Failure Load Prediction by Damage Zone

Journal of Composite MaterialsDOI: 10.1177/00219983093452952009; 43; 3031 originally published online Aug 17, 2009; Journal of Composite Materials Khanh-Hung Nguyen, Jin-Hwe Kweon and Jin-Ho Choi Carbon Composite and Aluminum Failure Load Prediction by Damage Zone Method for Single-lap Bonded Joints of /cgi/content/abstract/43/25/3031The online version of this article can be found at: Published by:On behalf of:American Society for Compositescan be found at:Journal of Composite Materials Additional services and information for/cgi/alerts Email Alerts:/subscriptions Subscriptions:/journalsReprints.nav Reprints:/journalsPermissions.nav Permissions:/cgi/content/refs/43/25/3031 CitationsFailure Load Prediction by Damage ZoneMethod for Single-lap Bonded Joints ofCarbon Composite and AluminumK HANH-H UNG N GUYEN,J IN-H WE K WEON*AND J IN-H O C HOI School of Mechanical and Aerospace engineering,Research Center for Aircraft PartsTechnology,Gyeongsang National University,Jinju,Gyeongnam660-701,KoreaABSTRACT:A damage zone method based on3D finite element analysis wasproposed to predict the failure loads of single-lap bonded joints with dissimilarcomposite-aluminum materials.To simulate delamination failure,interply resinlayers between any two adjacent orthotropic laminas of composite adherend wereassumed with a thickness of one-tenth of a composite lamina.Geometrically non-linear effects due to the large rotation of the single-lap joint were included in theanalysis.Analysis also considered the material nonlinearity of the aluminum adher-end due to the stress exceeding yield level.Based on the experimental observationthat the failure modes of the specimens were dominated by delamination anddebonding,the Ye-criterion was applied to account for the out-of-plane failure ofcomposite adherend and the Von Mises strain criterion was applied for the adhesivelayer.The failure indices were multiplied to the predicted damage zone as a weightfactor and the calculated damage zones were divided by an area or volume consid-ering the joint geometry.Predicted failure loads show deviation within18%fromexperimental results for nine different bonding lengths or adherend thicknesses.KEY WORDS:dissimilar materials,single-lap,bonded joint,damage zone.INTRODUCTIONA N AIRCRAFT STRUCTURE is the assembly of many parts such as skins,stiffeners,frames and spars,etc.These parts must be connected through joints:mechanical or bonded.Mechanical joints with fasteners such as bolts,screws,or rivets are simple and widely used when disassembly for maintenance is necessary.However,the fasteners them-selves are an important source of weight increase and the fastener holes induce stress concentrations and consequently reduce the strength of joints.*Author to whom correspondence should be addressed.E-mail:jhkweon@gnu.krFigures4 8,10,11and13appear in color online:Journal of C OMPOSITE M ATERIALS,Vol.43,No.25/200930310021-9983/09/253031 26$10.00/0DOI:10.1177/0021998309345295ßThe Author(s),2009.Reprints and permissions:/journalsPermissions.nav3032K.-H.N GUYEN ET AL. Adhesive bonding is another joining method that has been increasingly used.In adhe-sively bonded joints,there is no fastener at all and,therefore,no stress concentration due to fastener holes.The typical failure modes of bonded joints are cohesive failure,which is failure within the adhesive,interfacial failure(failure along the interface between adherend and adhesive),or adherend failure.Cohesive failure and interfacial failure are sometimes referred to as bond line failure.Bond line failure is the typical failure mode of metallic bonded joints.Adherend failure is mainly found in joints using composite laminate as the adherend.The adherend failure modes in joints with composite adherend are very com-plicated,and include such failures as matrix failure,fiber failure,and interlaminar and intralaminar failures.The research on bonded joints has a long history and has been conducted experimentally and/or numerically.Researchers have targeted stress analysis,failure mode and strength prediction,strength improvement,and the effects of various parameters such as material, geometry and bonding method,etc.One difficulty for failure load prediction in a bonded joint comes from the presence of the singularity at the ends of overlapped area.Harris and Adams[1]conducted finite element analysis to predict the failure mode of metallic single-lap bonded joints.They took into account the geometrical and material nonlinearity of single-lap joints.Their failure prediction method was based on