Effects of interfacial transition zones

Effects of interfacial transition zones on the stress –strain behavior of modeled recycled aggregate concreteJianzhuang Xiao a ,⁎,Wengui Li a ,b ,David J.Corr b ,Surendra P.Shah ba Department of Building Engineering,Tongji University,Shanghai 200092,PR ChinabCenter for Advanced Cement-Based Materials,Northwestern University,Evanston,IL 60208,United Statesa b s t r a c ta r t i c l e i n f o Article history:Received 27October 2012Accepted 2May 2013Available online xxxx Keywords:Concrete (E)Aggregate (D)Interfacial transition zone (B)Finite element analysis (C)NanoindentationBased on nanoindentation tests and analysis,the constitutive relationship of the Interfacial Transition Zones (ITZs)in Recycled Aggregate Concrete (RAC)is put forward.Together with the meso/micro-scale mechanical properties of each phase in Modeled Recycled Aggregate Concrete (MRAC),the plastic-damage constitutive models are employed in numerical studies on MRAC under uniaxial compression and uniaxial tension loadings to predict the overall mechanical behavior,particularly the stress –strain relationship.After the calibration and validation with the experimental results,a parametric study has been undertaken to analyze the effects of ITZs and new mortar matrix on the stress –strain relationship of MRAC.It is revealed that the mechanical properties of new mortar matrix and relative mechanical properties between ITZs and mortar matrices play a signi ficant role in the overall stress –strain relationship and failure patterns of MRAC under both uniaxial compression and uniaxial tension loadings.©2013Elsevier Ltd.All rights reserved.1.IntroductionThe behaviors of Recycled Aggregate Concrete (RAC)are deter-mined by properties of the waste concrete,the new mix composition,the mixing approach and the deterioration condition of Recycled Coarse Aggregates (RCAs)[1–3].It is generally accepted that the Interfacial Transition Zones (ITZs),the quality of the old mortar,and the old mortar content of the original concrete in fluence the properties of RAC.In recent years,RAC has been proven to be commercially and technically sound for both non-structural and structural applications [4–7].Xiao et al.found that properly designed and constructed RAC frame structures have good load-bearing capacity,deformation and energy dissipation ability to withstand earthquake-type loadings [8].Quasi-brittle multiphase materials,such as concrete,are widely applied in engineering.Most of them have intrinsic heterogeneous and nonlinear mechanical behaviors due to the random distribution of multiple phases over the nano-,micro-,meso-and macro-scales [9–15].A better understanding of mechanical properties including the failure processes by both experiments and computer modeling has become one of the most critical research topics for concrete [16–19].Corr et al.predicted the mechanical properties of concrete in tension with the consideration of meso-scale randomness in the cohe-sive interface properties [20,21].Mondal et ed a nanoindenter along with in-place scanning probe microscopy imaging to determine the nano-scale local mechanical properties of ITZs [22].Cusatis et al.formulated the Lattice Discrete Particle Model (LDPM)and simulated experiments include uniaxial compression and multiaxial compression,tensile fracture,shear strength,and cyclic compression tests [23,24].Yip et al.developed an irregular lattice model to simulate the fracture process of multiphase particles,such as concrete [25].Moreover,con-crete was simulated with plastic-damage constitutive model,and showed a very good correlation with the experimental results [26].To characterize the random heterogeneity in cementitious materials numerically,different phases in the material such as the mortar matrix,aggregates and ITZs can be explicitly modeled by the Finite Element Analysis (FEA),and the material mechanical properties are directly assigned to the elements [27–29].Al-Rub et al.and Nagai et al.simulat-ed the mortar matrix,coarse aggregate of random shapes and sizes and interfaces in concrete specimens under 2D tensile and compressive loadings [30,31].Rao et ed a unit cell approach to model the deformation and failure of single aggregate concrete [32,33].Xiao et al.numerically simulated the stress