Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear

合集下载

Isolation and characterization of fatty acid desaturase genes

ORIGINAL PAPERIsolation and characterization of fatty acid desaturase genes from peanut (Arachis hypogaea L.)Xiaoyuan Chi •Qingli Yang •Lijuan Pan •Mingna Chen •Yanan He •Zhen Yang •Shanlin YuReceived:8November 2010/Revised:27January 2011/Accepted:28February 2011/Published online:16March 2011ÓSpringer-Verlag 2011Abstract Fatty acid desaturases are responsible for the insertion of double bonds into pre-formed fatty acid chains in reactions that require oxygen and reducing equivalents.In this study,genes for FAB2,FAD2-2,FAD6and SLD1,were cloned from peanut (Arachis hypogaea L.).The ORFs of the four genes were 1,221,1,152,1,329and 1,347bp in length,encoding 406,383,442and 448amino acids,respectively.The predicted amino acid sequences of AhFAB2,AhFAD2-2,AhFAD6,AhSLD1shared high sequence identity of 79,76.2,73.4and 61%to the corre-sponding ones in Arabidopsis,respectively.Heterologous expression in yeast was used to conﬁrm the regioselectivity and the function of AhFAD2-2and AhFAD6.Linoleic acid (18:2),normally not present in wild-type yeast cells,was detected in transformants of these two genes.Quantitative real-time RT-PCR analysis indicated that the transcript abundances of AhFAB2and AhFAD2-1were higher in seed than that in other tissues examined.On the other hand,transcript of AhFAD2-2,AhFAD6and AhSLD1showed higher abundances in leaves.In addition,these ﬁve genes showed different expression patterns during seed devel-opment.These results indicated that the ﬁve genes may have different biochemical functions during vegetative growth and seed development.Keywords Fatty acid desaturase ÁPeanut (Arachis hypogaea L.)ÁPhylogenetic analysis ÁQuantitative real-time RT-PCR ÁSaccharomyces cerevisiae AbbreviationsFAB2Stearoyl-ACP desaturase FAD2Microsomal D 12desaturase FAD3Microsomal x 3desaturase FAD4Trans D 3desaturase FAD5D 7desaturaseFAD6Plastidial D 12desaturase FAD7Plastidial x 3desaturase FAD8Plastidial x 3desaturase ADS D 9desaturaseSLD1Sphingolipid D 8desaturase DES1Sphingolipid D 4desaturase D6D D 6desaturaseDesC Cyanobacterial D 9desaturase DesA Cyanobacterial D 12desaturase DesB Cyanobacterial x 3desaturaseIntroductionVegetable oils have become increasingly important eco-nomically because they are renewable resources of highly reduced carbon and are widely used in diets and industrial applications (Yang and Xu 2007).Peanut (Arachis hypo-gaea L.)is an allotetraploid species (2n =4x =40,AABB)and one of the ﬁve most important oilseed crops cultivated worldwide (Chen et al.2010).The peanut seed comprises around 50%oil,of which approximately 80%consists of oleic acids (36–67%)and linoleic acidsCommunicated by D.Zaitlin.X.Chi and Q.Yang are co-ﬁrst authors.X.Chi ÁQ.Yang ÁL.Pan ÁM.Chen ÁY.He ÁZ.Yang ÁS.Yu (&)Shandong Peanut Research Institute,Qingdao 266100,People’s Republic of China e-mail:yshanlin1956@Plant Cell Rep (2011)30:1393–1404DOI 10.1007/s00299-011-1048-4(15–43%)(Moore and Knauft1989).One of the major factors affecting the quality of peanut oil is the content of polyunsaturated fatty acids.Edible oils rich in oleic acid are suitable for human and animal consumption due to their improved stability,ﬂavor and nutrition(Heppard et al. 1996).It would be of great importance to investigate the fatty acid biosynthesis to improve oil quality and increase oil content of peanut.Fatty acid desaturases are enzymes that introduce double bonds into the hydrocarbon chains of fatty acids,and play an essential role in fatty acid metabolism and the mainte-nance of biological membranes in living organisms(Singh et al.2002).These desaturation processes take place in both the plastidial membrane and the endoplasmic reticu-lum(ER)membrane via two different pathways(Ohlrogge and Browse1995).With better understanding of fatty acid metabolic pathway,many desaturase genes with different regioselectivities were cloned(Wakita et al.2001;Thelen and Ohlrogge2002;Anai et al.2003;Nakamura et al. 2004;Peng et al.2010).They belong to a large gene family,containing conserved histidine regions.Histidine-rich boxes are thought to form a part of the diiron center where oxygen activation and substrate oxidation occur(Chi et al.2008a,b).For higher plants,most information on the function and speciﬁcity of fatty acid desaturases had been obtained from the characterization of Arabidopsis mutants,which were deﬁcient in speciﬁc desaturation activities(Somerville and Browse1991).The desaturase genes detected in Arabidopsis were divided into several subfamilies.FAB2was the only soluble desaturase characterized until now and catalyzed the desaturation of stearic acid(C18:0)to C18:1in the acyl carrier protein (ACP)-bound form(Murphy and Piffanelli1998).FAD2 and FAD6were x6desaturases that synthesized the di-enoic fatty acid,linoleic acid(C18:2),from oleic acid (C18:1)in the endoplasmic reticulum(ER)and plastids, respectively.FAD3,FAD7and FAD8were x3desatu-rases that synthesized linolenic acid(C18:3)from lino-leic acid(C18:2)in the ER(FAD3)and plastids(FAD7 and FAD8),respectively(Gibson et al.1994;Berberich et al.1998).FAD4and FAD5produced C16:1from C16:0speciﬁcally for PG and MGDG,respectively (Murphy and Piffanelli1998).ADS was D9acyl-lipid desaturase that participated in desaturation at the D9 position of C16:0in the ER(Fukuchi-Mizutani et al. 1998;Heilmann et al.2004).SLD1encoded a sphingo-lipid D8desaturase that led to the accumulation of8(Z/ E)-C18-phytosphingenine in the leaves and roots of Arabidopsis plants(Sperling et al.1998;Ryan et al. 2007).DES1encoded the sphingolipid D4desaturase responsible for the synthesis of D4-unsaturated LCBs such as sphingosine and sphinga-4,8-dienine in Arabid-opsis(Ternes et al.2002;Michaelson et al.2009).Two microsomal oleoyl-PC desaturase genes(AhFAD2-1A and AhFAD2-1B),each having its origin in different diploid progenitor species,have been isolated from the cultivated peanut(Jung et al.2000b;Lopez et al.2000). These two homeologous genes were expressed in normal oleate peanuts,but a G448A mis-sense mutation in AhFAD2-1A and a signiﬁcant reduction in the level of AhFAD2-1B transcript together resulted in high oleate phenotype in peanut varieties(8–2122and M2-225),and one expressed gene encoding a functional enzyme appeared to be sufﬁcient for the normal oleate phenotype (Jung et al.2000a).Patel et al.(2004)reported an insertion of the same miniature inverted-repeat transposable element (MITE)in AhFAD2-1B gene in a chemical-induced mutant Mycogen-Flavo and a previously characterized M2-225 mutant.This MITE insertion in AhFAD2-1B caused a frameshift,resulting in a putatively truncated protein.The insertion of this MITE in AhFAD2-1B,in addition to the point mutation in AhFAD2-1A,appeared to be the cause of the high-oleate phenotype in mutants Mycogen-Flavo and M2-225.Yu et al.(2008)reported that an extra A was inserted at the position?442bp of AhFAD2-1B sequence of radiation-induced high oleic acid genotypes,which resulted in the shift of open reading frame and a truncated protein.Yin et al.(2007)indicated that down-regulation of the FAD2-1in peanut resulted in a70%increase in oleic acid content in the seeds of transformed plants compared with a37.93%increase in untransformed plants.Analysis of transcript level showed that the expression of AhFAD2-1B gene in high oleic acid genotype was slightly lower than that in normal genotype.Recently,detection of FAD2-1 alleles was achieved by a cleaved ampliﬁed polymorphic sequence(CAPS)marker for the A genome(Chu et al. 2007)and a real-time polymerase chain reaction(PCR) marker for the B genome(Barkley et al.2010).Moreover, a simple PCR assay for detection of FAD2-1alleles on both genomes was developed by designing allele-speciﬁc primers and altering PCR annealing temperatures(Chen et al.2010).Varieties of fatty acids play crucial roles in plant phys-iology and possess high food and industrial values(Topfer et al.1995).However,only limited kinds of fatty acid desaturase genes in peanut have been functionally validated until now.It remains unclear if other kinds of desaturase genes are present in peanuts.In the present study,we iso-lated four novel desaturase genes from peanut and demon-strated the functions of two genes by heterologous expression in yeast(Saccharomyces cerevisiae).Also,the expression patterns of these genes were investigated in different tissues and seed developmental stages.Materials and methodsPlant materialsPeanut seeds(Arachis hypogaea L.cultivar Huayu19)were sown in sand and soil mixture(1:1),grown in a growth chamber under a16-and8-h light–dark cycle at26°C and 22°C,respectively.Three kinds of12-day-old tissues including roots,stems and leaves were collected as experimental materials for quantitative real-time RT-PCR analysis.In addition,immature peanut seeds25to60days after pegging(DAP)were also collected for expression analysis.Nucleic acid manipulationTotal RNA was extracted from samples using the RNeasy Mini Kit(Qiagen)according to the manufacturer’s instructions.Before cDNA synthesis,RNA was treated with RQ1RNase-free DNaseI(Promega,WI,USA) according to the manufacturer’s instructions to ensure no DNA contamination,and then theﬁrst-strand cDNA syn-thesis was carried out with approximately5l g RNA using an RT-PCR kit(Promega,WI,USA)according to the manufacturer’s procedure.Full-length cDNA sequence isolationPCR was performed with the LA PCR system(TaKaRa) using 2.5l l of109PCR buffer with MgCl2,1l l of 10l M of each primer, 4.0l l of10mM dNTPs,1l l cDNA samples,0.5l l LA Taq TM DNA polymerase and 15l l double distilled water.The PCR products were run on1%agarose gel and puriﬁed with Gel Extraction Kit (Takara)according to the manufacturer’s protocol.The puriﬁed products were then cloned into the pMD18-T Easy vector(Takara)and sequenced(Shangon,Shanghai).Sequence analysisOpen reading fragment(ORF)and encoded amino acid sequence of genes were deduced by BioXM2.6.Physico-chemical properties of the deduced protein were predicted by Protparam(http://www.expasy.ch/tools/protparam.html). Active sites of the protein sequence were analyzed by PROSITE database.The putative subcellular localizations of the candidate proteins were estimated by TargetP(http:// www.cbs.dtu.dk/services/TargetP/)and Predotar(http:// urgi.versailles.inra.fr/predotar/predotar.html).The potential N-terminal presequence cleavage site was predicted by ChloroP(http://www.cbs.dtu.dk/services/ChloroP/).Phylogenetic analysisAmino acid sequences were aligned using ClustalX pro-gram with the implanted BioEdit(Thompson et al.1994). The neighbor-joining(NJ)method in MEGA4(Tamura et al.2007)was used to construct the phylogenetic tree. Bootstrap with1,000replicates was used to establish the conﬁdence limit of the tree branches.Default program parameters were used.Quantitative real-time RT-PCRThe real-time RT-PCR analysis was performed using a LightCycler 2.0instrument system(Roche,Germany). b-actin gene was taken as the reference gene.Six pairs of gene-speciﬁc primers(Table1)were designed according to the AhFAB2cDNA(qFAB2-F and qFAB2-R),AhFAD2-1 (qFAD2-1-F and qFAD2-1-R),AhFAD2-2(qFAD2-2-F Table1DNA sequences of oligonucleotide primers used in this studyName Oligonucleotide sequence50–30Full-length cDNA sequence cloningFAB2-F ATGGCTCTGAGGCTGAACFAB2-R TTAGAGTTGCACTTCCCTATFAD2-2-F1ATGGGAGCTGGCGGCCGAFAD2-2-R1TCACAACTTATTGTTGTACCAGAATAC FAD6-F1ATGGCTTGCAGGCTTGCAGFAD6-R1TCAGGCATAATCAGGCATGACTSLD1-F ATGGCGGAACCACAATCAASLD1-R TCATCCATGAGTGTTAACAGCTTC Real-time RT-PCRqActin-F TTGGAATGGGTCAGAAGGATGC qActin-R AGTGGTGCCTCAGTAAGAAGCqFAB2-F CGGTTAGGTCTGCCACCTTCqFAB2-R ACGCCACGAGACTGCATACAqFAD2-1-F ATTCAAACCCTCCATTCAGTGTTG qFAD2-1-R GTGGTGGCAATGTAGAAGAGTAAG qFAD2-2-F CCTCACACTCACTATTACCCTCAC qFAD2-2-R TGACAAGACGGATAAGACCATAGG qFAD6-F TCCATATTCCGCACCACATATCC qFAD6-R TTGTCTTCATCAGTCTCCAGTTCC qSLD1-F TCTTGATGTGAGTTGTTCTTCTTGG qSLD1-R GCGTCCGAATCGTGAGAGCYeast expressionFAD2-2-F2TAGGATCCAAAATGGGAGCTGGCGGC FAD2-2-R2GGCCTCGAGTCACAACTTATTGTTGTA FAD6-F2TAGGATCCAAAATGGCTTGCAGGCTTG FAD6-R2TAACTCGAGTCAGGCATAATCAGGCATand qFAD2-2-R),AhFAD6(qFAD6-F and qFAD6-R),AhSLD1(qSLD1-F and qSLD1-R)and b -actin (qActin-F and qActin-R)sequences.The real-time RT-PCR reactions were performed using the SYBR Premix Ex Taq polymerase (TaKaRa,Japan)according to the manufacturer’s instruc-tions.Each 20l l reaction comprised 2l l template,10l l 29SYBR Premix and 0.4l l (200nM)of each primer.The reactions were subjected to an initial denaturation step of 95°C/10s,followed by 40cycles of 95°C/5s,60°C/30s and 72°C/10s.A melting curve analysis was performed at the end of the PCR run over the range 60–95°C,increasing the temperature stepwise by 0.5°C every 10s.Baseline and quantiﬁcation cycle (CP)were automatically determined using the LightCycler Software.Zero template controls were included for each primer pair,and each PCR reaction was carried out in triplicate.CP values were converted into rel-ative quantities via the delta-CP method using the sample with the lowest CP as calibrator.Expression in S.cerevisiaeThe auxotrophic S.cerevisiae strain INVSc1(MATa his3-D 1leu2trp1-289ura3-52)and the high copy number shuttle vector pYES2were used for analyzing expression of recombinant proteins (Invitrogen).The coding regions of AhFAD2-2and AhFAD6were ampliﬁed separately using speciﬁc primers with Bam HI or Xho I restriction site(underlined).The ampliﬁed AhFAD2-2and AhFAD6genes were digested by Bam HI and Xho I,connected to the plas-mid pYES2dual digested with the same restriction enzymes,which were located between the inducible yeast GAL1promoter and the yeast CYC1terminator,respec-tively.The constructs pYFAD2-2and pYFAD6,as well as the pYES2control,were transformed into the INVSc1cells using a lithium acetate method (Gietz et al.1995).Trans-formants were selected on minimal medium plates lacking uracil (SC-Ura).The yeast cells at logarithmic phase were incubated at 25°C for 48h.The cells were harvested by centrifugation and washed three times with sterile distilled water and then dried by lyophilization.Fatty acid analysisTotal lipids were extracted with dichloromethane/methanol (2:1)from dried cells,solidiﬁed under nitrogen gas ventila-tion and transmethylated with methanol containing 0.5M KOH–methanol/H 2O (95:5)at 100°C for 2h.The fatty acid methyl esters (FAMEs)were recovered with n -hexane.FAMEs analysis was carried out using a Finnigan Trace GC–MS equipped with a 30m 90.25mm DB-5ms cap-illary column.Fatty acids were identiﬁed by comparing their retention times with those of their FAME standards (Sigma Chemicals Co.,USA)separated on the same GC.Measure-ments were done using peak height area integrals expressedTable 2Fatty acid desaturase genes in peanutProtein Accession Len (aa)50upstream region (bp)30downstream region (bp)Molecular mass (kDa)PI FAB2FJ2303104061925946.2516 6.24FAD2-2FJ7687323839724743.82928.8FAD6FJ7687304429626451.6429.09SLD1FJ8246074481743351.36429.06Fig.1Alignment of the complete deduced amino acid sequences of stearoyl-ACP desaturase genes.The conserved histidine motifs are highlighted in black boxes .GenBank accession numbers are as follows:Arachis hypogaea (AhFAB2,FJ230310),Glycine max (GmFAB2,AAX86050),Arabidopsis thaliana (AtFAB2,NP_181899)as a percentage of the total of all integrals.The experiment was carried out in triplicate,and the data subjected to anal-ysis of variance using DPS software (Zhejiang University,China)Version 7.05.Duncan’s multiple range test was employed to determine the statistical signiﬁcance (P \0.05)of the differences between themeans.Fig.2Alignment of the complete deduced amino acid sequences of membrane desaturase genes.The conserved motifs are highlighted in black boxes .GenBank accession numbers are as follows:Arachis hypogaea (AhFAD2-1A,AAB84262;AhFAD2-1B,AAF82293;AhFAD2-2,FJ768732;AhFAD6,FJ768730;AhSLD1,FJ824607),Glycine max (GmFAD2-1A,AAX29989;GmFAD2-1B,ABF84062;GmFAD2-2,BAD89862;GmFAD6,P48628),Arabidopsis thaliana (AtFAD2,NP_187819;AtFAD6,NP_194824;AtSLD1,NP_191717),Stylosanthes hamata (ShSLD1,ABU98945)Results and discussionIsolation of fatty acid desaturase genes from peanut Four fatty acid desaturase genes namely stearoyl-ACP fatty acid desaturase (FAB2),microsomal D 12fatty acid desaturase (FAD2-2),plastidial D 12fatty acid desaturase (FAD6)and sphingolipid D 8desaturase (SLD1)were iso-lated from peanut seedling,respectively.Three of them were identiﬁed from a peanut seedling full-length cDNA library and one was cloned via reverse transcription poly-merase chain reaction (RT-PCR)and RACE (Rapid Ampliﬁcation of cDNA Ends)method.The ORF of the four genes were 1,218,1,149,1,326and 1,344bp in length,encoding 406,383,442and 448amino acids,respectively (Table 2).Prediction of subcellular location by two pro-grams,TargetP Server and Predotar,suggested that AhFAB2and AhFAD6protein were probably located in the chloroplast.The ﬁrst 65or 27amino acids at the N-ter-minal end of the deduced protein for AhFAB2or AhFAD6had a high proportion of hydroxylated and small,hydro-phobic amino acids,which was typical of chloroplast transit peptide.A Blast search revealed that the primary structure of AhFAB2,AhFAD2-2,AhFAD6,AhSLD1shared high sequence identity of 79,76.2,73.4and 61%to the corresponding ones in Arabidopsis,respectively.The amino acid sequence deduced from AhFAD2-2showed 87%identity to that of the soybean FAD2-2,and 86%identity to soybean FAD2-3.The AhFAD2-1(AhFAD2-1A and AhFAD2-1B)and AhFAD2-2were 75.1%identical in this study,compared with 72.5%(GmFAD2-1A and GmFAD2-2)and 70.5%(GmFAD2-1B and GmFAD2-2)in Glycine max .The four desaturase genes contained typical histidine-rich boxes (Figs.1,2),which was in accordance with the standard of different types of desaturase genes.For example,two histidine boxes of AhFAB2gene were con-sistent with those of plastidial stearoyl-ACP desaturases,which were represented as EENRHG,DEKRHE.Three histidine boxes of the AhFAD6gene matched the standard for plastidial D 12desaturase,i.e.,GHDCXH,HX 2HH andHXPHH.The third histidine box of AhSLD1contained a His to Gln substitution at the third histidine residue,which was also evident in several fatty acid desaturases such as the borage D 6desaturase and all the sphingolipid desatu-rases thus characterized (Sperling et al.1998;Sayanova et al.2001).Also,in common with other desaturases of this type,AhSLD1encoded a protein with a cytochrome b 5-like haem-binding domain at the N-terminus.The presence of this binding domain was characterized by the His-Pro-Gly-Gly motif,which indicated that this putative desaturase existed as a fusion protein.Phylogenetic analysisThe polyunsaturated fatty acids are synthesized by two distinct pathways in plants,known as the prokaryotic and eukaryotic pathways,which are located within the mem-brane of the plastid and the endoplasmic reticulum,respectively (Sato and Moriyama 2007).Therefore,plant desaturases fall into two major classes:soluble and mem-brane-bound desaturases.The soluble desaturases are ana-lyzed separately from membrane-bound desaturases because they are restricted to higher plants and show no evolutionary relationship with the more widely distributed membrane desaturases (Shanklin and Cahoon 1998).To examine the relationships among different sources of desaturase genes,the neighbor-joining method was used to construct the phylogenetic trees and all tree topologies were highly congruent (Figs.3,4).The plant stearoyl-ACP desaturase is the only soluble desaturase identiﬁed to date.In contrast,all other desatu-rases identiﬁed in plants,algae,animals and fungi are integral membrane proteins (Singh et al.2002;Yang et al.2005).The phylogenetic tree indicated that AhFAB2was grouped with stearoyl-ACP desaturases of higher plants and distinct from those of green algae (Fig.3).It might suggest that stearoyl-ACP desaturases in green algae and higher plants arose by independent gene duplication events.As shown in the phylogenetic tree,all of the membrane-bound desaturases fell into three distinct subfamilies:D 7/D 9desaturase subfamily,D 12/x 3desaturase subfamilyandFig.3Neighbor-joining tree based on the deduced amino acid sequences of stearoyl-ACP desaturase homologs.Sequences are shown by their accession numbers,strain names and labels.Bootstrap values from neighbor-joining analyses are listed to the left of each node and with values more than 50are shown‘front-end’desaturase subfamily (Fig.4).Based on func-tional criteria and the position of the clade integrated by D 9desaturases,D 9desaturase is assumed to be the ancestor of the remaining desaturases (Alonso et al.2003).The D 7/D 9-homologous genes of higher plants were grouped with D 7homologs of green algae,while the genes of cyanobacteria were placed in a basal position.Therefore,the D 9desat-urase may arise by independent gene duplication events in plant and green algae branches,and the cyanobacterial D 9desaturase was identiﬁed as the origin of plant/green algae D 7/D 9desaturase.In the D 12/x 3desaturase subfamily,the AhFAD6gene,grouped to chloroplastic D 12desaturase of higher plants,was situated along with D 12desaturases of cyanobacteria and green algae at the basal position of the tree.The microsomal D 12desaturases of higher plants formed a group and set apart from enzymes of green algae.The AhFAD2-1A and AhFAD2-1B genes clustered with FAD2-1Fig.4Neighbor-joining tree based on the deduced amino acid sequences of membrane desaturases.Sequences are shown by their accession numbers (locus tags),strain names and labels.Bootstrapvalues from neighbor-joining analyses are listed to the left of each node and values more than 50are showngenes of higher plants;whereas AhFAD2-2gene clustered with FAD2-2and FAD2-3genes of higher plants.Besides,the x 3desaturases of cyanobacteria were placed in a basal position,grouped with both microsomal and chloroplastic x 3desaturases of higher plants and green algae.Therefore,it can be speculated that the cyanobacterial D 12desaturase might be the origin of the plant D 12and x 3desaturases,including both chloroplast and endoplasmic reticulum (ER)isozymes.The ‘front-end’desaturases (D 6and sphingolipid D 8desaturases)formed a separate clade (Fig.4).The sphin-golipid D 8desaturase (AhSLD1)of peanut clustered with those of higher plants,forming a group with D 6desaturases of higher plants.Quantitative real-time PCR analysisQuantitative real-time PCR (qRT-PCR)was employed to conﬁrm the expression patterns of the four novel genes,as well as AhFAD2-1(AhFAD2-1A and AhFAD2-1B ),in four peanut tissues and at different developmental stages of seeds.b -actin was used as an internal reference control for total RNA input.Two microsomal oleoyl-PC desaturase genes (AhFAD2-1A and AhFAD2-1B )have been identiﬁed in peanut (Jung et al.2000b ).The open reading frames (ORFs)for FAD2-1A and FAD2-1B were 99%identical,encoding 379amino acids with no introns in the coding sequence (Jung et al.2000b ;Lopez et al.2000).In our analysis,the gene-speciﬁc primers used for ampliﬁcationofFig.5Expression analysis of ﬁve desaturase genes using quantitative real-time RT-PCR (RT-qPCR).The relative mRNA abundance was normalized with respect to the peanut actin gene.The bars are standard deviations (SD)of three technical repeatsAhFAD2-1recognized and ampliﬁed both AhFAD2-1A and AhFAD2-1B genes.As shown in Fig.5,theseﬁve genes displayed speciﬁc spatial expression patterns across dif-ferent tissues.The AhFAB2gene was expressed most strongly in seeds followed by leaves,and weakly in roots and stems.The AhFAD2-2gene showed the highest mRNA abundance in leaves compared with the other three tissues, whereas the expression of AhFAD2-1gene was largely restricted to seeds.Both AhFAD6and AhSLD1genes exhibited the highest transcript accumulation in leaves, whereas AhSLD1had relatively higher expression in stem and AhFAD6was preferentially expressed in seed.The expression patterns of theﬁve desaturase genes across six developmental stages of seeds are also illustrated in Fig.5.AhFAB2and AhFAD2-1RNAs were presented in high abundance across all stages compared with those of AhFAD6and AhFAD2-2,which were less abundant; whereas AhSLD1transcript was relatively rare and near the detection limit.AhFAB2and AhFAD6shared similar expression behaviors over the developmental stages with high expressions at25and39DAPs and much lower levels at other stages.AhFAD2-1and AhFAD2-2reached a maximum expression level at25DAP and decreased thereafter.In contrast,AhSLD1remained relatively high at the initial three stages,but showed dramatic decrease in abundance during later stages.Fatty acid composition of the different peanut plant tissues and seed developmental stagesThe relationship between the accumulation of transcripts ofﬁve desaturase genes with the distribution of fatty acids among different peanut tissues was investigated.To that end,the fatty acid compositions of different plant tissues used in the expression analysis(roots,stems, leaves,and seeds)were analyzed.The fatty acid com-position of peanut seeds has been analyzed in the past by many other groups.However,other tissues like stems or roots have not been analyzed in detail.As shown in Table3,the major fatty acid compositions of peanut were C16:0,C18:0,C18:1D9,C18:2D9,12,C20:0and C24:0.C18:1D9and C18:2D9,12represented more than 80%of the total fatty acids in seeds compared to approximately60%in other tissues.A higher amount of dienoic fatty acid(linoleic acid,18:2)was observed in roots and stems,whereas monoenoic fatty acid(oleic acid,18:1)was the most abundant detected in leaves and seeds.In seed,the C16:0levels reached9%,whichTable3Comparison of fatty acid distribution of peanut in four different tissuesFatty acid Fatty acid distribution(percent of total by mass)Roots Stems Leaves Seeds25DAP32DAP39DAP46DAP53DAP60DAPC12:00.0750.0490.041––––––C14:1D9–––0.009a0.016b0.015b0.016b0.016b0.010a C14:00.3470.2380.1350.009a0.016b0.015b0.016b0.016b0.011a C15:1D10––––0.002a0.001a0.001a–0.001a C15:00.4430.1010.032–0.001a0.001a0.002a–0.001a C16:1D90.1780.020.418––––––C16:034.6633.6622.8869.282ab9.6a9.291ab8.516c8.876bc7.890d C17:1D10––––––0.005a0.006a0.009b C17:00.230.1270.0770.009a0.027b0.024b0.031b0.031b0.035b C18:2D9,1234.19740.35217.25418.633d19.883b19.363c18.662d20.234a18.506d C18:1D924.19820.35655.10564.387bc63.132d63.91c66.077a64.701b65.544a C18:0 2.21 3.141 3.269 2.787a 2.593a 2.789a 3.338b 3.228b 4.476c C19:0–––0.253ab0.261a0.223abc0.245abc0.214bc0.206c C20:1D11–––0.519a0.565a0.523a0.365b0.338b0.383b C20:00.3380.460.235 1.076a 1.036a 1.015ab0.976ab0.868b 1.135a C22:00.9790.2910.211 2.447a 2.197a 2.199a 1.304b 1.104b 1.294b C23:00.4220.0910.035––––––C24:0 1.722 1.1150.3020.588a0.67a0.631a0.445bc0.369c0.499bNumbers with different letters are statistically signiﬁcant(P\0.05)Dashes indicate that the fatty acid was not detected.In the same row,the fatty acid alterations at six seed developmental stages are compared to each othermeans a reduction of about 60%with respect to its levels detected in other tissues.In addition,it was interesting that C16:1D 9was detected in roots,stems and leaves,but not in seeds.Moreover,fatty acid distributions at different develop-mental stages were analyzed in an attempt to ﬁnd any linkage between fatty acids alteration and seed develop-ment.As shown in Table 3,no signiﬁcant change was detected in C16:0and C18:0content at 39days after pegging.The earliest time point reﬂecting an alteration occurred at 46DAP,with the C18:0content exhibiting a gradual increase and the C16:0content exhibiting a gradual decrease.It was evident that the change in the C18:1content showed reverse trend compared to that of C18:2.For example,C18:1content increased signiﬁcantly at 46DAP,whereas C18:2content decreased at the same time course.AhFAB2and AhFAD2-1were the genes that were mainly expressed in seeds in high abundance compared with the other three.Although the transcript levels of these two genes were relatively low at 46DAP,the decrease of transcript accumulation for AhFAD2-1gene was larger than that of AhFAB2(Fig.5).These results indicated that the increase of C18:1content appeared to be due to the reduced ﬂux to C18:2fattyacid.Fig.6GC of FAME of recombinant yeast harboring pYES2(control,a ),pYFAD2-2(b )and pYFAD6(c ).The transformants at logarithmic phase were grown for 48h at 25°C,and FAMEs from whole cells were prepared and analyzed by gaschromatography (GC)as indicated in ‘‘Materials and methods ’’.The experiment was repeated in triplicate and the results of a representative experiment are shown。

