A comparative study of continuum damage models for crack propagation under gross yielding

In this paper, the problem of fracture initiation in an aluminum alloy thin plate containing a central crack is examined by employing several phenomenological continuum damage mechanics models. These models differ mainly in the selection of the kind of tensorial property the damage variable assumes, the nature of the equivalence postulate between damaged and pseudo undamaged material states, and the way damage evolution laws are formulated. Two formulations of damage effect tensor based on the engineering notation and the normative notation of stress and strain, respectively, are compared. In addition, the hypothesis of strain equivalence is compared to that of stress working equivalence. The error in the assumption of isotropic damage development in the crack tip process zone is also checked against that of anisotropic damage. In the numerical algorithm, both updated Lagrangian formulation and small displacement formulation of material non-linearity only are adopted and compared. The influence of non-proportionality in stress histories present in the crack tip region is accounted for by introducing a dynamic coordinate system of principal damage such that the principal direction of damage rotates in accordance with that of the loading. The calculated fracture initiation loads are finally compared with those determined experimentally.