distribution characteristics of Recycled Aggregate Concrete (RAC)by commercial FEA software the ABAQUS 6.8[11].However,for the previous investigations,the thick-ness,elastic modulus and strength of ITZs relative to the mortar matrix were not considered during the numerical simulation.Moreover,some numerical simulations even neglected the existence of the ITZs between aggregate and mortar matrix [34].With the emergence of nanoindentation technology,the proper-ties of the ITZs are available to be measured experimentally [9,22].Due to the recent advances in understanding the microstructure,thickness,and strength of the ITZ and the developments of computa-tional power,the micromechanical behavior of concrete can be effec-tively simulated to get a deeper insight into the effect of each phaseCement and Concrete Research 52(2013)82–99⁎Corresponding author.Tel.:+862165982787;fax:+862165986345.E-mail address:jzx@ (J.Xiao).0008-8846/$–see front matter ©2013Elsevier Ltd.All rights reserved./10.1016/j.cemconres.2013.05.004Contents lists available at SciVerse ScienceDirectCement and Concrete Researchj ou r n a l h o m e p a g e :h t tp ://e e s.e l s e v i e r.c o m /C E MC ON /d e f a ul t.a s p(such as aggregate size and shape,ITZ thickness and micromechanical properties,and the mortar matrix mechanical properties,etc.)[35].Compared to conventional concrete,RAC contains more types of ITZs [36,37].The old ITZ is between the original aggregate and the old paste matrix,while the new ITZ is between the old paste matrix and the new paste matrix.Xiao et al.[38]and Tam et al.[3]found that the microstructure of RAC was much more complicated than that of conventional concrete.It is well known that the compressive strength and elastic modulus of RAC are lower than those of conven-tional concrete.One of the major reasons for the lower strength exhibited by RAC is the weak ITZs and old adhered mortar.Etxeberria et al.[39]indicated that adhered old mortar on RCAs was the weakest point.Contrary to the common beliefs,Nagataki and Gokce et al.reported that adhered mortar is not always the primary parameter determining the quality of the RAC [40].Rasheeduzzafar and Khan [41]concluded that the weakest link in RAC depended on the relative strength of old mortar and new mortar or the relative quality of old ITZ and new ITZ.In this paper,Modeled Recycled Aggregate Concrete (MRAC)is a volume element of RAC which is used to simplify the real RAC for ex-perimental study [10,11].A plastic-damage model is adopted within FEA analysis.The mechanical properties of ITZs in MRAC are obtained by a nanoindentation technique.Due to the ratio of height to thick-ness being 3for the MARC,two-dimensional micro-scale numerical modeling is conducted in order to investigate the effects of ITZs on the overall behavior and failure process of MRAC under both uniaxial compression and uniaxial tension loadings.The experimental and numerical results show a good relation with each other.The results show that the micromechanical properties of ITZ have an obviousin fluence on the stress –strain relationship and failure patterns of MRAC.2.Modeled recycled aggregate concreteIn the current paper,a representative volume element of RAC is idealized as an MRAC consisting of nine recycled coarse aggregate surrounded by a mortar matrix [10,11].Recycled coarse aggregate is idealized to have a round shape.The MRAC used in numerical simula-tion is shown in Fig.1.In general,the MRAC was used to obtain the effective properties of multiphase composites.The MRAC means that the recycled coarse aggregates are embedded within new mortar matrix as a square array.This is an assumption made to simplify the real RAC and provide useful information regarding crack initiation and mechanical response of RAC under loadings.The previous exper-imental results show that the failure pattern of MRAC can provide in-sights into the in fluences of the mechanical properties of each phase on the failure mechanism of RAC [10,20,21,42,43].It has been found that idealization of regular distribution of recycled coarse aggregates in RAC not only simpli fies the problem but also assists in studying the effect of different phases on overall failure behavior of RAC.3.Constitutive relationshipsRecycled aggregate concrete,which is considered as a