a damage zone model for the failure analysis of adhesively bonded joints

International Journal of Adhesion & Adhesives 18 (1998) 385—400

A damage zone model for the failure analysis ofadhesively bonded joints

Andrew Sheppard!,", Don Kelly!,",* and Liyong Tong!,#

! Cooperative Research Centre for Advanced Composite Structures Ltd., 361 Milperra Road, P.O. Box 30, Bankstown, NSW 2200, Australia" School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, N.S.W.,2052, Australia

# Department of Aeronautical Engineering, University of Sydney, Sydney, N.S.W., 2006, Australia

Accepted 25 November 1997

Abstract

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lackof suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of thejoint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria isproposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failurelocus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of variouscomposite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicatethat by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of thedamage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It isconcluded that the damage zone model can be successfully applied across a broad range of joint configurations and loadingconditions. ( 1998 Elsevier Science Ltd. All rights reserved.

Keywords: B. composites; C. finite element stress analysis; C. joint design; strength of bonded joints

1. Introduction

Efficient design of structural joints is essential for aero-space structures because joints impose a significantweight penalty and often establish structural efficiency. Todesign efficient joints and to utilise the advantages of adhes-ive bonding, accurate joint failure predictions are required.

An adhesively bonded joint can fail by the followingmodes (see Fig. 1): (i) failure of the adherend due tobending, tension or compression (net-section adherendfailure), (ii) adherend—adhesive interface failure (surfacefailure), (iii) cohesive failure (entirely within the adhesive),and (iv) out-of-plane adherend failure (this failure modeonly occurs for composite adherends and is in the form ofintra-laminar and/or inter-laminar failure in the adherends).

Adherend—adhesive interface failure will occur on amacroscale when surface preparation or material qualityare poor and, consequently, this mode of failure cannotbe predicted using any theoretical techniques. In this

*Corresponding author.

paper, all joints are assumed to be manufactured tospecification and so adherend—adhesive interface failureis not expected to occur.

Failure of isotropic and anisotropic adherends due tobending, tension or compression can be predicted usingstandard in-plane failure criteria and therefore will alsonot be addressed. Cohesive and out-of-plane adherendfailure are the failure modes which pertain specifically tofailure of adhesively bonded joints. Cohesive and out-of-plane adherend failure will be collectively referred to asjoint failure and will be examined in detail in this paper.

At the present time bonded joint failure can only beaccurately predicted for joints with minimal overallflexural deflections (i.e. for symmetric joints with nobending). The failure load of these joints can be predictedusing simplistic analysis procedures and failure criteria[1,2]. While these procedures appear to be adequate forjoints with minimal flexural deflections, they are notapplicable to joints subjected to significant bending.With the introduction of postbuckling structures,bonded joints with thin postbuckling skins are suscep-tible to premature failure due to peel-induced loading.

0143-7496/98/$—see front matter ( 1998 Elsevier Science Ltd. All rights reserved.PII: S 0 1 4 3 - 7 4 9 6 ( 9 8 ) 0 0 0 2 4 - 4

Fig. 1. Typical failure modes of an adhesively bonded composite joint.

Consequently, a more robust procedure to predict jointfailure is required.

Adams [3—6] and his co-workers are renowned fortheir work on failure analysis of adhesively bondedjoints. In general, their approach to joint failure predic-tion is to use a plane strain, geometric and materialnonlinear finite element analysis (FEA) with eithera maximum principal stress or maximum principal strainfailure criterion.

The use of the finite element method with a failurecriterion applied at a point to predict joint failure (asintroduced by Adams and his co-workers) has beenutilised by a number of other workers with a variety offailure criteria to predict cohesive failure [7—10] andout-of-plane adherend failure [11—14].

Unfortunately, the problem with using FEA and in-deed the basic phenomenon which makes bonded jointfailure predictions very difficult is the presence of bothgeometric and material singularities at the ends of thejoint [15,16]. Even with an elastic/plastic analysisa strain singularity can exist. The accuracy with whichthe finite element solution will predict strains near theend of the joint will therefore depend heavily on therefinement of the finite element (FE) mesh.

In an attempt to overcome the FEA singularity prob-lem, a number of workers have used stress singularityparameter approaches to predict joint failure [17—19].However, in reality true singular points probably do notexist at the ends of the joint due to the fact that thecorners at the ends of the joint will not be perfectlysquare. In addition, the stresses at the ends of the jointwill be relieved due to zones of local damage which cantake the form of voids, local crazing, local cracking, etc.

As an alternative, Crocombe [20] proposed globalyielding of the adhesive layer as a failure criterion. Thiscriterion avoids many of the inherent problems with jointstrength predictions. Unfortunately, this approach is un-conservative for many joints because local failure couldoccur before global yielding.

To overcome the problems of these strength of mater-ials class approaches, a number of researchers have pro-posed using fracture mechanics class approaches topredict bonded joint failure [21—28]. In fracture mechan-

ics, a single sharp macroscopic crack is assumed to existin the material and fracture occurs due to the propaga-tion of this crack.

