On an Isotropic Damage Mechanics Model for Ductile Materials

A new model for combined elastoplasticity and damage is proposed. The model is based on the maximum dissipation principle and implements a strong coupling between plasticity and damage. First the evolution equations of different kinds of phenomenological damage models for ductile materials are discussed. Nonassociated flow rules violate the irreversibility postulate of Ilyushin, the stability postulate of Drucker and the maximum dissipation principle. Some other models use two independent associated flow rules for plasticity and damage. It will be shown that these models are a special case of maximal dissipative models with a weak coupling of plasticity and damage. A strong coupling can be obtained by using a single, smooth yield surface in the space of dissipative forces. This approach, which has not correctly been implemented before, is used in the new model. Uniaxial tension tests with unloadings have been performed to investigate the damage growth in a high strength steel. A good agreement between the experimental results and the model was obtained using elementary ansatz functions for the free energy and the yield function. Unfortunately, the model makes incorrect predictions for multiaxial loadings. A dependency of the damage term in the yield function on the damage variable is introduced to solve this problem. The modified model fits the experimental data for uniaxial stresses very well and shows a qualitatively correct behavior under multiaxial loadings.