Thermoviscoplastic shear instability and higher order strain gradients

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We examine the role of higher order strain gradients in the instability and localization of deformation during the shearing of a thermoviscoplastic material. We take the point of view that thermal softening is the leading mechanism of instability. A gradient dependent yield condition is assumed in order to stabilize the behavior within the softening regime. It turns out that the critical conditions for both instability and localization are different than those obtained in the absence of higher order strain gradients. Moreover, the thermomechanical constitutive parameters of strain hardening, strain rate sensitivity and thermal softening do not suffice to define the stability regime. In particular, a specific value of strain dependent on the aforementioned thermomechanical coefficients and the control parameter is required in order that loss of stability to occur. Such loss of stability may occur either "locally" through the growth of localized non-uniformities or "globally" throughout the material strip in a catastrophic manner. © 1991.

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International Journal of Engineering Science