Ductile damage model for metal forming simulations including refined description of void nucleation

Abstract

We address the prediction of ductile damage and material anisotropy accumulated during plastic deformation of metals. A new model of phenomenological metal plasticity is proposed which is suitable for applications involving large deformations of workpiece material. The model takes combined nonlinear isotropic/kinematic hardening, strain-driven damage and rate-dependence of the stress response into account. Within this model, the work hardening and the damage evolution are fully coupled. The description of the kinematics is based on the double multiplicative decomposition of the deformation gradient proposed by Lion. An additional multiplicative decomposition is introduced in order to account for the damage-induced volume increase of the material. The model is formulated in a thermodynamically admissible manner. Within a simple example of the proposed framework, the material porosity is adopted as a rough measure of damage.A new simple void nucleation rule is formulated based on the consideration of various nucleation mechanisms. In particular, this rule is suitable for materials which exhibit a higher void nucleation rate under torsion than in case of tension.The material model is implemented into the FEM code Abaqus and a simulation of a deep drawing process is presented. The robustness of the algorithm and the performance of the formulation is demonstrated.

Modelling of cyclic creep in the finite strain range using a nested split of the deformation gradient

“…The main conclusion of the paper is that the practically important phenomenon of the non-stationary creep can be described using the nested multiplicative split of the deformation gradient. Additional multiplicative decompositions can be introduced to capture the damage-induced porosity [56] and the thermal expansion [34,50] of the material. Moreover, the nested multiplicative split advocated here seems to be a reasonable tool for the construction of a unified model for creep-plasticity interaction.…”

“…For simplicity we assume here that both bulk and shear moduli deteriorate with the same rate. In a more general case one may introduce two different rates[56] or even two different damage variables[62,63].C 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.zamm-journal.org…”

On modelling the constitutive and damage behaviour of highly non-linear bio-composites – Mesh sensitivity of the viscoplastic-damage law computations

“…A great deal of work has been devoted to developing such models in order to combine the constitutive elasto-plastic material behaviour with the progressive stiffness degradation and subsequent fracture due to the nucleation, growth and coalescence of voids/microcracks as well as other damage processes (Zaïri, Naït-Abdelaziz et al 2008 (Basaran and Yan 1998) were the first to correlate these damage processes with entropy production rate in order to introduce damage evolution functions derived from statistical thermodynamic principles. Since then, thermodynamic models have been developed further to describe damage in a range of solids based on physical parameters (Voyiadjis, Shojaei et al 2011, Yao and Basaran 2013, Alfano and Musto 2017), whereas other empirical/phenomenological damage models have also found extensive use (Shutov, Silbermann et al 2015). Voyiadjis et al (Voyiadjis, Shojaei et al 2011) constructed a mathematical framework which incorporates the elastic, plastic, damage as well as recovery/healing components of the uniaxial compression response in shape memory polymers.…”

Efficient time stepping for the multiplicative Maxwell fluid including the Mooney‐Rivlin hyperelasticity

“…42 Further extension of this algorithm to the case of the Yeoh hyperelasticity was presented by Landgraf et al 43 Johlitz et al 9 and Ghobadi et al 8 extended the algorithm to the thermomechanical case. Silbermann et al 44 and Shutov et al 45 used the algorithm to stabilize numerical simulations within a hybrid explicit/implicit procedure for finite-strain plasticity with a nonlinear kinematic hardening. Schüler et al 46 used the algorithm to model the viscoelastic behaviour of a bituminous binding agent.…”