Yield surface for void growth and coalescence of porous anisotropic materials under axisymmetric loading

Ductile fracture in metallic alloys occurs by growth and coalescence of cavities. Growth, also referred to as homogeneous yielding, refers to rather diffuse plasticity around cavities, while coalescence, also termed as inhomogenous yielding, corresponds to the localization of plasticity along some planes or directions. Coalescence can develop in various patterns; three coalescence modes have been observed experimentally: internal necking, coalescence in columns and void sheeting. Plastic anisotropy of the material is known to have a significant effect on both homogeneous and inhomogeneous yielding. Therefore, in the present study, yield criteria accounting for the transition from homogeneous yielding to inhomogeneous yielding modes in anisotropic porous materials are obtained using kinematic limit analysis on a cylindrical unit cell with a coaxial cylindrical cavity. Two types of plastic anisotropy are considered: Hill (1948) plasticity and crystal plasticity. The proposed analytical yield criteria are compared to numerical limit analysis computations and are found to qualitatively agree with simulations. In particular, plastic anisotropy, void shape effects and their coupling are well captured, especially regarding yield stresses and deformation modes. Finally, an homogenized model for Hill porous materials is obtained by supplementing evolution laws for microstructural parameters (void aspect ratio and ligament size ratios) derived from sequential limit analysis. Proposed evolution laws are then discussed in the light of numerical results and experimental evidence.