Discontinuous crack model for piezoelectric materials and its application to CED evaluation

摘要

In order to study the influence of electric displacement saturation on fracture behavior of a piezoelectric material, the electric displacement strip-saturation model by [Gao H, Zhang TY, Tong P. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J Mech Phys Solids 1997;45:491-510] has been applied. However, this model is only applicable to problems such as that of a crack in an infinite plate for which it provides a singular solution. In order to overcome this situation, we developed a crack model for a piezoelectric material named discontinuous crack model that is presented in this paper, to evaluate crack energy density (CED) considering electric yielding and we studied its applicability through finite element analyses. The model is defined and methods to establish its constitutive equation are discussed. Moreover, it is shown that the model by Gao et al. and the ordinary crack model in continuum can be regarded as special cases of the discontinuous crack model. Subsequently, the CED and its derivatives for the discontinuous crack model are defined and their path independent expressions are also derived based on conservation laws. Finally, a finite element formulation is devised and the applicability of the model to the evaluations of CED and its derivatives is studied through finite element analyses of an example.