Rate Sensitive Continuum Damage Models and Mesh Dependence in Finite Element Analyses

Paper i proceeding, 2013

The experiences from the orthogonal machining simulations show that the Johnson Cook dynamic failure model appears to exhibit a significant element size dependence.Such pathological mesh dependence is a direct consequence of the use of damage models unless some type of egularization is introduced. The current contribution investigates the extent of possible pathological mesh dependence,and a comparison of the resulting behavior in the case of the Johnson Cook (JC) plasticity model combined with two types of damage evolutions. Both the plasticity and the damage models considered in the formulation are rate dependent and the damage evolutions for both models are defined as a post-processing of the effective stress response. The results show that both damage models, with a realistic representation of the pearlite material properties, exhibit a similar extent of mesh dependence and that viscous regularization effects do not suffice in the current investigation. As a remedy for the observed mesh sensitivity, it is proposed to use a continuum-damage approach for the modeling of continuous deformation behavior up to the critical point along the stress-strain curve where discontinuous bifurcation occurs. Whenever a critical stress-strain state has been diagnosed, a Cohesive Zone (CZ) is established to allow for objective fracture energy release as the stress is degraded in the CZ. The formulation is made in a completely general kinematical context thus allowing for large deformations, central in machining applications. To characterize the homogenized continuous/discontinuous macro-behavior, a discontinuous enhancement of XFEM--type is proposed at a sub-scale based on homogenization theory. It appears that the associated local momentum balance is manifested by the condition for traction continuity across the discontinuity surface. Thereby, the formulation generically contains e.g. the classical condition for diagnosing discontinuous bifurcation. In the corresponding FE-application, localized CZ damage is kinematically realized as an element embedded discontinuity, which is introduced elementwise, thereby facilitating the model implementation in standard FE-packages. Both pre-peak continuum behavior and post-peak CZ behavior are modeled using the concept of (visco)-plasticity coupled to damage, representing distributed and localized damage evolutions by separate constitutive modeling considerations, respectively. To arrive at a computationally attractive formulation, both the pre- and post--peak damage evolutions are defined as a post-processing of the effective stress response. In the considered numerical examples of typical shear and tensile deformation the new continuous/discontinuous ductile fracture modeling exhibits no significant element size dependence.