In recent years the general consensus in the literatureappears to be that as polymer structural components andadhesively bonded joints specifically do not inherentlycontain sharp macroscopic cracks, failure of these com-ponents will initiate from a zone of damaged material[28—37]. Based on these observations it can be concludedthat both fracture mechanics and classical strength ofmaterials-based models which use stresses/strains ata point are physically not valid for bonded joint strengthprediction. It appears that rather than trying to zoom inon the singular points at the ends of the joint, failureshould be predicted by backing away from the singular-ities and studying the stresses/strains over a finite zone atthe end of the joint.

One of the first workers who suggested that failureshould be calculated over a finite zone was McClintock[39]. McClintock stated that ‘‘fracture occurs in an elas-tic—plastic, nonwork-hardening material subjected topure shear when a critical shear strain is attainedthroughout a critical volume of material’’. Recently,Clark and McGregor [40] proposed that bonded jointfailure could be predicted when the maximum principalstress calculated over a finite zone exceeded the ultimatetensile stress of the adhesive. John et al. [41,42] proposedthat failure of bonded composite joints occurs when theadhesive over a critical portion of the joint exceeds theshear yield stress. Also in recent years Continuum Dam-age Mechanics (CDM) has been developed to describethe progressive degradation of a material prior to theinitiation of macrocracks [43—45].

Based on these statements it appears reasonable andplausible to assume that adhesively bonded joint failureoccurs after a damage zone at the end of the joint reachesa critical size. In this paper a damage zone model isproposed as an alternate procedure to predict both cohe-sive and out-of-plane adherend failure in adhesivelybonded joints. The versatility of this model is shown byusing it to predict the failure load of a number of alumi-nium and graphite/epoxy composite adhesively bondedjoints.

386 A. Sheppard et al. / International Journal of Adhesion & Adhesives 18 (1998) 385—400

Fig. 2. Damage zone model for a bonded joint suffering cohesivefailure.

Fig. 3. Damage zone model for a bonded joint suffering out-of-planecomposite adherend failure.

2. A damage zone model for joint failure prediction

2.1. The damage zone model

Based on the assumption that both cohesive and out-of-plane adherend crack initiation in adhesively bondedjoints will occur after a damage zone develops, the fol-lowing damage zone model has been proposed.

Under low load, localised damage will occur at the endof the joint. This damage occurs because the material islocally subjected to strains greater than the ultimatematerial strain. In the adhesive the damage will initiatefrom voids and flaws. If the joint has composite ad-herends a damage zone will develop in the adherends andwill consist of matrix cracking, fibre/matrix interfacefailure and fibre splitting/breakage. Under medium load,the damage zones will grow in size and the concentrationof points of specific damage will increase. As the ‘‘failure’’load is reached the damage zone in either the compositeadherend or the adhesive will grow to a critical size whenthe individual components of damage will coalesce andform a crack. Figs. 2 and 3 depict the failure process forcohesive failure and out-of-plane adherend failure, re-

spectively. The black zones in these figures representareas of crazing and other forms of micro-damage, whilethe visible cracks represent microcracking similar to thatobserved experimentally.

Once the crack has formed it will either continuegrowing leading to instant joint failure, or it may bearrested and additional loading will be required topropagate the crack to predict the ultimate failure load ofthe joint. However, in this paper, the joint is consideredto have failed as soon as a crack is formed. This isbecause water and other materials can get into the jointand degrade its strength.

The following is an outline of the procedure to predictthe critical load;

(i) Test one or more adhesively bonded joint(s) andrecord the load at which a crack initiates at the endof the joint, and the failure mode.

(ii) Analyse the joint(s) at the experimental crack initia-tion load using an appropriate analysis tool.

(iii) Using an appropriate failure criterion and the rel-evant material allowable(s) calculate the criticaldamage zone size in the region in which failure wasobserved in the experiment.

A. Sheppard et al. / International Journal of Adhesion & Adhesives 18 (1998) 385—400 387

Fig. 4. Aluminium single lap joint configuration (grip lengths of 25 mm at each end of the specimen not shown).

Table 1Joint dimensions of aluminium single lap joints

Joint group Joint type Adherend thickness t (mm)

SLJ1 Single lap joint 1.6SLJ2 Single lap joint 3.2SLJ3 Single lap joint 10.0

(iv) Use the critical damage zone size calculated in theprevious step to predict the critical load of bondedjoints with similar adherends, adhesives and loadpaths.

2.2. Failure criteria to characterise the damage zone

Using the damage zone model, failure criteria are re-quired to characterise the damage zones. Failure criteriaselection will depend upon the failure mode, the loadcomponents induced in the joint and the materials usedfor the adherends and adhesive. In addition to using anappropriate failure criterion, material allowables (ulti-mate stresses/strains) are required.

