A T-peel joint will be used as an example of the use of fracture mechanics in design. The example will show how the fatigue life of such a joint may be assessed. The joint consists of thin gauge steel (0.8 mm) substrates bonded with a toughened epoxy adhesive with a bondline thickness of 0.8 mm.
A two-dimensional finite element analysis was carried out using linear elastic material properties for the substrate and adhesive. The plane of crack growth was modelled through the centre of the bondline. A series of solutions were obtained for a unit load for various crack depths by removing the connectivity of nodes from adjacent elements on each side of the crack so that the crack length was increased by one element at a time. The deformed joint under load is shown in Figure 15, which also shows the concentration of stress around the crack tip in the adhesive layer for one particular crack length.
Figure 15: FEA plot of a deformed T-peel sample (with a crack along the centre of the bondline)
For each crack length the strain energy release rate was calculated from the appropriate nodal forces and displacements using the VCCT technique. For this case, the loading is completely Mode I. It was found that the analysis results were very sensitive to the size of the fillet at the edge of the adhesive layer. For the purposes of comparing with test data, the analysis was repeated for fillet sizes representing the largest and smallest fillets, which was a difference of 1 mm. The results are plotted in Figure 16 for the largest fillet size, together with a fit to the results used in the fatigue life calculation. The following is noted from Figure 16.
G/Ny2 increases with increasing crack length (i.e. the rate of crack growth is expected to increase with increasing crack length).
G/Ny2 increases rapidly over the first 0.2 mm, however an initial crack length (equivalent defect size) of 0.4 mm is assumed so that any crack initiation effects have been ignored.
Figure 16: Plot of G vs. a for T-peel sample
(with a crack along the centre of the bondline)
The fatigue life is calculated based on a final crack length of 6 mm from the variation in G/Ny2 vs. a and a crack growth model for the adhesive of the form da/dN = AGB , where A is 1.6 x 10-18 and B is 5.3. The results are compared with test data in Figure 17. Upper and lower predictions are given based on the range of fillet sizes considered. There is good agreement between the predicted range and the test data and the high level of variation in the test data is explained by small variations in fillet size between joints.
Figure 17: Comparison of predicted fatigue life with test data