material strength.The failure was assumed to occur when the maximum principal strain or maximum principal stress at one Gauss point close to the singular position inside the adhesive layer attained the ultimate stress or strain of the adhesive material.The method,therefore,is dependent on mesh refinement near the singularity point.The authors first applied this method to predict the failure mode and failure load of metal-to-metal single-lap joints[1]and then extended their work to lap joints with composite adherends[2].The point-based method proposed by Harris and Adams was shown by Kairouz and Matthews[3]to be useful in predicting the failure mode and strength of bonded single-lap joints made of cross-ply laminated adherends.To overcome the singularity problem,singularity parameter approaches[4,5]were also used.A generalized stress intensity factor and a parameter called strength of the singu-larity were defined and used successfully in the method for the prediction of fractures.In addition,the approach was used for the prediction of fatigue crack initiation in adhesive bonds[6,7].Ishii et al.[8]considered the concentrated multiaxial stress state in the adhe-sive layer in their analysis and proposed a method based on two-singularity parameters to estimate the fatigue strengths of adhesively bonded joints made of carbon fiber reinforced polymer and aluminum alloy.However,the singularity parameter approach did not con-sider the nonlinearity of the adhesive layer and therefore the obtained generalized stress intensity factor may not be correct when the adhesive layer shows highly nonlinear beha-vior.The method also requires additional tests to define the fracture criteria using stress singularity parameters.Crocombe[9]proposed another method to predict the bond line failure of single-lap bonded joints.Failure was assumed to occur as whole adhesive layers become plastic. It was shown that this method can make a good estimation of joint strength for a wide class of joints.In some cases,however,this approach can be incorrect because local failure can occur before global yielding.However,the method contributed to estab-lishing the concept of the damage zone method,in which a joint failure occurs after adhesion in some area fails rather than after adhesion fails at a certain point.Clark and McGregor[10]not only applied the point-based method but also proposed an approach based on ultimate stress over a zone to predict the failure load and failure mode ofFailure Load Prediction by Damage Zone Method3033 single-lap bonded joints.They showed that while the point-based method predicted lower failure loads and failure initiation near the singularity,in contrast to observed experi-ments,the damage zone-based method gave good predictions of failure loads of different joint geometries.As bonded joints with composite adherend are used,interlaminar failure(delamination) is usually found over the failure surfaces.Interlaminar failure is caused by weakness of composite adherends in the through-the-thickness direction.Assuming that both cohesive and out-of-plane adherend crack initiation of adhesively bonded joints will occur after a damage zone develops,Sheppard et al.[11]proposed a damage zone model to predict the joint failure loads of different ing their developed method,the authors showed that failure load predictions of aluminum joints and composite joints were within the experimental scatter range.Based on the fact that the intra/interlaminar failures occur in the layer close to the adhesive,Tong[12]conducted a2D analysis and tried six stress-based criteria to predict the failure loads of double-lap bonded joints.The stress was taken at the center of one ply element or one adhesive element at the free end where stresses were highly concentrated. The method is a point-based method and can be dependent on meshing near the singu-larity.In addition,3D effects such as the free edge effect,the anticlastic effect,and the bending-twisting coupling effect can play important roles in the failure initiation and failure load[13].To overcome the problem of singularity,Kim et al.[14]used a charac-teristic length method,which is widely used in failure prediction of mechanical joints. 