cementitious composite including natural aggregate,old ITZ,old mortar matrix,new ITZ and new mortar matrix (see Fig.1a),can be numerically modeled using finite element models.The details of each constitutive model used in this numerical simulation are described in the following.a) MRAC specimenb) MRAC schematicFig.1.Modeled Recycled Aggregate Concrete (MRAC).a) uniaxial tensionb) uniaxial compressionFig.2.Stress –strain relation under uniaxial loading.83J.Xiao et al./Cement and Concrete Research 52(2013)82–99Fig.3.Nanomechanical properties and characteristics of ITZs in RAC.84J.Xiao et al./Cement and Concrete Research 52(2013)82–993.1.Mortar matrixMortar matrix shows softening behavior after reaching its peak tensile stress or compressive stress,which is due to toughening me-chanics within the fracture process zone.Both micro-cracking devel-opment and irreversible deformations contribute to the nonlinear response of mortar matrix.A plastic-damage constitutive model for mortar matrix is developed by former investigators [26,30,44].Anisotropic damage with a plasticity yield criterion and a damage cri-terion is introduced to adequately describe the plastic and damaged behaviors of mortar matrix.Moreover,in order to account for differ-ent effects under tensile and compressive loadings,two damage criteria are adopted:one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components.For cyclic loading,stiffness recovery caused by crack opening and closing is also considered.The compressive stiffness is recovered upon crack closure as load changes from tension to com-pression.On the other hand,the tensile stiffness is not recovered as the load changes from compression to tension once crushing micro-cracks have developed.In this study,the tension and compres-sion stiffness recovery factors are 0.0and 1.0,respectively.The strain equivalence hypothesis is used in deriving the constitutive equations,so that the strains in the effective (undamaged)and damaged con fig-urations are set equal [26,30,45].This leads to a decoupled algorithm for the effective stress computation and the damage evolution.The following information is used for either isotropic or anisotrop-ic damage.And the damage tensor d ij (d t and d c )degenerates to the scalar damage variable in case of uniaxial loading.The plasticity and the compressive damage loading surface are more dominate in case of shear loading and compressive crushing (modes II and III cracking)whereas the tensile damage loading surface is dominant in case of mode I cracking.In the uniaxial loading,the elastic stiffness degrada-tion variables are assumed as increasing functions of the equivalentplastic strain ˜εpl t and ˜εpl c with ˜εpl t being the tensile equivalent plastic strain and ˜εplc being the compressive equivalent plastic strain.It should be noted that the material behavior is controlled by both plas-ticity and damage.It is assumed that the uniaxial stress –strain curves can be converted into stress versus plastic –strain curves.Thus σt ¼σt ˜εpl t ;_εpl t ;θ;f i σc ¼σc ˜εpl c ;_εpl c ;θ;f i8<:ð1Þ0.00000.00010.00020.00030.00040.00050.00060.00.51.01.52.02.53.03.5S t r e s s (M P a )Strain0.0000.0020.0040.0060.0080.0100.0120.0145101520253035404550S t r e s s (M P a )Straina) Uniaxial tensionb) Uniaxial compressionFig.4.Uniaxial stress –strain relation of ITZ and mortar matrix.Table 1Mechanical properties of each phase in MRAC.MRACThickness (μm)Elasticmodulus (E)(GPa)Poisson's ratio (ν)Strength (MPa)Compressive (f c )Tensile (f t )Natural aggregate –80.00.16––Old mortar (OM)–25.00.2245.0 3.00New mortar (NM)–23.00.2241.4 2.76Old ITZ (OI)5020.00.2036.0 2.40New ITZ (NI)6018.00.2033.12.21Fig.3(continued ).85J.Xiao et al./Cement and Concrete Research 52(2013)82–99where the subscripts t and c refer to tension and compression,respec-tively;˜εpl t and ˜εpl c are the equivalent plastic strains,_εpl t and _εpl c are the equivalent plastic rates,θis the temperature,and f i (i =1,2,…)are other prede fined field variables.When the mortar matrix specimen is unloaded from any point on the strain softening branch of the stress –strain curve,the unloading response is less stiff.The degradation of the elastic stiffness is charac-terized by two damage variables,d t and d c ,which are assumed to be functions of the plastic