sdarticle7

Probabilistic fatigue life prediction using AFGROW and accounting for material variabilityWilliam A.Grell,Peter z *Department of Mechanical and Materials Engineering,University of Denver,2390S.York St.,Denver,CO 80208,USAa r t i c l e i n f o Article history:Received 8July 2009Received in revised form 22October 2009Accepted 7December 2009Available online 16December 2009Keywords:Fatigue life prediction ProbabilisticMaterial variability Aluminum 2024AFGROW Lap jointa b s t r a c tThe fatigue performance of components contains signiﬁcant amounts of scatter,and variability has been characterized in initial crack sizes,crack growth rates,and material properties.Probabilistic methods have recently been gaining acceptance as an approach to account for uncertainty in various sources to predict component fatigue life.However,computation time associated with the accepted standard Monte Carlo method can be prohibitive during design phase evaluations.Accordingly,the objectives of the cur-rent study were to develop a probabilistic interface for the AFGROW life prediction software and to dem-onstrate the use of efﬁcient probabilistic methods,as an alternative to Monte Carlo analysis,to accurately predict fatigue lives for three veriﬁcation cases.The veriﬁcation cases were based on experimental data for compact tension,single edge notched tension,and single lap joint specimens from the literature.Based on experimentally determined distributions of crack growth rate,material properties,and initial crack size,predicted distributions of fatigue life agreed closely with replicate experimental test putation time with the Advanced Mean Value (AMV)and FORM methods were reduced by 100-fold compared to Monte Carlo,promoting the notion of utilizing probabilistic assessments within the design process.Ó2009Elsevier Ltd.All rights reserved.1.IntroductionComponent fatigue data contain signiﬁcant amounts of scatter [1,2].Variation in life of less than a factor of 2for high stresses and up to a factor of 100for low,uniform stresses is not uncom-mon [1].Inherent scatter has also been reported in crack nucle-ation sites [3–5]and crack growth rates [6,7].Additional uncertainties arise due to microstructure,processing,in-service loading,and environment.Historically,these uncertainties have been dealt with by applying experience-based safety factors to the fatigue analysis of critical components,driving the likelihood of failure to an acceptable level.In contrast to deterministic analy-ses,probabilistic methods represent the input parameters as distri-butions and predict distributions of performance.This allows assessment of performance at a corresponding probability level,which can aid in risk-related decision making for fatigue critical parts.In addition,similar to parametric studies,sensitivity factors are determined as part of the analysis to identify which input parameters are most critical to the performance distribution.Numerous studies have investigated probabilistic aspects of fa-tigue,including variability in stress-life (S –N )data [2,8],fatigue crack growth rate [6,7,9–13],and life prediction considering micro-structure [3,4,14–20],for structures [19,21–24]and under multi-axial conditions [25,26].In cases where a large amount of S –N data are available,statistical approaches may be used to quantify the scatter in the data [8].In more general approaches,probabilis-tic fracture mechanics based fatigue models are applied.The most straightforward probabilistic fracture mechanics models are ana-lytical and are based on randomizing the Paris relation (e.g.[10,11]).Typically these models describe the C-parameter in the Paris relation as a random variable,then numerically integrate the relation to determine a distribution of life.The limitations of this approach are that only one variable may be modeled as a dis-tribution and that the analysis is restrained to the Paris region of the material.More recently,models have been expanded to account for com-plex fatigue considerations (e.g.crack closure,variable amplitude loading)and multiple stochastic material behaviors (e.g.[14,21]).These models typically evaluate the crack growth process cycle-by-cycle while accounting for variability in crack growth rate.Other models accounted for the fatigue life variability by utilizing a distribution of material features or anomalies as the initial cracks [15,19]or incorporating initiation mechanisms [20].Fatigue life predictions using probabilistic fracture mechanics have typically employed time intensive Monte Carlo analysis,used simpliﬁed fracture mechanics models,or required complicated mathematical manipulation and formulation.Accordingly,the0142-1123/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.ijfatigue.2009.12.001*Corresponding author.Tel.:+13038713614;fax:+13038714450.E-mail address:plaz@ (z).International Journal of Fatigue 32(2010)1042–1049Contents lists available at ScienceDirectInternational Journal of Fatiguejournal homepage:w w w.e l s e v i e r.c o m/l o c a t e /i j f a t i g ueobjectives of the current study were to develop a probabilistic life prediction platform and to demonstrate the use of efﬁcient proba-bilistic methods,as an alternative to Monte Carlo analysis,to pre-dict the distribution of fatigue lives for three veriﬁcation cases.As an additional objective,the platform was to be developed with minimal software development in order to highlight the accessibil-ity of such an approach to engineers in the industry.The platform interfaced a commercially available probabilistic software package,NESSUS (Southwest Research Institute,San Antonio,TX)[27]or UNIPASS (PredictionProbe,Inc.,Irvine,CA),with the AFGROW (Wright-Patterson Air Force Base,OH)fatigue life prediction software.Wieland and Millwater [24]interfaced NESSUS and AFGROW to predict the sensitivity of fatigue life to probabilistic input parameters in T-38aircraft structures under spectrum loading;their study utilized Monte Carlo simulation,but did not consider the use of efﬁcient probabilistic methods.By interfacing with AFGROW,the model leverages all of the capabili-ties of the analysis package,including classical and user-deﬁned K-solutions,advanced weight function techniques,residual stress capabilities,multiple closure models,material databases,and ever improving numerical integration techniques.Further,the probabi-listic packages offer a wide array of numerical probabilistic tech-niques as well as useful tools to summarize results.Two probabilistic softwares were utilized to verify agreement in the probabilistic predictions independent of analysis package.The ver-iﬁcation cases evaluated in this study were based on experimental data from the literature for compact tension CT,single edge notched tension SENT,and single lap joint specimens of common engineering aluminum alloys.2.Methods2.1.Probabilistic analysis platformA probabilistic fatigue life prediction model was developed that interfaced commercially available probabilistic software and the AFGROW life prediction software (Fig.1).The AFGROW softwaremakes efﬁcient life predictions incorporating spectrum loading,crack closure,and inspection and repair features.The probabilistic modeling was demonstrated using commercially available proba-bilistic softwares,either NESSUS or UNIPASS.In the current study,the key input parameters were modeled as distributions,and the perturbed variables for the probabilistic methods were passed to AFGROW using the component object model (COM)capabilities and custom scripting.Life prediction was performed using AF-GROW with results passed back to the probabilistic software.The end result was a predicted distribution of fatigue lives.A variety of probabilistic methods were implemented and eval-uated to consider efﬁciency and accuracy for the various speci-mens.The most common and robust probabilistic method is Monte Carlo simulation,which involves repeated model evalua-tions with input values sampled at random according to their dis-tributions.Monte Carlo does not put restrictions on the number of random variables,nor the behavior of the response (e.g.linearity,continuity).However,Monte Carlo simulation is computationally expensive and may be prohibitive when trying to perform timely analyses within the design cycle.A series of approximate most probable point (MPP)methods have been developed that are more computationally efﬁcient than Monte Carlo simulation.The MPP represents the combination of input parameter values that predict performance,fatigue life in this study,at a speciﬁed probability level.The MPP methods typi-cally determine the most probable point using optimization on a ﬁrst-order Taylor series approximation of the performance func-tion [28].Some implementations map the original random vari-ables into independent standard normal variables to facilitate optimization with variables of similar magnitudes.The various techniques differ in terms of how performance is computed;for example,FORM (ﬁrst-order reliability method)uses a ﬁrst-order approximation.While the MPP methods are approximate,they have been shown in many analyses to be quite accurate in compar-isons with Monte Carlo simulation results,while requiring a small fraction of the number of computations.The low computational cost of the MPP methods comes with a tradeoff;these methods only provide information for a single point (e.g.probability),soResults (e.g. life)Perturbed variablesAFGROWCOMUNIPASSW.A.Grell,z /International Journal of Fatigue 32(2010)1042–10491043in order to construct a full PDF or CDF,the method must be applied repeatedly at each point of interest.The MPP methods work well with well-behaved monotonic systems,like fatigue life predictions.Further detailing the MPP family of methods,the mean-value (MV)method constructs a mean-based response function and computes the MPP for the speciﬁed probability levels.As aﬁrst-or-der method,it provides a good approximation of the solution near the mean.It is suitable for fairly linear problems,but can deviate signiﬁcantly toward the tails for non-linear problems.The MV method requires n+1trials,where n is the number of random vari-ables.The advanced mean-value(AMV)method utilizes the MV as a basis to achieve a better representation of the response.It does this by including corrective terms to approximate higher order ef-fects and requires n+1+m trials,where m is the number of spec-iﬁed probability levels[29].AMV takes the MV prediction and using data from the calculated MPP of interest,corrects this value for a single level of desired probability(or desired output).The higher-order approximation achieved by AMV cannot be applied at any point other than that for which it was derived;getting esti-mates for additional points requires additional applications of the AMV method.The advanced mean-value with iterations(AMV+) method involves the implementation of AMV but also includes iterations on the MPP to ensure that convergence to a speciﬁed le-vel is reached.AMV+has been shown to be very accurate even for non-linear problems,though the number of trials varies with the problem[29].2.2.Probabilistic sensitivity factorsIn addition to predicting the distribution of fatigue lives(e.g. cumulative distribution function),the probabilistic methods can identify the relative importance of each input parameter by com-puting sensitivity factors.Sensitivity factors can assess the change in probability with respect to a change in the mean or standard deviation of the input distribution.Sensitivity factors computedwith a partial differential equation,@p f@l and@p f@r,are calculated as partof the MPP methods.These values are typically nondimensional-ized by multiplying by the respective input standard deviation and probability to facilitate comparison across a variety of proba-bility levels in the CDF.The resulting sensitivity factors,@p f@l rpand@p f r r,provide a relative importance ranking of the inputparameters.3.Probabilistic fatigue life predictionsProbabilistic fatigue life predictions were performed for three veriﬁcation cases developed from the literature:CT specimens of aluminum2024-T351from Wu and Ni[12],SENT specimens of aluminum2024-T3from[15,30],and single lap joint geometries of aluminum2024-T3from Moreira et al.[31].These studies from the literature were selected as they contained a large number of re-peated tests.The parameters modeled as distributions varied for each geometry studied(Table1)and are discussed in the following sections on the respective geometries.The fatigue life predictions were performed in AFGROW utilizing the FASTRAN II plasticity in-duced closure model and the appropriate closed-form K-solutions for the CT and SENT specimens or tabulated solutions for the single lap joint.Parameters for the FASTRAN II[32]plasticity induced clo-sure model for Al2024-T3were based on the work by Newman et al.[33].3.1.Input distributionsIn the probabilistic analyses,input parameter variability was considered for fracture toughness,yield strength,initial crack size, and fatigue crack growth rate.Distributions for the input parame-ters were developed from available literature data for aluminum 2024in the-T3and-T351conditions.The fracture toughness of Al2024-T351was represented by a distribution with a mean of34MPa m0.5and a standard deviation of5.6MPa m0.5[34].The data was from testing on11specimens.It was assumed to be normally distributed based on observations made in the literature[7,21].The yield strength was considered be-cause of its impact in crack closure calculations.Yield strength data for2024-T3and2024-T351were very similar,and accordingly the same distribution was used for both.The yield strength distribu-tion was determined from A-basis and B-basis values of331and 345MPa,respectively[34].The A-and B-basis values represent the levels above which the actual yield strength falls99%and 90%of the time,respectively.The reporting of A-and B-basis im-plies that at least100samples were tested,though the exact num-ber was not reported[34].Here,it was assumed that the yield strength followed a lognormal distribution,and the distribution parameters were calculated from the A-and B-basis values as shape=0.03907and scale=5.8929(in ln(MPa))corresponding to a mean of362.7MPa and standard deviation of14.2MPa.The distribution of crack nucleating particles observed in Al 2024-T3SENT specimens were characterized in Laz et al.[15]. Based on180crack nucleation sites from31SENT and10double edge notch tension specimens[15],the study showed that the par-ticle widths,2a,and depths,c,were described well by lognormal distributions,and that the two exhibited a small degree of correla-tion.The corresponding mean and standard deviations were l a=4.478l m and r a=2.052l m for particle half-width(a)and l c=13.64l m and r c=5.582l m for depth.To model the fatigue crack growth rate(FCGR)relation,the baseline(mean)da/dN versus D K eff curve for Al2024-T3was rep-resented as a piece-wise curve from Newman et al.[33].Utilizing data from multiple sources,the extent of scatter for the material was evaluated by Wang[7,14],and standard deviations of da/dN were listed for ranges of D K eff values[14].The data were shown to be described well by a lognormal ing the infor-mation from these sources,a probabilistic crack growth rate curve was developed(Fig.2)with the mean piece-wise curve bounded by plus or minus three standard deviation scatter bands[14].The amount of scatter follows the expected trend in that the smaller crack region has larger standard deviations.Also included in the ﬁgure is the extrapolation which AFGROW performs when D K eff levels are less than the minimum from Newman et al.[33].This extrapolation is conservative because this region is below the threshold of crack growth for the material.Because of the similar crack growth rates for aluminum2024-T351[12],the probabilistic crack growth rate curve for2024-T3was used for both materials.To simulate specimen to specimen material property variability, each probabilistic variable was perturbed from its mean according to its distribution.This is a straightforward task for yield strength, fracture toughness,and initial crack size but is more complex forTable1Probabilistic inputs(U=active)for various specimens analyzed with the life prediction model.Material of specimens and input data source indicated in parenthesis.Probabilistic input CT(2024-T351)SENT(2024-T3)Single lap joint(2024-T3)Yield strength2024-T3/T351)U U–Fracture toughness(2024-T351)U––Fatigue crack growth rateoffset(2024-T3)U U UInitial crack size(2024-T3)–U U1044W.A.Grell,z/International Journal of Fatigue32(2010)1042–1049the crack growth rate variability.To set crack growth behavior for agiven specimen,the entire piece-wise curve is offset based on a single scale factor,‘‘FCGR Offset”.The piece-wise curve is deﬁned with mean and standard deviations for da/dN at each D K eff point. The FCGR Offset is a standard normal variate that is used to offset each point according to the mean and standard deviation.This pro-cess will offset the entire curve from the baseline and simulate overall variability in the crack growth rate rather than cycle-to-cy-cle variability.The overall crack growth rate variability contributes much more to scatter in fatigue life,as the cycle-to-cycle variabil-ity is averaged out over the entire fatigue life[11].Also,it has been observed that,when tested under identical conditions,a specimen with faster crack growth rates generally remained faster than other specimens over its life[6].pact tension(CT)specimen predictionsConstant amplitude fatigue experimental data on30identical CT specimens of Al2024-T351plate were taken from the work by Wu and Ni[12].Commonly used for material characterization, the CT specimens were50.0mm wide and12.0mm thick.Pre-cracking started at c=15mm and extended to c=18mm.Each specimen was tested under the same maximum and minimum loads of P=4.5and0.9kN at a frequency of15Hz for pre-cracking and the remainder of testing.Specimen failure occurred at56,314 cycles on average with a standard deviation of10,231cycles[12].The data from the work of Wu and Ni[12]are plotted in Fig.3as cumulative probability(CDF)versus cycles to failure.A lognormal distribution wasﬁt to the experimental data with the following parameters:shape=0.1802and scale=10.922.A Kolmogorov–Smirnov(K–S)test was conducted to show that the lognormal dis-tribution was acceptable(level of signiﬁcance a=0.05,D=0.170 was less than D0:0530=0.242).In addition to plotting the distribution ﬁt,Fig.3also includes the5%and95%conﬁdence intervals on the mean.The fatigue life data appears bimodal indicating the poten-tial for a different mechanism or growth rates in the short and long life specimens.In the current work,probabilistic life prediction analysis was performed for the CT geometry with dimensions and loading con-ditions from Wu and Ni[12].Variability in fracture toughness,yield strength,and fatigue crack growth rate was considered.The initial crack size wasﬁxed at c=18mm.The Monte Carlo(MC) method was implemented with NESSUS and UNIPASS for1000iter-ations each.More efﬁcient techniques were also considered, namely the MV and AMV methods with NESSUS and FORM with UNIPASS.Experimental and predicted fatigue life distributions are plotted as cumulative distribution functions(Fig.3),obtained by ordering the data from smallest to largest and uniformly distrib-uting them along the y-axis.The predictions compared reasonably well and captured the variability in the shortest fatigue lives(CDF values<0.5),but failed to predict the overall amount of scatter and the longest fatigue lives.The amount of variability in the crack growth rate curve must not have accounted for the amount of scat-ter present in the experimental data.The AMV and FORM results followed the MC predictions very closely,but required only a small fraction of the iterations.To evaluate the accuracy of the different probabilistic methods,their predictions of fatigue life for aﬁxed probability of failure,P f,of0.01were compared.This low probabil-ity was chosen on the grounds that conservatism dictates the shortest fatigue lives be considered in design to ensure a low P f.A summary of the predicted lives using the different methods is shown in Table2.A comparison with the AMV+method applied at this probability level was also performed to conﬁrm conver-gence and agreed well with results from the other methods.The analyses indicate that similar results can be obtained with AMV or FORM in less than one percent of the time required for MC.Nor-Table2Comparison of CT life prediction and efﬁciency for different probabilistic methods.(N=NESSUS,U=UNIPASS).The shortest experimental life was43,172cycles(P f=0.03)[12].Method Life(cycles)P f=0.01#of Trials Analysis timeN-MC-1k42,697100017hU-MC-1k43,671100016hN-MV43,29244minN-AMV43,49555minN-AMV+43,56555minU-FORM43,91187minW.A.Grell,z/International Journal of Fatigue32(2010)1042–10491045malized sensitivity factors at P f=0.01from the AMV analysis iden-tiﬁed the most important parameters(Fig.4).Yield strength and fracture toughness variability are not contributing signiﬁcantly to the scatter in fatigue life,and thus may be modeled as determinis-tic variables in order to expedite future predictions.3.3.Single edge notch tension(SENT)specimen predictionsData from constant amplitude fatigue experiments on similar single edge notch tension(SENT)specimens were taken from [15,30].Designed to simulate a rivet hole in an aircraft structure, the SENT specimens were machined from Al2024-T3sheet and had nominal dimensions of203mm long,45mm wide,and 2.54mm thick with a notch radius of r=2.813mm.The corre-sponding elastic stress concentration factor at the notch root was 3.165[15].Between the two studies,a total of24fatigue tests were conducted at the120MPa stress range with an R ratio(minimum-to-maximum stress)of0.01.While the tests were carried through to failure,the number of cycles to crack breakthrough,deﬁned as crack transitions from a nominally semi-elliptical crack to a through-thickness crack,was reported[15,30].Considering results from both studies,the life-to-breakthrough averaged198,515cycles with a standard devia-tion of146,200cycles.The results of the combined dataset are plotted as cumulative probabilities(CDF)versus the number of cy-cles to breakthrough in Fig.5.A K–S test(a=0.05)was again used to show that the lognormal distributionﬁt the SENT data accept-ably,resulting in the following distribution parameters: shape=0.6583and scale=11.982.The distribution along with the5%and95%bounds on the mean are also shown in Fig.5.In addition,tests were stopped periodically to create replicas of the notch root surface in order to observe and determine the details of crack formation at constituent particles[15].Crack nucleating particles were identiﬁed and their dimensions measured digitally.Probabilistic life predictions for the SENT specimens were con-ducted considering variability in yield strength,initialﬂaw size, and fatigue crack growth rate.As the simulations predicted fatigue life-to-breakthrough,fracture toughness was not a factor.The ini-tialﬂaw was assumed to be semi-elliptical with input distributions for the half-width,a,and depth,c.Again,the MC,MV,AMV,and FORM methods were implemented in NESSUS and UNIPASS.The predicted distributions of life-to-breakthrough showed good agreement with the experimental data over the entire CDF (Fig.5),with accurate predictions of the mean and important shortest lives.Furthermore,the AMV and FORM methods gave very similar results to the MC simulations in small fractions of the time. The MV predictions differed considerably from the experimental data for probabilities away from0.50;this result is somewhat ex-pected as the MV method assumes linear behavior which causes inaccuracies in non-linear systems.Each method’s predictions are compared for P f=0.01in Table3;again,the AMV+method was ap-plied at this probability level to conﬁrm convergence and agreed well with the AMV and FORM methods.This illustrates another case where AMV and FORM may be used to give similar predictions in small fractions of the time of MC.The sensitivity factors from the AMV analysis(Fig.6for P f=0.01)indicated that the initial crack size was most important,while the yield strength contributed neg-ligibly to fatigue life scatter.3.4.Single lap joint predictionsConstant amplitude fatigue experimental data were taken from the work by Moreira et al.[31].They conducted tests on45identi-cal single lap joint specimens at maximum remote stress of 160MPa and stress ratio of0.05[31].The single lap joint speci-mens consisted of a single column and three rows of rivets joining two160mmÂ20mmÂ1.2mm thick Al2024-T3sheets.TheTable3Comparison of SENT life prediction and efﬁciency for different probabilistic methods.(N=NESSUS,U=UNIPASS).The shortest experimental life was68,525cycles(P f=0.04)[15,30].Method Life to breakthrough(cycles)P f=0.01#of Trials Analysis timeN-MC-1k68,4651000 1.3hU-MC-1k72,8641000 1.3hN-MV24,035517sN-AMV75,327620sN-AMV+72,850937sU-FORM73,5051040s1046W.A.Grell,z/International Journal of Fatigue32(2010)1042–1049overlap was 60mm and the rivets rows were spaced 20mm apart.The specimen was designed to represent a normal rivet pitch of an aircraft fuselage.Fatigue cracks were observed to initiate at and grow from the ﬁrst (or third)rivet hole on the faying surface side [31].The faying surface is the surface of contact between the two sheets.In the work by Moreira et al.[31],the average fatigue life to fail-ure was 77,688cycles with a standard deviation of 18,320cycles.Their results are shown as cumulative probabilities (CDF)versus fatigue life in Fig.7.Based on a K–S test (a =0.05),a lognormal dis-tribution acceptably ﬁt the single lap joint life data,resulting in the following distribution parameters:shape =0.2348and scale =11.235.The distribution,along with the 5%and 95%bounds on the mean,is shown in Fig.7.The single lap joint specimen of Moriera et al.[31,35]was sim-ulated using the probabilistic AFGROW model incorporating vari-ability in initial crack size and crack growth rate.The yield strength and fracture toughness values were modeled as determin-istic as they did not affect the results in CT and SENT specimen pre-dictions.The crack was observed to be quarter elliptical in the lap joint study [31]and in typical observations for similar geometries [36].Three loading conditions were considered together:the by-pass stress from the remotely applied load,the bearing stress from the load transfer through the rivet,and the bending stresses due to the eccentricity of the joint.The stress intensity factor solutions for these cases have been developed by ﬁnite element techniques for the quarter elliptical crack [37,38]and the oblique through crack [39]and are implemented in AFGROW.Each loading condition is dealt with separately,and they are superposed to determine the stress intensity factor and crack growth rate.The solutions given by Newman and Raju [37],Zhao et al.[38],and Fawaz [39]are for any location along the elliptical crack front,denoted by u .;however,AFGROW uses values for u of 10°and 80°for the c and a solutions,respectively,to improve computational efﬁciency [40].The stress levels for the cases of tension,bending,and bearing loads were determined based on the geometry of the joint and a re-mote stress of 160MPa.At the ﬁrst (or third)rivet where failure occurs,the remote tensile load is divided into bypass and pin com-ponents.The bypass load is that which is transferred around the rivet hole through the top sheet.The pin load is that which is trans-ferred though the rivet to the bottom sheet.In this geometry,37.5%of the remote load is transferred through the ﬁrst rivet,leaving 62.5%as bypass load [35].In the analysis [35],friction between the sheets was neglected.Due to the eccentricity of the joint,a bending moment is produced inducing a bending stress in theExp. Moriera et al.Exp. log-normal fit Monte Carlo NESSUS MV NESSUS AMV NESSUS AMV+UNIPASS FORMSingle Lap JointTable 4Comparison of single lap joint life prediction and efﬁciency for different probabilistic methods.(N =NESSUS,U =UNIPASS).The shortest experimental life was 41,486cycles (P f =0.02)[31].Method Life (cycles)P f =0.01#of Trials Analysis time N-MC-1k 45,168100040min N-MV 26,40649s N-AMV 49,228512s N-AMV+46,0111229s U-FORM46,893821sW.A.Grell,z /International Journal of Fatigue 32(2010)1042–10491047。

