Plasticity Driven Damage and Void Growth

Sammanfattning: Plasticity induced damage evolution is considered using a thermodynamical approach. Different postulates on how to include the effects of damage in the constitutive equations have been studied. The results reveal that a mapping, similar to that of the stress, of both the kinematic and isotropic hardening variables is to be preferred. The undesired property that, irrespectively of the postulate employed, the elastic strain will not equal zero as failure takes place, is addressed and a simple modification of the postulate of strain equivalence that does not lead to this property is proposed. From the results it is also concluded that the postulate of (complementary) energy equivalence have some undesirable properties. A yield criterion for ductile porous materials is proposed based on the lower-bound solution for a cylindrical void model. Comparing the criterion with the Gurson yield criterion and cell model calculations for an axisymmetric cylinder with a spherical void shows good agreement. A constitutive model for porous materials is formulated using the proposed yield function. The corresponding thermodynamic formulation facilitates a natural modeling of damage, in which both the growth and the shrinkage of voids are allowed in the thermodynamic process. Both the elastic and the plastic properties in the model are dependent on the void-volume fraction. The model was found to fit naturally into the thermodynamical framework.