A nonlinear thermoviscoelastic stress and fracture analysis of an adhesive bond

Abstract

The evolution of residual stresses resulting from cooling an adhesive bond configuration on its lateral surfaces at a constant rate through the glass transition of the polymer are considered. A nonlinear, viscoelastic (free-volume) model serves for the thermoviscoelastic characterization of the polymer. The simultaneous solution to the heat diffusion and the transient thermoviscoelatic problems are addressed. Both an infinite (one-dimensional) and a finite (two-dimensional) domain are studied. A "critical" cooling time exists, in the present case on the order of a few seconds, which separates the control of the solidification process according to whether the relaxation or thermal diffusion time scale governs. The short time "quenching process," i.e., when the time scale is governed by thermal diffusion, leads to essentially constant residual stresses. Slower cooling increasingly invokes the time and rate sensitive properties of the polymer and leads to monotically decreasing residual stresses with longer cooling times. To reduce residual stresses by a factor of two from their maximal values requires cooling times on the order of one or two days. These results are not drastically altered by changes in the thicknesses of the bond components. Apart from singular behavior of the stress components in the two-dimensionally finite domain "quenching" has the effect of producing significantly different stress distributions (including stress "spikes") than slow or thermoelastic analyses would suggest. This observation is attributed to the interaction of the bending response of the metal components early in the cooling history under the high thermal gradients, which deformations are then partially frozen in during the subsequent cooling of the polymer. Implications of these results for systems possessing geometric and material differences subjected to various thermal cooling ranges are also discussed. The results demonstrate the importance of knowing the bulk relaxation or creep spectrum for the polymer. In the second part of the thesis the effect of the residual stresses on fracture behavior of an adhesive bond are addressed within the context of linear fracture mechanics for dissimilar materials. The crack faces are found to be in contact at the fractured end during the (residually stress) unloading process. A significantly error results if this contact zone is not taken into account. The combined effect of the mechanical loads and the residual stresses on the energy release rate is also studied. The total energy release rate from the combined effect is not necessarily higher or equal to the sum of the individual contribution from external loads and from residual stresses separately.