strain,temperature,and field variables:d t ¼d t ˜εpl t ;θ;f i ;0≤d t ≤1d c ¼d c ˜εpl c ;θ;f i ;0≤d c≤1:8<:ð2ÞThe damage variables can take values from zero,representing theundamaged material,to one,which represents total loss of strength.If E 0is the initial (undamaged)elastic modulus,the stress –strain relations (ε−σ)under uniaxial tension and compression loading are respectively as shown:σt ¼1−d t ðÞE 0εt −˜εpl tσc ¼1−d c ðÞE 0εc −˜εpl c8<:ð3ÞThe model assumes that the uniaxial tensile and compressive re-sponse are characterized by damaged plasticity,as shown in Fig.2[30,45],where εt el and εc elare the tensile and compressive equivalent elastic strain,respectively.a) Overall FEA model b) Details of each phaseFig.5.2D micro-scale FEA model of MRAC.Table 2Mixture proportion of cement mortar in MRAC [10].MRACOld mortar(w/c ratio)Mass,kg/m 3New mortar (w/c ratio)Mass,kg/m 3Water Cement SandWater Cement Sand MRAC-30-200.451603565650.55160276589MRAC-30-300.451603565650.45160356565MARC-30-400.451603565650.36160444539a) Test and DIC setupb) Failure patternFig.6.Experimental study on MRAC under uniaxial compression.0.0000.0010.0020.0030.0040.00551015202530354045S t r e n g t h (M P a )Strainparison of compressive stress –strain curves (MRAC30-30).86J.Xiao et al./Cement and Concrete Research 52(2013)82–993.2.ITZsDue to the difficulties in determining the properties of ITZ with traditional testing methods,the understanding of the thickness,and elastic modulus and strength of ITZ related to mortar matrix is limit-ed.With the emergence of nanoindentation techniques,it is now possible to directly measure the micromechanical properties of the quite thin ITZ.The nanoindentation involves performing indents at micro or nano scale[46,47].In this study,four indentation areas(150μm×100μm)were taken randomly for nanoindentation within the old ITZ and new ITZ regions,respectively.Total341indents were performed in an array at each studied area(Fig.3(a)and(b)).These four studied areas were used for statistical analysis including the average and standard deviation.Hardness testing on cement paste found that there is a linear relationship between hardness and strength[46,47].The hard-ness obtained from nanoindentation is assumed to provide a linear relationship between hardness and strength.As the indentation hard-ness characteristics at the ITZs in RAC were observed to generally be similar to those of the elastic modulus[9,35],this study will focus on the elastic modulus in the following analysis.Fig.3(c)and(d)re-spectively shows the contour maps of elastic modulus of old and new ITZs.The darker areas mean the lower modulus region,while the brighter areas mean the higher modulus regions.In this study,the distribution of elastic modulus was used as a basis for the property characteristics of old ITZ and new ITZ,such as the thickness,elastic modulus and strength related to old and new mortar matrices,re-spectively.Fig.3(e)and(f)shows the elastic modulus distributions with the distance across old ITZ and new ITZ.It is well established that the microstructure in the ITZ region is quite different from thata) Experimental (point a)b) Numerical (point a) c) Experimental (point b)d) Numerical (point b) e) Experimental (point c)f) Numerical (point c)Fig.8.Micro-scale crack development at different loading levels.87J.Xiao et al./Cement and Concrete Research52(2013)82–9988J.Xiao et al./Cement and Concrete Research52(2013)82–99a) Experimental (Point b)b) Numerical (Point b)c) Experimental (Point c)d) Numerical (Point c)e) Experimental (Point d)f) Numerical (Point d)g) Experimental (Point e)h) Numerical (Point e)pressive failure pattern at different loading levels.of the mortar matrix.In this test,greater porosity in the ITZs caused the reduced elastic modulus and strength,relative to those of related mortar matrix [9,11,35,48].In this study,the ITZ thickness was estimated by locating the place where there is slight variation in the elastic modulus with the distance from the natural aggregate or old mortar matrix surface,and the elastic modulus distribution of the ITZs seems to be close to that of mortar ma-trix.Based on the nanoindentation results,the thicknesses of old ITZ and new ITZ are found to be around 50μm and 60μm,respectively.Moreover,the average elastic modulus of old ITZ and new ITZ were found to be approximately 80%and 85%of those of old mortar matrix and new mortar matrix,respectively [9,35].It is assumed that there is a linear relationship between indentation hardness and strength.Considering that the hardness has a similar distribution with the mod-ulus in the ITZ regions (see Fig.3(g)–(j)),the strengths of old ITZ and new ITZ are assumed to be 80%and 85%of those of old mortar matrix and new mortar matrix,respectively [35,46,47].Based on the current and previous experimental data,the ratios of ITZs'mechanical proper-ties to those of mortar matrix are assumed to be mainly ranged 0.5to 1.0[22,49,50].The constitutive relation of ITZ is simulated with dam-aged plasticity model,which is similar to that of mortar matrix,but the elastic modulus and strength are a little lower than those of mortar matrix.For the mortar matrix,elastic modulus,the strength (peak stress),and deformation capacity (peak strain and ultimate strain)parameters are obtained according the experimental data from Refs.[20,21,51].In case of the ITZs,the relative mechanical properties (elastic modulus and strength)to that of mortar matrix can be provided by the nanoindentation test,however,recently it is still a big challenge to obtain the deformation capacity parameters of ITZs.So in this study,the deformation capacity of ITZs is assumed to be similar with that ofmortar bining the descriptions in this and above sections,the predicted uniaxial tensile and compressive stress –strain relation-ships for both ITZ and mortar matrix based on the plastic-damage con-stitutive model are shown in Fig.4.3.3.Natural aggregateGranite cylinders are used as natural aggregate in the MRAC.Based on the experiment results [10],there were no cracks or damage observed in the natural aggregates during loading.In the current study,natural aggregate is modeled as linear-isotropic material.It behaves linearly throughout the analysis.For the numer-ical calibration validation,the material parameters of each phase in MRAC,which were determined according to the experimental data,are listed in Table 1[10,35].However,the Poisson's ratios of new ITZ and old ITZ were de fined as 0.20according to the study by Ramesh et al.[52].4.FEA simulation and test veri fication4.1.FEA modelThe software program (ABAQUS 6.11)was used for the FEA analyses.4-node plane stress quadrilateral (CPS4R)elements were used to mesh the MRAC.The 2D micro-scale FEA model of MRAC is shown in Fig.5.The model was subjected to a uniformly distributed displacement at the top edge,as the displacement-controlled loading scheme was used.The Y degrees of freedom were fixed at the bottom edge,while the X degrees of freedom and rotation were not constrained.The FEA model has a total of 34,240elements in this simulation.4.2.Modeling implementationIn this paper,ABAQUS/explicit quasi-static analyses were applied for the numerical simulation [53,54].The explicit method was origi-nally developed,and is primarily used to solve dynamical problems involving deformable bodies.Acceleration and velocity at a particular point in time are assumed to be constant during a time increment and are used to solve for the next point in time.ABAQUS/explicit uses a forward Euler integration scheme as follows [55,56]:ui þ1ðÞ¼ui ðÞþΔti þ1ðÞ_ui þ1ðÞð4Þ_ui þ12ðÞ¼_u i −12ðÞþΔti þ1ðÞþΔti þ1ðÞ2€ui ðÞð5Þwhere u is the displacement and the superscripts refer to the timeincrement.The term ‘explicit ’refers to the fact that the state of the0.00000.00010.00020.00030.00040.00050.00.51.01.52.02.53.03.5S t r e s s(M P a )StrainFig.10.Numerical tensile stress –strain curve of MRAC30-30.a) Point a b) Point b c) Point cFig.11.Simulated micro-scale crack development at different loading levels.89J.Xiao et al./Cement and Concrete Research 52(2013)82–99analysis is advanced by assuming constant values for the velocity _u,and the acceleration €u,across half time intervals.The accelerations are com-puted at the start of the increment by €ui ðÞ¼M −1⋅F i ðÞ−Ii ðÞð6Þwhere F is the vector of externally applied forces,I is the vector of in-ternal element forces and M is the lumped mass matrix.As the lumped mass matrix is diagonalized it is a trivial process to invert it,unlike the global stiffness matrix in the implicit solution method.Therefore each time