Prediction of energy release rate due to the growth of an interface crack by variational analysis

In our previous studies (Wu W, Verpoest I, Varna J. A novel axisymmetric variational analysis of the stress transfer into fibre through a partially debonded interface. Composites Science and Technology 1998;58:1863–77 and Wu W, Jacobs E, Verpoest I, Varna J. Variational approach to the stress transfer problem through partially debonded interfaces in a three phase composite. Composites Science and Technology 1999;59:519–35) on the stress transfer problem for a single fragment of a fibre or a fibre with an additional interphase, embedded in an infinite matrix with a partially debonded interface, we presented two axisymmetric models, based on the principle of minimum complementary energy. In this paper, some parts of models, useful in the application of fracture mechanics, are first summarised. An expression is then given for the strain energy release rate due to a crack extension in an arbitrary composite system subjected to mixed traction-displacement boundary conditions and with thermal residual stresses included. This expression is suitable for a stress-based variational model. An important advantage is that it can include the friction work at the crack surfaces, in a rather simple but exact way, without using both the displacement and stress distributions at the crack surfaces as inputs. As an application of the expression, we illustrate how to calculate the energy release rate due to the growth of an interface crack in a single fibre fragment with a partially debonded interface under thermomechanical load, by using models in the above references. It is found that the energy release rate can be calculated by using only the rate of change of the strain energy related to the perturbation stress components. A second application is the energy change which is due to fibre breakage. The numerical results indicate that the energy release rate due to the growth of an interface debond or a similar problem can now be determined in a reliable way for both 2- and 3-phase composites.