Fatigue Strength and Residual Stress Analysis of Deep Rolled Crankshafts

Fatigue Strength and Residual StressAnalysis of Deep Rolled CrankshaftsImran M Quraishi1, Mrs Madhavi S Harne21Student, ME (Mechanical Design) Govt. College of Engineering, Aurangabad (MS)2Professor, (Mechanical Design) Govt. College of Engineering, Aurangabad (MS)1 (imranquraishi@),2 (msharne11@)AbstractThe endurance life of an engine crankshaft is closely related to its fatigue strength, in addition to other material properties and shape parameters. Deep rolling, moreover, enhances the fatigue limit by applying compressive residual stress within the fillet radius area as a major surface hardening technique. The objective of this paper is to maximize fatigue life of engine through crankshaft design optimization by quantifying fatigue strength for microalloyed steels versus Cr-Mo alloy steel, and to examine the effects of deep rolling load and rolled fillet geometry.Fatigue tests have been made with standard rotary bending test samples from both bar and forged blanks. Rig tests for actual crankshafts have been made to show how the fatigue strength correlates with different sample types. A correlation of stress distribution with bending moment was demonstrated by applying a strain gauging technique on crankshaft specimens. Therefore, an analysis of combined stresses could be made by considering the effect of static residual stress in addition to the applied dynamic bending stress.Optimum conditions for rolling load, fillet geometry and material were identified. Consequently, these results will be adapted to CAE analysis database to enable an optimization of safety factors.Key Words: Deep rolled crankshaft, Fatigue strength, residual tresses, design and optimization.1.IntroductionPreliminary performance prediction is the goal of all automotive designers. For the crankshaft this will be achieved by the quantification of material and the strengthening process. Deep rolling of the fillet area is a significant surface treatment of an engine crankshaft by which the fatigue life of a crankshaft is increased by developing a compressive residual compressive stress in the fillet area.Two types of forged crankshaft were made by using medium carbon microalloyed steels and a Cr-Mo alloy steel. The quantification of deep rolling on cast iron and carbon steel has been widely studied so far. [1][2]. However, the effects of fillet rolling were determined mostly on standard test samples rather than on actual crankshafts. Needless to say, the quantification of rolling on crankshafts used in engines was greatly lacking. Although a former study [3] revealed the effects of fillet rolling by load control, it is still difficult to explain the correlation of stress and moment on the enhancement of the design. In this research, a correlation was made between stress and moment by utilizing moment control that could support the design. The database extracted from these tests could directly enhance the design and FE analysis. Crankshafts from a V6 engine application were selected for testing as shown in Fig.1.The fatigue strength was investigated in terms of different materials and rolling load. Standard rotating bending fatigue specimens were prepared from the bar steel and forged crankshaft. Also, bending fatigue testing was conducted on crankshafts by a magnetic resonance system.Fig. 1 Shape of V6 crankshaftAttempts to apply a strain gauging technique to a production crankshaft have been successful. The correlation of stress distribution with the bending moment of a production crankshaft with a deep rolled area was demonstrated. An analysis of the effect of residual stress under normal conditions to bending stress at dynamic load was performed as well.2Experimental procedure2.1 MaterialTable 1 shows detailed chemical compositions of the steels used for the crankshaft study. Samples ‘A and B’ are microalloyed steels while sample ‘C’ represents a typical alloy steel that is quenched and tempered.Table 1 . Chemical composition of crankshaft steels (wt%)- A: Microalloyed steel – Only controlled cooling after forging- B: Alloy steel - Quenched and tempered after forging2.2 Rotating bending fatigue testIn this test, bending fatigue tests were conducted in order to determine how deep rolling could improve the fatigue strength of production crankshafts. Sections from actual forged crankshafts were extracted and used as test samples. Fig. 2 shows the method of specimen preparation from the forged part, (1) longitudinal (2) perpendicular to the direction of metal flow. The Ohno-type rotary bending fatigue test was used to determine the fatigue limit. .(a) (b)Fig. 2 Specimen preparation for actual crankshaft(a) Forged crankshaft (b) Standard bending fatigue specimen (c) A schematic of the machined area (hatched) in mm2.3 Crankshaft fatigue test methodActual crankshafts were prepared from the various steels to compare the bending fatigue limit which is defined by a bending moment. Fig. 3 shows the crankshaft magnetic resonance bending fatigue test rig. Specimens of each material were deep rolled at an optimized condition that was determined empirically. For the rig test, a half-cut of the crankshaft was used as a specimen. A bending moment was applied to the round area between crank pin and journal, the maximum stress was concentrated at the fillet radius(R) location. The mean stress was set to zero while an alternating moment was applied to simulate an engine load of compressive and tensile conditions.Fig.3 Schematic diagram of magnetic resonance bending fatigue tester.2.4 Stress measurement methodThe analysis of surface stress was conducted using strain gauges. As shown in Fig. 4, four gauges were used to acquire the strain signal of amplitude and mean strain.Fig. 4 Machined crank specimen used for fatigue rig test and strain gauging location.3Results and discussion3.1 Rotating bending fatigue strength3.1.1 Effect of metal flow and hardnessFig. 5 shows a difference in fatigue strength of coupon samples machined from the front-end and web of crankshaft. The fatigue strength of the front-end sample is 10 % higher than that of web sample. The front end sample has a metal flow parallel to the machined surface while the web sample has a metal flow perpendicular to the surface as shown in Fig. 6. In addition, the front end sample has higher hardness of HB 25 on average than the web sample due to a faster cooling rate. It is an indication that the geometry of metal flow is a predominant parameter to enhancing the fatigue limit along with hardness. Therefore, it should be noted that the design of the crankshaft should be optimized to accommodate the parallel metal flow especially in the fillet radius area where crack formation can be initiated. The safety factor should also be considered on the basis of the actual mechanical properties of the fillet radius area.Fig.5 Fatigue strength of Cr-Mo steel vs. microalloyed steels for 3.3L forged crankshaftFig. 6 Metal flow of specimen from fillet radius area.3.1.2 Microalloyed steel vs. alloy steelFig. 7 illustrates the fatigue strength data of the micro-alloy steels and that of the quenched and tempered (Q-T) alloy steel. Microalloy steels show a fatigue strength ranging from 370 to 390 MPa whereas the Q-T alloy steel exhibits a fatigue strength of 410 MPa. This data is in good agreement with Richards et al.[2]. The fatigue strengths in this study are within 5~10% of those steels. It should be noted the microalloy steels have different fatigue strengths presumably due to differences in vanadium content. The average vanadium content of microalloy steel A is 0.14% whereas that of B is 0.12%. The minor increase in the vanadium content of steel A compared to steel B could achieve a 5% increase in fatigue strength due to an increase in tensile strength resulting from the higher vanadium content. When it comes to the development of a better alloy design for microalloy steels, the goal is to achieve an equivalent level of fatigue strength with a Q-T alloy steel. Thus, it is proposed that the chemistry be modified such that the vanadium content is more than 0.15% when substituting microalloy steels for Q-T alloy steels.Fig. 7 Fatigue strength of standard sample from forged steel crankshaft variations3.2 Crankshaft rig test resultsA crankshaft is a component on which a torsional bending mode or so called combined stress is exerted. Yet, the bending stress significantly exceeds the torsion stress. In fact, most of the crankshafts that failed in fatigue were due to bending fatigue. In this test, the primary focus was on bending fatigue using bending moment control. 3.2.1Bending moment of microalloyed steel vs. alloy steelThe bending fatigue limit obtained for the crankshafts is shown in Fig. 8. This figure shows that the bending fatigue limit of microalloyed steel is 1100~1150N.m and bending fatigue limit of alloy steel is 1200N.m. These results follow the same trend as the results obtained from rotating bend testing which are shown in Fig. 7. These results demonstrate that the effect of fatigue stress can be evaluated by a dynamic bending moment test.Fig.8 bending moment of a 3.3L crankshaft3.2.2 Effect of deep rollingFig. 9(a) shows the difference in results between deep rolled and un-rolled crankshafts for a 1L engine. The bending fatigue limit for the deep rolled crankshaft was 500N.m whereas the bending fatigue limit for the groove machined crankshaft was 240N.m. Hence, the deep rolled crankshaft’s bending fatigue limit was enhanced by 108% compared to that of the groove machined crankshaft. Fig. 9(b) depicts the results from the deep rolled and un-rolled crankshafts for a 2.5L engine application. Here, the bending fatigue limit for the rolled crankshaft was 800N.m whereas the bending fatigue limit for the un- rolled crankshaft was 300N.m. Thus, the deep rolled crankshaft showed a 166% improvement as compared to that of the un-rolled version. The rolling loads of crankshafts are 4.5kN and 7.0kN, respectively. Improvement of the bending fatigue limit for deep rolling indicates that surface strengthening is a major portion of the fatigue limit for crankshaft.(a) Deep rolled and un-rolled crankshafts for the 1L engine (b) Deep rolled and un-rolled crankshafts for the 2.5L engineFig.9 Results of dynamic bending moment test3.2.3 Correlation of bending moment and stressIn line with the fatigue moment strength obtained from the above rig test, the following test was conducted in order to quantify the fatigue strength. Stress measurements were made with different applied moments by bonding the strain gauges to the main locations: fillet radius and the centre of pin journal. The signal produced from the strain gauge is shown in Fig. 10(a). In addition, the amplitude, the mean stress of the fillet radius and the pin surface are defined in Fig. 10(b). The stress measurements from the dynamic bending test were nearly identical regardless of the types of steel that were used and when the design of the crankshafts stayed the same. The area of interest is the amplitude stress on the fillet radius.Fig. 10 Stress measurement method by strain gauging(a) Signal of strain gauge (b) Definition of amplitude and mean stress, * A: amplitude, M: mean, U: upper, L: lowerFigure 11 plots applied stress against the bending moment for the 1L crankshaft. Figs. 11(a) and (b) show the 1L crankshaft with 4.5kN rolling load. The mean stress is nearly zero, that is, R=-1 and the amplitude stress is significantly higher at the fillet radius than at centre of the pin surface. This figure shows the linear relationship of stress and moment. The applied stress for fillet radius area was compared to quantify the effect of deep rolling. The evaluation revealed that applied stress of the unrolled crank was 332MPa at a bending moment fatigue limit of 240N.m whereas the nominal stress of the rolled crank was 688MPa at the bending moment fatigue limit of 500N.m. It was found that the surface nominal stress is increased 107% as the bending moment fatigue limit is increased up to 500N.m.(a) Stress analysis of un-rolled for 1L engine(b) Stress analysis of deep rolled 1L engineFigure 11(c) also shows the result of stress vs. moment for 3.3L type crankshaft with 7.0kN rolling load. The bending moment fatigue limit of this crankshaft was 1100~1200N.m as shown in Fig.8. Since the strain gauge can be used only up to 600N.m, a linear regression was made to obtain the nominal stress at 1100N.m~1200N.m. The nominal stresses are in the range of 1239MPa~1352MPa. By applying the fatigue strength of the former results, 370MPa and 410MPa for microalloyed and alloy steel, it is estimated that the surface nominal stress of the fatigue limit increased up to 230%~235%.(c) Stress analysis of deep rolled 3.3L engineFig.11 Correlation of applied moment and stress3.2.4 Effect of residual stressIt should be noted that the increase of fatigue limit referenced in this paper is considerably higher than the results from Richards et al.[3] where fatigue limit increases 51~63% after deep rolling. Our results are from an actual crankshaft sample test where the nominal stress represents only the crack initiated area in the subsurface while the fatigue strength of standard sample [3] is calculated from the cross section area of specimen. Considering the distribution of residual stress after deep rolling, the subsurface area has the maximum compressive stress which contributes to the fatigue strength increase at the crank-web area. Therefore, there is a good agreement between rig test and standard sample fatigue results. Besides, it is found that one should recognize the real applied stress value at the tip of fillet radius surface to optimize crankshaft design.A detailed map is under development of the fillet radius area in terms of the hardness distribution to confirm the effect of residual stress at different locations.4ConclusionsThe conclusions obtained in this work are as follows.1. Correlation of bending moment and stress has been evaluated to quantify the effect of deep rolling. It wasdemonstrated that the bending moment of deep rolled and unrolled crankshaft vs. applied stress of the fillet radius area. The design safety factor can now be calculated directly by quantifying the stress.2. The optimal chemistry for the microalloyed steel, which provides the same level of fatigue strength as the alloy steel, was established. The fatigue strength varied accordingly with the different chemistry.3. It was demonstrated that the geometry of metal flow is a predominant parameter to enhance the fatigue limit along with hardness. Therefore, the design of the crankshaft should be optimized to accommodate the parallel metal flow in the fillet radius area.5AcknowledgementsThe authors wish to acknowledge the guide Mrs Madhavi S Harne and the assistance from Nipas Forging ltd who helped to perform many of difficult experiments on the stress analysis.6References[1]T.Shimamoto, T.Yamaguchi, Y.Suzuki, R. Ohmi,” Improvement of fatigue strength on crankshaft by fillet rolling”, JSAE Vol.44, No.6, 1990.[2]T.C. Chatterley, P.Murrell, “ADI Crankshaft – An Appraisal of Their Productin Potential,” Society of Automotive Engineers, Inc.,980686, 1998,[3] 3. M.D.Richards, D.K.Matlock, J.G.Speer, “Deep rolling response of notched medium carbon bar steels”, SAE 2004-01-1528,2004.[4]H.Park, Y.S.Ko, S.C.Jung, “Fatigue life analysis of crankshaft at various surface treatments”, Society of Automotive Engineers, Inc.,01ATT193, 2001[5]Kamimura, T., 1985, “Effects of Fillet Rolling on Fatigue Strength of Ductile Cast Iron Crankshaft,” SAE Technical Paper No.852204, Society of Automotive Engineers, Warrendale, PA, USA.[6]Hoffmann, J. H. and Turonek, R. J., 1992, “High Performance Forged Steel Crankshafts – Cost Reduction Opportunities,” SAETechnical Paper No. 920784, Society of Automotive Engineers, Warrendale, PA, USA.[7]Chien, W. Y., Pan, J., Close, D., and Ho, S., 2005, “Fatigue Analysis of Crankshaft Sections Under Bending with Consideration ofResidual Stresses,” International Journal of Fatigue, Vol. 27, pp. 1-19.[8]Williams, J., 2007, “Fatigue Performance Comparison and Life Predictions of Forged Steel and Ductile Cast Iron Crankshafts,”Masters Thesis, The University of Toledo, Toledo, OH, USA.。

非特异性腰痛的研究进展

腰痛可分为由非脊柱或脊柱起源的特定病理生理机制引起的疼痛及其他症状和非特异性腰痛，非特异性腰痛是指通过客观检查不能确定腰痛原因，没有组织结构的改变，也不能发现病理变化的一种腰痛，可能是生物、心理和社会因素共同作用的结果，占腰痛的80%~90%[1]。

