| Adiabatic shear localization at high strain rates is investigated by considering the simple shearing of a heat of a heat conducting thermoviscoplastic material with a gradient-dependent flow stress. Understanding of the thermo-mechanical instability and localization is developed through the classical perturbation analysis, the relative perturbation analysis accounting for non-steadiness, and numerical solutions of the fully nonlinear system of partial differential equations which govern the deformation. Two key parameters, the threshold wavelength representing the shear band width and the maximum growth rate controlling evolution rate of shear banding, are derived, respectively, from the classical perturbation method and relative perturbation method. The two perturbation methods respectively provide instability and localized criteria which are compared. With the two key parameters, the effects of various factors such as the strain hardening, strain rate sensitivity, thermal softening, strain gradient and thermal conductivity on adiabatic shear banding are studied. Combined with the numerical nonlinear study, this study is compared with those of several main investigators in this area. Some contradictions and inconsistencies among the previous are clarified.; As an application of the above study, a simple one dimensional model of the primary shear zone, proposed by Dudzinski and Molinari [1997], is adopted incorporating with the strain gradient theory of thermo-viscoplastic materials to describe the shear localized chip formation. Approximating the one dimensional model with the simple shearing, a dimensionless threshold wavelength is derived via the localization analysis. This wavelength generalizes various effects including the thermal softening, strain and strain rate hardening, heat production, heat conduction and the strain gradient. The numerical simulation of the one dimensional model for various cases indicates that the value of threshold wavelength is an appropriate measure inversely for the severity of localization and proportional to the shear band width. It turns out that the simple shear model is a good approximation for the cutting process as long as the flow normal to the shear zone is slow compared to relative motion between the lower and upper layer of the shear zone or the time considered is short. |
