A Dislocation Pile-Up Computation for Adiabatic Shear Banding
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A Dislocation Pile-Up Computation for Adiabatic Shear Banding Stephen D. Antolovich1 and Ronald W. Armstrong2 1
Schools of Materials Science and Mechanical Engineering, Georgia Tech, Atlanta, GA,303320245 USA & School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920 USA 2 Center for Energetic Concepts Development, University of Maryland, College Park, MD 20742 USA. ABSTRACT A model is presented for computing the temperature increase associated with the formation of an adiabatic shear band. The hypothesis is that the heating is supplied by the difference in energy of a pile-up of n dislocations and the energy of n individual dislocations. The heating is assumed to occur within a volume determined by the grain size (i.e. slip band length) and an effective thermal length determined by the dislocation velocity. The model predicts increases in temperature with increasing shear modulus (G), increasing numbers of piled up dislocations (n), increasing Burgers vector (b), increased grain size (d), and increased dislocation velocity (vd). Increasing temperature is also predicted with decreasing heat capacity (c*) and thermal diffusivity () as would be expected. The model was applied to low carbon steel for which considerable data are available. Application to low carbon steel gives a temperature increase of about 1400K. The implied result that untempered martensite should be observed after adiabatic shear banding is in agreement with examples cited in the literature. Further investigation into the dynamics of pile-up release and the associated heat transfer mechanisms is discussed.
Definition of Symbols = Effective applied shear stress b = Dislocation Burgers vector n = Number of dislocations v = Dislocation velocity K = Thermal conductivity L = Length of the slip band d = Grain size = Effective thermal length ks = Hall-Petch microstructural stress intensity parameter = Thermal conductivity c* = Specific heat at constant volume = Poisson’s ratio xi = Representative spacing of dislocations at the tip of the pile-up = Elastic energy of n discrete dislocations = Elastic energy of n piled up dislocations G = Shear modulus Q = Energy available for localized adiabatic heating T = Temperature increase due to slip band collapse. = Thermal diffusivity t = Time 2x = Width of heated region around slip band ys = Yield strenght of mild steel kph = Phonon component of the thermal conductivity
INTRODUCTION Adiabatic shear banding refers in a formal sense to the case in which a localized shear band forms with no transfer of heat to or from the external environment (i.e. . The behavior is favored in metals under conditions of low heat capacity and low thermal conductivity when deformed at high loading rates and/or low temperatures. The mechanical work associated with formation of the shear band is mainly transformed into heat and thereby manifested by an increase in temperature. Unlike the Portevin-Le Chatelier (PLC) effect, which is self-exhausting, the formation of adiabatic shear
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