本文总结近年来诊疗非特异性腰痛的相关文献，以期为该病在结合医院实际情况下，为临床医生、治疗室选择更加合理的诊疗放法提供参考。

1　非特异性腰痛的流行病学腰痛（LBP）是临床上一种极为常见的疾病，给社会带来了巨大的负担[2]。

不仅如此，腰痛也会对个人健康和经济状况产生不可忽视的影响。

在健康方面，腰痛会导致与腰痛有关的症状和功能障碍，限制日常或娱乐活动，以及严重残疾。

腰痛对个人的经济负担主要表现在腰痛后寻求医疗康复的直接治疗费用，以及占用大量工作时间的间接费用[3]，80%以上的人在其一生中至少经历过一次腰痛。

当腰痛从急性或亚急性转变为慢性腰痛时，就很难完全康复，只有5%的患者会完全消失[4]。

非特异性腰痛是全世界残疾的主要原因。

急性非特异性腰痛患者通常有良好的预后，在两个月内迅速改善。

然而，大多数患者会发展成慢性非特异性腰痛，反复发作[5]。

2　非特异性腰痛的发病机制2.1　椎旁肌问题椎旁肌的问题可能是导致非特异性腰痛发生的最重要因素。

脊柱的稳定性主要取决于椎旁肌的支持。

因此，当椎旁肌肌肉萎缩或其肌纤维特性发生改变时，将导致非特异性腰痛的发生。

研究表明，非特异性腰痛患者的背部肌肉力量和活动水平明显低于健康人[6-7]。

2.2　心理因素大多数非特异性腰痛的患者都有慢性疼痛。

在长期忍受疼痛的过程中，他们会逐渐产生不健康的心理问题，如抑郁症和焦虑症。

这种不健康的心理往往导致疾病的加重和复发。

因此，社会心理因素在腰痛中起着重要的作用。

在慢性腰痛中，良好的心理健康是促进非特异性腰痛患者缓解疼痛的重要因素[8]。

我们应将抑郁症等不健康状态视为公共卫生的重点，着力解决患者的不健康心理问题，鼓励患者积极接受治疗。

Research on drive fatigue detection using wavelet transform

Abstract —Driver fatigue is an important factor causing serious traffic accidents and often results in many people deaths or injuries. Therefore, many countries have made great effort on how to detect driver fatigue. This paper presents a new approach to detect driver fatigue based on discrete wavelet transform which has been used to extract the key features for constructing the classifier to identify driver fatigue. . The analyzed data are obtained from experiments using driving simulator. The result proves the algorithm is valid.I. I NTRODUCTIONriver fatigue is one of the main causes of traffic accidents, and endangers traffic safety increasingly. However, the drivers are unable to be aware of forthcomingaccident by themselves. Therefore, vehicle detection sensorsare always used to monitor the driver's driving behaviors andphysiological information to make sure that the vehicle is on its usual driveway. If the vehicle deviates too much, the console will buzz and a precautionary measure will be done to prevent accidents. Now, detection of driver fatigue is a hot topic for intelligent transport system in home and abroad [1]. The methods for detecting driver fatigue can be divided into subjective and objective. Recently, most of the researchers are concentrating on objective detecting method. The former include Fatigue Assessment Questionnaire (FAQ), Stanford Sleepiness Scale and Pearson-Byers Fatigue Feeling Checklist (FFC) so on. For example, the Transport Department in EU requires each bus equip a vehicle data recorder for safe. But these methods will not consider thedifference in body, mind, diet and health. The effect of detecting and preventing driver fatigue is not satisfied. The later could estimate different drivers, and the result is better, including EEG (electroencephalography), EKG (electrocardiogram), PERCLOS (Percent Eyelid Closure), etc. But these methods are hard to be applied in real time for the device limitation [2-5].Many literatures have used wavelet analysis to detecting driver fatigue. Gabor wavelet was used to extract texture facial features of drivers [6-7]. Wavelet coefficients are alsoproposed as features for identifying muscle fatigue [8].This paper mainly introduces the application of theWavelet Analysis on vehicle parameters to detecting driverfatigue. Data are collected through a driving simulator M. W. Mao is with the National Institute of Standards and Technology, Boulder, CO 80305 USA (e-mail: mmw85108@).L. P. Du is with University of Science and Technology, Beijing, China 100083. (corresponding author, Phone: 86-10-62332991; e-mail: liping199@).including normal driving state and abnormal driving state. While analysis result in the time-domain cannot characterize the state of mind well, the data has been computed in the frequency-domain using wavelet transform. After the wavelet decomposing by Haar wavelet function, the feature vectors have been extracted. Then the minimum distance classifier has been constructed to identify the driving state.II. E XPERIMENTAL D ESIGNThe experiment is performed on a high fidelity drivingsimulator for sufficient duration in order to test changes between normal and fatigue driver state. A. Driving SimulatorThe study is conduced on the VR-4 driving simulator which is produced by our own lab and has been applied to simulating exam for driving school. The simulator is a fixed-base device which provides real-time, interactive feedback to the driver through a combination of visual, auditory, and tactile cues, wide-view visual scene, a steering torque controller, and high-fidelity vehicle dynamics models. The visual scene is generated by a computer, and is presented on a 160° wrap-around front projection screen. The vehicle used for the test was a full body Santana. The roadway image presented to the drivers was that of a four lane highway at night which contains the curved and straight roads. The image of VR-4 driving simulator is shown in Fig.1.Fig. 1. VR-4 driving simulatorB. Experimental Design The test duration was about 2 h and began at or near 1:30 in the afternoon. Driver subjects were asked to sleep 3h less the night preceding the test. Vehicle speed is asked to maintain about 110km/h. And the test will be terminated if the driver subjects fall on sleep.RESEARCH ON DRIVE FATIGUE DETECTION USINGWA VELET TRANSFORMMingwang Mao, and Liping DuD1-4244-1266-8/07/$25.00 ©2007 IEEE.The collected data in the experiment are as follows: V (The vehicle speed), α (the steering wheel angle), γ (the state of accelerator), the status of turning lamp, as well as images of drivers. The track profile s is obtained according to the vehicle dynamics model.III. DATA PROCESSA. Data PreprocessThe data is the track collected from the driver simulator. Firstly, load the original data in Matlab, resample the data and divide it into segment. Each segment contains data collected within 100s, which is shown in Fig. 2. The resample data shows the same profile as original data.Fig. 2. One segment of original data and its resample data. Each segment is denoised by using WDEN function. Matlab achieve it in the way [XD, CXD, LXD] =WDEN (X, TPTR, SORH, SCAL, N, ’wname’).The string ‘TPTR’ includes threshold selection rules and the string ‘SCAL’ define present the definition of the threshold adjustment. The function returns a de-noised version XD of input signal X and additional output arguments [CXD, LXD] which are the wavelet decomposition structure of de-noised signal XD.The denoising procedure proceeds in three steps:--First, decomposition. Compute the wavelet decomposition of the signal X at level 5 by ‘db3’ wavelet. We got approximation coefficients AD and detail coefficients DD --Second, detail coefficients thresholding. For each level from 1 to 6, select a threshold and apply soft thresholding to the detail coefficients DD. Here we select ‘minimaxi’ as the threshold selection rule, which means it gives the extremumof standard deviation, not without error. The modified detail coefficients are expressed as DD’. --Third, reconstruction. Compute wavelet reconstructionbased on the original approximation coefficients AD and themodified detail coefficients DD’. The reconstructed signal is XD.Take one segment for example, the original and thede-noise signal are compared in Fig. 3.Fig. 3. Orignal signal and denoised signal.The de-noised signal is processed by wavelet transform. Here WAVEDEC function is used which performs a multilevel 1-D wavelet analysis using either a specific wavelet 'wname' or a specific set of wavelet decomposition filters. ‘Bior 3.1’wavelet is used to analysis the signal.B. Feature Extraction Based on Wavelet AnalysisGiven a wavelet decomposition structure (C and L), WRCOEF function is used to reconstruct the coefficients of a 1-D signal at level N. Based on the experiment, ’bior 3.3’ wavelet is chosen for the reconstruction filter. The low frequency coefficients (approximate coefficients) and high frequency coefficients (detailed coefficients) are shown in fig. 4 and fig. 5. As the data is divided into segments per 100s, each segment can be considered as stationary signal. As shown in fig. 4, low frequency coefficients of each level have little changes and are unfit for feature vectors. Fig. 4. Low frequency coefficients of one segment (a1~a7 presentreconstructed coefficients from level one to level seven).Here we choose the high frequency coefficients as the feature vectors.Fig. 5. High frequency coefficients of one segment (d1~d7 present reconstructed coefficients from level one to level seven).According to the fig. 5, signal d1~d5 contain a lot of noise, level 6 (d6) reflects the signal characteristics well and used as feature vectors. Each 100 seconds data of d6 forms a row of matrix B. Then, matrix B contains the entire characteristic coefficient. The row vectors are divided into two groups, normal driving state and abnormal driving state, according to experimental records for the next step to construct distance classifier.C. Distance classifierWe compute element-by-element mean of feature vectors belonging to the normal state group. The resulting vector is considered as the distinguishing vector of normal state. In a similar way, the distinguishing vector of abnormal state is determined. The two distinguishing vectors are shown in Fig. 6.Fig. 6. Normal and abnormal distinguishing vectors of track.Each segment of the data array is compared with the resulting normal and abnormal distinguishing vectors, and the different values give two arrays 'g'and'b'. If g>b, the driver is considered as to be fatigue; If g ≤b, the state is normal. Theoverall process is shown as fig. 7:Fig. 7. The flowchart of our method.Through the classifier, the driving state of segments can be judged; the results are shown in Fig. 8. Upper part is the segments which are driving fatigue. Lower part shows the distance comparison.Fig. 9. The track results of distance classifier.In addition, the normal and abnormal distinguishing vectors of steering wheel angle are shown in Fig. 9. The resultof detecting driving fatigue is shown in fig. 10.Fig. 9. Normal and abnormal distinguishing vectors of steering angle.Fig. 10. The steering angle results of distance classifier.IV.C ONCLUSIONThe detection of driver fatigue is performed by using wavelet analysis. The analysis data are vehicle track and steering angle collected through driving simulator. The data was preprocessed by noise reduction and resampling. The high frequency coefficients of wavelet analysis are used as feature vectors and distance classifier is applied to distinguish the driving state. The results show that it is feasible for the application of wavelet analysis methods to detect driver fatigue.A CKNOWLEDGMENTThis paper is supported by Professor Yanjiong Zhong, University of Science and Technology Beijing.R EFERENCES[1]White paper on Traffic Safety in Japan.International Association ofTraffic and Safety Sciences, IATSS 2001. 10.[2]X. J. Shi, and H. W. Xie, “Review on driver fatigue detectiontechnology,” The First International Conference on Transportation Engineering, vol. 1, pp. 1715-1717, 2007.[3] D. F. Mix, and K. J. Olejniczak, Elements of Wavelets for Engineersand Scientists., NJ: Wiley-Interscience, 2003.[4]Y. C. Huang, “Fault Identification of Power Transformers UsingGenetic based Wavelet Networks,” IEE Proc.Sci.Meus.Teclinol.，vol.150, no. 1, pp. 25-29, 2003.[5]M. M. Saied, “Capacitor Switching Transients: Analysis and ProposedTechnique for Identifying Capacitor Size and Location,” IEEE Trans.Power Deliv., vol. 19, no. 2, pp. 759-765, 2004.[6]R. B. Wang, K. Y. Guo, S. M. Shi, and J. W. Chu, “A monitoringmethod of driver fatigue behavior based on machine vision,” IEEE Proceedings of Intelligent Vehicles Symposium, pp. 110-113, June 9-11 2003.[7]Q. Ji, Z. W. Zhu, and P. Lan, “Real-Time Nonintrusive Monitoring andPrediction of Driver Fatigue,” IEEE Transactions on Vehicular Technology, vol. 53, no. 4, July 2004.[8] D. Moshou, I. Hostens, G. Papaioannou and H. Ramon, Waveletcoefficients are proposed as features for identifying muscle fatigue.Applied Soft Computing, vol. 5, no. 4, pp. 391-398, July 2005.。

international journal of fatigue简介

international journal of fatigue简介International Journal of Fatigue (IJF) is a leading academic publication in the field of fatigue and structural integrity. With a focus on providing a platform for researchers and practitioners to share their knowledge and advancements, IJF plays a crucial role in disseminating cutting-edge research and promoting innovation in fatigue analysis and design.As one of the most respected journals in the field, IJF publishes high-quality papers that contribute to the understanding and prediction of fatigue behavior in various materials and structures. The journal covers a wide range of topics, including experimental investigations, theoretical studies, and numerical simulations related to fatigue and fracture mechanics.IJF welcomes submissions from both academia and industry, fostering collaboration between researchers and practitioners. The journal's editorial board comprises renowned experts from around the world, ensuring a rigorous and impartial peer-review process. This process ensures the quality and integrity of the published articles, making IJF a trusted source of information for scientists, engineers, and professionals in the field of fatigue.The scope of the journal encompasses several key areas, including fatigue crack growth, fatigue life prediction, fatigue testing techniques, and durability analysis. Additionally, IJF explores emerging topics such as multiscale fatigue modeling, environmental effects on fatigue, and fatigue in advanced materials and structures. By covering a broad range of subjects, IJF offers a comprehensive and up-to-date perspective on fatigue research.IJF aims to bridge the gap between fundamental research and practical applications. The journal encourages the submission of papers that have direct implications for industry, addressing real-world challenges and proposing practical solutions. By providing a platform for knowledge exchange, IJF facilitates the transfer of innovation from academia to industry, enabling technological advancements and enhancing the reliability and safety of engineering systems.In addition to regular research articles, IJF publishes review articles, technical notes, and case studies, further enriching the readers' experience and providing comprehensive insights into the field of fatigue. These diverse types of contributions enhance the journal's value as a reference for researchers, engineers, and practitioners seeking both in-depth analysis and practical advice.Furthermore, IJF embraces international collaboration and diversity, publishing articles from researchers around the globe. This global perspective ensures a wide range of perspectives and promotes the exchange of ideas and methodologies across different cultures and scientific communities.In conclusion, International Journal of Fatigue serves as a vital platform for the dissemination of knowledge and advancements in the field of fatigue and structural integrity. By fostering collaboration, promoting innovation, and providing a comprehensive perspective, IJF contributes significantly to the advancement of fatigue research and its practical applications. Researchers, engineers, and professionals can rely on IJF as a trusted sourceof high-quality research, helping them stay at the forefront of this critical field.。

GCK对高脂饲料诱导的小鼠肥胖模型的降脂减肥作用

Hans Journal of Food and Nutrition Science 食品与营养科学, 2020, 9(1), 1-7Published Online February 2020 in Hans. /journal/hjfnshttps:///10.12677/hjfns.2020.91001Inhibition of GCK on High Fat Diet-InducedMouse ObesityJianqin Mao1, Xiaofang Zhong1, Lifei Liu1,2,*1Zhejiang HISUN Pharmaceutical CO., Ltd., Taizhou Zhejiang2Wuhan Optics Valley Yatai Pharmaceutical Research Institute Co, Ltd., Wuhan HubeiReceived: Dec. 12th, 2019; accepted: Dec. 23rd, 2019; published: Dec. 30th, 2019AbstractObjective: To investigate the effect of GCK on high fat diet-induced mouse obesity model. Methods: Mice were fed a high-fat diet for 12 months to develop an obesity model. GCK was intragastrical administered for 6 weeks, while the food intake and body weight were recorded. The mice were sacrificed at the end of the experiment. The plasma levels of ALT, AST, TC and TG were detected by automatic biochemical analyzer. The liver was prepared by paraffin section and stained by HE staining kit. The RNA was extracted from the liver homogenate, and the levels of lipid metabolism related proteins FAS and PPARα were detected by RT-PCR. Results: GCK did not affect the food in-take of mice, but high dose of GCK could cause weight loss in obese mice. GCK can effectively re-duce plasma ALT, AST, TC, TG levels in mice; GCK can reduce the fat content in mouse liver. The mechanism of those effects may be to induce the FAS decrease and PPARα increase. Conclusion: GCK can inhibit the HFD-induced obesity.KeywordsGinsenoside Compound k, Mouse Obesity Model, Fat Loss, Lipid Metabolism-Related GeneGCK对高脂饲料诱导的小鼠肥胖模型的降脂减肥作用毛剑琴1，钟晓芳1，刘礼飞1,2*1浙江海正药业股份有限公司，浙江台州2武汉光谷亚太医药研究院有限公司，湖北武汉收稿日期：2019年12月12日；录用日期：2019年12月23日；发布日期：2019年12月30日*通讯作者。

统计学随机分组(实验动物含小鼠)-PPT

[4] 赵伟，孙国志. 常用实验动物随机分组方法，实验动物，2009年第4期
[5]万霞, 刘建平. 临床试验中的随机分组方法. 中医杂志2007 年第 48 卷第3 期
阳性对照组：通常是给予疾病模型动物已知应该有效的药物或者其他有效因素的处理；目的是对比某受试药物与阳性药物对比，是否有效；举例：已知阿霉素对乳腺癌肿瘤生长有抑制作用，因此我们可以选用阿霉素作为阳性对照，来判断此受试药物的治疗效果。
问题二：每组几只合适？
动物实验设计应遵循实行“3R原则”，包括实验动物的替代、减少和优化原则，其中减少即指尽量减少实验动物的数量。查阅文献，并未发现对实验动物数目有绝对要求，但在减少的同时，一定要满足统计学要求。统计学上要求一般至少每组有6个可用数据，才有意义。
[2] Festing M F, Altman D G. Guidelines for the Design and Statistical Analysis of Experiments Using Laboratory Animals[J]. Ilar Journal, 2002, 43(4): 244-258.
一般小鼠的每组一般不少于10只；一般大鼠每组不少于6只；大动物等级越高，价格越贵，根据情况可适当
减少，但一般不能少于4-5只。
问题三：如何进行随机分配？
根本不同的实验目的，实验对象，分组时常用的方法有：完全随机设计、随机区组设计等[3-4]。实现随机分组时需要利用随机数字表以及随机数余数分组法。
优势：区间分组将保证了实验组间的生物差异减到了最小，遵循了一致性原则与随机性原则，使实验结果更具有统计学意义。
注：有时候我们会碰到多个因素，则需要依次分区，如：40只体重差异较大的小鼠，雌雄不一，此时我们不能只按照体重区组分配，需要先把雌雄分开，然后各自按体重分层。即它要求随机先按某一因素分成相等的几组，再在组内按另一因素分成几个区。

Fatigue of structures and materials

2. Fatigue of materials as a physical phenomenon 2.1. Fatigue crack initiation . . . . . . . . . . . . . 2.2. Fractographic observations . . . . . . . . . . . 2.3. More about fatigue crack growth . . . . . . .
Nomenclature CA VA OL Sf Constant amplitude Variable amplitude Overload Fatigue limit
1. Introduction An evaluation of fatigue of structures and materials in the 20th century raises the question what happened in the 19th century? The answer is that fatigue of structures became evident as a by-product of the industrial revolution in the 19th century. In some more detail, it was recognized as a fracture phenomenon occurring after a large numbers of load cycles where a single load of the same magnitude would not do any harm. Fatigue failures were frequently associated with steam engines, locomotives and pumps. In the 19th century, it was considered to be mysterious that a fatigue fracture did not show visible plastic deformation. Systematic fatigue tests were done at a few laboratories, notably by August ¨ hler. It was recognized that small radii in the Wo geometry of the structure should be avoided. Fatigue was considered to be an engineering problem, but the fatigue phenomenon occurring in the material was still largely in the dark. Some people thought that fatigue implied a change from a ﬁbrous to a crystalline, brittle structure in view of the absence of visible plastic deformation. A fundamental step regarding fatigue as a material problem was made in the beginning of the 20th century by Ewing and Humfrey in 1903 [1]. They carried out a microscopic investigation which showed that fatigue crack nuclei start as microcracks in slip bands. Much more evidence about fatigue as a material phenomenon was going to follow in the 20th century. Fatigue as a technical problem became evident around the middle of the 19th century. About 100 years later, in the middle of the 20th century, the development of fatigue problems were reviewed in two historical papers by Peterson in 1950 [2] and Timoshenko in 1954 [3]. Both authors were already well-known for important publications. Peterson reviewed the discussion on fatigue problems during meetings of the Institution of Mechan-

211245384_基于直观汉字构形原理的C3-GAN字体生成优化方法

第44卷第10期包装工程2023年5月 PACKAGING ENGINEERING 193收稿日期：2022–12–02基金项目：2023年河北省教育厅人文社会科学研究重大课题攻关项目（ZD202327）阶段性成果。

作者简介：秦嘉霖（1994—），女，硕士，主要研究方向为字体设计。

基于直观汉字构形原理的C 3-GAN 字体生成优化方法秦嘉霖1,2，刘维尚1（1.燕山大学，河北秦皇岛 066004；2.河北省设计创新及产业发展研究中心，河北秦皇岛 066004）摘要：目的为了提升生成对抗网络汉字风格迁移的图像生成质量，实现汉字智能生成在字库产业中的实际应用，提出了一种基于直观汉字构形学的条件生成对抗网络字体生成优化方法（Optimization of Conditional Fonts Generation with Chinese Character Configuration GANs ，C 3-GAN ）。

方法建构了直观汉字构形模组（C 3Module ），该模组包含了利于条件生成对抗网络进行汉字构形语义特征学习的全特征汉字字符集。

C 3-GAN 在条件生成对抗网络模型下进行字体生成训练，降低了必要训练样本数量，实现对字体生成效果的优化。

结果使用C 3-GAN 生成汉字图像的清晰度更高、字形更准确。

在图像相似性定量评估中，使用C 3-GAN 的实验组相比于其他模型，获得了更高的相似值和更小的误差值。

结论使用C 3-GAN 可以降低必要训练样本数量、提升汉字图像质量。

在实际项目中具有一定的应用性和可操作性。

关键词：生成对抗网络；汉字构形；人工智能；深度学习；汉字字体；C 3-GAN 中图分类号：TB472 文献标识码：A 文章编号：1001-3563(2023)10-0193-09 DOI ：10.19554/ki.1001-3563.2023.10.019C 3-GAN Fonts Generation Optimization Based on IntuitiveChinese Character ConfigurationQIN Jia-lin 1,2, LIU Wei-shang 1(1.Yanshan University, Hebei Qinhuangdao 066004, China;2.Hebei Design Innovation and Industrial Development Research Center, Hebei Qinhuangdao 066004, China) ABSTRACT: The work aims to propose a method for Optimization of Conditional Fonts Generation with Chinese Character Configuration GANs (C 3-GAN) of the intuitive Chinese character configuration to improve the image generation quality of Chinese character style transferring with generative adversarial networks, and achieve the practical application of Chinese character intelligent generation in the font industry. An intuitive Chinese character configuration module (C 3 Module) was constructed, which contained Chinese character sets with all features. It was beneficial to generating an adversarial network for the learning process of semantic features of Chinese character configuration. Performing font generation training with C 3-GAN under the model of the conditional generative adversarial network reduced the number of compulsory training samples, and optimized the font generation effect. C 3-GAN could generate Chinese characters with higher images definition and more accurate glyphs. In the quantitative evaluation of image similarity, the experimental group using C 3-GAN obtained higher similarity values and smaller error values than other models. C 3-GAN can reduce the number of compulsory samples, and improve the image quality of Chinese characters. It has certain applicability and operability in practical projects.KEY WORDS: generative adversarial networks; Chinese character configuration; artificial intelligence; deep learning; Chinese character font; C 3-GAN194 包装工程 2023年5月近年来人工智能技术以其强大的数据分析能力和运算能力被广泛应用。

