COMPUTATIONAL WELDING MECHANICS
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]:
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{Mm) |
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£p = Aexp(-^^-) RT |
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sinh(^—) s and for evolution of the internal variable: |
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(5-39) |
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s = {hc |
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(1~) |
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Sign( --)}£P s |
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(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(—)
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є A |
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(5-41) |
RT
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Note that A , h() |
exponents m and 1 and dimensionless
activation volume c, generally, are temperature and microstructure dependent material properties.
