Dislocations accelerating through the shear-wave speed barrier and effect of the acceleration on the Mach front curvature Surong Huang a , Xanthippi Markenscoff b,⇑ a Dept. of Aeronautics, Xiamen University, Fujian 361005, China b Dept. of Mech and Aerospace Engineering, University of California, San Diego 92093-0411, USA article info Article history: Received 20 October 2010 Accepted 15 March 2011 Available online 19 May 2011 Keywords: Dislocation dynamics Supersonic motion Mach fronts abstract In a transient analysis of a dislocation accelerating through the shear wave speed barrier the stress on the forming Mach front is analyzed, as well as the effect of the acceleration on the curvature of the front from which, inversely, information about the motion may be inferred. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Accelerated dislocation motion plays an important role in high strain rate deformation in metals under shock wave load- ing (e.g. Bringa & Caro, 2005; Holian & Lomdahl, 1998; Meyers et al., 2003), but despite a surge of recent activity (Gumbsch & Gao, 1999; Li & Shi, 2002; Dunham & Archuleta, 2004; Vandersall & Wirth, 2004; Marian & Caro, 2006; Mordehai, Kelson, & Makov, 2006; Nosenko, Zhdanov, & Morfill, 2007; Olmsted, Hector, Curtin, & Clifton, 2005; Sharma & Zhang, 2006), disloca- tion motion crossing the shear wave speed barrier and traveling with supersonic (transonic for edge) speeds (exceeding the shear-wave speed c 2 ) is still not well understood until recently. The classical works of Weertman (1967, 1969) present the analysis of the stress field and the energetics of the steady- state supersonic motion, which concludes that the crossing of the barrier is assumed prohibitive due to the ðc 2 2  _ l 2 ðtÞÞ  1 2 sin- gularity in the steady-state analysis. Different from steady-state analysis, in the transient analysis to the second-order terms that account for the acceleration, the term that yields ðc 2 2  _ l 2 Þ is not zero any longer but depends on the acceleration € lðtÞ at the instant when the velocity is equal to c 2 . The transient analysis here focuses on addressing the effect of dislocation acceleration on the stress at the Mach wave front after crossing the barrier by means of the analysis of a screw/edge dislocation in a general motion x = l(t) evaluated at the instant when the velocity _ lðtÞ equals the shear-wave speed in the presence of acceleration € lðtÞ and after the motion has become supersonic. In a continuum analysis of a Volterra dislocation in general motion the field quantities (stress, strain, velocity) depend on the radiated wavelets from the interval of the dislocation motion that can contribute to the field point. At the transition from subsonic to supersonic, at which transition instant an envelope (Mach cone) starts to form, a pair of complex conjugate roots becomes a double real one, splitting subsequently into two real roots (Markenscoff & Huang, 2008). The asymptotic analysis for the stress on the developing Mach front is performed at this double root (also, Freund, 1972; Huang, 2007; Huang & Markenscoff, 2008). 0020-7225/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijengsci.2011.03.009 ⇑ Corresponding author. E-mail address: xmarkens@ucsd.edu (X. Markenscoff). International Journal of Engineering Science 49 (2011) 1461–1469 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci