A micromechanics based ductile damage model for anisotropic titanium alloys

The hot-workability of Titanium (Ti) alloys is of current interest to the aerospace industry due to its widespread application in the design of strong and light-weight aircraft structural components and engine parts. Motivated by the need for accurate simulation of large scale plastic deformation in metals that exhibit macroscopic plastic anisotropy, such as Ti, a constitutive model is developed for anisotropic materials undergoing plastic deformation coupled with ductile damage in the form of internal cavitation. The model is developed from a rigorous micromechanical basis, following well-known previous works in the field. The model incorporates the porosity and void aspect ratio as internal damage variables, and seeks to provide a more accurate prediction of damage growth compared to previous existing models. A closed form expression for the macroscopic yield locus is derived using a Hill-Mandel homogenization and limit analysis of a porous representative volume element. Analytical expressions are also developed for the evolution of the internal variables, porosity and void shape. The developed yield criterion is validated by comparison to numerically determined yield loci for specific anisotropic materials, using a numerical limit analysis technique developed herein. The evolution laws for the internal variables are validated by comparison with direct finite element simulations of porous unit cells. Comparison with previously published results in the literature indicates that the new model yields better agreement with the numerically determined yield loci for a wide range of loading paths. Use of the new model in continuum finite element simulations of ductile fracture may be expected to lead to improved predictions for damage evolution and fracture modes in plastically anisotropic materials