A model for creep of porous crystals with cubic symmetry

A model for description of the creep response of porous cubic single crystal is presented. The plastic potential is obtained by specializing the orthotropic potential of Stewart and Cazacu (Int. J. Solids Struct., 48, 357, 2011) to cubic symmetry. The crystal matrix material response is characterized by power law creep. The predictions of this porous plastic constitutive relation are presented for various values of stress triaxiality (mean normal stress divided by Mises effective stress) and various values of the Lode parameter L (a measure of the influence of the third invariant of the stress deviator). A strong influence of crystal orientation on the evolution of the creep strain and the porosity is predicted. For loadings along the < 100 > directions of the cubic crystal, void growth is not influenced by the value of the Lode parameter. However, for loadings such that the maximum principal stress is aligned with the [110] direction there is a strong influence of the values of the Lode parameter and the fastest rate of void growth occurs for shear loadings (one of the principal values of the applied stress deviator is zero). For loadings such that the maximum applied stress is along the [111] crystal direction the fastest rate of void growth corresponds to L=-1, while the slowest rate corresponds to L=1. These predictions are compared with corresponding predictions of the three dimensional finite deformation unit cell analysis of Srivastava and Needleman (Mech. Mater., 90, 10, 2015). It is found that the phenomenological model predicts the same trends as the cell model calculations and, in some cases, gives good quantitative agreement.