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]:

{Mm)

£p = Aexp(-^^-) RT

sinh(^—)

s

and for evolution of the internal variable:

(5-39)

s = {hc

(1~)

Sign( --)}£P s

(5-40)

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:

exp(—)

є

A

(5-41)

RT

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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