On the simulation of plastic forming under consideration of thermal effects

Abstract

A new model of finite strain thermo-viscoplasticity is constructed. The model takes a combined nonlinear isotropic-kinematic hardening into account in a thermodynamically consistent manner. The yield stress and some of the hardening parameters are temperature dependent. The equation of the heat conduction is obtained directly using the energy balance. In particular, the thermoelastic effect and the mechanical dissipation are obtained in a natural way. Unlike the classical Taylor-Quinney rule, which yields in the case of a strong kinematic hardening inconsistent simulation results, the developed model enables physically reasonable computations. In order to capture the energy storage associated with the inelastic deformation more precisely, an additional component of the free energy -the so-called detached free energy -is introduced. Using this constitutive assumption, a better fitting of the model prediction concerning the real temperature evolution can be achieved.Keywords: thermo-plasticity / viscoplasticity / large strains / kinematic hardening / detached free energy / Ein neues Modell der Thermoviskoplastizität bei finiten Deformationen wurde konstruiert. Mit dem Modell wird eine kombinierte nichtlineare isotrop-kinematische Verfestigung auf eine thermodynamisch konsistente Weise berücksichtigt. Die Fließspannung und einige der Verfestigungsparameter sind temperaturabhängig. Die Wärmeleitungsgleichung wurde direkt aus der Energiebilanz abgeleitet. Dabei wurden der thermoelastische Effekt und die mechanische Dissipation auf einem natürlichen Wege erhalten. Im Gegensatz zum klassischen Taylor-Quinney-Ansatz, der bei großer kinematischer Verfestigung auf inkonsistente Simulationsergebnisse führt, werden mit dem entwickelten Materialmodell physikalisch sinnvolle Berechnungen ermöglicht. Mit dem Ziel, die Energiespeicherung infolge inelastischer Vorgänge noch genauer zu erfassen, wurde eine zusätzliche Komponente der freien Energie eingeführt -die sogenannte abgetrennte freie Energie. Mit dieser konstitutiven Annahme kann eine bessere Anpassung der Modellvorhersage bezüglich der tatsächlichen Temperaturentwicklung erreicht werden.

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

“…A similar decomposition is obtained for some models of thermoplasticity due to the similar description of kinematics(Lion , 2000;Shutov and Ihlemann , 2011).…”

“…8 More precisely, ψ kin + ψ iso is a part of the free energy stored in the defects of the crystal structure. Remaining parts of the "defect energy" which are detached from any hardening mechanism (Shutov and Ihlemann , 2011) are neglected here. An accurate description of the energy storage becomes especially important within thermoplasticity with nonlinear kinematic hardening (Canadija and Brnic , 2004;Canadija and Mosler , 2011;Shutov and Ihlemann , 2011). Here, constant parameters BRR ≥ 0 and SRR ≥ 0 stand for "bulk reduction rate" and "shear reduction rate" respectively.…”

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.…”

“…Using the procedure which is similar to that described in[50], the model can be extended to the general thermo-mechanical case in a straightforward manner. The most difficult part of the generalization is that some of the material parameters are strongly temperature dependent.www.zamm-journal.org C 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim…”

On the thermodynamics of pseudo-elastic material models which reproduce the M ullins effect

“…The resulting stress-strain curves are equal for both models and are shown inFig. 2.5 The consideration of such stored energy component becomes important if the equation of heat conduction is derived directly from the energy balance(Shutov and Ihlemann, 2011).…”