increment is computationally inexpensive to solve.A stability limit determines the size of the time increment:Δt ≤2ωmaxð7Þwhere ωmax is the maximum element eigenvalue.A conservative and practical method of implementing the above inequality is:Δt ¼min Le cð8Þwhere L e is the characteristic element length and c d is the dilatational wave speed:c d¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλþ2μρs ð9Þhere,λand μare the Laméelastic constants and ρis the material den-sity.A quasi-static problem solved using the explicit method would have much smaller time increments than an equivalent problem solved by implicit method.Although the incremental solution is easy to obtain using the implicit method,it is unusual for an analysis to take 100,000increments to solve.In order to maintain ef ficiency ofc) Point d d) Point ea) Point b b) Point cFig.12.Simulated tensile failure pattern at different loading levels.Table 3Mechanical properties of each phase in parametric analysis.New mortar matrixOld ITZNew ITZr ¼0:8ENME OM;f NMf OM;E NI E OI ;f NI f OI¼0:8 :MRAC30-20;r ¼0:5EOIE OM;f OI f OM¼0:5;r ¼0:5ENIE NM;f NI f NM¼0:5;r ¼1:0E NM E OM ;fNM f OM ;E NI E OI ;fNIf OI¼1:0 :MRAC30-30;r ¼0:8EOI E OM ;fOIf OM¼0:8 ;r ¼0:8ENI E NM ;f NIf NM ¼0:85 ;r ¼1:2ENME OM;f NMf OM ;E NI E OI ;f NI f OI ¼1:2:MRAC30-40r ¼1:0EOIE OM;f OIf OM¼1:0;r ¼1:0ENI E NM ;fNI f NM¼1:0;Note:E OM and f OM are elastic modulus and strength of old mortar,respectively.E NM and f NM are elastic modulus and strength of new mortar,respectively.E OI and f OI are elastic modulus and strength of old ITZ,respectively.E NI and f NI are elastic modulus and strength of new ITZ,respectively.90J.Xiao et al./Cement and Concrete Research 52(2013)82–99the analyses,it is important to ensure that the sizes of the elements are as regular as possible.This is so that on small element does not reduce the time increment for the whole model.On the other hand, the implicit FEA method encounters numerical difficulties when solv-ing non-linear quasi-static problems.The iterative approach may have trouble achieving convergence in analyses with a highly non-linear material behavior,such as the plastic-damage model for cement-based materials.In the case of the explicit method,the solver equations can be solved directly to determine the solution without iteration,thus providing an alternative method.It is important when performing a quasi-static simulation that the inertial forces do not affect the mechanical response and provide unrealistic dynamic results.To reduce the dynamic effects,the ratio of the duration of the load and the fundamental natural period of the method should be greater thanfive.It has been shown that by keeping the ratio of kinetic energy to the total internal energy at b5%the dynamic effects in the model are negligible[57,58].This is the criterion for quasi-static behavior that is employed in this study.The ABAQUS/explicit quasi-static solver used an analysis time of 0.1s(period time).A displacement-controlled loading scheme was adopted in this simulation.After trial and comparison,the damage variables for the plastic-damage constitutive model are determined. In order to obtain complete stress–strain curves,all the analyses for uniaxial tension and compression were ended at a displacement d=0.09mm(ultimate strain0.0006)and0.9mm(ultimate strain 0.006),respectively.A computer with an Intel®Core I7processor and8GB physical memory was used for all the simulations.In this study,the FEA numerical response depends on two sets of parame-ters.Thefirst set is relevant to the tensile and compressive stress data which are provided as a tabular function of strain,which is directly obtained from the constitutive relation of each phase in MRAC.These mechanical properties are provided by experimental study and mix design.The other one is the definition of the damage variable as a tabular function of the inelastic strain for both the ten-sion and compression.If the damage variable is specified,ABAQUS au-tomatically calculates the inelastic and plastic strain values.The calibration of the damage variables is obtained through the best fitting of the complete compressive stress–strain curves as well as failure patterns(crack initiation and propagation)of MRAC with dif-ferent mixture proportions.4.3.Simulation