The damage zone will be identified by marking ele-ments for which a failure criterion is exceeded on theelement. The adhesive used in the joints analysed in thispaper is a toughened ductile adhesive which is expectedto suffer a yielding failure. Consequently, the failure cri-terion used for cohesive failure of the adhesive layer is theequivalent Von Mises strain criterion:

e%26*7.

"

1

J2 (1#l)

]J(e11!e

12)2#(e

12!e

13)2#(e

13!e

11)2 . (1)

For out-of-plane composite adherend failure (intra/in-ter-laminar failure), which is a brittle resin dominatedfailure, a principal strain criterion will be used. Thiscriterion is satisfied when the maximum principal strainin the material reaches the ultimate principal strain. Foreach failure criterion an ultimate strain will be definedand the corresponding damage zone size at failure deter-mined.

The proposed damage zone model is an extension ofthe average stress approach and the point stress ap-proach for predicting failure at discontinuities in com-posite structures [38]. These approaches have been usedextensively to predict out-of-plane adherend failure ofcomposite structures [46—52]. It should also be notedthat the physical arguments used for this model aresimilar to those used in the damage zone models inpost-yield fracture mechanics [53,54]. In post-yield frac-ture mechanics, fast fracture is predicted when the mater-ial, a certain distance ahead of the crack tip, reachesa specified condition. The material between the crack tipand the critical distance is considered to have failedlocally.

It is noted that the damage zone model is applicablefor the detection of crack initiation, while traditionalfracture mechanics should be used for crack growth,prediction of the maximum strength of the joint anddamage tolerance analyses.

3. Damage zones for adhesively bonded lap joints

To characterise the damage zones for aluminium andcomposite lap joints, a number of joints were tested andanalysed.

3.1. Aluminium and graphite/epoxy composite joints

3.1.1. Configuration of aluminium jointsThe experimental results from the testing of three alu-

minium adhesively bonded single lap joints were ob-tained [55], and the joints numerically analysed.Diagrams and complete dimensions of the joints are inFig. 4 and Table 1. Not included in Fig. 4 are the griplengths of 25 mm at each end of the joint which givestotal adherend lengths of 63 mm each. The adhesivethickness was held constant at 0.15 mm. The joint dimen-sions were selected to force a cohesive failure. Althougha cohesive failure mode indicates an inefficient joint, itwas required so that the validity of the damage zonemodel could be determined. It is expected that an effi-cient, well-designed, aluminium bonded lap joint (i.e.long overlap length and thin adherends) would suffera net tensile adherend yield failure.

The adhesive fillets were removed from the ends of thejoints to avoid the possibility that different-sized adhes-ive fillets could produce excessive scatter in the recordedjoint failure loads. It was hoped that by removing theadhesive fillets, consistent minimum failure loads for eachjoint type would be determined. This approach also


Table 2Joint dimensions of graphite/epoxy composite bonded lap joints

Joint group Joint type Ply layup Overlap length ¸ (mm) Adherend thickness t (mm)

A1 Single lap joint (0, 90, 90, 0)4

89.4 1.12B1 Single lap joint (0

2, 90

2, 0

2)4

134.2 1.68C1 Single lap joint (0

2, 90

2, 90

2, 0

2)4

178.8 2.24A2/A3 Double strap joint (0, 90, 90, 0)

433.6/22.4 1.12

B2/B3 Double strap joint (02, 90

2, 0

2)4

50.4/33.6 1.68C2/C3 Double strap joint (0

2, 90

2, 90

2, 0

2)4

67.0/44.8 2.24

Fig. 5. Graphite/epoxy composite single lap and double strap joint configurations (grip lengths of 25 mm at each end of the specimens not shown).

removes the adhesive fillet size as an additional para-meter from this investigation. The adhesive fillets areremoved to allow the damage zone model to bebenchmarked with consistent adhesive ends. It is certain-ly not suggested that adhesive fillets should be removedfrom production bonded joints. Details of joint fabrica-tion procedures and material properties are available inRefs. [55,58].

The joints were tested in an Instron test machine underdisplacement control. During testing the joints sufferedinstant ultimate joint failure with little, if any, priorwarning. The recorded joint failure loads are shown inTable 3.

3.1.2. Configuration of composite lap jointsThree composite adhesively bonded single lap joints

and six composite adhesively bonded double strap jointswere tested and analysed. All the joints had adherendsmade of unidirectional graphite/epoxy tape. Diagramsand dimensions of the joints are shown in Fig. 5 andTable 2. Not included in Fig. 5 are the grip lengths of25 mm at each end of the lap joint specimens. The adhes-ive thickness was held constant at 0.15 mm and theadhesive fillets at the ends of the joints were removed forthe same reasons as noted for the aluminium joints.Details of joint fabrication procedures and materialproperties are available in Ref. [58].

As for the aluminium joints, the composite joints weretested in an Instron test machine under displacement

control. During testing the joints emitted high pitchedcracking sounds which were followed later by instantultimate joint failure. The recorded joint failure loads areshown in Table 4.

