MTS Adhesives Project 2 Failure Modes and Criteria Report ... 2/P2r6a3.pdf · A final report on Task 3.1, Project 2, Development of failure criteria B H Le Page, AD December 1995

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MTS Adhesives Project 2 Failure Modes and Criteria

Report No. 6: Annex 3

Prediction of Failure Criteria for Adhesive Joints Subjected to Short

Term Static Loading B H Le Page*, A D Crocombe” and P A Smith*

December 1995

AEAT-0743

The work described in this report was funded by the Department of Trade and Industry under the Measurement Technology and Standards Programme. AEA Technology plc accepts no liability for the use by third parties of any information contained in the report.

I Copyright AEA Technology plc 1996. Enquiries about copyright and reproduction should be addressed to John McCarthy at the address below.

AEA Technology * University of Surrey Harwell Guildford Didcot Surrey. GU2 5XH Oxfordshire. OX11 ORA United Kingdom United Kingdom Telephone 01235432476 Facsimile 01235432481

Prediction of failure criteria for adhesive joints subjected to short term static loading

A final report on Task 3.1, Project 2, Development of failure criteria

B H Le Page, AD

December 1995

ME-CDR621/95

Crocombe and P A Smith

Department of Mechanical Engineering University of Surrey Guildford GU25XH United Kingdom

University of Surrey

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MTS Adhesives Project 2: Report No. 6: Annex 3: Prediction of Failure Criteria for Adhesive Joints

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Summary

Linear and non-linear analyses were undertaken for a number of different configurations of

joints bonded with AV119 adhesive for which the failure loads had been determined. Two

sets of non-linear analyses were carried out, with and without pressure sensitive yielding.

A coarse-mesh model was used to represent the design type joints stress analyses that are

available. Results from models having more refinement have been obtained as a separate

study. Failure criteria resulting from this work are “strain at a distance” type criteria where

the distance is typically the adhesive layer. It was not possible to identify a component of

adhesive stress or strain that could be used with confidence as a failure criterion for all the

joint configurations. A possible reason for this is that different failure mechanisms might be

active.

Using linear analyses and the UTS of the adhesive it was found that the strengths could

only be predicted to within about 30% but that this could be significantly improved if the

thin lap shear joint with the 1.lmm bondline was not considered. Further, it was found that

extensive yielding occurred, generally in both substrate and adhesive. In the von Mises

analyses the lap joint strains were found to be significantly lower than the strains in the peel

and thick adherend shear tests. However by omitting the lap joint data a sensitivity analysis

showed that a maximum principal strain of about 7% allows prediction of failure to within

about 5% in the other joints. This is close to the maximum strain obtained from bulk

adhesive tests and so this criterion has physical relevance. The Drucker-Prager analyses

show that the maximum principal strain (taken from the centre line of the fringe plot) varies

by less than 20% from the mean value of 3.5%. As it is a non-linear analysis the errors in

the failure loads based on a critical value of this strain would be much less than this.

However it should be noted that if strains were taken at the element centroid (a more

meaningful location) they are much higher for the peel configuration and the predicted

strengths are thus worse.

— . .. —. ——— - —. —. ——. — .——. . ____ .

Thus using this level of mesh refinement the Drucker-Prager analyses give a less accurate

and less physically meaningful prediction of joint failure than the von Mises analyses.

However the Drucker-Prager based prediction does apply to the complete range of joints

whilst the von Mises based prediction excludes thin lap shear joints.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...0.. . . . . . . . . . . . . . . . . . . . . 1

1.1. Joint Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l

1.2. Mesh Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Linear Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...*.. . . . . . ...*. ● *........ 3

3. Von Mises Analyses . . ...*.... . . ...0.... . . . . . . ...* . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...5

3.2. TAST Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...6

3.2.1. TAST0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...6

3.2.2. TASTl.O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...6

3.3. TPEEL Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...7

3.3.1. TPEEL0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...7

3.3.2. TPEELl.O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...7

3.4. TLS Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8

3.4.1. TLS2.0/0.51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8

3.4.2. TLSl.47/0.51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8

3.4.3. TLsl.47/l.l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.6. Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..lO

4. Drucker Prager Cap Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..ll

4.2. TAST Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2.1. TAST0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l2

4.2.2. TASTl. O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l2

4.3. TPEEL Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l3

4.3.1. TPEEL 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l3

4.4. TLSJoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l3

4.4.1. TLS2.0/0.51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l3

4.4.2. TLSl.47/0.51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..l4

5. Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figures

Appendix A

Joint dimensions

Appendix B

Material data

1. Introduction

1.1. Joint Types

The purpose of this work was to analyse the stress and strain distributions in some of the

joints tested elsewhere in the program with the aim of finding a common failure criterion.

