Continuum Damage Mechanics (CDM) Based Local Approach to the Sheet-Bulk Metal Formability Prediction

摘要

Since sheet-bulk metal forming processes inherit properties of both sheet and bulk metal forming processes, their analysis requires on one side following certain methods conventionally devised in these process classes' analyses whereas on the other side leaving certain customs out. For instance, inherent anisotropy of the rolled sheet has to be taken into account whereas due to non-vanishing out of plane stress component, analysis with thin shells using the plane stress state assumption is no more applicable. Similarly, methods based on necking instabilities, i.e. forming limit diagrams, which are typically used in sheet metal formability assessment; fall short in sheet-bulk metal formability prediction. In the present study, we propose a local approach to fracture, more specifically a phenomenologically based Lemaitre variant CDM model, devised frequently in bulk metal forming analysis, as an alternative. For this purpose, a combined nonlinear isotropic-kinematic hardening plasticity with Hill'48 type initial anisotropy is fully coupled with isotropic damage. Together with the concept of effective stress and equivalent strain principle, quasi-unilateral damage evolution is used, where the energetic contribution of the compressive stress state to the damage driving force is scaled with a so-called crack closure parameter, 0 ≤ h ≤ 1. The framework devises state coupling between elasticity and damage and kinematic coupling between plasticity and damage which increases the relative effect of h on the eventual damage development. To this end, a direct extension to the finite strains for metal forming analysis is realized using a corotational formulation and the developed framework is implemented as a VUMAT subroutine for ABAQUS Explicit. For evaluation of the predictive capability of the model, teeth forming process results for DC04 reported in [1] are used. Mechanical material characterization studies are realized using a hybrid experimental-numerical procedure. The simulations show that a correct prediction of the zone and time of fracture is possible for the selected process whereas since the teeth formation process is mainly a compressive process, once the quasi-unilateral damage development is not used, i.e. for h = 1, a premature crack prediction is recorded which is not compatible with the experimental findings.