Fatigue testing under variable amplitude loading

Fatigue testing under variable amplitude loadingC.M.SonsinoFraunhofer-Institute for Structural Durability and System Reliability LBF,Darmstadt,Germany Received 22May 2006;received in revised form 7September 2006;accepted 4October 2006Available online 28November 2006AbstractThere are many publications about variable amplitude test results.However,very often information on load–time histories,spectra and testing details are missing.This fact does not allow the interpretation of test results with regard to fatigue liﬁng and structural dura-bility design.Therefore,this paper aims at presenting how spectra and test conditions should be clearly described and how statistics can be applied when variable amplitude test results are presented.Ó2006Elsevier Ltd.All rights reserved.Keywords:Variable amplitude loading;Constant amplitude loading;Cumulative damage;Load–time histories;Multichannel loading;Presentation of spectrum;Level crossings;Range pairs;Rainﬂow matrix;Safety;Risk1.IntroductionThe major reason for carrying out variable amplitude loading (VAL)tests is the fact that a prediction of fatigue life under this complex loading is not possible by any cumulative damage hypothesis.Therefore,for the purpose of fatigue liﬁng,experiences must be gained by such tests which allow to derive real damage sums by comparing Woehler-and Gassner-lines,Fig.1.Applying the because of its simplicity still mostly used Palmgren–Miner-Rule modiﬁed by Haibach [1],the dam-age content of a spectrum with the size L s can be determined X n Ni ¼D spec ð1Þand with this value the real damage sum is calculated from the experimental results:D real ¼D specL sÁN exp ð2ÞA broad investigation on cumulative fatigue [2]displays the scattering of the real damage sum over almost three dec-ades,Fig.2.About 90%of all results are below the conven-tionally used value D =1.0,i.e.a fatigue life estimation with D =1.0is in these cases at the unsafe side.This knowledge justiﬁes the need of variable amplitude testing,necessary on one hand for the investigation of cumulative damage behaviour of components or structures and on the other hand for the structural durability proof [3].For this,the most important prerequisite,the load–time history,must be given [1,4].The cumulative frequency dis-tribution of load amplitudes or ranges (spectrum)is derived afterwards from the load–time history.Generally,load–time histories applied in testing are derived from service load–time histories,Fig.3,compiled to load sequences corresponding to a deﬁned mission,e.g.wave spectrum for one year,a ﬂight between two des-tinations or a deﬁned driving distance.The ﬁrst variable amplitude loading spectrum was intro-duced by Gassner for aeronautical structures,the historical Eight-Block-Programme Test,Fig.4[5].The reason of the blocking was that random loading processes could not be yet simulated by existing simple testing machines at that time.In the 1960s due to the access of servo hydraulic testing machines random processes could be simulated fairly well and the historical Eight-Block-Programme Test could be substituted by a more realistic load–time process,e.g.the Gaussian random load distribution,Fig.5.0142-1123/$-see front matter Ó2006Elsevier Ltd.All rights reserved.doi:10.1016/j.ijfatigue.2006.10.011E-mail address:c.m.sonsino@lbf.fraunhofer.de/locate/ijfatigueInternational Journal of Fatigue 29(2007)1080–1089International Journalof FatigueAs load–time histories depend on the particular appli-cation(oﬀshore,aeronautics,railways,automotive, bridges etc.)and function of the components,in the past 65years diﬀerent application related standard spectra were developed,Tables1and2[6],and are still under develop-ment.Thus,this paper will not address the methodologies for deriving testing spectra,but the principles to be respected,when tests have to be performed with a given spectrum.2.Documentation and presentation of the loadingA testing spectrum is characterized mainly by following parameters,Fig.6:–Maximum and minimum values,–load(stress)ratio R of the maximum values,–spectrum(sequence)length(size)L s and–shape.These parameters must be documented and presented by a cut-out of the load–time history,by the rainﬂow matrix, by the load ratio R of the maximum load values of the spec-trum,the irregularity factor I,and by the conventional cycle counting methods level crossings and range pairs. The maximum value of the level crossings counting indi-cates the level of the maximum spectrum stress with regard to the yield strength of the material as well as how far the high-cycle fatigue strength is exceeded.The comparison of the spectra accounting to both counting methods,level crossings and range pairs,in term of ranges gives the infor-mation about present mean-load(stress)ﬂuctuations, which have an additional damaging inﬂuence[3];this is dis-played if the spectra for both counting methods are notNomenclatureC probability of conﬁdenceD damage sumF loadL s sequence lengthL T,L TR spectrum size,test,test prolonged by risk factor N,N number of cycles,constant and variable ampli-tude loadingN k fatigue life at knee pointP s,P f,P o probability of survival,failure,occurrenceR x,R x load,stress or strain ratio R x=X min/X max for constant and variable amplitude loadingT N,T N fatigue life scatter between P s=10%and90%, for constant and variable amplitude loadingr, r stress,constant and variable amplitudeloading r ak knee point of the S–N curvee straina amplitudeeq equivalentf frequency,failurej R,C risk factorj N safety factork,k0slope of the S–N curve,slope of the prolonga-tionl longitudinalm meann number of tests,number of cycles,nominals N standard deviation(s N=0.39lg(1/T N))t timeD rangeC.M.Sonsino/International Journal of Fatigue29(2007)1080–10891081identical.If in term of cycles or cumulative frequency the ratio of 1:3between the two counting methods is exceeded,a much lower real damage sum D real than for a spectrumwithout mean-load ﬂuctuations has to be selected for a fati-gue life assessment [3,4], e.g.D real =0.2versus 0.5for welded joints,0.1versus 0.3for not welded components basing on experiences.However,more research for a dam-age mechanics founded approach is necessary.Figs.7and 8present the documentation of two diﬀerent spectra,one without a mean-load ﬂuctuation (narrow band)and the other one with a large mean-load ﬂuctuation (wide band).The load history for performing a variable amplitude test is stored usually as a peak (turning point)sequence,Fig.9,and by the appertaining rainﬂow matrix.(In the past also the Markovian matrix was used.)Generally,a spectrum does not contain the information about the loading frequency.Often,the testing frequency depends on the interaction between the testing machine and the stiﬀness of the test object,as well as on the elec-tronical control possibilities of the frequency.However,for variable amplitude tests of dynamic (swinging)as well as non-linear systems, e.g.mass-damper-systems,where the frequency content is required,the storage of the load–time history has to contain also theinformationFig.2.Real damage sum distributions for steel andaluminium.Fig.3.Diﬀerent load–time histories.1082 C.M.Sonsino /International Journal of Fatigue 29(2007)1080–1089about the frequency spectrum,e.g.the power spectral den-sity (PSD)[4],Fig.10.The sequence length L s of a test spectrum may be a value obtained after an omission of small,as non-damag-ing assumed amplitudes.However,in case of an omission it must be noted that the obtained test cycles to failure cor-respond to service cycles to failure given by N service ¼N test ÁL s ;before omissionL sð3Þ3.Performance of variable amplitude loading tests Variable amplitude loading (VAL)tests are principally carried out like constant amplitude loading tests (CAL)on diﬀerent load levels,Fig.11.The only diﬀerence is that in case of VAL a given sequence must be continuously repeated until a failure is obtained,while under CAL the amplitude (or range)remains unchanged.For a valid VAL test,the sequence must be repeated at least 5–10times in order to achieve a service-like load mixing [7].There are diﬀerent failure criteria which must be deﬁned according to the particular application:a crack with a deﬁned depth,a deﬁned decrease of stiﬀness,a total rupture etc.The diﬀerence between the load levels is only a linear ampliﬁcation of the amplitudes (or ranges)of the spectrum;shape and length L s of the spectrum remain independent of the load level.As long as the frequency does not aﬀect the fatigue life,or particular attention of the frequency content isnotFig.5.Gaussian load spectrum.Table 1Overview of existing uniaxial variable amplitude loading standards NamePurposeStructural detailYear Eight-Block Programme General purpose,block-wise variable amplitude loadingComponents of transportation vehicles,heavy machinery components,etc.1939Twist Transport aircraft wingWing root bending moment1973Gaussian General purpose random sequence Narrow-band,medium-band,wide-band random 1974FalstaﬀFighter aircraft Wing root 1975MiniTwist Shortened versionAs above1979Helix,FelixHelicopters,hinged and ﬁxed rotors Blade bending 1984Helix/32,Felix/28Shortened versionsAs above 1984Cold turbistan Tactical aircraft engine discs Bore1985Wisper Wind turbines Blade out-of-plane bending1988Wash I Oﬀshore structures Structural members of oil platforms 1989Wawesta Teel mill driveDrive train components1990CarlosCar loading standard Sequence (uniaxial)Vertical,lateral,longitudinal forces on front suspension parts1990Table 2Overview of existing multi-channel variable amplitude loading standards Name PurposeStructural detailYear Eurocycle I passenger car wheels Vertical and lateral loads wheels,wheel/hub/bearing units 1981Eurocycle II truck wheelsVertical and lateral loads wheels,wheel/hub/bearing units 1983EnstaﬀAlstaﬀ+temperatureWing root1987Hot turbistan Tactical aircraft engine discs Cold turbistan +temperatureRim (hot section)1989Carlos multi Car loading standard (multiaxial)4-Channel load components for front suspension parts 1994Carlos PTM Car power train (manual shift)torques +speeds +gear pos.Power train components,e.g.clutch,gear-wheels,shafts,bearings,and universal joints1997Carlos PTA Car power train (autom.shift)torques +speeds +gear pos.Ower train components e.g.gear-wheels,shafts,bearings,and universal joints2002CarloS TCCar trailer coupling (multiaxial)Trailer coupling device and vehicle supporting structure2003C.M.Sonsino /International Journal of Fatigue 29(2007)1080–10891083required,the frequency can be increased for shortening the testing time.However,depending on the interaction between the testing machine and the stiﬀness of the speci-men,the overall testing frequency can be limited.In such cases,especially low load amplitudes can be accelerated by an amplitude and frequency adaptive control,Fig.12[8].During the testing,control and real signals must be compared and registered with regard to turning points,amplitude distribution,rainﬂow matrix and ifrequiredFig.7.Gaussian spectrum with constant meanload.Fig.8.Truck spectrum with ﬂuctuating mean load.)a(a F σoP ,R Cycles N (log) L Preload (prestress) F values from which the maximum load (stress) amplitude and the load(stress) ratioand )(F max max σAmplitude distribution (shape)S pectrum size L (total number of cycles N),probability of occurance P min max min /F /F R σσ==)(F a a σsFig.6.Main parameters of a spectrum.1084 C.M.Sonsino /International Journal of Fatigue 29(2007)1080–1089the power spectral density.In case of multichannel VAL,especially of dynamic or/and of non-linear systems,e.g.automotive suspensions or car body structures,also the time order and the phase diﬀerences between the particular channels must be controlled,Fig.13[9].For the durability proof of components or structures tests are carried out usually only on the service–load level.4.Statistics and required amount of testsThe statistics applied to VAL tests is principally the same as the statistics applied to CAL tests [1,4,10,11].The mostly assumed distribution type is the Gaussian Log-Normal-Distribution,but other distributions, e.g.according to Student [10]or Weibull [12,13]can be applied,too,for deﬁning the course of the Gassner curve with the probability of survival P s =50%and the scatter band with P s =10%and 90%or 2.5%and 97.5%.(Within P s =10%and 90%the type of distribution does not inﬂuence the position of the curves signiﬁcantly,but an extrapolation to much lower or higher probabilities results signiﬁcant dif-ferences [13].)As VAL tests are more complicated and often more time consuming than CAL tests,at least two levels with each ﬁve tests or three levels with each three tests can be consid-ered to be suﬃcient,to determine the slope k ,the scatter T and the standard deviation s:Fig.10.Power spectral density and joint density distribution.Fig.9.Cut-out of a peak (turning point)sequence from a load time history.C.M.Sonsino /International Journal of Fatigue 29(2007)1080–10891085k¼lgðN2=N1ÞlgðD r1=D r2Þð4ÞT x¼1:xðP s¼10%ÞxðP s¼90%Þð5Þx¼ r a;D r or Nð6Þs x¼12:56lg1T xð7ÞIn Fig.14Woehler-and Gassner-curves are displayed with their mean values(P s=50%),the appertaining scatter bands between P s=10%and90%and the particular slopes k.For the durability proof of big structures the amount of test objects is very restricted;in the worst case an assess-ment may be required by only one test.In such cases the risk given by a few amount of tests must be covered by sta-tistics;the mean value of fatigue lives obtained by few tests must be reduced by the risk factor j R,C to obtain the‘‘real’’mean value[1]:N Ps¼50%¼N mean;testsjR;Cð8ÞjR;C¼1T N1=ﬃﬃﬃﬃ4n pðÞð9Þwhile n is the amount of tests performed and T N is the scat-ter which would be obtained for a high amount of tests(ba-sic population);it is not the scatter resulting from few tests. It can be estimated by testing experiences with a larger number of specimens manufactured in a comparable way. The risk factor in Eq.(8)is valid for a probability of con-ﬁdence P c=90%.To calculate a fatigue life for an allowable probability of survival P s>50%,the‘‘real’’mean value must be reduced by the safety factor j N[1,14]:N Ps>50%¼N Ps¼50%jNð10ÞjN¼1T Nexp2:36ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃlgð1ÀP sÞj jpÀÁ2:56À1"#ð11ÞIn case of few testing objects,the durability proof can also be conducted on such a way that the spectrum for the re-quired life cycle(the spectrum can be composed by a high amount of repeated sequences,e.g.for25years life of anFig.13.Documentation example of a multichannel variable amplitude loading. 1086 C.M.Sonsino/International Journal of Fatigue29(2007)1080–1089oﬀshore rig25repetitions of the1years sequence)has to be repeated according to the risk factor[15,16],Fig.15.If a failure is not caused,the durability is proved.5.Documentation and presentation of test resultsAs mentioned before,test results must be documented in following way:Description of the spectrum by its rainﬂow matrix, sequence length,visualization by level crossings and range pairs counting;for dynamic or/and non-linear behaving test objects additionally the power spectral density.Storage of the peak(turning point)sequence.Tabulation of applied maximum load levels of the sequence(all other amplitudes or ranges are related lin-early to the maximum value)and the number of cycles to failure or the number of repetitions of the spectrum. Deﬁnition of the failure criterion, e.g.crack,break through,total failure,and stiﬀness loss.Testing frequency.Environmental conditions,e.g.temperature,corrosion.For the graphical presentation of the test results in the double-logarithmic plot the maximum load(stress)of the spectrum versus the number of cycles to failure should be preferred[3–5,17,18].This is justiﬁed by following argu-ments which are important for the design of structures: Distance between the maximum spectrum stress and the structural yield strength can be evaluated.However,this requires the determination of the local stress in the crit-ical area of the component.Exceedance of the Woehler-curve can be evaluated with regard to exploitable light-weight design potential in dependency of the spectrum applied[3],Fig.16.In case of a spectrum with a Gaussian distribution of the amplitudes for achieving a fatigue life of e.g.N¼1Â108 cycles the constant amplitude high-cycle fatigue strength can be exceeded by a factor of1.50,in case of a straightline Fig.14.Woehler-and Gassner-curves of a laserbeam welded hatproﬁle.Fig.15.Testing requirement for covering the risk of a low number of determining fatigue life with few tests.C.M.Sonsino/International Journal of Fatigue29(2007)1080–10891087distribution even more,1.90.Light-weight design can be performed by allowing higher-stresses in the structure and thus reaching the required fatigue life:compared to constant amplitude design of a steering rod with a diameter of d =22mm,by considering the spectrum shape a diame-ter of d =18mm for a Gaussian distribution,and d =16mm for a straight-line distribution is obtained.This diameter reduction renders a weight decrease of 50%.In some design codes or recommendations [19,20]the calculation of an equivalent stress or load of the spectrum is suggested:D r eq ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃX h 1n i D r k i L s k v u u t ð12ÞThis kind of presentation for comparing the VAL –results with the CAL –results assumes on one hand a dam-age sum of D =1.0which is mostly on the unsafe side,Fig.2,[17,18]and on the other hand it does not allow to recognize at one glance the light-weight design potential (exceedance of the Woehler-curve)as well as the risk of glo-bal plastiﬁcation (distance of the maximum value of the spectrum from the yield strength).The equation assumes also the same slope for the Woehler-and Gassner-curves,which is seldom the case.6.SummaryThe lack in fatigue life assessment despite more then 70cumulative damage hypothesis [21]necessitates experimen-tally based knowledge for the design practice [22].How-ever,as the performance of variable amplitude fatigue tests are not as simple as constant amplitude tests,a guid-ance on the particular testing principles,the documentation of testing details and results and ﬁnally the presentation of the results is needed.The major points to be respected in variable amplitude loading (VAL)tests are:Description of the load spectrum (maximum values,shape,sequence length)and documentation by storage of the peak (turning point)sequences as well as by the rainﬂow matrix;in case of systems with dynamic response or/and non-linear testing objects additionally the power spectral density (frequency content).Deﬁnition of the failure criterion (crack length,total failure,stiﬀness loss,etc.).Description of the experimental devices and conditions (frequency,environment).Presentation of the maximum spectrum loads versus cycles to failure or/and number of repetitions of the sequence length in a double-logarithmic plot as well as in a table.In comparison to an already existing ISO-draft [23],this paper gives more information,especially on testing details and presentation of results.References[1]Haibach E.Betriebsfestigkeit –Verfahren und Daten zur Berechnung (Structural durability –Methods and data for calculation).2nd ed.Du ¨sseldorf:VDI-Verlag;2003.[2]Eulitz KG.Kotte,KL.In:Damage accumulation–limitations and perspectives for fatigue life assessment Materials week 2000–Proceedings,Werkstoﬀwoche-Partnerschaft,Frankfurt,25–28Sep-tember 2000.Available from:/proceedings .[3]Sonsino CM.Principles of variable amplitude fatigue design and testing Fatigue testing and analysis under variable amplitude loading conditions.In:McKeighan PC,Ranganathan N,editors.ASTM STP,vol.1439.West Conshohocken,PA:ASTM International;2005.p.3–23.[4]Buxbaum O.Betriebsfestigkeit –Sichere und wirtschaftliche Bemes-sung schwingbruchgefa ¨hrdeter Bauteile (Structural durability –Safe and economic fatigue design of components),2nd ed.Du ¨sseldorf:Verlag Stahleisen;1992.[5]Gassner E.Festigkeitsversuche mit wiederholter Beanspruchung im Flugzeugbau (Strength tests under repeated loading for aeronotical engineering).Luftwissen 1939;6:61–4.[6]Heuler P,Kla ¨tschke H.Generation and use of standardized load spectra and load–time histories.Int J Fatigue2005;27(8):974–90.Fig.16.Inﬂuence of spectrum –shape on fatigue life and component dimensions.1088 C.M.Sonsino /International Journal of Fatigue 29(2007)1080–1089[7]Schijve J.Fatigue of structures and materials.AH Dordrecht:KluwerAcademic Publishers;2001.[8]Sonsino CM.Versuchszeitverku¨rzung in der Betriebsfestigkeit(Reduction of testing time for structural durability proof).Materi-alpru¨fung2003;45(4):133–44.[9]Kla¨tschke H,Schu¨tz D.Das Simultanverfahren zur Extrapolationund Raﬀung von mehraxialen Belastungs-Zeitfunktionen fu¨r Schwingfestigkeitsversuche(The simultaneous method for extrapola-tion and shortening of multiaxial load–time histories for fatigue testing).Mat-wiss U Werkstoﬀtechnik1995;8:404–15.[10]Schneider CRA,Maddox SJ.Best practice guide on statisticalanalysis of fatigue Data Report No.13604.01/02/1157.02,2002The Welding Institute(TWI),Abington Hall,UK.[11]Bastenaire F.New method for the statistical evaluation of constantstress amplitude fatigue test results.In:Probabilistic aspects of fatigue.ASTM STP,vol.511.Philadelphia:ASTM;1972.p.3–28.[12]Castillo E,Fernandez Canteli A.A general regression model forlifetime evaluation and prediction.Int J Fracture2001;107:117–37.[13]Fuchs HO,Johns MV.The risks of extrapolations of metal fatiguedata.J Test Eval,JTEVA1988;16(3):276–9.[14]Filippini M,Dieterich K.An approximate formula for calculating theprobability of failure.Fraunhofer-Institute for Structural Durability (LBF)Technical Information TM-No.111;1997.[15]Grubisic V.Determination of load spectra for design and testing.JVehicle Des1994;15(1/2):8–26.[16]Grubisic V.Fatigue evaluation of vehicle components-State of theart,restrictions and requirements-Keynote address to section ‘‘Fatigue research and application’’SAE International Congress, Detroit,February24–27;1997[LBF-Publication No.633].[17]Sonsino CM.Limitations in the use of RMS-values and equivalentstresses in variable amplitude loading.Int J Fatigue 1989;11(3):142–52.[18]Lagoda T,Sonsino parison of diﬀerent methods forPresentino variable amplitude loading fatigue results.Mat-wiss U Werkstoﬀtechnik2003;34(11):13–20.[19]Eurocode No.3.Part1:General design rules for steel constructions.DIN-V ENV1993-1-1/A2.[20]Hobbacher A.Fatigue design of welded joints and components.IIW-Doc.XIII-1539-96/XV-845-961996Abington Hall,UK.[21]Fatemi A,Yang L.Cumulative fatigue damage and life predictiontheories:a survey of the state of the art for homogeneous materials.Int J Fatigue1998;20(1):9–34.[22]Sonsino CM,Maddox SJ,Hobbacher A.Fatigue life assessment ofwelded joints under variable amplitude loading–State of the present knowledge and recommendations for fatigue design regulations.In: Proceedings of the IIW international conference on technical trends and future prospectives of welding,2004.p.84–99.[23]ISO/WD12110-1.Metallic materials–fatigue testing–variableamplitude fatigue testing–Part1:General principles test method and reporting requirements document state,September2006.C.M.Sonsino/International Journal of Fatigue29(2007)1080–10891089。

高考英语阅读理解科普类说明文4篇--较难(有答案)