The finite element (FE) analyses conducted were intended to be equivalent in accuracy to a

typical engineering design analysis. To this end a reasonably coarse mesh was used. This

work complements the more detailed FE analyses that have been carried out at AEA

Technology.

Average results of failure loads were taken for each type and configuration of joint. These

data are listed in table 1.

Substrate Bond line Bond line Joint Fillet Load (N) Range thickness thickness length width -/+% (mm) (mm) (mm) (mm)

TLS2.O/O.51 2.0 0.51 12.5 10 full 45° 4360 6.2/10.6

TLSl.47/0.51 1.47 0.51 12.5 10 full 45° 3180 2.5/2.2

TLSl.47/l.l 1.47 1.1 12.5 10 full 45° 2410 10.7/7.9

TAST0.5 6.0 0.5 12.5 10 none 5388 1.3/1.3

TAST1.O 5.75 1 12.5 10 none 4925 1.7/1.7

TPEELO.5/25 2.0 0.5 26 10 25% 933 14.3/17.9

TPEEL1 .0/25 2.0 1 26 10 25% 910 4.4/4.4

Table 1. Joint configurations analysed.

It should be borne in mind that the loadings used are experimentally obtained values and as

such there is a certain amount of scatter associated with them as shown by the range of the

results in table 1 above. Dimensioned drawings of these joints are shown in Appendix A.

1

1.2. Mesh Design

As mentioned previously the mesh used in this work was kept fairly coarse. The elements

at critical areas in the bondline, for example the ends in the TAST joints, were 0.5mm

square. This means that there were two rows of elements across a 1.0mm bondline and one

row of elements across a 0.5mm bondline, The elements were allowed to reach an aspect

ratio of 3:1 in less critical areas, for example the centre of the bondline of a TAST joint. The

elements that form the adherends were not allowed to exceed an aspect ratio of 5:1, for

example at the constrained ends of the adherends. This allowed the minimum number of

elements to be used in the analysis and so reduced its complexity and requirement for

computing power, whilst not compromising the accuracy.

Diagrams of the meshes used are given in figures 1 to 7. The fringe plots shown in the

following sections have the same orientations as these diagrams. The constraints used were

similar for each configuration and are shown in figure 8. These model built in conditions at

each end of the joint.

The adhesive used in the joints examined in these analyses was AV119. All adherends were

steel. Both linear and non linear analyses were undertaken. The non linear analyses used

two different adhesive material models, von Mises and Drucker Prager Cap. The Drucker

Prager model shows a hydrostatic stress sensitivity whereas the von Mises model does not.

For the analyses that used a von Mises adhesive model the same non-linear steel model was

used for all substrates. However as the set of analyses that used the Drucker-Prager model

for the adhesive were intended to be the most realistic, different models for steel were used

based on experimental test data. The 2mm thick TLS and TPEEL used one model, the

1.47mm TLS joint another and in the TAST analyses (which used a high carbon steel) a

linear model was used. Material data for the various analyses are presented in Appendix B.

For each analysis the results are presented in different ways to show possible failure

criterion.

2

.-

2. Linear Analyses

The results from the linear analyses are summarised in table 2. Adhesive data are the peak

centroid values in the adhesive, extrapolated from the nodal values.

Joint Peel stress Shear stress Major principal von Mises von Mises adhesive adhesive stress adhesive stress stress (MPa) (M Pa) (M Pa) adhesive substrate

(M Pa) (M Pa)

TLS2.0/0.51 33 38 76 68 863

TLS1.47/0.51 27 33 65 59 909

TLS1.47/1.1 19 23 45 40 842

TAST0.5 34 49 75 86 318

TAST1 .0 20 42 56 73 321

TPEEL0.5125 127 0 129 94 660

TPEEL1.0/25 100 0 105 82 647

Table 2. Stress values taken from numerical data obtained from analyses,

The graphs of centreline stress from which the tabulated data above was taken are shown in

figures 9 to 15. Fringe plots of the adhesive von Mises stress in these joint configurations

are shown in figures 16 to 22.

It can be seen that the maximum von Mises stress in the adhesive of most of the joints has

exceeded the UTS of the adhesive (60-70 MPa). In addition to this, the substrate von Mises

stress has exceeded the yield stress of the adherends, with the possible exception of the two

TAST joints. Further, the adherends in the TLS joints and the TPEEL joints undergo plastic

deformation when they are tested. This means that the linear analyses cannot be relied upon

as we are no longer in the region where the materials of the joint behave in a linear manner.

At this point the need to carry out non-linear analyses is clear.

