A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence

A phenomenological anisotropic damage progression formulation for porous ductile metals with second phases is described through mechanisms of void nucleation, growth and coalescence. The model is motivated from fracture mechanisms and microscale physical observations. To describe the creation of new pores, the decohesion at the particle–matrix interface and the fragmentation of second phase particles, the void-crack nucleation equation is related to several microstructural parameters (fracture toughness, length scale parameter, particle size, volume and fraction of second phase), the plastic strain level, and the stress state. Nucleation is represented by a general symmetric second rank tensor, and its components are proportional to the absolute value of the plastic strain rate components. Based on the Rice and Tracey model, void growth is a scalar function of the trace of damage tensor and the positive triaxiality. Like nucleation, coalescence is a second rank tensor governed by the plastic strain rate tensor and the stress state. The coalescence threshold is related to the void length scale for void impingement and void sheet mechanisms. The coupling of damage with the Bammann–Chiesa–Johnson (BCJ) plasticity model is written in the thermodynamic framework and derives from the concept of effective stress assuming the hypothesis of energy equivalence. A full-implicit algorithm is used for the stress integration and the determination of the consistent tangent operator. Finally, macroscale correlations to cast A356 AL alloy and wrought 6061-T6 AL alloy experimental data are completed with predictive void-crack evolution to illustrate the applicability of the anisotropic damage model.