A simple finite strain non-linear visco-plastic model for thermoplastics and its application to the simulation of incremental cold forming of polyvinylchloride (PVC)

This paper introduces a finite strain extension of a non-linear visco-plastic material model, previously proposed by the authors, and its application to the finite element simulation of incremental cold forming processes of thermoplastics, demonstrated on PVC. Preserving the original structure of the model, its finite strain extension does not rely on any presumed kinematic split, either multiplicative or additive, among elastic and inelastic parts. It uses a systematic replacement of the strain and stress tensors and their rates by their respective spatial counterparts. A deviatoric Oldroyd rate is introduced to preserve the objectivity as well as the deviatoricity of the integration of the rate forms of deviatoric tensors. To cope with the incremental loading paths within the process, where through-thickness variations of the variables gain importance, the material model is posed in 3D formulation. The developed model is implemented as an ^ABAQUS®/UMAT subroutine and used in the simulations following parameter identification studies. The numerical results are compared with analogous experimental ones to evaluate the performance of the material model where PVC sheets of three different thicknesses are formed incrementally with path controlled tool force monitoring. The investigations have the following consequences: the deformation-limited homogeneous stress-strain portion at uni-axial tensile tests, which is generally used in parameter identification of the constitutive model, is not able to reflect the post necking regime and its extrapolation ends up with a stiffer response with much less retained strains. Once a semi-inverse parameter identification is followed by taking into account the overall experimental outputs, one ends up with a considerable improvement in the tool force, geometry and the wall thickness predictions. Nevertheless, these improvements are inversely proportional with the sheet thickness where the local indentation effects (strains and stresses) become larger.