However if the possibility of predicting failure based on a linear analysis is considered it

can be seen that the von Mises stress appears the most appropriate adhesive stress

3

component to consider. If a critical value of von Mises stress of 67MPa were used

(consistent with the measured UTS for AV119) the strength of all the joints can only be

predicted to within about +/- 30%. By omitting the lmm TLS joint this can be improved to

about +/- 20% but the reason for such an omission is not entirely clear.

4

3. Von Mises Analyses

3.1. Introduction

These analyses were carried out to enable comparison with the analyses already undertaken

by AEA Technology having a higher degree of mesh refinement. The material data for these

“von Mises” analyses are shown in Appendix B. The adhesive post-UTS hardening is a

little unrealistic but was used to enable comparison with the AEA Technology analyses. In

fact it will be seen that only a small amount of post-UTS hardening was encountered in the

analyses. The same meshes were used as in the linear analyses. Non linear geometric

behaviour was used in Abaqus as was automatic load stepping. The initial load increment

was 5’%, All analyses converged without any serious problems.

Table 3 shows the maximum values of various components of adhesive stress and strain

found at the centroids of the elements. Where there are two rows of elements the centroid

values for adjacent elements are averaged.

Configuration

TLS1.47/1.1

TLS2. 0/0.51

TAST0.5

TAST1 .0

TPEEL0.5

TPEEL1.0

Ivon Mises Maximum principal Maximum principal Equivalent plastic

stress stress strain strain

48.0 55.0 0.034 0.017

35.9 41.1

55.6 63.7

76.1 58.1

69.2 47.6

74.7 114.3

66.7 90.8

0.022 0.009

0.043 0.024

0.078 0.062

0.062 0.048

0.084 0.059

0.066 0.043

Table 3. Results from von Mises analyses.

5

More detailed results can be found in the following sections. The graphs of stress and strain

in the following sections are found from the adhesive element centroid values. The x-axis

refers to the distance between adhesive element centroids. The zero value of distance

represents the centroid of the left hand adhesive element in each joint, or the top element in

the case of the TPEEL joints, and not the edge of the bondline.

3.2. TAST Joints

3.2.1. TAST0.5

Figure 23 shows the levels of stress along the bondline. The adhesive has yielded along its

entire length. Figure 24 shows the levels of strain along the bondline. The maximum

principal strain is only slightly in excess of the failure strain experienced in the bulk tensile

test. The overall distribution of von Mises stress in the TAST0.5 joint can be seen in figure

25. It can be seen that the maximum adherend stress is concentrated around the loaded ends

of the overlap. Figures 26, 27 and 28 show fringe plots of adhesive maximum principal

stress, maximum principal strain and equivalent plastic strain respectively.

3.2.2. TAST 1.0

Figure 29 shows the levels of stress along the bondline. Once again it can be seen that the

adhesive has yielded along its entire length. Figure 30 shows the levels of strain along the

bondline. Again the maximum principal strain is close to the failure strain experienced in the

bulk tensile test. The overall distribution of von Mises stress in the TAST 1.0 joint can be

seen in figure 31. It can be seen that the maximum adherend stress is concentrated around

the loaded ends of the overlap. Figures 32, 33 and 34 show fringe plots of adhesive

maximum principal stress, maximum principal strain and equivalent plastic strain

respectively.

6

.-

3.3. TPEEL Joints

3.3.1. TPEEL0.5

Figure 35 shows the levels of stress along the bondline. Unlike the TAST joints which are

dominated by shear the hydrostatic loading in the TPEEL joints enables the major principal

stress to exceed the von Mises stress. The differences between the two configurations

suggests that maximum principal stress would not be a suitable failure criterion. Figure 36

shows the levels of strain along the bondline. It can be seen that the levels of maximum

strains are similar to those found in the TAST joints. This suggests the possibility of a

strain based failure criterion. The overall distribution of von Mises stress in the TPEEL0.5

joint can be seen in figure 37. It can be seen that the maximum adherend stress is

concentrated around the loaded ends of the overlap. It can be seen that there is a significant

plastic zone forming in the substrate. Figures 38, 39 and 40 show fringe plots of adhesive


respectively.

3.3.2. TPEEL1.0

Figure 41 shows the levels of stress along the bondline. Again, the level of maximum

principal stress is higher than the von Mises stress. Figure 42 shows the levels of strain

along the bondline. As before the maximum strains are similar to those found in the bulk

tensile tests. Levels of strain in the thicker TPEEL joint is lower which is consistent with

lower strains in the thicker TAST joint. The overall distribution of von Mises stress in the

TPEEL 1.0 joint can be seen in figure 43. It can be seen that the maximum adherend stress

is concentrated around the loaded ends of the overlap. The levels of substrate stress and the

formation of a plastic hinge are comparable to the TPEEL0.5 joint. Figures 44,45 and 46

show fringe plots of adhesive maximum principal stress, maximum principal strain and

equivalent plastic strain respectively.

