A nonlinear thermoviscoelastic stress and fracture analysis of an adhesive bond

Abstract

We consider 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 and evaluate the effect of these residual stresses on bond failure through associated changes in the energy release rate. A nonlinear, viscoelastic (free-volume) model serves for the thermoviscoelastic characterization of the polymer. The simultaneous solution to the heat diffusion and the transient therrnoviscoelastic problems are addressed. A “critical” cooling time on the order of a few seconds exists for the chosen design configuration, 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. To reduce the stresses from their maximal value by a factor of two requires cooling times of the order of a day or two. For the fracture analysis, a crack of variable length is introduced into the polymer layer at or near an interface, and glassy (elastic) properties are allowed to dominate (only) for the fracture process. The crack faces are found to be in contact away from the tip during the unloading process. For a finite dimensioned geometry there exists a maximal energy release rate for a given crack penetration, which is roughly proportional to the ratio of the layer thickness to the adherend thickness. This peak energy release is reduced by a factor of about a hundred as one passes from quench cooling to (pronouncedly) slow cooling. The total energy release rate resulting from combined loading and from the residual stresses is also studied. One finds that ignoring the crack face contact leads to sizable errors in estimating the interface fracture energy.