On the dynamics and the role of imperfections for localization in thermo-viscoplastic materials

We employ an adaptive Chebyshev pseudo-spectral method for the computation of adiabatic shear bands in materials with temperature-dependent viscoplastic materials coupled with heat conduction. The method allows very high resolution of the spatial structure of the band with a relatively small number of computational degrees of freedom. The method is used to study the dynamics of band formation and the spatial structure of the resulting bands with special emphasis on the role of the imperfection. We find that the spatial structure of the band can be characterized by an inner band, in which the field quantities, (e.g. viscoplastic strain or temperature) attain a nearly constant large value, and an outer band connecting the inner band to the undeformed portion of the specimen. The outer band is sensitive to the spatial structure of the imperfection while the inner band is sensitive to the structure of the imperfection during the early stages of severe localization but not during the later stages. The dynamics of shear-band formation during severe localization can be divided into three stages. In the first stage (stage A), the band narrows but the spatial extent of the inner band is sensitive to the imperfection. In the second stage (stage B) the band continues to narrow, but the spatial structure of the inner band is insensitive to the imperfection. A length scale for the smallest width of the temperature band is derived and shown to be in reasonable agreement with the computations. In the third stage (stage C), the band widens as diffusion and elastic effects become important. A residual effect of the imperfection persists in the outer band throughout all three stages.