7

3.4. TLS Joints

3.4.1. TLS2.0/0.51

Figure 47 shows the levels of stress along the bondline. The level of von Mises adhesive

stress is fairly uniform along the overlap. Figure 48 shows the levels of strain along the

bondline. The general level of strain appears to be somewhat lower than in the TAST and

TPEEL joints, although it does rise at the toe of the fillet. The overall distribution of von

Mises stress in the TLS2.O/O.51 joint can be seen in figure 49. It can be seen that the

maximum adherend stress is concentrated around the loaded ends of the overlap where a

significant plastic zone has formed. Figures 50, 51 and 52 show fringe plots of adhesive


respectively.

3.4.2. TLS1.47/0.51

Figure 53 shows the levels of stress along the bondline. This also is a little lower than the

last configuration. Figure 54 shows the levels of strain along the bondline. The overall

distribution of von Mises stress in the TLS 1.47/0.5 1 joint can be seen in figure 55. It can

be seen that the maximum adherend stress is concentrated around the loaded ends of the

overlap and is a little lower than that developed in the 2mm substrate joint (TLS2.O/O.51 )

discussed previously. Figures 56, 57 and 58 show fringe plots of adhesive maximum

principal stress, maximum principal strain and equivalent plastic strain respectively. This

shows similar trends as the TLS2.O/O.51 joint.

3.4.3. TLS1.47/l.l

Figure 59 shows the levels of stress along the bondline. Figure 60 shows the levels of

strain along the bondline. The overall distribution of von Mises stress in the TLS 1.47/1.1


concentrated around the loaded ends of the overlap. These substrate stresses are the highest

of all of the TLS configurations. Again, a more complete plastic hinge is formed than in the

8

TLS 1.47/.51 joint. Figures 62, 63 and 64 show fringe plots of maximum principal stress,

maximum principal strain and equivalent plastic strain respectively.

3.5. Comments.

The maximum values of maximum principal stress, maximum principal strain and

equivalent plastic strain are found at the interface of the bondline and the substrate in all of

the above configurations as shown in the relevant fringe plots. This is the location at which

adherend rotation occurs in the analyses and also where it is seen in practice when testing

the TPEEL and TLS joints.

In order to investigate the relevance of various adhesive parameters as failure criterion,

charts of maximum adhesive stress values for all of the configurations are shown in figure

65. This shows that there is not a satisfactory failure criterion in the results obtained from

the stresses. We can now look at the strains in the same manner in figure 66. It can be seen

that the strains in the TLS joints are generally lower than the other two configurations and

there does not appear to be a unique failure strain across all the joints. However if there was

a reason for excluding the TLS joints a value of failure strain of 7% would produce very

reasonable predictions for all TAST and TPEEL joints. It is possible that a different failure

mechanism is active in the TLS joints. The errors in predicted strength should be

significantly less than the errors in maximum strain values because the analyses are non-

linear and a small change in load will result a much larger change in strain. These errors can

only be found by undertaking sensitivity analyses and these are discussed in section 3.6.

It was decided to look at the values of strain at two other locations. The first location was

the maximum centroid value. This differs from the data presented in the previous graph for

the TAST 1.0 and TLS 1.47/ 1.1 joints as the two rows of bondline centroid values are not

averaged in this case. The second location was the maximum value encountered on the

fringe plot on the centre line of adhesive layer. These results are shown in figures 67 and

68 for maximum principal strain and equivalent plastic strain respectively.

9

.

If we look at the maximum centroid results (without averaging) the TLS 1.47/1.1 and

TAST 1.0 values have been raised slightly. If we look at the maximum centre line fringe

results the TLS 1.47/0.51 and TLS2.O/O.51 and the TAST 1.0 values have been raised

while the TPEEL0.5 and TPEEL 1.0 have been lowered, There are however no significant

improvements in strength predictions. Again the un-averaged maximum centroid results

have made little difference to the graph.

3.6. Sensitivity analysis

As these analyses are non-linear it is not possible to scale the loadings to see what

difference this would make to the results and to find a critical value of stress or strain that

would give a minimum error for all of the analyses. In order to investigate what effect

varying the applied load would make, the analyses were re-run so that results were obtained

for a range of applied loads that were above and below the experimental failure load to

cover the range of critial adhesive strains being considered. Results were output for each of

the applied loads for the maximum (non-averaged) centroid value of maximum principal

strain as this appears to be the best criterion. The root mean square error for each of the

results for a given critical value of maximum principal strain was found. The accumulated

error was minimised by varying the critical value. The resulting optimum strain was found

to be 6.7%.