3.2. Numerical analysis

To analyse the adhesively bonded joints describedabove, the finite element method (FEM) software pack-age MSC/NASTRAN (Version 68.2) was used [57].Isoparametric, three- and four-noded elements were usedto create plane strain models of the joints. A geometricnonlinear analysis procedure was used to correctly cap-ture the large out-of-plane deflections experienced insome of the joints. Material nonlinearity was also incorp-orated in each analysis to model the stress/strain relationof the adhesive and the aluminium adherends. Typically,a yield criterion including both a hydrostatic term anda deviatoric energy term is required for adhesives. How-ever, Lee [56] showed that the Von Mises yield criterionis suitable to model the stress/strain behaviour of theadhesive used in these joints. Consequently, for thiswork, the Von Mises yield criterion was used for theadhesive layer for all the joints and for the adherends ofthe aluminium joints.

For cohesive failure the ultimate equivalent Von Misesstrain was set to 0.2. Beyond this strain the stress/strainbehaviour of the material was modelled as showing noincrease in the equivalent stress. Under tensile loading


Fig. 6. Example of a typical FE mesh used to analyse the aluminium joints.

the adhesive can achieve strains up to 0.1, but undershear load the shear strain at failure at room temperaturecan be as high as 0.3. The value selected is not criticalsince the damage zone is a two-parameter model basedon the criterion for definition of elements inside thedamage zone, and the damage zone size at the failureload. The value of 0.2 was found to produce damagezones of the shape and size anticipated from the review ofprevious work.

For out-of-plane adherend failure the ultimate princi-pal strain for the resin was set to 0.01. This ultimatestrain is lower than the manufacturer’s published neatresin ultimate strain. However, when fibres are combinedwith the resin the off-axis resin dominated stiffnessis usually double the neat resin stiffness while the ulti-mate strain decreases towards 0.01. It is noted thatthe out-of-plane failure mechanism is characterisedby resin/fibre interface failure which was occurringat a lower strain than pure resin failure. Again the se-lected strain is not critical to the success of the modeland the value selected produced damage zones atfailure anticipated by the authors. In the numericalmodel the composite adherends are modelled as linearelastic, so no loss of stiffness is modelled as the damagezone grows.

It is well known that once a certain joint overlaplength has been reached, any further increase in overlaplength will not change joint strength. Consequently, forthis paper joints in groups A2 and A3, B2 and B3, and C2and C3 are considered equivalent, respectively.

3.3. Damage zones for adhesively bonded lap joints

The adhesively bonded joints described above wereexperimentally tested and their failure loads used tovalidate the damage zone model approach. Due to space

restrictions, details of the experimental testing and jointfailure modes will not be discussed in this paper but areavailable in Ref. 58.

3.3.1. Aluminium lap jointsTo validate the damage zone model for cohesive

failure, a relatively fine FE meshing scheme typical ofthe mesh shown in Fig. 6 was used to discretise thealuminium single lap joints. This mesh uses nine ele-ments through-the-thickness to model the adhesivelayer at the end of the joint. Although the adhesive filletswere removed from the ends of the joints, examination ofthe joints revealed that very small adhesive fillets stillremained. Consequently, a single three-noded elementwas used at the ends of the joints to model the adhesivefillets and thus remove the sharp corners at theselocations.

Running the finite element models at the average ex-perimental failure load for each joint produced damagezones similar to that depicted in Fig. 7. For the uniformmesh used the number of elements is a direct measure ofthe size of the damage zone. The average of the damagezone sizes was found to be 34 elements or 0.012 mm2. Theexact location and shape of the damage zone in each jointwas allowed to vary, only its size (area/volume) wasrecorded at the experimental failure load.

The selection of the critical damage zone size wasbased on a requirement to ensure the predicted failureload for all joints lay within the experimental scatterrange. It was found that if the damage zone size wasreduced to 27 elements or 0.01 mm2, this criterion wasmet (Table 3). Consequently, the critical damage zonesize was set at 27 elements or 0.01 mm2. It is important tonote that the damage zone model is implemented inconjunction with experimental results to ensure realisticdamage zone sizes are used.


Fig. 7. Typical damage zone for aluminium single lap joints based on a Von Mises strain criterion with 0.2 ultimate strain.

Table 3Experimental and numerical strength predictions based on critical damage zone size

Joint No. tested Experimental failure load (kN) Damage zone size atthe average failureload

Load for 27element damagezone size

Ratio(FEA/Av.Exp)

Min. Max. Av. (Elements) (kN)

SLJ1 5 9.9 11.2 10.4 27 10.4 1.0SLJ2 5 10.5 11.9 11.4 18 11.9 1.04SLJ3 5 13.0 14.9 13.7 57 13.4 0.98

Table 3 summarises the experimental and numericalstrength predictions which would be obtained for thealuminium bonded lap joints based on the critical dam-age zone size of 27 elements. The Von Mises straincriterion produced numerical joint failure predictionswithin 4% of the average experimental joint failure loads.It is argued that this is very good correlation with theexperimental joint failure loads given the wide range ofadherend thicknesses used for the specimens.