高考英语说明文4篇1make Here is an astonishing and significant fact: Mental work alone can’ｔus tire. It sounds absurd/?b's??d/荒谬的. But a years ago, scientists tried to find outhow long the human brain could labor without reaching a stage 阶段of fatigue /f?'ti?g/(疲劳). To the amazement of these scientists, they discovered thatblood passing through the brain, when it is active, shows no fatigue at all! If wetooka drop of blood from a day laborer劳动者, we would find it fullof fatigue toxins /'t?ks?n/ (毒素) and fatigue products. But if wetook blood from the brain of an Albert Einstein, it would show nofatigue toxins at the end of the day.So far as the brain is concerned, it can work as well and swiftly很快地at the end of eight or even twelve hours of effort as at the beginning. The brainistotally tireless. So what makes us tired?Some scientists declare that most of our fatigue comes from our mentalm ost outstandingand emotional(情绪的) attitudes. One of England’ｓscientists, J.A. Hadfield, says, “The greater part of the fatigue from which wesuffer is of mental origin /'?r?d??n/起源. In fact, fatigue of purely physical origin is Dr. Brill, a famous American scientist, goes even further. He declares, “One rare.”hundred percent of the fatigue of sitting worker in good health is due toemotional problems.”What kinds of emotions make sitting workers tired? Joy? Satisfaction?No! A feeling of being bored, anger, anxiety/??'za??t?/焦虑, tenseness紧张, worry, a feeling of not being appreciated---those are the emotions that tiresitting workers. Hard work by itself seldom causes fatigue. We get tiredbecause our emotions produce nervousness in the body.1. What surprised the scientists a few years ago?s blood.A. Fatigue toxins could hardly be found in a laborer’work.feel worn after a day’ｓB. Albert Einstein didn’ｔC. The brain could work for many hours without fatigue.D. A mental worker’ｓblood was filled with fatigue toxins.2. According to the author, which of the following can make sitting workerstired?A. Challenging mental work.B. Unpleasant emotions.C. Endless tasks.D. Physical laboidea?attitude towards the scientists’the author’ｓ3. What’ｓA. He agrees with them.B. He doubts them.C. He argues against them.D. He hesitates to accept them.4. We can infer from the passage that in order to stay energetic, sitting workers need to ________.A. have some good food.B. enjoy their workC. exercise regularlyD. discover fatigue toxins2They baby is just one day old and has not yet left hospital. She is quietbut alert /?'l??t/（警觉）. Twenty centimeters厘from her face researchershave placed a white card with two black spots on it. She stares at it carefully.A researcher removes the card and replaces it by another, this time with the spots differently spaced. As the cards change from one to the other, her gaze（凝视）starts to lose its focus — until a third, with three black spots,is presented. Her gaze returns: she looks at it for twice as long as she did atthe previous card. Can she tell that the number two is different from three,just 24 hours after coming into the world?Or do newborns simply prefer more to fewer? The same experiment, butwith three spots shown before two, shows the same return of interest whenthe number of spots changes. Perhaps it is just the newness 名，新奇? When slightly older babies were shown cards with pictures of objects (a comb, a key, an orange and so on), changing the number of objects had an effect separate from changing the objects themselves. Could it be the pattern that two thingsmake, as opposed to three? No again. Babies paid more attention to squaresmoving randomly on a screen when their number changed from two to three,or three to two. The effect even crosses between senses. Babies who were repeatedly shown two spots became more excited when they then heard three drumbeats than when they heard just two; likewise （同样地）when the researchers started with drumbeats and moved to spots.5. The experiment described in Paragraph 1 is related to the baby’s__.A. sense of hearingB. sense of sightC. sense of touch D sense of smell6. Babies are sensitive to the change in______.A. the size of cardsB. the colour of picturesC. the shape of patternsD. the number of objects7. Why did the researchers test the babies with drumbeats?A. To reduce the difficulty of the experiment.B. To see howbabies recognize sounds.C. To carry their experiment further.interest.D. To keep the babies’8. Where does this text probably come from?literature.A. Science fiction.B. Children’ｓC. An advertisement.D.A science report3Last night’ｓmeteor(流星) 英/'mi?t??/ shower left many people in the community dissatisfied and demanding 苛求的；要求高的；吃力的answers. Accordingmayor市长, people gathered in theto Gabe Rothsclild, Emerald Valley’ｓsuburbs /'s?b??b/of the city, carrying heavy telescopes, expecting to watch the brightly burning meteors passing through the sky. What they found instead was a sky so brightene lights that it darkened the light of the meteors passing overhead.by the city’ｓadmitted town resident Duane Cosby, “We “My family was so frustrated,”wanted to make this an unforgettable family outing, but it turned out to be ahuge disappointments.”Astronomers- /?'str?n?m?/n. 天文学家--scientists who study stars and planets---- have beencomplaining about this problem for decades. They say that light pollution prevents them from seeing objects in the sky that they could see quite easily in the past. They call on people and the government to take measures tofightagainst it.There is yet a population besides professional and amateur /??m?t?(r)/美 /'?m?.t??r/n. 爱好者star observers that suffers even more from light pollution. This population consists of birds, bats frogs, snakes, etc. For example, outdoor lighting severely affects migrating(迁徙的)birds. According to the International Dark-Sky Association. “100million birds a year throughout North America die in crashes 撞碎with lighted buildings and towers.”Countless more animals casualties(伤亡）result from the use of artificial lighting. Clearly, people enjoy the benefits of lighting their evenings, but some scientists think it can be harmful for humans, too. They worry that exposure to light while sleeping can increase person’ｓchances of getting cancer. Emerald Valley is only one community that is becoming aware of the negative effects of light pollution. For years, Flagstaff, Arizona/,?ri'z?un?/美 /,?ri'z?un?/n. 美国亚利桑那州, has enforced lighting regulations in its city in order to assist astronomers at the Lowell Observatory.英 /?b'z??v?t(?)r?/美 /?b'z?v?t?ri/n. 天文台；气象台；瞭望台Similar efforts have been made worldwide, and a movement isunderway 进行中的to remind us to turn off lights when we are not using them, so thatother creatures can share the night.9.It happened last night thatlights affected the meteor watchingA. the city’ｓB. the meteors flew past before being noticedC. the city light show attracted many peopleD. the meteor watching ended up a social outing10. What do the astronomers complain about?A. Meteor showers occur less often than beforeB. Their observation equipment is in poor repairC. Light pollution has remained unsolved for yearsD. Their eyesight is failing due to artificial lighting11. What the author concerned about according to Paragraph 4?A. Birds may take other migration pathsB. Animals living habits may changesuddenlyC. Varieties of animals will become sharplyreducedD. Animals’survival is threatened byoutdoor lighting12. Lighting regulations in Flagstaff, Arizona areput into effect toA. Lessen the chance of getting cancerB. create an ideal observation conditionC. ensure citizens a good sleep at nightD. enable all creatures to live in harmony13.What message does the author most want to give us?A. Saving wildlife is saving ourselvesB. Great efforts should be made to save energyC. Human activities should be environmentally friendlyD. New equipment should be introduced for space study4Almost every machine with moving parts has wheels, yet no one knows exactly when the first wheel was invented or what it was used for. We do know，however，that they existed over 5,500years ago in ancient Asia.The oldest known transport wheel was discovered in 2002 in Slovenia. It is over 5，100 years old. Evidence suggests thatwheels for transport didn't become popular for .while, though . Thiscould be because animals did a perfectly good job of carryingfarming tools and humans around.But it could also be because of a difficult situation. While wheels need to roll on smooth surfaces, roads with smooth surfacesweren't going to be constructed until there was plenty of demandfor them. Eventually, road surfaces did become smoother, but thisdifficult situation appeared again a few centuries later. There had been no important changes in wheel and vehicle design before thearrival of modern road design.In the mid-1700s,a Frenchman came up with a new design ofroad--a base layer (层)of large stones covered with a thin layer of smaller stones. A Scotsman苏格兰人improved on this design in the 1820s and a strong, lasting road surface became a reality. At around thesame time, metal hubs英 /h?b/美 /h?b/n. 中心；毂；木片(the central part of a wheel)、came into being, followed by the Wheels were invented in 1967, sixty years after the appearance of tarmacked roads(泊油路). As wheel design took off,vehicles got faster and faster.14. What might explain why transport wheels didn’ｔb ecome popular for some time?A. Few knew how to use transport wheels.B. Humans carried farming tools just aswell. C. Animals were a good means oftransport.D. The existence of transport wheels was not known.15. What do we know about road design from the passage?A. It was easier than wheel design.B. It improved after big changes in vehicle design.C. It was promoted by fast-moving vehicles.D. It provided conditions for wheel design to develop.16. How is the last paragraph mainly developed?A. By giving examples.B. By making comparisons.C.By following time order.D.By making classifications.17.What is the passage mainly about ?A.The beginning of road deaign.B.The development of transport wheel.C.The history of public transport.D.The invention of fast-moving vehicles.。

不锈钢的疲劳裂纹扩展有限元模拟-英文版(另有中文翻译)

Modeling of fatigue crack growth of stainless steel 304LFeifei Fan,Sergiy Kalnaus,Yanyao Jiang *Department of Mechanical Engineering (312),University of Nevada,Reno,NV 89557,USAa r t i c l e i n f o Article history:Received 7November 2007Received in revised form 9June 2008Keywords:Damage accumulation Fatigue crack growth Fatigue criteriona b s t r a c tAn effort is made to predict the crack growth of the stainless steel 304L based on a newly developed fatigue approach.The approach consists of two steps:(1)elastic–plastic ﬁnite element (FE)analysis of the component;and,(2)the application of a multiaxial fatigue cri-terion for the crack initiation and growth predictions based on the outputted stress–strain response from the FE analysis.The FE analysis is characterized by the implementation of an advanced cyclic plasticity theory that captures the important cyclic plasticity behavior of the material under the general loading conditions.The fatigue approach is based upon the notion that a material point fails when the accumulated fatigue damage reaches a cer-tain value and the rule is applicable for both crack initiation and growth.As a result,one set of material constants is used for both crack initiation and growth predictions.All the mate-rial constants are generated by testing smooth specimens.The approach is applied to Mode I crack growth of compact specimens subjected to constant amplitude loading with differ-ent R -ratios and two-step high–low sequence loading.The results show that the approach can properly model the experimentally observed crack growth behavior including the notch effect,the R -ratio effect,and the sequence loading effect.In addition,the early crack growth from a notch and the total fatigue life can be simulated with the approach and the predictions agree well with the experimental observations.Ó2008Elsevier Ltd.All rights reserved.1.IntroductionLoad-bearing engineering components are often sub-jected to cyclic loading and failure due to fatigue is of a great concern.Generally,fatigue process consists of three stages:initiation and early crack growth,stable crack growth,and ﬁnal fracture.Traditionally,the crack growth rate (d a /d N )is expressed as a function of the stress inten-sity factor range (D K )on a log–log scale.The stable crack growth results under constant amplitude loading with dif-ferent R -ratios (the minimum load over the maximum load over a loading cycle)are often represented by the Paris law (Paris and Erdogan,1963)and its modiﬁcations (Walker,1970;Kujawski,2001).Different materials behave differ-ently under constant amplitude fatigue loading.Some materials display a R -ratio effect:crack growth rate curves are coincided for the same R -ratio,but a higher R -ratio re-sults in a higher crack growth rate (Kumar and Garg,1988;Pippan et al.,2005;Wu et al.,1998;Zhao et al.,2008).Other metallic materials do not reveal any R -ratio effect,and the curves for constant amplitude loading overlap in a log–log scale (Crooker and Krause,1972;Kumar and Pan-dey,1990;Wang et al.,to appear ).The fatigue crack growth behavior under variable amplitude loading is another subject that has been studied for a number of years.The application of an overload (ten-sile load of high magnitude applied over one cycle pre-ceded and followed by constant amplitude loading)or change in the loading amplitude (so-called high–low se-quence loading experiments)can introduce profound effects on the fatigue crack growth.For most metallic materials,the application of the abovementioned loading schemes results in a crack growth rate retardation.Based on the linear elastic fracture mechanics (LEFM)concept,such a transient behavior is often modeled by using the stress intensity factor concept and by introducing correc-tion factors to the Paris law on the stable crack growth0167-6636/$-see front matter Ó2008Elsevier Ltd.All rights reserved.doi:10.1016/j.mechmat.2008.06.001*Corresponding author.Tel.:+17757844510;fax:+17757841701.E-mail address:yjiang@ (Y.Jiang).Mechanics of Materials 40(2008)961–973Contents lists available at ScienceDirectMechanics of Materialsj o u r n a l h o m e p a g e :/loc ate/mechmatregime.A model of such a type was introduced by Wheeler (1972)and can be viewed as a practical way of treating the effects of variable amplitude loading.Several modiﬁcations on Wheeler’s model have been proposed(Kim et al.,2004; Yuen and Taheri,2006;Zhao et al.,2008)targeting the par-ticular shapes of the crack growth curves for different materials subjected to variable amplitude loading.These models have little or no physical basis and the results of the crack growth experiments are needed in order to ob-tain a set ofﬁtting constants to calibrate the models.Since its introduction by Elber(1970),the crack closure concept is often used to explain crack growth behavior.The retardation in crack growth rate generated by a single ten-sile overload was explained by using the crack closure con-cept in Elber’s later study(Elber,1971).The concept of K op was introduced as a stress intensity factor corresponding to the crack opening load,and the effective stress intensity factor range from K op to K max was considered as a crack driving parameter.As a result,the contribution to crack propagation comes from a part of the total stress intensity factor range corresponding to the part of the cycle when the crack is open.Such an approach is used to explain the R-ratio and variable loading effects.However,the crack closure method has been under criticism based upon experimental observations(Lang and Marci,1999;Sada-nanda et al.,1999;Silva,2004;Feng et al.,2005)and numerical simulations(Jiang et al.,2005;Mercer and Nich-olas,1991;Zhao et al.,2004).Crack-tip blunting has been used to explain the crack advance(Gu and Ritchie,1999;Tvergaard,2004).The retardation caused by an overload is attributed mainly to the compressive residual stresses ahead of the crack tip, plasticity induced crack closure behind the crack tip,or the combination of these two.The initial acceleration in the crack growth immediately after the application of an overload was explained as a result of the tensile residual stress due to crack-tip blunting(Makabe et al.,2004).The ﬁnite element analysis was used to analyze the stress dis-tribution and the crack opening displacement which was related to the variable amplitude loading effects(Zhang et al.,1992;Ellyin and Wu,1999;Tvergaard,2006).Generally,a fatigue crack is nucleated at a notch due to the stress concentration.The so-called notch effect on short crack behavior exists and the crack growth rate may be higher or lower than that expected based on the stable growth.Extensive research has been carried out to study the crack initiation and early crack growth behavior from a notch.Around a notch,a transition zone exists and the fatigue crack growth rate may decelerate,accelerate,or non-propagate after the crack initiation under constant amplitude loading.In order to model the short crack growth behavior from a notch,efforts were concentrated on the‘‘effective stress intensity factor”near the notches (Sadanandam and Vasudevan,1997;Dong et al.,2003; Teh and Brennan,2005;Vena et al.,2006),notch tip plas-ticity(Li,2003;Hammouda et al.,2004),and the combina-tion of crack tip cyclic plasticity and the contact of the crack surfaces(Ding et al.,2007a).A recent effort by Jiang and co-workers(Ding et al., 2007a,b;Feng et al.,2005;Jiang and Feng,2004a)at-tempted to use a multiaxial fatigue criterion to unify the predictions of both crack initiation and crack growth.The notion is that both crack initiation and the subsequent crack growth are governed by the same fatigue criterion.A material point fails to form a crack once the accumula-tion of the fatigue damage reaches a certain critical value. The approach has been applied to1070steel with success. The predictions of the early crack growth from notches (Ding et al.,2007a;Jiang,Ding and Feng,2007),the stable crack growth(Feng et al.,2005;Jiang and Feng,2004a; Jiang,Ding,and Feng,2007),the overload effect(Jiang and Feng,2004a;Jiang,Ding,and Feng,2007),the R-ratio effect(Jiang and Feng,2004a;Jiang,Ding,and Feng, 2007),and the crack growth under direction-changing loading(Ding et al.,2007b)agreed well with the experi-mental observations.All the predictions of the crack growth were based on the material constants generated from testing the smooth specimens.In the present investigation,the aforementioned ap-proach is used to simulate the crack growth from the notched specimens made of the AISI304L austenitic stain-less steel.The notch effect on the early crack growth,the R-ratio effect,and the inﬂuence of the loading sequence are modeled.The stress analysis is conducted by using theﬁ-nite element method implementing a robust cyclic plastic-ity model.The predicted results are compared with the results of the crack growth experiments.2.Crack growth modelingIn the present investigation,the fatigue approach devel-oped by Jiang and co-workers(Jiang and Feng,2004a;Jiang et al.,2007)is used to model the crack growth of the stain-less steel304L.The approach is based on the assumption that any material point fails if the accumulation of the fa-tigue damage reaches a critical value on a material plane.A fresh crack surface will form on the material plane at the material point.Essentially,the approach consists of two major computational steps:a)Elastic–plasticﬁnite element(FE)stress analysis forthe determination of the stress and strain history atany material point of a component,and,b)Application of a multiaxial fatigue criterion utilizingthe stress and strain obtained from the previous stepfor the determination of crack initiation and crackgrowth.The following sub-sections describe the methods em-ployed in the current study.2.1.Cyclic plasticity model and multiaxial fatigue criterionEarlier studies indicate that an accurate stress analysis is the most critical part for the fatigue analysis of the mate-rial(Jiang and Kurath,1997a,b;Jiang and Zhang,2008; Kalnaus and Jiang,2008;Jiang et al.,2007).If the stresses and strains can be obtained with accuracy,fatigue life can be reasonably predicted by using a multiaxial fatigue criterion.The elastic–plastic stress analysis of a notched or cracked component requires the implementation of a962 F.Fan et al./Mechanics of Materials40(2008)961–973cyclic plasticity model into FE software package.The selec-tion of an appropriate cyclic plasticity model is crucial for an accurate stress analysis of a component subjected to cyclic loading.Cyclic plasticity deals with the non-linear stress–strain response of a material under repeated external loading.A cyclic plasticity model developed by Ohno and Wang (1993,1994)and Jiang and Sehitoglu (1996a,b)is used in the present FE simulations of the stress and strain response in a notched or cracked component.The model is based on the kinematic hardening rule of the Armstrong–Frederick type.Basic mathematical equations constituting the model are listed in Table 1.A detailed description of the plasticity model together with the procedures for the determination of material constants can be found in corresponding refer-ences (Jiang and Sehitoglu,1996a,b ).The choice of the cyc-lic plasticity model was based on its capability to describe the general cyclic material behavior including cyclic strain ratcheting and stress relaxation that occur in the material near the notch or crack tip.The plasticity model listed in Table 1was implemented into the general purpose FE package ABAQUS (2007)through the user deﬁned subroutine UMAT.A backward Euler algorithm is used in an explicit stress update algo-rithm.The algorithm reduces the plasticity model into a non-linear equation that can be solved by Newton’s meth-od.The corresponding consistent tangent operator is de-rived for the global equilibrium iteration,which ensures the quadratic convergence of the global Newton–Raphson equilibrium iteration procedure (Jiang et al.,2002).A critical plane multiaxial fatigue criterion developed by Jiang (2000)is used for the assessment of fatigue dam-age.The criterion can be mathematically expressed as follows,d D ¼r mrr 0À1m 1þr r fb r d e p þ1Àb s d cpð1ÞIn Eq.(1),D represents the fatigue damage on a material plane and b and m are material constants.r and s are the normal and shear stresses on a material plane,and e p and c p are the plastic strains corresponding to stresses r and s ,respectively.r 0and r f are the endurance limit and the true fracture stress of the material,respectively.r mr is a memory stress reﬂecting the loading magnitude.For constant amplitude loading,r mr is equal to the maximum equivalent von Mises stress in a loading cycle.The use ofMacCauley bracket hi ensures that when r mr 6r 0the fati-gue damage is zero.The critical plane is deﬁned as the material plane where the fatigue damage accumulation ﬁrst reaches a critical value,D 0.The Jiang multiaxial fatigue criterion has been success-fully applied to the fatigue predictions of a variety of mate-rials (Ding et al.,2007a,b;Feng et al.,2005;Gao et al.,to appear;Jiang,Ding,and Feng,2007;Jiang et al.,2007;Zhao and Jiang,2008).The incremental form of the criterion (Eq.(1))does not require a separate cycle counting method for general loading conditions.Any fatigue criterion making use of the stress/strain amplitude or range requires the deﬁnition of a loading cycle or reversal.Therefore,a cycle counting method is needed to deal with the variable ampli-tude loading.Although the rain-ﬂow cycle counting meth-od is widely accepted for counting the loading reversals/cycles,it is not well deﬁned for general multiaxial loading.The second feature of the criterion expressed by Eq.(1)is its capability to predict the cracking behavior.The Jiang fa-tigue criterion is a critical plane approach which is capable of predicting different cracking behavior through the intro-duction of constant b in Eq.(1).The value of constant b is selected to predict a particular mode of cracking based on the smooth specimen experiments.It has been shown (Jiang et al.,2007;Zhao and Jiang,2008)that the predic-tions of the cracking behavior based on the Jiang criterion are generally more accurate than the predictions based on the other multiaxial criteria such as the Fatemi–Socie mod-el (Fatemi and Socie,1988),the Smith–Waltson–Topper model (Smith et al.,1970)and the short-crack based crite-rion (Döring et al.,2006).Table 2lists the material constants used in the cyclic plasticity model and the fatigue model for stainless steelTable 1Cyclic plasticity model used in the ﬁnite element simulations Yield functionf ¼ðe S À~a Þ:ðe S À~aÞÀ2k 2¼0e S ¼deviatoric stress~a¼backstress k =yield stress in shear Flow lawd ~e p ¼1hh d ~S :~n i ~n ~n¼normal of yield surface h =plastic modulus function ~e p ¼plastic strain Hardening Rule~a¼P Mi ¼1~aði Þ~aði Þ¼i th backstress part d ~a ði Þ¼c ði Þr ði Þ~n À~a ði Þk k r ði Þ v ði Þþ1~a ði Þ~aði Þk k !dp M =number of backstress parts (i =1,2,3,...M )dp =equivalent plastic strain increment c (i ),r (i ),v (i )=material constantsTable 2Material constants for SS304L Cyclic plasticity constantsElasticity modulus E =200GPa Poisson’s ratio l =0.3k =115.5MPac (1)=1381.0,c (2)=507.0,c (3)=172.0,c (4)=65.0,c (5)=4.08r (1)=93.0MPa,r (2)=130.0MPa,r (3)=110.0MPa,r (4)=75.0MPa,r (5)=200.0MPa v (1)=v (2)=v (3)=v (4)=v (5)=8.0Fatigue constants r 0=270MPa;m =1.5;b =0.5;r f =800MPa;D 0=15000MJ/m 3F.Fan et al./Mechanics of Materials 40(2008)961–973963304L.The cyclic plasticity material constants were ob-tained from the cyclic stress–strain curve which was ob-tained from the experiments on the smooth specimens under fully reversed tension-compression loading.A com-plete description of procedure for determination of mate-rial constants can be found in corresponding references (Jiang and Sehitoglu,1996a,b ).The fatigue material con-stants were determined by comparing the fatigue data un-der fully reversed tension-compression and that under pure torsion (Jiang,2000).2.2.Finite element modelRound compact specimens with a thickness of 3.8mm were used in the crack growth experiments.The geometry and the dimensions of the specimen are shown in Fig.1.The crack growth experiments were conducted in ambient air.The specimens were subjected to constant amplitude loading with different R -ratios (the minimum load over the maximum load in a loading cycle)and high–low se-quence loading.All of the experiments started without a pre-crack,except two specimens tested under the follow-ing loading conditions:R =0.85,D P /2=0.54kN and R =À1,D P /2=5.0kN.More detailed information of the experiments and the experimental results were reported in a separate presentation.Due to the small thickness,plane-stress condition was assumed for the round compact specimen.Four-node plane-stress elements were used in FE mesh model.The FE mesh model shown in Fig.2was created by using the FE package HyperMesh (Altair HyperMesh,2004).Due to the symmetry in geometry and loading,only half of the specimen was modeled.To properly consider the high stress and strain gradients in the vicinity of the notch or crack tip,very ﬁne mesh size was used in these regions.The size of the smallest elements in the mesh model was 0.05mm.There were approximately 3058to 5067ele-ments used in the mesh model depending on the cracksize.The knife edges for the attachment of the open dis-placement gage in the specimen (Fig.1)were not modeled because the free end of the specimen does not affect the stress and strain of the material near the crack tip or notch.Referring to the coordinates system employed in Fig.2,the tensile external load,P ,is applied in the y direction uni-formly over nine nodes on the upper surface of the loading hole.To mimic the actual loading condition,the compres-sive load is applied in the negative y direction uniformly over nine nodes on the lower surface of the loading hole.The displacements in the x direction of the middle nodes on the upper edge of the loading hole are set to be zero.The displacements in the y direction for all the nodes on the plane in front of the crack tip or the root of the notch are set to be zero.In order to consider the possible contact between the upper and lower surfaces of a crack,the FE model incorpo-rates the contact pairs deﬁned in ABAQUS (2007).The crack surface of the lower symmetric half of the specimen is considered as a rigid surface which acts as the master surface.The corresponding crack surface of the upper half of the specimen serves as the slave surface.2.3.Determination of crack growth rateFor continuous crack growth under constant amplitude loading with small yielding,a simple formula was derived for the determination of the crack growth rate (Jiang and Feng,2004a ),d a d N ¼AD 0;ð2Þwhere,A ¼Zr 0D D ðr Þd r ;ð3Þr is the distance from the crack tip and r 0is the damaging zone size ahead of the crack tip where the fatigue damage is non-zero.D D (r )is the maximum fatigue damage per loading cycle with respect to all possible material planes at a given material point.D D (r )is determined by integrat-ing Eq.(1)over one loading cycle,D D ¼Icycler mrr 0À1m 1þr r fb r d e p þ1Àb s d cpð4ÞFig.1.Geometry and dimensions of the round compact specimen (all dimensions inmm).Fig.2.Finite element mesh model.964 F.Fan et al./Mechanics of Materials 40(2008)961–973for a given material point once the stress–strain response at the point is known.In Eq.(3),A denotes the damaging area enclosed by the D D(r)–r curve.Fig.3shows the distribution of D D(r)along the x-direc-tion for Specimen C01which was subjected to constant amplitude loading with R=0.1and D P/2=2.475kN. According to the fatigue criterion,Eq.(1),a material plane will accumulate fatigue damage when the memory stress is higher than the endurance limit and the material point experiences plastic deformation.For a cracked component, only the material near the crack tip accumulates fatigue damage.The values of D D(r)are determined along all ra-dial directions in a polar coordinate system with its origin being at the crack tip.The direction at which the crackgrowth rate is a maximum or the value of A is a maximum is the predicted cracking direction.The corresponding crack growth rate is the predicted crack growth rate.2.4.Crack initiation and early crack growth from notchThe approach described in the previous sub-sections as-sumes that a material point fails to form a fresh crack on the critical plane when the accumulation of the fatigue damage on the critical material plane reaches a critical va-lue,D0.The rule applies to the initiation of a crack and the crack extension after a crack has been formed.Therefore, the approach uniﬁes both the initiation and the subse-quent crack propagation stage.The distribution of the stress-plastic strainﬁeld in the vicinity of a notch root, however,inﬂuences the early crack growth,which should be properly considered.The deﬁnition of crack initiation used in the current study is different from that of the traditional way.The crack initiation of a fatigue crack is judged by using the fa-tigue criterion,Eq.(1).Once the fatigue damage on a mate-rial plane for the material point at the notch root reaches the critical fatigue damage,D0,the notched member is called to have initiated a fatigue crack.The FE stress analysis is conducted with the notched member for the designated loading condition.For a notched component,the maximum fatigue damage occurs at the notch root.The fatigue damage per loading cycle can be determined and it can be plotted as a distribution along the radial direction from the notch root.Fig.4shows an example for Specimen C20(R=0.2,D P/2=2.0kN,notched depth a n=7.38mm,notch radius=2.0mm).The distance,r,from the notch root is along the x-axis(refer to Fig.1).D D i denotes the fatigue damage per loading cycle on the critical plane during crack initiation.D D i is a function of the location of the material point.The maximum fatigue damage occurs at the notch root during crack initiation.The crack initiation life is predicted to be,N i¼D0D D in;ð5Þwhere N i is the predicted crack initiation life,D0is a mate-rial constant,and D D in is the fatigue damage per loading cycle on the critical plane at the root of the notch.D D in is D D i shown in Fig.4when r=0.During crack initiation,the fatigue damage is also accu-mulated in the vicinity of the notch root and should be considered in the determination of the crack growth near the notch.The area where the fatigue damage accumula-tion is non-zero during crack initiation(Fig.4)is referred to as the notch inﬂuencing zone(NIZ).For a specimen un-der a given loading condition,the NIZ can be determined by applying the fatigue criterion,Eq.(1),with the stress and strain histories outputted from the FE analysis.For Specimen C20shown in Fig.4,the NIZ size is approxi-mately0.85mm ahead of the notch root.For each material plane at any material point,the total fatigue damage at the end of the fatigue crack initiation is N i D D i.It should be reiterated that the discussion is based on the assumption that the material is stable in stress–strain response and the applied loading is constant ampli-tude.The crack growth rate within the NIZ can be deter-mined by using the following equation with the consideration of pre-existing fatigue damage accumulation (Ding et al.,2007a):d ad N¼AD0ÀN i D iðrÞ:ð6Þwhere A is the damage area enclosed by the D D(r)–r curve, as explained in Section2.3.In Eq.(6),N i and D D i(r)are re-lated to the fatigue damage accumulation during crack ini-tiation in the NIZ.For a given crack size within the NIZ the FE analysis is conducted.The distribution of the fatigue damage per loading cycle,D D(r),can be determined as a function of the distance from the crack tip,as shown in Fig.3.The enclosed area made by the D D(r)–r curve is A in Eq.(6).For any direction radiated from the crack tip, the direction which has the highest crack growth rate isF.Fan et al./Mechanics of Materials40(2008)961–973965the predicted cracking direction and the corresponding crack growth rate is the predicted crack growth rate.It can be seen that the difference between the crack growth rate determination near the notch(Eq.(6))and that away from the notch root(Eq.(2))lies in the consideration of the fatigue damage caused during the crack initiation stage.Generally,the stress–strain response becomes stabi-lized after a limited number of loading cycles.It was shown (Jiang and Feng,2004a)that the predicted crack growth re-sults obtained based on the stress–strain response from the10th loading cycle were very close to those based on the stabilized stress and strain response.Therefore,the FE analysis for a given notch or crack length under a desig-nated loading amplitude is conducted for10loading cycles. The stress and strain results at the10th loading cycle are used for the fatigue analysis.The stress and strain results obtained from analyzing the notched component during crack initiation will deter-mine the fatigue damage per loading cycle for each mate-rial plane at each material point.Eq.(5)is used to determine the crack initiation life.FE stress analyses are conducted with different crack lengths for a given loading condition.When the crack tip is within the notch inﬂuenc-ing zone,Eq.(6)is used for the crack rate determination.D D i(r)in Eq.(6)is the fatigue damage per loading cycle for a given material point during crack initiation.Once the crack grows out of the NIZ,Eq.(2)is used for the crack growth rate determination.In fact,D D i(r)is determined during crack initiation.As a result,Eq.(6)can be used for both situations since D D i(r)is zero for the material points out of the notch inﬂuencing zone.It should be noticed that the FE simulation is conducted cycle by cycle mimicking the real crack growth procedure. The crack initiation life is determinedﬁrst.The crack growth rates at several crack lengths are predicted by using the approach.Therefore,the prediction is the relationship between the crack growth rate,da/dN,and the crack length for a given notched component.With the crack initiation life obtained from using Eq.(5),the relationship between the crack length and the number of loading cycles can be established through a numerical integration.Simulations are also conducted for the high–low step loading conditions.In a high–low step loading experiment, an external load with higher loading amplitude is applied until a crack length reaches a certain value.The amplitude of the external load is switched to a lower value in the sec-ond loading step.In the simulations for the high–low load-ing sequence,one special consideration is made.The memory stress,r mr,in Eq.(1)is kept the same before and immediately after the change of the external load from a higher amplitude to a lower amplitude.After an extension of the crack in the second loading step,the memory stress returns to that under the lower constant amplitude loading.3.Results and discussion3.1.Crack growth experimentsThe material under consideration in the present study is AISI304L austenitic stainless steel which belongs to the class of metastable steels of300-series.Austenitic steels display a R-ratio effect when subjected to constant ampli-tude loading,as has been shown for AISI304(Mei and Morris,1990)and AL6-XN(Kalnaus et al.,2008).The experimental data used in the present investigation was the results of a series of experiments conducted by the authors.Fatigue crack growth experiments were performed using round compact specimens made of stainless steel 304L.The compact specimens were machined from an as-received cold rolled round bar.The bar had a diameter of41.28mm.The dimensions of the specimens are shown in Fig.1.The U-shaped notches were made through EDM (Electric Discharge Machining).The width of the slot in the specimen is0.2mm.One side of the specimen was pol-ished to facilitate the observation of the crack growth using an optical microscope with a magniﬁcation of40. The loading conditions included constant amplitude load-ing with R-ratios ranging fromÀ1to0.85and two-step high–low sequence loading.Detailed description of the experiments and the results were reported in a separated presentation.Fig.5shows the experimental results under constant amplitude loading with different R-ratios.Ten specimens were subjected to constant amplitude loading with different loading amplitudes and six R-ratios.Clearly, the R-ratio has an effect on the crack growth of the mate-rial.The notch effect is reﬂected in the crack growth results presented in Fig.5.It can be found that,except in the case of the specimen with a relatively large notch radius under R=À1loading,the notch effect on the crack growth is not signiﬁcant.For the R=À1case(Specimen C24,notch966 F.Fan et al./Mechanics of Materials40(2008)961–973。