results4.3.1.Uniaxial compressionAccording to the above parameters and descriptions,the complete compressive stress–strain curve and failure process of MRAC under uniaxial compression loading were calculated.In order to calibrate and validate the FEA,the simulation results will be compared with the test results the authors had completed by using Digital Image Cor-relation(DIC)technique on the displacement and strain measure-ments at microscale[10,51].The DIC technique was applied to record the initiation and propagation of surface microcracks for the tested samples.The experimental data are relevant to compression tests on MRAC specimens with the same old cement mortar mixture design(w/c=0.45)but three different new cement mortar mixture designs(w/c=0.36,0.45,and0.55).The mixture proportion details of MRAC specimens are listed in Table2.The experimental setup and basic failure pattern are shown in Fig.6.Fig.7shows the comparison between experimental and numerical complete stress–strain curves.The strain is evaluated by dividing the prescribed displacement by total height,and the stress is computed by the reaction force over the cross-section area.It can be found that the agreement between experimental data and numerical results is excellent,which is sufficient to assess the modeling capability of this numerical simulation.In addition to matching the stress–strain curves,the model also simulated crack initiation and propagation correctly.Fig.8shows the comparison on the plastic strain progres-sion(damage parameter)of MRAC30-30between experimental and numerical results at different loading levels.Each snapshot represents the strain levels in the Y direction.It should be noted that the contour map is scaled differently in each snapshot in order to show the strain range.The strain localization phenomenon was apparent at both new and old ITZs.The bond initiation and propagation of bond cracks were evident ahead of the macro-crack formation.For both the experimental and numerical results,the bond cracksfirst appeared around the weak ITZs and then connected with each others.As the load increased,the localized bond cracks increased and propagated around the aggregate.As the macro-crack formed at the ITZs,the strain contour map became less meaningful,while the crack estimation became dependent on the displacement contour map.Fig.9shows lateral displacement(failure pattern)comparison of MRAC30-30at different loading levels between experimental and numerical results[10,51].It is observed that the bond cracks around old and new ITZs developed across old mortar matrix,and propagates into new mortar matrix.In thefinal crack pattern,most cracks lined up vertically with the loading direction for both experimental and numerical results.Overall,the FEA analyses predict remarkably well the whole failure pattern of the MRAC under compression including the crack initiation,propagation and pattern.4.3.2.Uniaxial tensionBecause the uniaxial tensile test is still a big challenge,there is no available experiment data of MRAC under tensile for validation at this moment.In the tensile numerical simulation,the parameters applied for the simulation were assumed based on previous calibration of compression modeling.Additionally,parameter adjustments were not permitted except the displacement-controlled loading.Fig.10 shows the predicted stress–strain behavior of MRAC30-30resulting from the FEA simulation.The model is capable of predicting the com-plete stress–strain curve quite well considering the inelastic behavior of MRAC including strain softening,localization of deformation,and micro-crack pattern at different loading levels.Besides predicting the stress–strain curve,the model can also simulate the micro-crack initiation and propagation reasonably by the plastic strain progres-sion(see Fig.11).The fracture process starts around the aggregates as the cracks form,and propagates along both old and new ITZs. With the loading increased,the vertical displacement progression shows that one main crack dominates and propagates through the whole MRAC,while all the other micro-cracks closed(see Fig.12).0.0000.0010.0020.0030.00451015202530354045Stress(MPa)Strainpressive stress–strain curves with different new mortar matrices.91J.Xiao et al./Cement and Concrete Research52(2013)82–99。