The constitutive model due to Kocks, Mecking and Estrin, the so-called One Internal Variable Model, which was developed to describe quasi-static stress-strain behaviour of metallic materials, has been extended to provide modular modelling of the material behaviour under strain rates relevant for automotive applications (10-3/s to 250/s). The extended description applies to particle strengthened, fine grained and lamellar microstructures and also accounts for the effect of deformation induced heat release. Strain rate dependence of the yield stress in ferritic steels has been included. A first application of the extended model to the response to dynamic loading of a deep drawing quality (DC06) and a microalloyed steel grade (HX420LAD) is presented. Other possibilities of modular modelling mentioned are the prediction of work hardening behaviour at high strains, extension of model to cyclic behaviour and the prediction of deformation instabilities.
Basics of the ModelA constitutive relation between the true stress a and the true strain 8 for the plastic region of a stress-strain curve can be represented through the so-called kinetic equation, in which E denotes the plastic strain rate and S is a state variable that is to represent the microstructural state of the material; T denotes the absolute temperature. This quantity, in tum, varies with the plastic strain and may also be strain rate and temperature dependent: account for various microstructural mechanisms contributing to strain hardening in metallic materials. Model calculations performed on this basis and verified through comparison with experimental data are presented in this paper, with special emphasis on high-speed deformation behaviour of two ferritic steel grades.(2)(1)
The one internal variable model by Kocks, Mecking and Estrin has been applied for the description of the hot tensile and creep behaviour under constant loading conditions of Alloy 800H, a carbide precipitation strengthened high temperature alloy. The model was extended by incorporating an expression for a mean free path of mobile dislocations which depends on the kinetics of the precipitation and ripening process of the secondary carbides. Microscopy and mechanical data for three different heats of Alloy 800H at 900°C were evaluated to enable comparison between calculations using the extended model and experimental data. Difficulties were caused by the complex precipitation behaviour of the alloy in which both larger carbides of type M23C6 and smaller ones of type M(C,N) are formed in the investigated range of temperature. Although the microstructural data available is not sufficient for a reliable quantitative description of the evolution with time of the average carbide spacing a qualitative agreement between calculations and mechanical data gives a preliminary verification of the developed extended model.
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