2D analysis considering geometrical and material nonlinearity was conducted with the use of a global yielding criterion for the adhesive layer and a quadratic delamination criterion,which was proposed by Brewer and Palage[15],for the composite adherend. Interfacial stresses in the specimens were calculated under the test failure loads.The char-acteristic length was determined as the distance from the overlapped end along the inter-face to a location of the finite element model in which the quadratic delamination criterion was satisfied.The optimal joint strength was found and a new joint strength improvement technique was also suggested.Shin and Lee[16]performed a3D analysis considering the thermal load of co-cured single-lap and double-lap joints without any additional adhesive.They predicted failure load of the joints considering two criteria:the Ye-delamination failure criterion and the3D Tsai Wu failure criterion.In the case of single-lap co-cured joints,failure loads predicted by the Ye-criterion were in good agreement with the experimental results.Otherwise,using the Tsai Wu criterion was better for failure load prediction for double-lap bonded joints. Other research[17 20]has utilized fracture mechanics to predict the failure loads of bonded joints.An initial crack is usually assumed to exist in the adhesive,at the interface of the adherend/adhesive,or in the composite adherend.The crack propagates as the strain energy release rate exceeds a critical value.The strain energy release rate can be computed by the virtual crack closure technique in conjunction with finite element ana-lysis.However,this energy-based approach relies on the existence of a crack in the inter-face,and on the assumption of small-scale bridging and linear elasticity.If any of these conditions are violated,an alternative approach such as cohesive zone modeling is required[20].The cohesive zone model,however,has some limitations such as mesh sensitivity,lack of convergence,computing inefficiency,and so on.An improvement of the cohesive zone model was done with the implementation of the discrete cohesive zone model by Xie and Waas[21].The authors showed that this model is not sensitive to the mesh size and the load putation time was also reduced.Progressive failure is another method to predict the strength of bonded joints.Apalak and Apalak [22]performed a progressive damage analysis for unidirectional composite single-lap joints in tension with the Hashin failure criteria.After the damage modes were checked in each ply of the composite plate,degradation of failed plies was applied based on a set of suitable rules.The main objective of this article is to develop an efficient failure prediction method based on material strength for single-lap joints with different geometries and materials.While most previous researchers have conducted 2D analyses,a damage zone method based on 3D failure analysis is proposed.Interlaminar failure is considered as the failure of interply resin-rich layers inside the composite adherend.Adhesive is assumed to fail by yielding and the material nonlinearity of aluminum is considered.Predicted failure loads are compared with the experimental results in the author’s previous paper [23].FAILURE LOAD PREDICTIONExperimental ProcedureThe experimental details of the joints considered were reported in Seong et al.[23]and therefore are only briefly described here to help understand the failure loads and modes.A typical specimen configuration is shown in Figure 1,where the overlap length between the composite laminate and the aluminum plate is denoted as ‘b .’Two different stacking sequences were used for the composite adherend:[Æ45/90/0]2S and [Æ45/90/0]4S.70(a)(b)60504030S t r e s s (M P a )20100.000.010.02Strain 0.030.04Aluminum Figure 1.Configuration of a typical single-lap bonded joint.3034K.-H.N GUYEN ET AL .The former was used to manufacture the thin specimens and the latter to make the thick specimens.The aluminum adherend was made with anodized aluminum 2024-T3and bonded to a composite adherend using adhesive FM73m by Cytec.The mechanical prop-erties of the composite unidirectional prepreg (USN125by SK Chemicals),adhesive layer,and aluminum adherend are given in Table 1.The thicknesses of the anodized aluminum 2024-T3adherend are 1.58mm and 3.01mm.The stress strain curve for the tension test of the adhesive experimentally obtained is shown in Figure 2(a),and that of the aluminum is shown in Figure 2(b)[24].Detailed dimensions of the specimens are given in Table 2and experimental failure loads are shown in Figure 3.The experimental result shows that higher overlap length yieldsTable 1.Material properties of USN125prepreg,adhesive,and aluminum 2024-T3.USN125AL2024-T3FM73m Tensile modulus E 11(GPa)16273 2.8E 22(GPa)9.6E 33(GPa)9.6Shear modulus G 12(GPa)6.1G 13(GPa)6.1G 23(GPa)3.5Poisson’s ratio m 120.2980.330.38m 130.298m 230.47Tensile strength X T (MPa)2552Y T (MPa)43Z T (MPa)43Shear strengthS 12(MPa)94S 13(MPa)94S 23(MPa)40S t r e s s (M P a )5004003002001000.000.010.020.03Strain 0.040.050.06Figure 2.Tensile stress strain curve of (a)FM73m adhesive,and (b)aluminum 2024-T3.Failure Load Prediction by Damage Zone Method 3035a higher failure load.Increase of the specimen thickness also affects the failure load of single-lap bonded joints.However,failure loads increase only 12 32%as the thicknesses of the specimens nearly double.In a metal-to-metal joint,a bond line failure is the typical failure mode.However,the weakness of the composite material in the out-of-plane direction leads to a different failure mode.Typical failure surfaces of specimens are shown in Figure 4.The failure surface of the specimens is dominated by the delamination of composite adherend,and intralaminar failures are locally observed.In addition to out-of-plane failure of the composite adherend,partial bond line failure is also found.F a i l u r e l o a d (k N )25201510.712.814.714.216.416.518.221.611.9105FM15FM20FM25FM30FM35FM40FM15D FM25D FM35DFigure 3.Failure loads of specimens.Table 2.Dimensions of composite-to-aluminum single-lap bonded joint.Thickness (mm)IDb (mm)Al Composite FM73m Total No.of specimens FM1515 1.58 1.680.112 3.3725FM2020 1.58 1.680.123 3.3835FM2525 1.58 1.680.143 3.4035FM3030 1.58 1.680.132 3.3925FM3535 1.58 1.680.137 3.3975FM4040 1.58 1.680.199 3.4596FM15D15 3.01 3.380.168 6.5586FM25D25 3.01 3.380.187 6.5776FM35D 35 3.01 3.380.193 6.58363036K.-H.N GUYENET AL .Finite Element AnalysisMODELING STRATEGYThree-dimensional finite element analysis of single-lap joints was conducted by MSC.Marc.A typical finite element model for joint FM15is shown in Figure 5.A 3D isometric element,Element 7[25],was used to model the adherend and adhesive.The spew fillet shape was modeled approximately as a right triangle with 0.4mm long legs,as shown in the right side of the figure.The mesh was created more finely at both ends and side edges of the overlap area.Twenty elements were created along the width of the joints.The smallest width (along the Y -direction)of the element at the free side edges was 0.0475mm.The effects of the mesh density of the model are discussed later in this article.Geometrical nonlinearity from the large displacement and rotation caused by the eccentricity of applied loads in single-lap joints were taken into account.Material nonlinearity was also considered in the analysis,as the adhesive layer and aluminum adherend show nonlinear stress strain curves before failure.The Von Mises yield criterion was used to model the stress strain behavior of both the aluminum adherend and adhesive layer,which are isotropic.The boundary conditions are shown in Figure 6.Interlaminar stresses are the source of delamination in composite laminate.Delamination failure can be defined as the failure of the interply resin-rich layers that are made during the manufacturing process of composite laminate.InterlaminarstressesFM25FM25DFigure 4.Typical failure surface of the joint FM25(left)and FM25D (right).zYX0.4 mm0.4 mmFigure 5.Finite element model of bonded joint specimens.Failure Load Prediction by Damage Zone Method 3037can be considered as stresses on the interface between two adjacent plies or as stresses inside these thin resin layers.Fenske and Vizzini [26],when investigating the delamination of a plate subjected to an axial strain,found that the onset of delamination can be pre-dicted by considering the failure of interply resin layers.In this article,the composite adherend is modeled as a combination of orthotropic plies and isotropic interply resin layers.An interply resin layer is modeled to exist between any two adjacent orthotropic plies.Consequently,delamination is considered as the failure of these interply layers.Moduli of the interply resin layer are assumed to be the same as the matrix properties of an orthotropic lamina.A schematic cross section at the overlapped area of the joint is shown in Figure 7.As in the work of Fenske and Vizzini,all interply resin layers are assumed to have a constant thickness that is equal to 10%of one ortho-tropic ply thickness.DAMAGE ZONE METHODIn this article,four slightly different approaches based on the damage zone method are applied to predict the failure load of single-lap bonded joints.The first approach is the damage area method [11].This approach assumes that the specimen fails as the damage area inside it exceeds a critical value.In other words,the specimen fails as follows:DA ¼CDA ð1Þwhere DA and CDA are the total damage area inside a specimen and a critical damage area,respectively.The second approach is the weighted damage area method proposed by Choi and Chun[27]to predict the failure load of mechanical joints.This method considers not only the damage area but also the magnitude of the failure index by using a given failure criterion and the geometrical effects.The joint is assumed to fail as the weighted damage area ratio equals a critical value:DAR n ¼P FI n ÁD A A G¼CDAR n ð2Þwhere DAR n ,FI ,DA ,A G ,n ,and CDAR n are the damage area ratio,the failure index by a failure criterion,the damage area,the area that is responsible for the geometrical effects,the weighting power factor,and the critical damage area ratio,respectively.X XDistributeuniformlyF i x e d bZW YFigure 6.Boundary conditions for the finite element analysis.3038K.-H.N GUYEN ET AL .In the above two approaches,the damage area is the main concern.As a 3D analysis is conducted in this article,the damage volume approach can be obtained by expanding the damage area concept.Simply put,damage volume can be used instead of damage area.Equation (1)can be rewritten as follows:DV ¼CDV ð3Þwhere DV and CDV are the total damage volume inside a specimen and a critical damage volume,respectively.A weighted damage volume approach is given in Equation (4):DVR n ¼P FI n ÁD V V G¼CDVR n ð4Þwhere DVR n ,FI ,DV ,V G ,n ,and CDVR n are the damage volume ratio,the failure index by a failure criterion,the damage volume,the volume the relates to geometrical effects,the weighting power factor,and the critical damage volume ratio,respectively.It is noted that the damage area is the in-plane damage area in the adhesive,interply resin layers,and orthotropic plies.The area A G and the volume V G should account for the differences in geometry of the joints such as bonded length,thickness,and width.The details of A G and V G are given in the next chapter.The weighting power factor n is an integer such as 0,1,or 2.When n equals 0,the failure index has no effect on the damage volume ratio (DVR ).The general procedure to predict failure load of the joints was reported in Sheppard et al.[11]and is rewritten here with a difference in the damage zone size,which may be the size of the damage area,the damage volume,the damage area ratio,or the damage volume ratio:(1)Test one or more bonded joint(s)to record the failure load(s)and mode(s).(2)Analyze the joint(s)under the experimental failure load(s)using an appropriate ana-lysis tool.Z YInterply resin layersAluminum adherend Adhesive layer45°–45°90°0°45°Figure 7.Cross section of the single-lap joint at the bonding area.Failure Load Prediction by Damage Zone Method3039(3)Use appropriate failure criterion and the relevant material allowable(s)to calculate thedamage zone size(s)in the joint and choose a value to be the critical value.(4)Use the critical damage zone size calculated in the previous step to predict the criticalload of bonded joints with similar adherends,adhesives,and load paths.FAILURE CRITERIAFailure criteria selection depends on the failure mode of the specimens.The failure mechanism of the bonded single-lap joint was out-of-plane failure and partial bond-line failure.Based on the experimental failure modes,the Ye-delamination criterion[28]was applied to the interply resin layers to take into account the interlaminar failure,and was also applied to the orthotropic plies to account for the intralaminar transverse failure. The Ye-delamination criterion is as follows:2 33 Z2þ213S213þ223S223¼1ð 33!0Þ2 13 S 13þ223S23¼1ð 3350Þ8>>><>>>:ð5Þwhere 33, 13, 23,Z,S13,and S23are the peel stress in interply layer or orthotropic ply, out-of-plane shear stresses in interply layer or orthotropic ply,interlaminar normal strength,and transverse shear strengths,respectively.The adhesive used in this article shows a nonlinear stress strain curve.Consequently, the Von Mises strain criterion is applied to the adhesive layer:"VM¼ffiffiffi2p3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið"1À"2Þ2þð"2À"3Þ2þð"3À"1Þ2qð6Þwhere e1,e2,and e3are the principal strains.RESULTS AND DISCUSSIONDamage Area in AdhesiveFigure8shows the Von Mises stress distribution in the mid-plane of the adhesive layer(Z¼0)of joint FM15subjected to its experimental failure load(10.67kN),assum-ing a linear elastic adhesive.The same load was applied to obtain the results given in Figures9 14.The Von Mises stress distribution is uniform along the width direction (Y-direction)of the joint,with the exception of the bonding area corners.The stress is very high at the ends of the overlapped area(along the X-direction)where geometry(thickness) changes discontinuously.The stress at the left end of the overlapped area(aluminum end) is higher than that at the right end(composite end).This suggests that the left end of the overlapped area is more in danger of debonding than is the other bonded area.This analysis result concurs with the experimental observation[22],in which bond line failures are mainly found at the end of aluminum parts.The material linear analysis is used to easily show only this observation.The other results that follow come from the analysis with both geometrical and material nonlinearities.V o n m i s e s s t r e s s (M P a )200180160140120100806040200–1.0–0.5–1.0–0.51.00204060801001201401601802000.50.02Y /W0.02X /b0.51.0Figure 8.Von Mises stress distribution in the adhesive of the joint FM15without considering material nonlinearity .–1.0020*********V o n m i s e s s t r e s s (M P a )120140Nonlinear adhesiveLinear elastic adhesive 1601800.5 1.00.0–5.02X /bFigure 9.Von Mises stress distribution along the center of the adhesive of joint FM15with and without considering material nonlinearity (Y ¼Z ¼0).YbXFigure10.Damage area in the adhesive of joint FM15according to Von Mises strain criterion.The Von Mises stress distribution along the centerline in the X-direction of the adhesive (Y¼Z¼0)on the overlapped area(2X/b is fromÀ1to1)considering the material non-linearity is compared with the results of the linear elastic adhesive model in Figure9.While the stress in the elastic adhesive model shows peaks at the ends of the bonding area on both overlap free ends,the stress of the nonlinear adhesive model is nearly constant in the end areas.Consequently,the inner overlapped area(far from ends)carries a larger load and then shows higher stress compared with the results of the elastic adhesive model. Figure10shows the failure areas considering the material nonlinearity of the adhesive, based on the Von Mises strain criterion.As expected,the failure of the adhesive is focused over the end areas of the overlapped area where stresses are highly concentrated.The failure area is slightly larger in the aluminum end area than in the composite end area. Damage Area in Interply Resin LayersFigure11(a)shows the delamination failure index distribution by the Ye-criterion in the interply layer between the first45 and the firstÀ45 layers of joint FM15from the adhesive layer.Obviously,along the ends of the overlap area and free side edges of the composite adherend,the stress is highly concentrated.Consequently,a high failure index and large damage area are predicted over the regions.Pagano[29]reported that the high stress along the free side edges area can be attributed to the stress singularity along the edges.Figure12shows the failure index in the same layer at various positions of X-along the Y-axis.The figure obviously shows that the failure index is high at the overlapped area ends(2X/b¼À1.0)and shows a peak value at the very limited free side edges.The delamination failure index of the second(between firstÀ45 and90 layers)and the third interply layers(between the first90 and0 layers)of joint FM15are shown in Figure11(b)and(c),respectively.Similarly,the damage area and high failure index are found near the ends of the bonded area and free side edges.It is interesting that failure indices are very high along the free side edges of the non-overlapped region of the composite adherend.However,delamination was not visually observed over theseareas in the experiment.As noted by Pagano [29],it is guessed that there is a singularity along the free side edges between two plies.Therefore,a high-density mesh was created at the free side edges.Consequently,high stresses were obtained at these singular positions.However,the delamination should be predicted by the stress at some distance from the singularity rather than at the singularity point itself because the singularity occurs in a very limited area.Therefore,even though the failure index obtained is higher than unity at both free edges far away from the bonding area,this does not mean that delamination occurs there experimentally.The peak failure index in Figure 11(a)is smaller than that in Figure 11(b)and (c).This can be explained in terms of the compressive interlaminar peel stress at the free side edges–2.0–1.5–0.5–0.50.00.00.50.51.01.0–1.0–1.0268402468(a)(b)Y e f a i l u r e i n d e x–2.0–1.5–0.5–0.50.00.00.50.51.01.0–1.0–1.0268402468Y e f a i l u r e i n d e x2Y /W2Y /W2X /b2X /bFigure 11.Ye failure index in interply layers (a)between the first 45 and À45 layers,(b)between the first À45 and 90 layers,and (c)between the first 90 and 0 layers.。