A criterion for void coalescence in anisotropic ductile materials

• A criterion for void coalescence in anisotropic ductile materials is developed.
• The criterion accounts for the combined effect of material anisotropy and void shape.
• The criterion has a functional form similar to the Gurson model for void growth.
• The model shows good agreement with numerical upper-bound coalescence loci.

Plastic anisotropy in the form of texture development and void shape evolution can significantly affect damage growth rates and overall strain to failure in ductile materials. A criterion for the onset of coalescence, which is the transition from void growth by diffuse plastic deformation to localized plasticity in the ligament connecting neighboring voids, is a critical component of any predictive model for ductile fracture. In this paper, a new micromechanics-based criterion for void coalescence, combining both forms of anisotropy above, is developed using homogenization and limit analysis of a hollow cylindrical representative volume element made of an orthotropic material of the Hill type. Two possible modes of coalescence, corresponding to necking instability and shear strain localization in the transverse inter-void ligament, are accounted for in the analysis. The final form of the coalescence criterion has an interesting symmetry with Gurson-type yield criteria for porous materials and is shown to be an improvement over existing models for the special case of isotropic matrix behavior. For validation of the analytical model, quasi-exact numerical coalescence loci are computed using a finite elements based limit analysis method for the special case of transversely isotropic materials. The analytical model is shown to be in good agreement with the numerical data, except for highly oblate void shapes approaching penny shape cracks. A heuristic modification for the model is proposed, which significantly improves the model predictions in that limit.