3.3.2. Graphite/epoxy composite lap jointsTo validate the damage zone model for the composite

joints, a relatively fine FE meshing scheme typical of themesh in Fig. 8 was used. Nine elements through-the-thickness were used to model the surface adherend plyand three elements through-the-thickness were used tomodel the adhesive layer at the end of the joint. Verysmall adhesive fillets remained on all test specimens evenafter removal of the spew fillet. Consequently, three ele-ments were used to model small adhesive fillets at theends of the joints.

The procedure used for the aluminium joints was thenrepeated. The FE models of all the composite bondedjoints were analysed at the average experimental failure

load for the joint and at the maximum and minimumfailure loads in the experimental range defined in Table 4.There was a wide range of damage zone sizes, with mostjoints exhibiting rapid damage zone growth near thefailure load as the applied load was increased. It is alsonoted that there is considerable scatter in the recordedexperimental failure loads.

To ensure the numerically predicted failure loads forall joint groups were within the experimental scatterrange, the damage zone size was set at seven elements or0.0018 mm2. The predicted failure loads for all the singleand double strap composite joints based on this criticaldamage zone size are summarised in the table. Based onthe principal strain criterion, numerical joint failure pre-dictions for all the joints were within 19% of the averageexperimental failure loads. Due to the complexity ofpredicting bonded joint failure and out-of-plane ad-herend failure, and due to the wide range of adherendthickness and geometry used in the joints, the accuracy ofthe failure predictions presented in this section is believedto be very good.

Also included in the table are the results for a damagezone size of 24 elements (0.0062 mm2). This is 60% of thedamage zone size that appeared in the adhesive in the


Fig. 8. FE mesh used for the analysis of the graphite/epoxy composite joints.

Table 4Experimental and numerical strength predictions for the selected critical damage zone size

Joint No. tested Experimental failure load (kN) Predicted failure loadfor seven elementdamage zone

Ratio(FEA/Av.Exp)

Load for 24elementdamage zone

Min. Max. Av. (kN) (kN)

A1 5 12.5 18.5 16.25 13.1 0.81 13.8B1 7 17.5 23.5 21.0 23.5 1.12 24.7C1 4 23.5 29.0 26.75 23.7 0.89 24.8A2/A3 10 18.0 25.5 22.0 19.0 0.86 19.8B2/B3 8 31.75 38.75 35.75 35.2 0.98 36.2C2/C3 9 29.0 36.75 33.75 35.4 1.05 36.5

Fig. 9. Principal strain damage zone for composite out-of-plane adherend failure of joint group C1 with 0.01 ultimate strain.


Fig. 10b. Fine FE mesh with corner rounding showing the cohesivedamage zone of a double lap joint based on an equivalent Von Misesstrain criterion.

Fig. 10a. Fine FE mesh showing the cohesive damage zone of a doublelap joint based on an equivalent Von Mises strain criterion.

Fig. 10d. Coarse FE mesh showing the cohesive damage zone ofa double lap joint based on an equivalent Von Mises strain criterion.

Fig. 10c. Medium FE mesh showing the cohesive damage zone ofa double lap joint based on an equivalent Von Mises strain criterion.

aluminium joints and therefore would not be acceptedfor the brittle resin failure. However, this critical damagezone size only marginally increased the predicted failureloads. This error margin is still within engineering accu-racy indicating the procedure is robust.

3.4. Evaluation of the damage zone model

To evaluate how sensitive the damage zone model is toFE mesh refinement, a plane strain analysis was conduc-ted on an aluminium double lap joint at its ultimate load.Fig. 10 shows four different FE mesh refinements thatwere used for this study. The shaded elements in eachplot are considered to be the damage zone for cohesivefailure. The damage zones are characterised by the equiv-alent Von Mises strain criterion.

A comparison of Fig. 10a and b shows that the damagezone model is relatively insensitive to the micro-ge-

ometry at the end of the joint. In reality, a perfectlysquare corner is unlikely to exist at the end of the jointand areas of localised high stress will be relieved due tolocal cracking and crazing. Consequently, it is desirablefor the damage zone size to be the same with variations inthe micro-geometry at the end of the joint. Clark andMcGregor [40] found no variation in experimental jointstrength of bonded aluminium double strap joints withadhesive fillets and corner radii ranging from 3 to 15 lm.

Fig. 10a and c show that because we are looking ata damage zone over an area, different mesh refinementsgive similar results and do not appear to be adverselyaffected by the singularities at the end of the joint. Theproblem of FE mesh-dependent results has been a majorstumbling block for FE bonded joint analysis in the past.

