Local damage models are known to produce pathological mesh dependent results. Regularization techniques are therefore mandatory if local damage models are used for academic research or industrial applications. The viscoplastic framework can be used for regularization of local damage models. Despite of the easy implementation of viscoplasticity, this method of regularization did not gain much popularity in comparison to the non-local or gradient damage models. This work is an effort to further explore viscoplastic regularization for quasi-static problems. The focus of this work is on ductile materials. Two different types of strain rate hardening models i.e. the Power law (with a multiplicative strain rate part) and the simplified Bergström van Liempt (with an additive strain rate part) models are used in this study. The modified Lemaitre's anisotropic damage model with a strain rate dependency was used in this study. It was found that the primary viscoplastic length scale is a function of the hardening and softening (damage) parameters and does not depend upon the prescribed strain rate whereas the secondary length scale is a function of the strain rate. As damage grows, the effective regularization length gradually decreases. When the effective regularization length gets shorter than the element length numerical results become mesh dependent again. This loss of objectivity can not be solved but the effect can be minimized by selecting a very fine mesh or by prescribing high deformation velocities.

The Lemaitre's continuum damage model is well known in the field of damage mechanics. The anisotropic damage model given by Lemaitre is relatively simple, applicable to nonproportional loads and uses only four damage parameters. The hypothesis of strain equivalence is used to map the effective stress to the nominal stress. Both the isotropic and anisotropic damage models from Lemaitre are implemented in an in-house implicit finite element code. The damage model is coupled with an elasto-plastic material model using anisotropic plasticity (Hill-48 yield criterion) and strain-rate dependent isotropic hardening. The Lemaitre continuum damage model is based on the small strain assumption; therefore, the model is implemented in an incremental co-rotational framework to make it applicable for large strains. The damage dissipation potential was slightly adapted to incorporate a different damage evolution behavior under compression and tension. A tensile test and a low-cycle fatigue test were used to determine the damage parameters. The damage evolution was modified to incorporate strain rate sensitivity by making two of the damage parameters a function of strain rate. The model is applied to predict failure in a cross-die deep drawing process, which is well known for having a wide variety of strains and strain path changes. The failure predictions obtained from the anisotropic damage models are in good agreement with the experimental results, whereas the predictions obtained from the isotropic damage model are slightly conservative. The anisotropic damage model predicts the crack direction more accurately compared to the predictions based on principal stress directions using the isotropic damage model. The set of damage parameters, determined in a uniaxial condition, gives a good failure prediction under other triaxiality conditions.

Plasticity-induced damage development in metals is anisotropic by nature. The anisotropy in damage is driven by two different phenomena: anisotropic deformation state i.e. load-induced anisotropic damage (LIAD) and anisotropic microstructure i.e. material-induced anisotropic damage (MIAD). The contribution of second-phase particles can be anisotropic in terms of shape as well as distribution. Most of the continuum anisotropic damage models mimic the phenomenon of LIAD only. Not much attention has been paid to MIAD. This work shows the existence of MIAD in a (pre-production) grade of dual-phase steel (DP600). The aim is to see the influence of MIAD on post-localization deformation behavior and final failure mode. The deformation in this material is almost isotropic up to localization but the post-localization deformation and final failure mode is different when loaded in 0 and 90 to rolling direction. Tensile specimens were deformed up to final failure. A few specimens were stopped just before the final failure. Scanning electron microscopic analysis was carried out to study martensite morphology and damage in these specimens. The martensite morphology showed anisotropy in shape and orientation in the undeformed specimens. Significant MIAD was observed in the deformed tensile specimens due to the anisotropic martensite morphology. MIAD explains direction-dependent post-localization deformation, final failure mode, and formability of this material. Lemaitre's anisotropic damage model is modified to account for MIAD in a phenomenological manner. The MIAD parameters were determined from tensile tests carried out in 0 , 45 , and 90 to the rolling direction.

Abstract. Local damage models are known to produce pathological mesh dependence in finite element simulations. The solution is to either use a regularization technique or to adopt a non-local damage model. Viscoplasticity is one technique which can regularize the mesh dependence of local damage model by incorporating a physical phenomenon in the constitutive model i.e. rate effects. A detailed numerical study of viscoplastic regularization is carried out in this work. Two case studies were considered i.e. a bar with shear loading and a sheet metal under tensile loading. The influence of hardening / softening parameters, prescribed deformation rate and mesh size on the regularization was studied. It was found that the primary viscoplastic length scale is a function of hardening and softening parameters but does not depend upon the deformation rate. Mesh dependency appeared at higher damage values. This mesh dependence can be reduced by mesh refinement in the localized region and also by increasing the deformation rates. The viscoplastic regularization was successfully used with a local anisotropic damage model to predict failure in a cross die drawing process with the actual physical process parameters.

The accuracy of material models can have a large impact on the overall accuracy of material forming simulations in general and sheet forming simulations in particular. For large strain plastic deformations, the material model usually consists of a yield function and a hardening relation, optionally including the influence of temperature and strain rate. In large-scale simulations it is favourable to keep the model as simple as possible. The ‘allowable’ error in a material model should be in balance with other errors, like the discretisation error and errors in contact and friction modelling. The required accuracy depends on the application and the goal of the analysis. In many occasions, strain rate and temperature dependency can be ignored, but for warm forming this is clearly not the case. Furthermore, numerical simulation of the onset of necking requires a much better material model than needed for the calculation of the global deformation field before necking.