The assessment has only been carried out for the TAST and PEEL joints. The results of the

sensitivity analysis are shown in figure 69. The maximum errors with respect to the critical

value are +5% and -7%. This means, for example, that the principal strain in the TAST0.5

joint reaches 6.7% at a load that was 93% of its experimental failure load.

10

4. Drucker Prager Cap Analyses

4.1. Introduction

These analyses should be seen as the most advanced of these “coarse-mesh” type analyses.

The material models for the adhesive and substrates were different to those used in the von

Mises analyses. The adhesive used the Drucker Prager model which not only allows for a

hydrostatically-sensitive material response but also removes the unrealistic post UTS-

hardening in the previous set of analyses. The constants for this model were calculated

from a combination of shear and tensile data, and are shown in Appendix B. The substrate

models used were more representative than the generic “mild” steel used in the von Mises

analyses. This adherend data was obtained from mechanical tests, with the exception of the

TAST adherends. These were treated as being linear elastic as the levels of substrate

stresses are lower than the yield stress in the high carbon steel used in these joints. These

substrate models are also shown in Appendix B. The same meshes were used as in the von

Mises analyses. Non linear geometric behaviour was used in Abaqus as was automatic load

stepping. The initial increment was 5%.

Maximum principal Maximum principal Magnitude of plastic

stress strain strain

TLS1.47/0.51 61.22 0.028 0.008

TLS1 .47/1.1 41.11 0.017 0.001

TLS2.0/0.51 65.36 0.0419 0.019

TAST0.5 51.99 0.0266 0.0072

TAST1.0 49.01 0.02 0.0022

TP1.0 76.06 0.082 0.052

Table 4. Results from Drucker Prager analyses.

Table 4 shows the maximum values of stress and strain found at adhesive element

centroids. Where there are two rows of elements the centroid values for adjacent elements

are averaged as they were in the von Mises analyses.

More detailed results can be found in the following sections. The graphs of stress and strain

are found from the adhesive element centroid values. The x-axis refers to the distance

between adhesive element centroids. The zero value of distance represents the centroid of

the left hand adhesive element in each joint, or the top element in the case of the TPEEL

joints, and not the edge of the bondline. The levels of strain are generally lower than with

the von Mises analyses. This is because most joints have some shear component which has

a lower hydrostatic stress level and hence restricted yielding.

4.2. TAST Joints

4.2.1. TAST0.5

Figure 70 shows the levels of stress along the bondline. Major principal stress in this joint

is similar to that in this configuration detailed in section 3. Figure 71 shows the levels of

strain along the bondline. It would appear that the compressive peel stress actually prevents

yield of the adhesive in the centre region of the overlap, thus restricting the levels of strain

being generated. The overall distribution of von Mises stress in the TAST0.5 joint can be

seen in figure 72. It can be seen that the maximum adherend stress is concentrated around

the loaded ends of the overlap. The general level of substrate stress is higher than that in the

von Mises analysis because the steel has a high yield strength. Figures 73, 74 and 75 show

fringe plots of maximum principal stress, maximum principal strain and equivalent plastic

strain respectively.

4.2.2. TAST1.0

Figure 76 shows the levels of stress along the bondline. Again, levels of maximum

principal stress similar to TAST0.5 and those in section 3. Figure 77 shows the levels of

strain along the bondline. The strains however are slightly lower, with less predicted

12

yielding. The overall distribution of von Mises stress in the TAST 1.0 joint can be seen in

figure 78. It can be seen that the maximum adherend stress is concentrated around the

loaded ends of the overlap. Levels of substrate stress are similar to the previous joint with a

thinner bondline. Figures 79, 80 and 81 show fringe plots of maximum principal stress,


4.3. TPEEL Joints

4.3.1. TPEEL0.5

At the time of writing a converged solution for this configuration had not been obtained.

4.3.2. TPEEL1.0

Figure 82 shows the levels of stress along the bondline. As expected it was not possible to

sustain the high level of principal stress seen in section 3 because this promotes earlier

yielding. Figure 83 shows the levels of strain along the bondline. The strains are higher

because of higher levels of hydrostatic tension in the joint. The overall distribution of von

Mises stress in the TPEEL1.0 joint can be seen in figure 84. It can be seen that the

maximum adherend stress is concentrated around the loaded ends of the overlap forming a

plastic hinge of similar size to that seen in section 3. Figures 85, 86 and 87 show fringe

plots of maximum principal stress, maximum principal strain and equivalent plastic strain

respectively.

4.4. TLS Joints

4.4.1. TLS2.0/0.51


strain along the bondline. Again, levels of maximum principal strain correspond to those in

section 3 whilst there is much less predicted yield. The overall distribution of von Mises

stress in the TLS2.O/O.51 joint can be seen in figure 90. It can be seen that the maximum

adherend stress is concentrated around the loaded ends of the overlap, the distribution being

13

similar to that in section 3. Figures 91, 92 and 93 show fringe plots of maximum principal

stress, maximum principal strain and equivalent plastic strain respectively.