脂肪测定FatDetermination

0,2 2-3 25-30 21-26 0.4-1 0.5 1-4 8-13 25-32 8-13 0.4-2 1-2
2-3 39-42 0.3 2-5 22-29 0.2-15
coconut椰子 5-9 4-10 44-51 13-18 7-10 1-4
5-8 0-1
maize oil玉米油
0-2 8-10 1-4
11 August, 2020 2
Fat Determination acc. to WeibullStoldt
Agenda（演讲内容）
1. Introduction（绪言） 2. Fat determination methods（脂肪测定方
法） 3. Preparation of fat containing samples
Chemical quick methods: Gerber, butyrometer, and others（化学快速测定方法: 盖勃法, 乳脂计等）
（脂肪样品的制备） 4. Digestion in hydrochloric acid（盐酸水解
过程） 5. Extraction（萃取过程） 6. Quality assurance（质量保证） 7. Discussion（讨论）
11 August, 2020 3
Fat Determination acc. to WeibullStoldt
Lipids: fat + lipoids（脂类：脂肪+类脂）
11 August, 2020 8
Occurrence and Composition成分构成
Fat Determination acc. to WeibullStoldt
Type类型

基于正则极限学习机的驾驶员疲劳状态分类方法

收稿日期：2020-03-06基金项目：国家自然科学基金项目（61771178）作者简介：李冰（1994-），男，杭州电子科技大学电子信息学院硕士研究生，研究方向为机器学习；陈龙（1979-），男，博士，杭州电子科技大学电子信息学院教授、硕士生导师，研究方向为嵌入式系统设计与应用、神经网络与机器学习。

本文通信作者：陈龙。

0引言近年来，随着汽车等交通工具的普及，交通事故发生率越来越高。

其中驾驶员疲劳驾驶是引发交通事故的主因。

疲劳驾驶指驾驶在长时间连续驾车后，生理机能进入失调状态，从而影响正常驾驶［1］。

目前对于疲劳驾驶的检测方法多为单一信号检测，常用检测方法主要包括：①基于驾驶员生理信号的检测。

该方法主要通过检测不同疲劳状态下人体脑电信号、心电信号或呼吸信号等出现的变化，判别驾驶员疲劳状态。

该方法需在驾驶员体表安装相应检测装置，这会影响驾驶员安全驾驶，可行性较低；②基于驾驶员面部表情特征的检测，该方法通过视频监测驾驶员面部表情特征，如眨眼、打哈欠等动作，并运用图像处理等方法提取分析数据以判断驾驶员疲劳状态。

该方法受驾驶员佩戴口罩、眼镜等行为的影响较大，疲劳检测准确度会随之降低。

针对目前疲劳驾驶检测方法存在的问题，本文采用多源信息结合的方式，将多种检测方法的优势结基于正则极限学习机的驾驶员疲劳状态分类方法李冰，陈龙（杭州电子科技大学电子信息学院，浙江杭州310018）摘要：为避免接触式疲劳检测方法给驾驶员带来干扰，解决单一信号源对于反映疲劳程度可靠性低的问题，实现对疲劳状态高精度、高速度的检测，提出一种基于正则极限学习机的驾驶员疲劳状态分类方法。

该方法通过多普勒雷达模块采集驾驶员生理信号，包括呼吸信号和心跳信号，作为神经网络输入数据。

通过多源信息结合的方式提高疲劳状态检测可靠性。

设计正则极限学习机（RELM ）模型对数据集进行训练。

实验结果显示，基于RELM 算法模型检测驾驶员疲劳状态的准确率达92%。

Pseudoalteromonas carrageenovora芳香基硫酸酯酶突变文库热稳定性提高突变

Pscudoaltcvomonas c a r r a g c c n o v o v a H M H 酯酶突变文库热稳定性提高突变体的筛选及鉴定乔超超s王新侠、李鹤宾2,倪辉\肖安风s朱艳冰w(1.集美大学食品与生物工程学院，福建厦门 361021; 2.厦门医学院药学系，福建厦门 361023)摘要：利用易错聚合酶链式反应技术引入随机诱变，构建一个芳香基硫酸酯酶突变体库。

经过筛选，获得一个芳香基硫酸酯酶热稳定性提高的突变株4-153。

序列分析表明，该突变体有2个氨基酸替换，包括D84A和H260L。

以对硝基苯硫酸钾为底物，突变酶4-153 (M4-153)的最适反应温度为55X：,在45、50、55、60 °C处理30 min后，M4-153分别保留85%、83%、48%和13%的残留酶活力。

野生型酶（WT)在45、50、55、60°C处理30min后，分别保留79%、68%、21%和1%的残留酶活力。

M4-153与WT相比具有更好的热稳定性。

M4-153的最适反应pH值为8.0,在pH5.0〜9.0范围内保持稳定。

EDTA对突变酶的抑制作用表明，金属离子在突变酶的催化过程中起重要作用。

M4-153对一些洗涤剂，包括Triton X-100、Tween20、Tween80和Chaps,有好的耐受性。

M4-153对龙须菜粗多糖硫酸基团的脱硫率为79.5%。

关键词：芳香基硫酸酯酶；易错聚合酶链式反应；热稳定性提高；突变体性质Screening and Characterization of Mutant with Improved Thermostability from a Random Mutant Library ofPseudoalteromonas carrageenovora ArylsulfataseQIAO Chaochao1, WANG Xinxia1, LI Hebin2, NI Hui1, XIAO Anfeng1, ZHU Yanbing1 *(1. College of Food and Biological Engineering, Jimei University, Xiamen 361021, China;2. Department of Pharmacy, Xiamen Medical College, Xiamen 361023, China)Abstract: A library of Pseudoalteromonas carrageenovora arylsulfatase mutants was constructed by random mutagenesis using error-prone PCR. After screening, one mutant strain named 4-153 was obtained whose arylsulfatase had improved thermal stability. It was found that there were two amino acid substitutions in the mutant, including D84A and H260L. When /?-nitrophenyl sulfate was used as a substrate, the optimal reaction temperature for the mutant enzyme was 55 °C. Mutant arylsulfatase 4-153 (M4-153) retained 85%, 83%, 48%, and 13% of its initial activity after incubation at 45, 50, 55 and 60 °C for 30 min, respectively. Meanwhile, wild-type arylsulfatase (WT) retained 79%, 68%, 21%, and 1% of its initial activity after incubation at 45, 50, 55 and 60 °C for 30 min, respectively. These results showed that M4-153 had a better thermal stability than WT. M4-153 had an optimum pH of 8.0, and it was stable over the pH range of 5.0-9.0. Inhibition assay with EDTA indicated that metal ions played an important role in the catalytic process of the mutant enzyme. The recombinant arylsulfatase 4-153 showed a relatively strong tolerance to some detected detergents including Triton X-100, Tween 20, Tween 80, and Chaps. The desulfuration ratio of t he crude polysaccharides from Gracilaria lemaneiformis by M4-153 was 79.5%.Key words: arylesterase; error-prone PCR; improved thermostability; mutant propertyD01:10.7506/spkxl002-6630-201710004中图分类号：Q814.9 文献标志码：A 文章编号：1002-6630 (2017) 10-0018-06引文格式：乔超超，王新侠,李鹤宾，等.■P jeMifoa/teromowos camigeenovora芳香基硫酸醋酶突变文库热稳定性提高突变体的筛选及鉴定[J].食品科学，2017, 38(10): 18-23. D01:10.7506/spkxl002-6630-201710004. QIAO Chaochao, WANG Xinxia, LI Hebin, et al. Screening and characterization of mutant with improved themostability from a random mutant library of Pseudoalteromonas carrageenovora arylsulfatase[J]. Food Science, 2017, 38(10): 18-23.(in Chinese with English abstract) D01:10.7506/spkxl002-6630-201710004. 收稿日期：2016-09-02基金项目：国家自然科学基金青年科学基金项目（31401632);福建省高校新世纪优秀人才支持计划项目（B15139)作者简介：乔超超（1991—)，男，硕士研究生，主要从事食品科学研究。

脂肪组织材料本构模型参数力学响应灵敏度分析

河南科技Henan Science and Technology化工与材料工程总第875期第4期2024年2月收稿日期：2023-10-16作者简介：段海彤（1994—），女，硕士，工程师，研究方向：车辆被动安全及损伤生物力学。

脂肪组织材料本构模型参数力学响应灵敏度分析段海彤　郑光洁　韩菲菲　胡帛涛　梁亚妮（中汽研（天津）汽车工程研究院有限公司，天津 300300）摘　要：【目的】确定脂肪组织材料各材料本构的参数灵敏度，以便合理简化参数反求变量，提高材料对标效率。

【方法】采用对4种常用的脂肪组织材料本构模型进行无约束压缩试验，研究各材料参数对力学响应的影响情况。

【结果】线性黏弹性材料本构中短效剪切模量与衰减常数对接触力影响显著，Mooney-Rivlin 超弹性本构中材料常数对接触力值影响较大，Ogden 超弹性本构模型中Og⁃den 系数对接触力值影响最显著，软组织材料本构中材料常数对接触力影响显著。

【结论】为脂肪组织材料力学性能研究、参数反求及材料对标工作的合理简化提供了参考，极大地提高了计算效率。

关键词：脂肪组织；本构模型；材料参数；试验设计与分析中图分类号：U467.14；R318.01 文献标志码：A 文章编号：1003-5168（2024）04-0093-05DOI ：10.19968/ki.hnkj.1003-5168.2024.04.017Analysisof Constitutive Model Parameters of Adipose Tissue Materials on Mechanical Response SensitivityDUAN Haitong ZHENG Guangjie HAN Feifei HU Botao LIANG Yani（CATARC （Tianjin ） Automotive Engineering Research Institute Co., Ltd., Tianjin 300300, China ）Abstract: [Purposes ] The parameter sensitivity of each material constitutive of adipose material was de⁃termined in order to simplify the inverse parameter variables reasonably and improve the efficiency ofmaterial calibration. [Methods ] Unconstrained compression tests were carried out on four commonly used material constitutive models of adipose tissue, and the parameters of each material constitutive model were and analyzed to study the influence of each material parameter on the mechanical response of each material constitutive model. [Findings ] The results show that the short-time shear modulus and decay constant have significant effects on the maximum contact force in the linear viscoelastic material. In the Mooney-Rivlin hyperelastic constitutive, the material constant has a greater influence on the maxi⁃mum contact force, the Ogden coefficient has the most significant effect on the maximum contact force in the Ogden hyperelastic constitutive model.The influence of material constants on the maximum contact force is significant for soft issue constitutive model. [Conclusions ] It provides a reference for the rationalsimplification of adipose tissue material mechanical properties research and parameter inversion work,and greatly improves the calculation efficiency.Keywords: adipose tissue; constitutive mode; material parameters; design of experiment0 引言国内外对人体生物组织材料力学性能的研究已经开展了几十年［1］。

无机与有机混合物的含量分析——以探究鼻可乐成分为例

大学化学Univ. Chem. 2022, 37 (2), 2105058 (1 of 6)收稿：2021-05-24；录用：2021-06-21；网络发表：2021-07-01*通讯作者，Email:******************.cn基金资助：南京师范大学教改重点项目(2021NSDJG015)•化学实验• doi: 10.3866/PKU.DXHX202105058 无机与有机混合物的含量分析——以探究鼻可乐成分为例王雨欣1，丁淑媛1,2，张守林1，徐林1，唐亚文1,*1南京师范大学教师教育学院，化学与材料科学学院，南京 2100232江苏省海门中学，江苏南通 226100摘要：在化学实验课堂上，以生活中常见药品作为实验对象更能激发起学生对化学学习的兴趣。