Fig. 11 shows the large strain concentration at the endof the adhesive layer of the joint analysed in Fig. 10.Obviously, if too coarse a mesh is used, the correct size


Fig. 11. Typical strain concentration at the end of an adhesivelybonded joint.

and shape of the damage zone cannot be modelled asshown in Fig. 10d.

An important feature of any physically plausible fail-ure model is that it must be able to predict the locus offailure. Figs. 7 and 9 appear to show that the damagezones follow the typical locus of failure for adhesivelybonded joints. Fig. 7 shows that the typical damage zonefor the aluminium joints is in the adhesive close to theloaded adherend. Figure 9 shows that the typical damagezone for the composite joints is in the adherend travellingjust below the interface of the adhesive and the adherend.Both of these failure loci have been observed experi-mentally.

4. A modified damage zone model for joint failureprediction

The FE meshes used in the examples above are un-realistically refined for industry design analysis. Thecomputational expense is increased not only because ofthe large number of elements used in the analysis, butalso because the mesh is being refined around a singularpoint. If the damage zone size is ‘‘fixed‘‘, and the ultimatematerial strain not to be exceeded at the edge of thedamage zone determined by calibration with testing ofa joint, then it is possible to define coarse FE meshes forthe analysis process. Indeed for an efficient and cost-effective engineering analysis, an FE model of only oneelement across the adhesive thickness and relativelycoarse elements around the critical area of the jointshould be used (ie. one element through-the-thickness percomposite ply). The damage zone size is then defined asa single element in the region where failure is expected tooccur. The damage zone size defines the mesh size re-quired for the analysis. This modified damage zonemodel consisting of using a relatively coarse FE mesh

and a ‘‘calibrated’’ material ultimate strain has beenimplemented in Ref. [58].

For some bonded joint FE modelling strategies (e.g.plate/shell elements modelling adherends and brick ele-ments modelling adhesive) and when using one-dimen-sional shear lag algorithms, it may also not be possible tocalculate adherend through thickness stresses andstrains. Consequently, it becomes very difficult to predictout-of-plane composite adherend failure. In these situ-ations the only indication of how close the joint is tofailure comes from the adhesive stresses and strains, eventhough failure occurs in the adherends.

The justification for this simplified modelling lies inthe damage zone model. As the joint is loaded the adhes-ive strain at the end of the joint increases. This is becausethe two adherends are trying to split apart. It wasobserved from the FE analysis in the examples abovethat the length of the damage zones in the surface plies ofadherends of composite joints depends linearly on themean adhesive peel strain at the ends of these joints. Toillustrate this point, the mean adhesive peel strain at theend of the joint (calculated using a single square elementthrough the adhesive thickness) was plotted against thedamage zone length in the composite adherend (cal-culated using the principal strain criterion) for jointgroups B1 and B2/B3 (see Section 3.1.2) in Fig. 12. Thisfigure shows that there is essentially a linear relationshipbetween the mean adhesive peel strain at the end of thejoint and the adherend damage zone length. It is arguedthat the magnitude of the mean adhesive strain at the endof the joint is inherently linked to the length of thedamage zone in the composite adherend. This is analog-ous to the situation in fracture mechanics where theopening displacement of a crack is used to determine theenergy release rate (COD method). John et al. [41,42]used a similar approach which entailed using adhesiveshear stresses to predict out-of-plane adherend failure incomposite joints. Consequently, it is proposed that analternate procedure to predict out-of-plane adherend fail-ure of composite joints is to calculate a critical ‘‘calib-rated’’ adhesive strain and use this strain to predict thejoint failure load.

5. Failure predictions for adhesively bonded compositejoints based on the modified damage zone model

In this section the modified damage zone model is usedto predict the failure load of a range of adhesively bondedjoints with adherends made from graphite/epoxy tape.The adhesive peel strain criterion will be used to imple-ment the modified damage zone model. The joints ana-lysed comprise all the composite bonded lap jointspresented in Section 3.1.2 and composite bonded post-buckling doubler joints which will be introduced in thefollowing section.


Fig. 12. Comparison of mean adhesive peel strain at the end of the joint versus adherend damage zone length for joint groups B1 and B2/B3.

Fig. 13. Adhesively bonded doubler joint configuration and dimen-sions (grip lengths of 40 mm at each end of the specimen not shown).

Table 5Summary of panel and flange layups

Specimen group Panel layup Flange layup

A ($45,0,90)4

($45,0,90)24

B ($45,0,90)4

($45,0,90)4

C ($45,0,90)4

($45)4

D ($45,0,90)4

($45)24

E (0,90,$45)4

(0,90,$45)24

F (0,90,$45)4

(0,90$45)4

G (0,90,$45)4

(0,90)4

5.1. Graphite/epoxy bonded postbuckling doubler joints

5.1.1. Configuration of the graphite/epoxy bonded post-buckling doubler joints

An experimental and numerical study was undertakento analyse graphite/epoxy adhesively bonded doublerjoints loaded in compression [58,59]. Fig. 13 shows thegeometric configuration and generic dimensions of thesejoints. The nominal ply thickness was 0.17 mm andthe nominal adhesive layer thickness was 0.15 mm. Notincluded in Fig. 13 are the grip lengths of 40 mm at eachend of the specimen.