4.4.2. TLS1.47/0.51


strain along the bondline. The overall distribution of von Mises stress in the TLS 1,47/0.5 1


concentrated around the loaded ends of the overlap. Figures 97, 98 and 99 show fringe

plots of maximum principal stress, maximum principal strain and equivalent plastic strain

respectively.

4.4.3. TLS1.47/l.l


strain along the bondline. The overall distribution of von Mises stress in the TLS 1.47/ 1.1

joint can be seen in figure 102. This has the most significant plastic hinge of all TLS joints.

It can be seen that the maximum adherend stress is concentrated around the loaded ends of

the overlap. Figures 103, 104 and 105 show fringe plots of maximum principal stress,


4.5. Comments

As with the von Mises analyses different ways of extracting the maximum adhesive stress

were considered.

Figure 106 shows maximum averaged centroid values for peel stress and maximum

principal stress. The range in the maximum principal stresses is much lower than in either

of the two previous sets of analyses. However in an elasto-plastic analyses adhesive

stresses are generally much less sensitive than strains and are thus not usually appropriate

as failure criterion. Figure 107 shows maximum averaged centroid values for maximum

principal strain and magnitude of plastic strain. Here it can be seen that using a hydro-

statically sensitive material model leads to the maximum adhesive strains in the TLS and

14

TAST joints being similar with the TPEEL joint strains being larger. This is in contra-

distinction to the trend in the linear and von Mises analyses and is because the TPEEL

experiences much less shear and thus less suppressed yielding than the other joints. Figure

108 shows a comparison between maximum averaged centroid values, un-averaged

centroid values and centre line fringe values of maximum principal strain. Taking un-

averaged values as a failure criterion and excluding the TPEEL1.0 result, 3.1% maximum

principal strain gives a maximum error of 23%. If however the centreline maximum from

the contour plots were taken the maximum variation in the principal strain from a mean

value of 3.470 was only 189Z0 across all joint configurations. As the analyses are non-linear

the errors in predicted failure load would be much better than 23% and 18% respectively.

15

—. . .

5. Concluding Comments

A “coarse mesh” type finite element model has been used to analyse seven different joint

configurations bonded with AV119 for which the experimental failure load was known.

For most of these joints the experimental scatter was much better than +/-10% .By using

elements of the same size at the region of maximum adhesive stress (i.e. 0.5x0.5mm) this

is essentially an implementation of “stress at a distance” and “strain at a distance” type

failure criteria where the distance is a typical bond line thickness. One of the reasons for

carrying out this work is that there are an increasing number of continuum type adhesive

joint stress analyses, linear and non-linear, which give adhesive stresses and strains as

averaged values across the adhesive layer. This work will consider how best to interpret the

results from such analyses. Three different types of analyses were undertaken; linear, non-

linear with von Mises adhesive plasticity and non-linear with Drucker-Prager adhesive

plasticity. The linear analyses showed that significant non-linearity would occur in all joints

and thus a non-linear analysis was essential. In the Drucker-Prager analyses a converged

solution for the thinner TPEEL joint could not be obtained. Interestingly this was the joint

that experienced a considerable amount of experimental scatter.

No component of adhesive stress or strain could be identified as being an appropriate

failure criterion across the complete range of joints. In the von Mises analyses the TPEEL

and TAST joints had similar levels of adhesive strain whilst those calculated for the TLS

joints were much lower. Indeed a failure strain of 6.7% (the maximum levels measured in a

very good quality bulk tensile tests) predict joint strengths of the TPEEL and TAST joints

very accurately. A possible explanation for the lack of fit for the TLS joints is that a

different failure mechanism may have occurred. The TAST and TPEEL joints have been

monitored during loading in previous studies and the mode of failure was identified as

damage and cracking along the interface.

16

The Drucker-Prager analyses generally exhibited lower levels of adhesive strain because of

the suppression of yield. With this model of adhesive yield the two shear configurations

(TAST and TLS) resulted in similar levels of adhesive strain, with the peel configuration

having higher levels. The accuracy of an adhesive centroid strain based failure criterion

appears worse than with a von Mises model (used only TPEEL and TAST joints only).

This has not been quantified as sensitivity studies (required for non-linear analyses) were

only carried out for the von Mises analyses. However, when the maximum strain was

extracted from the centreline of the contour plot the criterion was applicable across all joint

configurations and gave a reasonable level of accuracy. The critical strain was about half

that used in the von Mises analyses and is about the average failure strain measured from

bulk tensile tests. It is then less quantifiable (and justifiable) than the critical strain used in

the von Mises analyses but appears to be applicable over the complete range of joints

analysed.