鼻可乐是一种常见的市售洗鼻剂，主要成分为氯化钠、柠檬酸与柠檬酸钠，是一种典型的无机物与有机物的混合体系。

本文设计了对鼻可乐的组成进行定量分析的方法，并且通过实验验证其合理性，以期为鼻可乐成分分析实验进入高校分析化学实验课堂提供指导方法。

学生通过该实验不仅能掌握恒重坩埚、沉淀滴定等实验基本操作方法，而且能更好地理解定量分析数据的方法。

关键词：热分解；恒重实验；沉淀滴定；鼻可乐中图分类号：G64；O6Content Analysis of Inorganic and Organic Mixtures: A Case Study of the Compositional Analyses of NasalcareYuxin Wang 1, Shuyuan Ding 1,2, Shoulin Zhang 1, Lin Xu 1, Yawen Tang 1,*1 School of Chemistry and Materials Science, School of Teacher Education, Nanjing Normal University, Nanjing 210023, China.2 Haimen Middle School, Nantong 226100, Jiangsu Province, China.Abstract: For chemistry experimental teaching, using the common medicine in daily life as the experimental object can greatly arouse students’ interest in chemistry learning. Nasalcare is a commonly commercial nasal detergent which mainly contains sodium chloride, citric acid and sodium citrate, representing a typical mixture of inorganic substances and organic substances. In this paper, a quantitative analysis method for the composition analyses of Nasalcare is designed, and the rationality is verified by experiments. This work is anticipated to provide the methodological guidance for the involvement of compositional analyses of Nasalcare experiment into the university analytical chemistry experiment class. Through this experiment, students can not only master the basic laboratory skills, such as constant weight of crucible and precipitation titration, but also have a better understanding of the method of quantitative analysis of data.Key Words: Thermal decomposition; Constant weight test; Precipitation titration; Nasalcare2017年，教育部高等学校化学类专业教学指导委员会发布了化学类专业化学理论教学和实验教学建议内容。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves Jin-Yeon Kim,Laurence J.Jacobs,a͒and Jianmin QuG.W.Woodruff School of Mechanical Engineering,Georgia Institute of Technology,Atlanta,Georgia30332-0405Jerrol W.LittlesPratt&Whitney,Materials and Processes Engineering,400Main Street,M/S114-40,East Hartford,Connecticut06108͑Received10February2006;revised14June2006;accepted16June2006͒This research develops a robust experimental procedure to track the evolution of fatigue damage ina nickel-base superalloy with the acoustic nonlinearity parameter,␤,and demonstrates itseffectiveness by making repeatable measurements of␤in multiple specimens,subjected to both high-and low-cycle fatigue.The measurement procedure developed in this research is robust in that it is based on conventional piezoelectric contact transducers,which are readily available off the shelf,and it offers the potential forﬁeld applications.In addition,the measurement procedure enables the user to isolate sample nonlinearity from measurement system nonlinearity.The experimental results show that there is a signiﬁcant increase in␤linked to the high plasticity of low-cycle fatigue,and illustrate how these nonlinear ultrasonic measurements quantitatively characterize the damage state of a specimen in the early stages of fatigue.The high-cycle fatigue results are less deﬁnitive͑the increase in␤is not as substantial͒due to increased uncertainties involved in the high-cycle fatigue tests,but still show a clear relationship between␤and remaining fatigue life.One application of the measured␤versus fatigue-life data is to potentially serve as a master curve for life prediction based on nonlinear ultrasonic measurements.©2006Acoustical Society of America.͓DOI:10.1121/1.2221557͔PACS number͑s͒:43.25.Zx,43.25.Dc,43.25.Ba͓MFH͔Pages:1266–1273I.INTRODUCTIONRecent experimental studies and new physical models are demonstrating the potential of nonlinear ultrasonics͑or the second-harmonic generation technique͒to quantitatively detect and characterize fatigue damage in metals.1–10This fatigue damageﬁrst appears in the form of dislocation sub-structures,such as veins and persistent slip bands͑PSBs͒, and these PSBs accumulate at grain boundaries to produce strain localization and,thenﬁnally,microcrack initiation with increasing fatigue cycles.These dislocations͑and re-sulting microplastic deformation͒do not cause a large change in the linear macroscopic properties͑such as elastic moduli,sound speed,and attenuation͒of a material;the changes in the linear ultrasonic values are not large enough to be accurately measured with conventional linear ultrasonic techniques.However,the accumulation of dislocations throughout the continuum͑with increasing fatigue͒will cause a nonlinear distortion in an ultrasonic wave propagat-ing in the material,and thus generate higher harmonic com-ponents in an initially monochromatic ultrasonic wave sig-nal.For this reason,nonlinear ultrasonic͑acoustic͒waves can be used to quantify the presence and the density of dis-locations in a metallic material,and thus measure fatigue damage in a quantitative fashion.In addition,nonlinear ul-trasonics has the potential to promote an understanding of the evolution and accumulation of the dislocation substruc-tures in the very early stages of fatigue.To date,a number of investigators1–8have applied non-linear ultrasonic techniques to assess fatigue damage in dif-ferent materials under relatively controlled laboratory condi-tions.Yost and Cantrell1and Cantrell and Yost6 experimentally observed changes of the acoustic nonlinearity parameter,and attributed the changes to the effects of fatigue-induced dislocations.Frouin et al.5,8performed in situ nonlinear ultrasonic measurements during fatigue test-ing,and related the measured increase in the acoustic non-linearity parameter—in the vicinity of the fracture surface—to an increase in the dislocation density.Among these studies,only Frouin et al.8reported using nonlinear ultrasonic results to track fatigue damage throughout the en-tire fatigue life of a specimen.Oneﬁeld application of non-linear ultrasonics examined fatigue damage in stainless-steel turbine blades.7In spite of the recognized potential of non-linear ultrasonics,there are very few examples of its success-ful application to monitor fatigue damage.This is probably due to instrumentation issues that make accurate and consis-tent nonlinear ultrasonic measurements difﬁcult,plus a lack ofﬂexibility in the measurement setup needed to interrogate real fatigue test specimens.A critical next step—for the in-corporation of nonlinear ultrasonic techniques into life-prediction strategies of structural components—is a system-a͒Also at:School of Civil and Environmental Engineering,Georgia Institute of Technology,Atlanta,GA30332-0355;electronic mail: laurence.jacobs@atic study that quantiﬁes the robustness,accuracy,and validity of nonlinear ultrasonics to detect the early stages of fatigue damage͑prior to crack initiation͒in metallic materi-als.Of particular interest is the development of an experi-mental procedure with the capability of performingﬁeld in-spections of an absolute and repeatable nature.The objective of the current research is to develop a robust experimental procedure to track the evolution of fa-tigue damage in metallic materials with the acoustic nonlin-earity parameter,␤.The effectiveness of this proposed mea-surement procedure is demonstrated by making repeatable acoustic measurements of␤,in nickel-base superalloy speci-mens,subjected to three types of damage:Quasi-static monotonic,low-,and high-cycle fatigue.These nonlinear ul-trasonic measurements are used to track the evolution of damage in multiple specimens with a series of interrupted mechanical tests—ﬁrst by making a baseline measurement of ␤in an undamaged specimen,then introducing some damage into the specimen,repeating the measurement of␤in thissame͑unloaded͒specimen,then introducing more damage into the specimen,and repeating the procedure.It is important to note that the acoustic nonlinearity pa-rameter,␤,is an absolute material constant,which can be related to the higher-order elastic constants,of a material;the ␤parameter is a directly measurable acoustic parameter that is linked to the state of material damage.As a result,nonlin-ear ultrasonics is unparalleled in its potential to provide a robust and quantitative characterization of fatigue damage in in-service structural components.However,the acoustic non-linearity associated with fatigue damage is very small,and can be easily overwhelmed by a number of other factors ͑especially instrumentation nonlinearity͒inherent to the mea-surement procedure.Therefore,a critical contribution of this research is a systematic experimental procedure that can identify and remove spurious sources of nonlinearity,isolat-ing only those contributions due to the material and associ-ated damage.II.GENERATION OF HIGHER HARMONICS AND THE ACOUSTIC NONLINEARITY PARAMETER,␤The equations of motion of a solid element,in the ab-sence of body forces,are written in material coordinates,X, as␳ץ2u iץt2=ץ␴ijץX j,͑1͒where t is time,␳is the mass density,u i is the displacement vector,and␴ij is the stress tensor.The stress in a nonlinear ͑fatigued͒solid can,in general,be written as␴ij=␴ij0+A ijkl ץu kץX l+12A ijklmnץu kץX lץu mץX n+¯,͑2͒where␴ij0is the residual stress in the material,and A ijkl and A ijklmn are the Huang coefficients,9which are related to the second-and third-order elastic constants by A ijkl=␴jl0␦ik +C¯ijkl and A ijklmn=C¯ijklmn+C¯jlmn␦ik+C¯ijnl␦km+C¯jnkl␦im.C¯ijkl and C¯ijklmn are modified by fatigue damage͑dislocation substructures͒9from their initial values,C ijkl and C ijklmn.11Expressions for the modified elastic constants during fatigue have been presented in terms of the residual stress and plastic strain.12The density of a material undergoing finite deforma-tion is given by␳=␳0/det F where␳0is the constant den-sity in the unstressed configuration and F is the deforma-tion gradient tensor,defined as F ij=␦ij+ץu j/ץX i. Substituting Eq.͑2͒into Eq.͑1͒,and considering one-dimensional wave propagation of a longitudinal wave in an isotropic solid,one getsץ2u1ץt2=c2ץ2u1ץX12ͩ1+␤ץu1ץX1ͪ,͑3͒where c=ͱ͑C¯1111+␴110͒/␳is the longitudinal wave speed and␤is the acoustic nonlinearity parameter defined as␤=C¯111111+3C¯1111C¯1111+␴110.͑4͒It is well known that the second-order elastic constant͓C¯1111 in Eq.͑4͔͒changes very little,and that the residual stress ͑␴110͒is relatively small compared to the elastic constants. Therefore,it is the third-order elastic constant͓C¯111111in Eq.͑4͔͒which causes the increase in the acoustic nonlin-earity parameter,␤,during fatigue.Consider a time-harmonic plane͑displacement͒wave A1cos͑kX1−␻t͒,where A1is the amplitude,k is the wave number,and␻is the angular frequency.Assuming that the nonlinearity in the solid is small,the solution to Eq.͑3͒for this time-harmonic wave is obtained by a perturbation analy-sis as13u1=−18␤k2A12X1+A1cos͑kX1−␻t͒+18␤k2A12X1cos͓2͑kX1−␻t͔͒+¯=A0+A1cos͑kX1−␻t͒+A2cos͓2͑kX1−␻t͔͒+¯.͑5͒It is noted that the amplitude of the second-harmonic dis-placement is proportional to the acoustic nonlinearity param-eter and a subharmonic;that is,the static displacement is induced by the material nonlinearity.14The acoustic nonlin-earity parameter is determined experimentally by measuring the absolute amplitudes of the fundamental͑A1͒and the second-harmonic͑A2͒displacement signals,or␤=8A2k2X1A12.͑6͒Finally,note that Eq.͑6͒neglects the effect of attenua-tion losses that may be present in the fundamental and second-harmonic.If the difference in attenuation rates at the fundamental and the second-harmonic frequencies is large, then a correction factor must be included in the measurement of␤.The speciﬁc superalloy examined in this research is IN100,which is produced by powder metallurgy and has a veryﬁne grain structure.Attenuation measurements are made in IN100through the range of1–15MHz before fa-tigue tests.These results show that the attenuations at the fundamental and the second-harmonic frequencies are about0.14Neper/cm and0.34Neper/cm,respectively,which cor-respond to a maximum correction of less than2%in␤.Fur-thermore,the fatigue specimens show no noticeable change in attenuation in the frequency range considered here,so no attenuation corrections are made for the following␤calcu-lations.III.EXPERIMENTAL PROCEDUREA.Measurement system and procedureFigure1shows a schematic of the proposed nonlinear ultrasonic measurement system.A tone burst signal of7–9 cycles͑depending on the specimen thickness͒at5.3MHz is generated by a function generator͑80MHz Agilent33250A͒and is fed into a high-power gated ampliﬁer͑Ritec RAM-10000͒.In order to ensure one-dimensional wave propaga-tion in a single direction͑only right or left propagating͒,the exact number of cycles of the tone burst is selected as the maximum number of cycles that canﬁt within the thickness of the specimen—the spatial length of the tone burst is less than the specimen thickness.This eliminates any possible spurious͑apparent͒higher harmonics generated by the inter-ference of the incident and reﬂected wavefronts,as well as the effects of boundary conditions.The ampliﬁed high-voltage signal passes through a4dB attenuator͑pad͒and a 50⍀termination to suppress the transient behavior due to the mismatch in electrical impedances between the ampliﬁer and the mercial narrow-band PZT͑Lead Zir-conate Titanate͒-base piezoelectric transducers,with center frequencies of5MHz and10MHz,are used as a transmitter and a receiver,respectively.The transducers are coupled to the specimen with light lubrication oil.A specialﬁxture is designed to keep both the transmitting and receiving trans-ducers aligned on the same centerline axis,and to also allow for the removal of either transducer͑transmitter or receiver͒without disturbing the coupling͑and position͒of the other; this capacity is critical for the calibration procedure de-scribed next.The receiver is terminated with a50⍀passive load to have the same terminal load in the calibration.Both voltage and current signals of the transmitted ultrasonic waves are recorded and averaged256times with an oscillo-scope,and then transferred to a computer for further signal processing.Then,diffraction corrections are made to the measured fundamental and the second-harmonic signal am-plitudes.The calibration procedure for the͑piezoelectric͒receiv-ing transducer is based on the principle of self-reciprocity,15 and is employed in order to obtain a conversion transfer function͑from the measured electrical signal to the absolute amplitude of the particle displacement͒,and to compensate for any͑small͒variations in the coupling of the receiving transducer.Note that this calibration is performed prior to every nonlinear measurement,with the transmitter transducer removed.A50MHz pulser/receiver͑Panametrics,5072PR͒is used to transmit͑through the receiver transducer͒a wide-band ultrasonic pulse through the specimen.The current and voltage signals of the incident and the reﬂected pulse from the bottom surface of the specimen that is kept stress-free ͑when the transmitter is removed͒,are measured and used to calculate a transfer function that converts the measured cur-rent signal to the particle displacement of the incident wave at the receiver.15Finally,the pulse-inversion technique16,17is applied to accentuate the contribution of the even͑second͒harmonic signal,while reducing the dominance of the fundamental contribution.The pulse-inversion technique is very efﬁcient in extracting this second-harmonic amplitude by canceling out the odd harmonics͑which are mainly due to the instru-mentation͒;the even harmonic signal is extracted by adding two180°out-of-phase input signals.18Figure2illustrates the pulse-inversion technique by showing both the0°phase,and the180°out-of-phase͑inverted͒signals,the respective Fou-rier spectra before and after addition͑in the time domain͒, and the second-harmonic signal extracted.For the actual pro-cedure,ﬁrst,two transmitted time domain signals with180°out-of-phase inputs are measured consecutively with all other conditions unchanged.A function generator performs phase inversion of the input pulse.Then,two separately mea-sured output signals are combined in the time domain,ex-tracting the second-harmonic signal.Note that this combina-tion is performed with two raw signals without introducing any adjustments,such as time shifts or amplitude modiﬁca-tion.Figure2clearly demonstrates how the fundamental fre-quency contribution is completely canceled out,leaving only the second-harmonic contribution.Note that the remaining subharmonic component͑at zero frequency͒corresponds to theﬁrst term in Eq.͑5͒,and appears as a result of the static displacement induced by the acoustic radiation;this compo-nent should have an amplitude proportional to the amplitude of the second-harmonic,19but it is not systematically ana-lyzed in this study.The frequency spectra of the signal origi-nally transmitted,and the extracted signal shown in Fig.2͑b͒are independently calculated with a rectangular window.Fi-nally,to obtain a more accurate estimation of the amplitudes of the fundamental and second-harmonics,the signals are digitallyﬁltered in the frequency domain and inverse Fourier transformed.An additional advantage of using the pulse-inversion technique is that one can readily monitor the shape of the second-harmonic signal.Since the amplitude of the second-harmonic signal produced by material nonlinearity is very small in comparison to the amplitude of thefundamen-FIG.1.͑Color online͒Experimental setup.tal,small variations in coupling—that are usually accompa-nied by spurious interface nonlinearity—can have a signiﬁ-cant inﬂuence on the repeatability of the proposed measurement procedure.Experience shows that the shape of this second-harmonic signal is an excellent indicator of the quality of the transducer to specimen coupling.Figure 3illustrates the linear relationship that exists be-tween the measured absolute amplitudes of the second-harmonic and the squared fundamental ͑both displacements ͒,as a function of increasing input voltage amplitude.These absolute displacement amplitudes are calculated using the transfer function described previously.Figure 3shows the results of two independent measurements on the same speci-men,where the transducers and the couplant are completely removed,and then reattached and recalibrated for the second measurement.It is seen that the slopes from these two inde-pendent measurements are nearly constant,which conﬁrms that the measurements are repeatable,and that removal andreplacement of the transducers ͑and couplant ͒will not have a dominant ͑negative ͒inﬂuence on the results.The variability ͑error bars ͒due to measurement error is determined by av-eraging ﬁve measurements on the same undamaged speci-men,and results in a variability of ±0.45on all ␤values reported henceforth.Finally,Fig.3can be used as a guide for the required input voltage needed to avoid inconsistencies caused by a low fundamental amplitude.20The measurement system is calibrated by measuring ␤in borosilicate.It is known that borosilicate has a very low degree of nonlinearity,and researchers 21have shown that the ratio of the second-harmonic amplitude to the fundamental amplitude is on the order of −120dB ͑this unpublished ref-erence value illustrates that the ␤of borosilicate is almost zero ͒.A ␤of 9.0is measured in borosilicate using the pro-posed measurement procedure,and this nonzero value of ␤is believed to be associated with the inherent nonlinearity of the transmitting piezoelectric transducers used in the mea-surement system.This is in agreement with previous researchers 22who examined the nonlinear properties of PZT ͑polarized K1͒and measured its ␤to be on the order of 8.0.Therefore,a ␤of 9.0will be used to calibrate the measure-ment system by subtracting this value from all measured ␤values.Although such a calibration method neglects the in-teractions between different frequencies in a nonlinear sys-tem,it can be easily argued that the effects of such interac-tions on ␤are higher ordered.This is further veriﬁed by performing a ␤measurement on fused silica.The directly measured value of ␤for fused silica is 21.0.After calibration ͑subtracting 9.0͒,a ␤of 12.0is obtained for fused silica,which is in agreement with published values.23The good agreement between these results and published values,plus the consistency and repeatability of the results reported in Sec.IV ,validate the accuracy of the proposed procedure as a working method to track changes in ␤as a function of fatigue life in multiple specimens.B.SpecimensThree different types of specimens are used;each type machined from IN100cylindrical rods—128mm longandFIG.2.͑a ͒Typical time domain signals:Thin continuous and dotted lines are the transmitted signals with 0ؠphase ͑uninverted ͒and 180ؠout-of-phase ͑inverted ͒inputs,respectively.The thick line is the second-harmonic signal extracted by the pulse-inversion technique.͑b ͒Fourier spectra of the origi-nal transmitted signal ͑fundamental ͒and the second-harmonic signal ex-tracted by the pulse-inversion technique,demonstrating that the second-harmonic amplitude can be measured without being inﬂuenced by the large fundamentalamplitude.FIG.3.͑Color online ͒Second-harmonic amplitude ͑A 2͒versus the ampli-tude of the fundamental squared ͓͑A 1͒2͔for increasing input voltage ob-tained from two independent measurements.27mm in diameter.Note that the surface ﬁnishes on all specimens in this study are “as-machined.”The ﬁrst type is a standard fatigue specimen with a constant rectangular cross section—a constant gauge width of 12.5mm and a thickness of 6.4mm.One of these specimens is used for the low-cycle fatigue tests,and one is used for the high-cycle fatigue tests.The second specimen has an hour-glass shape ͑starting from a width of 12.5mm and a constant thickness of 6.4mm ͒with a varying cross section that gradually reduces to create a region of higher stress at its center;this specimen is used exclusively for the high-cycle fatigue tests.The third speci-men is a nonstandard rectangular bar specimen;it is simply a 120mm long by 14.3mm wide rectangular bar—having a constant thickness of 4.7mm.This specimen is used for both the monotonic and low-cycle fatigue tests,and for a concur-rent set of Rayleigh wave measurements.24IV.EXPERIMENTAL RESULTS AND DISCUSSION A.Monotonic load resultsFirst,consider a quasi-static monotonically loaded ͑non-standard rectangular bar ͒specimen.This specimen is used to validate the repeatability of a set of nonlinear ultrasonic mea-surements made on a specimen subjected to an interrupted mechanical test—a test specimen that is mechanically loaded,removed to make a set of nonlinear ultrasonic mea-surements,and then the procedure is repeated at speciﬁed intervals,typically until the specimen fails.In this monotonic test,the specimen is loaded ͑at a rate of 890N/s ͒to a ﬁrst-load equivalent to 125%of the yield stress ͑absolute strain of 7.463%͒,and then is unloaded at the same rate.The nonlin-ear ultrasonic measurements are then performed on the un-loaded specimen.The same procedure is repeated for in-creasing maximum loads equivalent to 135%and 145%of yield stress ͑strains of 10.66%and 13.77%,respectively ͒.These calibrated results are presented in Fig.4,and note that these measured acoustic nonlinearity parameters,␤,are ab-solute values.It is important to note that the ␤value of 23.1—measured in the undamaged specimen ͑before anymechanical load is applied ͒—is a measure of the intrinsic nonlinearity of the undamaged IN100material;and that the nonlinearity associated with the transmitting piezoelectric transducers ͑␤=9.0͒has already been subtracted from this and all other values.Figure 4shows that there is a signiﬁcant increase in ␤with increasing plastic stress;the increase is largest from the unloaded ͑undamaged ͒state to 125%yield stress,and then the increase is less substantial at the higher stresses.This observed behavior of a large increase in the acoustic nonlinear parameter,once the specimen is loaded above its yield stress,makes sense because dislocations ͑or microplasticity ͒create signiﬁcant material nonlinearity;the literature reports that the second-͑order ͒harmonic ampli-tudes associated with dislocations should be larger than the intrinsic material nonlinearity due to the elastic lattice anharmonicity.25Most importantly,the results in Fig.4show that the proposed measurement procedure is capable of mak-ing an absolute measurement of the evolution of the acoustic nonlinear parameter,␤͑as a function of stress in this case ͒in these interrupted mechanical tests on an IN100specimen.B.Low-cycle fatigue resultsLow-cycle fatigue in this paper refers to a fatigue test where the maximum stress is above yield,so there is plastic deformation even at the beginning of the fatigue test.Of equal importance is that cyclic loading promotes the forma-tion of dislocation dipoles,which is the strongest source of nonlinearity among a list of potential sources.6,9,10The fre-quency of cyclic loading is 0.5Hz,R ͑=␴min /␴max ͒is zero ͑strain controlled ͒,the maximum stress level is 105%of the yield stress ͑strain of 0.48%͒,and the fatigue tests are inter-rupted to perform the nonlinear ultrasonic measurements at different numbers of fatigue cycles.Three different speci-mens are tested,and there will be some level of variability associated with the initial microstructure of each specimen.As a result,the measured acoustic nonlinearity parameters will be normalized by the value measured in each undam-aged specimen ͑␤0͒,before any mechanical load is applied.This normalization procedure ͑which will be repeated for the high-cycle fatigue results ͒removes some of the variability associated with the initial microstructures of each specimen,enables a direct comparison of the evolution of the acoustic nonlinearity of all the specimens tested,and normalizes the nonlinearity associated with the transmitting piezoelectric transducers.The evolution of the normalized acoustic non-linearity parameter ͑␤/␤0͒,as a function of normalized fa-tigue life ͑fatigue cycle normalized to the total number of cycles,where 100%means the total fatigue life ͒,together with a best-ﬁt curve,is shown in Fig.5.Note that the speci-mens failed at 12,640,13,012,and 50,221cycles ͑the third specimen is the standard fatigue specimen;while the ﬁrst two are the nonstandard rectangular bars ͒and the ͑calibrated ͒␤0measured in each specimen is 21.4,22.2,and 22.4,re-spectively.Figure 5shows a rapid increase in ␤/␤0͑up to 30%͒during the ﬁrst 40%of fatigue life,which demonstrates that these nonlinear ultrasonic measurements can be used to quantitatively characterize the damage state of thismaterialFIG.4.͑Color online ͒Monotonic load results—acoustic nonlinearity pa-rameter ␤versus applied stress ͑or strain ͒level.in the early stages of fatigue life.This is somewhat different from other experimental results,5which show a slower initial increase in ␤.The difference in behavior is most likely due to the high maximum stress ͑strain ͒level beyond the yield stress ͑strain ͒,and a signiﬁcant amount of plasticity—due to the dislocation motions—probably starts accumulating in the specimen from the ﬁrst loading cycle,which reduces the time period for dislocation reassociation at the beginning of fatigue.The measurement data show increasing scatter with increasing number fatigue cycles,which is most likely due to a combination of two factors:The intrinsic material behavior,and issues with the measurement procedure.There is an in-herent randomness in the progression of fatigue damage dur-ing fatigue testing ͑more so in high-cycle fatigue,as dis-cussed in the next section ͒,which should manifest itself as a corresponding randomness in the resulting acoustic nonlin-earity.There is a somewhat unrelated issue with the measure-ment procedure in the later stages of fatigue—the surface deformation associated with the increased plasticity makes it difﬁcult to consistently couple the transducers to the speci-men surface.Finally,note that a best-ﬁt curve,such as the one developed in Fig.5͑but based on a larger number of specimen and data points ͒,has the potential to serve as a master curve for life prediction based on nonlinear ultrasonic measurements.A companion study makes nonlinear ultrasonic measure-ments with Rayleigh surface waves on the ﬁrst two speci-mens;the procedure used to make these ͑relative ͒nonlinear Rayleigh wave measurements is reported elsewhere.24Figure 6shows a comparison of the best-ﬁt curve from Fig.5͑lon-gitudinal waves ͒with those from the nonlinear Rayleigh wave measurements.There is excellent agreement with these two sets of results,demonstrating that both longitudinal and Rayleigh waves can be used to track nonlinear material be-havior.Note that the sharp drop in the acoustic nonlinearity ͑the single data point in Fig.6͒,at 87%of fatigue life forSpecimen No.1,is most likely due to the emergence of surface-breaking microcracks whose depths are larger than the wavelength of the second-harmonic.24C.High-cycle fatigue resultsHigh-cycle fatigue in this study refers to fatigue tests where the maximum stress level is below yield;in this case,the maximum stress is 95%of yield stress,the frequency of cyclic loading is 1Hz,and R ͑=␴min /␴max ͒is zero ͑load controlled ͒.Five different fatigue specimens are tested,with failure occurring at 55,432,102,392,203,220,328,341,and 350,985cycles.As with the monotonic and low-cycle fatigue tests,these fatigue tests are interrupted to perform the non-linear ultrasonic tests.Figure 7shows the change in the nor-malized acoustic nonlinearity parameter ͑␤/␤0͒over the nor-malized fatigue life of each specimen.Note that the ͑calibrated ͒␤0measured in each specimen is 22.1,21.3,19.8,22.4,and 21.2,respectively.FIG.5.Low-cycle fatigue results—normalized acoustic nonlinearity param-eter ␤/␤0as a function of the percentage of fatigue life for three different fatigue specimens.The continuous line is the best-ﬁt curve obtained from the discrete experimentaldata.parison of longitudinal and Rayleigh wave ͑Ref.24͒results showing the normalized acoustic nonlinearity parameter ␤/␤0as a function of the percentage of fatigue life for the low-cycle fatigueresults.FIG.7.High-cycle fatigue results—normalized acoustic nonlinearity param-eter ␤/␤0as a function of the percentage of fatigue life for ﬁve different fatigue specimens.The continuous line is the best-ﬁt curve obtained from the discrete experimental data.。