Anisotropic yield functions in a co-rotating reference frame

In metal forming simulations large deformations are often treated based on objective formulations. Large rotations are accounted for by rotating the stress tensor or approximating the rotation by some integration rule for the rate of rotation. For isotropic material behavior, this is easily done. For anisotropic material behavior however, not only the stresses, but also the relation between stress rate and strain rate must be updated. In this case it is easier to take a co-rotating reference frame and apply the constitutive relations on a strain measure that is neutralized for rigid body translations and rotations. This paper presents an algorithm that is based on the latter idea. The algorithm directly uses the increments in the deformation gradient, avoiding as much as possible to take time derivatives that should then be integrated subsequently. The algorithm is applied to a constitutive model including an initial anisotropic yield function and isotropic and kinematic hardening. The kinematic hardening makes use of a maximal back stress surface [1] to account for behavior observed in cyclic loading

The implementation of the vegter yield criterion and a physically based hardening rule in finite elements

A new material description for sheet metal forming using Finite Elements has been developed. The description consists of a yield criterion and a hardening rule. In contrast to most former criteria the new criterion is based on multi-axial stress states. The yield criterion is extended with a physically based hardening rule, in which the flow stress depends on the strain and strain rate. A Limiting Dome Height test is used to examine the material description

Characterisation and modelling of the plastic material behaviour and its application in sheet metal forming simulation

The application of simulation models in sheet metal forming in automotive industry has proven to be beneficial to reduce tool costs in the designing stage and for optimising current processes. Moreover, it is a promising tool for a material supplier to optimise material choice and development for both its final application and its forming capacity. The present practice requires a high predictive value of these simulations. The material models in these simulation models need to be developed sufficiently to meet the requirement of the predictions. For the determination of parameters for the material models, mechanical tests at different strain paths are necessary 1. Usually, the material models implemented in the simulation models are not able to describe the plastic material behaviour during monotonic strain paths sufficiently accurate 2. This is true for the strain hardening model, the influence of strain rate and the description of the yield locus in these models. A first stage is to implement the improved material models which describe this single strain path behaviour in a better way. In this work, different yield criteria, a hardening model and their comparison to experiments are described extensively. The improved material model has been validated initially on forming limit curves which are determined experimentally with Nakazima strips. These results will be compared with predictions using Marciniak-Kuczinsky-analysis with both the new material model and the conventional material model. Finally, the validation on real pressed products will be shown by comparing simulation results using different material models with the experimental data. The next challenge is the description of the material after a change of strain path. Experimental evidence given here shows that this behaviour cannot be treated using the classical approach of an equivalent strain as the only history variable