In this paper the bonded doubler joint specimen will beused to demonstrate the validity of the damage zonemodel for joints with postbuckling skins. This specimenis an idealisation of rib or stiffener flanges bonded toa thin skin.

Seven groups of bonded doubler joint specimens werestudied (Table 5). Three specimens were fabricated andtested for each specimen group. The bonded doublerjoints were fabricated from T300/934 graphite/epoxy uni-directional tape from the Fiberite Corporation. All thejoints were bonded with FM 300K adhesive from Cytec.Details of joint fabrication procedures and materialproperties are documented in Ref. [58,59].

All specimens were tested in a 10 kN INSTRON testmachine. During testing, joint failure was characterisedby a sharp drop in load which was often accompanied bya loud cracking sound from the specimen.

5.1.2. Numerical analysis of the graphite/epoxy bondedpostbuckling doubler joints

Because the #45 and !45° plies in the laminates ofthe bonded doubler joints induce a coupling betweenbending and twisting, the geometric symmetry of thejoints cannot be used to reduce the size of the FE models

and the assumption of plane strain is invalid. As thisanalysis was part of a larger investigation, detailedstress/strain information from the adhesive and ad-herends was required. Consequently, a hybrid modellingstrategy was used comprising a combination of four-nodequadrilateral shell elements and eight-node solid ele-ments.

Fig. 14 shows a typical FE mesh used to model thebonded doubler joint specimens. The adhesive layer andthe composite plies in the panel area above and slightlybeyond the end of adhesive layer were all modelledindividually using solid elements. Anisotropic material


Fig. 14. Side view of typical FE meshing scheme used for the bonded doubler joints.

Fig. 15. Experimental and numerical comparison of load versus axial crosshead displacement for specimen group B.

matrices were calculated for each composite ply. Thedoublers (flanges) and the portion of the panel away fromthe actual doubler joints were modelled using shell ele-ments. Laminate theory was used to give the shell ele-ments the correct stiffness. The shell elements modellingthe flanges were offset from the brick elements modellingthe adhesive by using an offset facility in the MSC/NAS-TRAN PCOMP card [57]. The rotational degrees offreedom in the shell elements (modelling the panel) weretransferred to the solid elements by building the shellelements one row into the solid elements and giving theseelements 1% of their membrane stiffness and 100% oftheir bending stiffness. At the end of the joints (which isthe critical region) the elements were refined down to0.15 mm by 0.15 mm in the X-½ plane for the adhesivelayer and 0.15 mm by 0.17 mm in the X—½ plane for thecomposite plies (where X is the longitudinal directionand ½ is the thickness direction). Five elements were usedacross the width of the joint (Z direction).

The FE models of the specimen groups were analysedusing MSC/NASTRAN V68.2 [57] with a geometric andmaterial nonlinear analysis. The adherends were as-

sumed to be material linear elastic while the elastic/plas-tic behaviour of the adhesive was modelled using the VonMises yield criterion. Both ends of the models wereconstrained in all degrees of freedom. Load was appliedto the models using an enforced displacement. An ap-plied force could not be used to load the models becauseonce buckling occurs the load does not increase(see Fig. 15). Fig. 16 shows a typical deformed plot ofthe doubler joint specimens with the distinctive firstmode buckle configuration which was observed experi-mentally.

5.2. Selection of a bonded joint coupon specimen

In Section 3.3 the damage zone model was assessed bydetermining the ability of the models to match knownexperimental failure loads and failure modes. In thissection the modified damage zone model will be appliedin a predictive mode to illustrate the way it would beimplemented in a practical design/analysis environment.As noted in the beginning of this section the modifieddamage zone model will be used to predict the failure


Fig. 16. A typical deformed FE plot of the bonded doubler specimens.

Fig. 17. Typical FE mesh used to model the bonded single lap anddouble strap joints when using the modified damage zone model.

load of the composite bonded joints presented in Section3.1.2 and the composite bonded doubler joints presentedin Section 5.1.1.

Because all the joints were bonded with Cytec FM300K adhesive and the two types of graphite/epoxy tapehave similar properties, the same critical ‘‘calibrated’’material ultimate strain can be used for both types ofbonded joint. To determine the critical ‘‘calibrated’’ ma-terial ultimate strain, an appropriate bonded joint cou-pon specimen is required. From experience it is suggestedthat double strap joints with adherend thicknessesranging from 1.5 to 3 mm make appropriate bonded jointcoupon specimens. Consequently, the graphite/epoxytape double strap joint B2/B3, presented in Section 3.1.2,is used as the bonded joint coupon specimen.

To determine the critical ‘‘calibrated’’ peel strainallowable, joint B2/B3 was numerically analysed at itsaverage experimental failure load using a plane strain,geometric and adhesive material nonlinear analysis.A relatively course FE mesh of one element through-the-thickness for the adhesive layer and one elementthrough-the-thickness for each composite ply was usedfor the analysis (see Fig. 17). At the end of the joint theelements modelling the adhesive were refined down to0.15 mm by 0.15 mm. It was found that the adhesive peelstrain in the last adhesive element at the end of the jointwas 0.048. Consequently, the critical ‘‘calibrated’’ peelstrain allowable was set to 0.048. This ‘‘calibrated’’ allow-able should be calculated over a single 0.15 mm by0.15 mm element at the end of the adhesive layer and canbe used to predict the failure load of bonded joints withsimilar adhesive and adherends.

5.3. Failure predictions for graphite/epoxy tape bondedjoints

To implement the modified damage zone model, thecomposite bonded single lap and double strap joints were

analysed using the same analysis approach and FE mesh-ing scheme as described for the bonded joint couponspecimen above. The composite bonded doubler jointswere analysed as described in Section 5.1.2. Failure waspredicted to occur in each joint when the adhesive peelstrain in the last element in the adhesive layer reached thecritical ‘‘calibrated’’ peel strain allowable of 0.048 definedin Section 5.2. In every FE analysis the last element in theadhesive layer was square and essentially of the samesize.

Table 6 shows the comparison of experimental andnumerical strength predictions for each of the graph-ite/epoxy tape bonded joints. It is argued that due to thewide range of bonded joint types, the accuracy of thefailure predictions in Table 6 is very good.

6. Conclusion

A review of the literature reveals that there is nouniversally accepted procedure to accurately predict ad-hesively bonded joint strength. A numerical techniquesuch as the finite element method appears to be the most


Table 6Comparison of experimental and numerical strength predictions for graphite/epoxy tape bonded joints

Joint group Joint type Loading Av. experimental failureload or deflection

FEA predicted failure loador deflection

A1 Single lap Tension 16.25 kN 16.9 kNB1 Single lap Tension 21.0 kN 22.5 kNC1 Single lap Tension 26.75 kN 22.6 kNA2/A3 Double strap Tension 22.0 kN 27.1 kNB2/B3 Double strap Tension 35.75 kN 35.75 kNC2/C3 Double strap Tension 33.75 kN 35.0 kNA Bonded doubler Compression 2.3 mm 2.9 mmB Bonded doubler Compression 3.3 mm 5.0 mmC Bonded doubler Compression 17.6 mm 14.3 mmD Bonded doubler Compression 4.7 mm 5.8 mmE Bonded doubler Compression 2.0 mm 1.9 mmF Bonded doubler Compression 3.0 mm 3.1 mmG Bonded doubler Compression 9.4 mm 7.3 mm

effective and flexible tool for joint strength prediction.Unfortunately, as points of geometric and material singu-larity are a feature of adhesively bonded joints, FEA willbe mesh-dependent.

To overcome this problem a joint analysis procedurehas been proposed based on a damage zone model andstrain based failure criteria. The damage zone model wasvalidated for both cohesive failure and out-of-plane ad-herend failure. Cohesive failure of the aluminium jointswas predicted to within 4%, while the out-of-plane ad-herend failure of the composite joints was predicted towithin approximately 19% of the average experimentaljoint failure loads. All joint failure predictions were with-in the experimental scatter range. The critical damagezone size was smaller for the composite joints thanthe aluminium joints because of the brittle nature of thecomposite resin.

It was then demonstrated that a modified form of thedamage zone model can be implemented relatively quick-ly and cheaply by using a critical ‘‘calibrated’’ materialallowable. Using the adhesive peel strain failure criterion,relatively accurate joint failure predictions for adhesivelybonded composite joints were obtained. The significanceof these failure predictions should not be overlookedconsidering that the joint types ranged from single lapand double strap joints loaded in tension to bondedpostbuckling doubler joints loaded in compression. Themodified damage zone model can be implemented usingone-dimensional shear lag algorithms in a similar fashionas it is for the finite element method using a critical‘‘calibrated’’ material allowable.

It appears that there is no loss of accuracy when goingfrom the computationally expensive damage zone modelto the relatively cheap modified damage zone model. It issuggested that this is because both approaches are‘‘tuned’’ to experimental results. It is noted that

a strength of the damage zone approach is that interac-ting with experimental test results ensures accurate andrealistic damage zone sizes and ‘‘calibrated’’ materialultimate strains.

It is suggested that the damage zone model can beapplied to structural discontinuities in general, as well asadhesively bonded joints.

Acknowledgements

The authors wish to thank Cameron Spencer, anundergraduate student from the University of New SouthWales, and Peter Chalkley, a research scientist with theAeronautical and Maritime Research Laboratory, De-fence, Science and Technologies Organisation, Depart-ment of Defence, Australia, for help with fabrication andexperimental testing of the graphite/epoxy joints.

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a damage zone model for the failure analysis of adhesively bonded joints

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