17

I I I I : . . .

Figure 1. The mesh of the TLS joint.

,,.,,

Figure 2. The mesh of the TLS 1.47/0.51 joint.

Figure 3. The mesh of the TLS 1.47/1.1 joint.

X ANDY CONSTRAINTS

FIXED GRIP END

LOAD .

MOVING GRIP END -

Figure 8. Configuration of constraints and loading used on all joints in this work

—.

60

40

20

0

-20

-40

,., .. ----- , \ ,/

I \

I / I

Distance along bondline (mm)

PEEL

‘-- SHEAR

‘–- MAJOR PRINC.

– – – - VON MISES

Figure 9. Centroid adhesive stresses in the TLS2.0/0.51 joint.

70

60

50

.

Distance along bondline

15 20

(mm)

PEEL

-- SHEAR

— - – - MAJOR PRINC.

– - VON MISES


50

40

30

-lo

-20

\ I 1 I I I

15 20


PEEL

‘-- SHEAR

- – - MAJOR PRINC.

Figure 11. Centroid adhesive stresses in the TLS1.47/l.l joint.

100

T 80 -

‘._ ,

60 \

-:\- /

40 -

20

0

c -20


PEEL

. . -- SHEAR

- – - MAJOR PRINC.

— – – - VON MISES

—

Figure 12. Centroid adhesive stresses in the TAST0.5 joint.

80

60

40

20

0

-20

-40

\

\

along bondline

10

(mm)

PEEL

- ‘- SHEAR

— - – “ MAJOR PRINC.

— – – - VON MISES

Figure 13. Centroid adhesive stresses in the TAST1.O joint.

140

120

100

80

60

40

20

0

-20

-40 1 ., \.-


30

(mm)

-- PEEL

– - MAJOR PRINC.

VON MISES

Figure 14. Centroid adhesive stresses in the TPO.5 joint.

120

100

80

o

-20

-40

along

20

bondline

VON MISES

— – - MAJOR PRINC.

“ - PEEL

30

(mm)

Figure 15. Centroid adhesive stresses in the TP1.O joint.

80

70

60

50

40

30

20

10

0

-lo

-20

—-——_ _ ———— .

___

. . . . ..-” ------ .. ---- --

\ \ /

— . —

I

.

14



0.01

0 ! , , , I

o 2 4 6 8


10 12 14

Figure 24. Centroid adhesive strains in the TASTO.5 joint.

70

60

50

40

10

0

-lo

/— ‘— ——-—

‘\

—

.

\ \

— . — S vm

S hyd

S peel

Smj

,

4–---–-C-–” –-Z 10 14


—

-J

0.05

\ 0.04 \

0.02

0.01

I , (

o 2 4 6 8


10 12 14

Figure 30. Centroid adhesive strains in the TAST1.O joint.

120

100

80

60

-40

-60

-80

S hyd

— — – - S mises

‘- Smj

— ‘–- Speel

[

15 20 25 30

Distance along bond[ine (mm)

-J

9.00E-02

8.00E-02

7.00E-02

6.00E-02

L

E mj

5.00E-02 - ~ . — ‘- PEeq c

3.00E-02 -

2.00E-02 -

\ -\

\ 0.00E+OO 1 I I , I I

o 5 10 15 20 25 30


Figure 36. Centroid adhesive strains in the TP0.5 joint.

0 -- , t

S hyd

— — – - S mises

“-- Smj

— ‘–- Speel

, I

-20 15 20 25 30

-40

-60


—

Figure 41. Centroid adhesive stresses in the TP1.0 joint.

0.07

0.06

0.05

0.04 I

E mj

. ‘–- PEeq

\

0.02 -

\ 0.01 -

\

o 1 , ! I

o 5 10 15 20 25 30


Figure 42. Centroid adhesive strains in the TP1.0 joint.

6-

70

60

50

40

30

20

10

0

-10

-20

-30

-40

---- _— -- . —

.

‘.. . ..”


Shyd

— — ‘–-Svm

-- Smj

— — - – - Speel


0.045 Emj

0.04 — — —

0.035 – - PEeq

0.03

—— __ __ —-- -- 0.01

0 I , I I I

0 5 10


15 20

Figure 48. Centroid adhesive strains in the TLS2.0/0.51 joint.

60

50

40

30

c _ --- 5 20


Shyd

— —

— – - Speel


0.035

0.03

0.025

0.02

\ I

0.01 _\/\ I ,“

___ Emj 0.005

— — – – - PEeq

o

0 5 10 15 20


Figure 54. Centroid adhesive strains in the TLS1.471O.51 joint.

50

40

30

20

10

0

-lo

-20

--—_ ____ —

. ‘.


—

—

Figure 59. Centroid adhesive stresses in the TLS1.4711.1 joint.

0.025

0.02

0.015

\ \

0.005 —\

0. I I , I

o 5 10 15 20


Figure 60. Centroid adhesive strains in the TLS1.47/l.l joint.

120

Joint configuration

Figure 65. Maximum centroid adhesive stresses.

0.09 T

008

T

- Maximum principal strain

Maximum principal strain (un-

averaged)

-------- Maximum principal shin (centre line

fringe)

Figure 67. Adhesive principal strains taken at various locations.

008

0.07

O 05

O 03

002

+

Figure 68. Adhesive equivalent plastic strains taken at various locations.

T 98% 93%

003

0.07

, , I

Figure 69. Results of the sensitivity analysis.



003

T 0.025

0.02

!

Figure 71. Centroid adhesive strains in the TAST0.5 joint.

30

0.025


Figure 77. Centroid adhesive strains in the TAST1.0 joint.

80

60

40

20

-20

-40

,-2

Figure 83. Centroid adhesive strains in the TP1.O joint.

70 T

004

0,035

0.03

0.025

0015 .



70

60

2 4 6 6 10 12 14 16



50 T

40 -


Figure 101. Centroid adhesive strains in the TLS1.47/l.l joint.

I I TLS1 471051 TLS1 .47/1.1 TLS2 0/051 TASTO.5 TAST1.0 TPEEL1.0

Joint configuration

Figure 108. Adhesive strains taken at various locations.

.—- . . ..—. . . . —- . . —. —.. .-. ———

Appendix A

Joint dimensions

AV119 TAST JOINT

Length Overlap blt A B c D E

228 12.5 0.5 6 10 17.5 120.3 12.5 228 12.5 1 5.75 10 17.5 120.3 12.5

cure 120 degrees C for 2 Hours

E

–B

blt (mm) bll (mm) Fillet(%) Chamfer Temp. ( “c) rate (mm/min) ShearStrength (MPa) 0.5 12.5 0 Y rt 0.5 43.1 1 12.5 0 v rt 0.5 39.4

2

AV119 T PEEL JOINT

,

0.5 28 25 20 0.5 93.3

1 28 25 20 0.1 91

AVI 19 TLS JOINT

)

A 1.47 1.47 2 B 0.51 1.1 0.51 c 0.51 1.1 0.51 D 10 10 10 E 12.5 12.5 12.5 Fillet 45° Y Y Y Av. Load (N) 3.18 2.41 4.36

cure 120 degrees C for 2 Hours

Appendix B

Material data

Adhesive material model used for the von mises analyses

200

180

160

40

20

Stress (M Pa) Total strain Plastic strain

o 0 0 13.5 0.005

26.75 0.0149 38.25 0.0242

47 0.0324 54 0.04

57.5 0.0463 60 0.0522

200 0.3826

0 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300 0.3085

Poissons ratio: 0.3

Modulus: 2.7 GPa

Steel material model used in the von mises analyses

450

400

50

0 o 0.05 0.1 0.15 0.2 0.25

Strain

—

Stress (MPa) Total strain Plastic strain

o 0.0 0 220 0.0010 0 430 0.2020 0.2

Poissons ratio: 0.3

Modulus: 210 GPa

Adhesive material response for the Drucker Prager analyses

/

o 0.02 0.04 0.06

Total Strain

Poissons ratio: 0.3

Modulus: 3 GPa

Using values for yeild in tension 63.3 MPa and in shear of 45 MPa

The Drucker Prager constants are :

d=77.94

ß=34.69°

Steel material model used in the Drucker Prager analyses

on the TLS2.0/0.51 and TPEEL configurations

Total strain

o 0 156 0.001 185 0.002 214 0.01 262 0.04

Poissons ratio: 0.3

Modulus: 210 GPa

PIastic strain

o 0

0.00111 0.00897

0.03874

0.0486

0.1085

Steel material model used in the Drucker Prager analyses

on the TLS1 .47/0 .51 and TLS1 .47/1.1 configurations

250

175 18C 187 196 204 248 248

Total strain Plastic strain

o 0 0.00086 0 0.00133 0.00045 0.00180 0.00088 0.00279 0.00182 0.00428 0.00328 0.03000 0.02878 0.10000 0.09878

Poissons ratio: 0.3

Modulus: 200 GPa

Documents

MTS Adhesives Project 2 Failure Modes and Criteria Report ... 2/P2r6a3.pdf · A final report on Task 3.1, Project 2, Development of failure criteria B H Le Page, AD December 1995