Rate dependent isotropic plasticity (General case)

For steel at temperatures from 700 to 1300 °С we adopt a rate dependent plasticity model using the constitutive functions proposed by Brown [38] for the effective plastic strain rate was adopted in [31]:


£p = Aexp(-^^-) RT



and for evolution of the internal variable:


s = {hc


Sign( --)}£P s


where the temperature dependent term in (5-39), A exp(-AG/RT), is the reference ( for a given temperature) strain rate, m is a rate sensitivity, the hyperbolic sine accounts for the contribution of stress to thermal activated slip, h() is the reference hardening parameter

and s’ is the saturation value of deformation resistance s:






Note that A , h()

exponents m and 1 and dimensionless

activation volume c, generally, are temperature and microstructure dependent material properties.

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