THE 2-DIMENSIONAL STRUCTURE OF DYNAMIC BOUNDARY-LAYERS AND SHEAR BANDS IN THERMOVISCOPLASTIC SOLIDS

A general boundary layer theory for thermoviscoplastic solids which ac counts for inertia; rate sensitivity, hardening,;thermal coupling, hea t convection and conduction, and thermal softening is developed. In ma ny applications of interest, the boundary layer equations can be consi derably simplified by recourse to similarity methods, which facilitate s the determination of steady-state and transient fully non-linear two -dimensional solutions. A simple analysis of the asymptotic behavior o f the steady-state solutions leads to a classification of stable and u nstable regimes. Under adiabatic conditions, the resulting material st ability criterion coincides with that previously derived by Molinari a nd Clifton [(1987) Analytical characterization of shear localization i n thermoviscoplastic solids. J. Appl. Mech. 54, 806-812] by a quasi-st atic, one-dimensional analysis. The transition from initially stable t o unstable behavior can also be conveniently described by similarity m ethods. This provides a powerful semi-analytical tool for the interpre tation of impact tests exhibiting dynamic shear bands, and For the cha racterization of the two-dimensional structure of such bands. It follo ws from the theory that, if the velocity of the impactor is held stead y, the leading tip of the sheer band propagates at a constant speed. T his shear band tip speed follows readily from the theory as a function of the impact velocity and material parameters. The two-dimensional v elocity, stress, temperature and plastic work fields attendant to the propagating shear band are also determined.