Is Intersonic Dislocation Motion Possible? Singularity Analysis for an Edge Dislocation Accelerating through the Shear Wave Speed Barrier S. Huang & X. Markenscoff Received: 28 August 2007 / Accepted: 7 January 2008 / Published online: 5 March 2008 # Society for Experimental Mechanics 2008 Abstract The analysis of Markenscoff and Clifton (J Mech Phys Solids 29:253–262, 1981) for a generally nonuni- formly moving Volterra edge dislocation, valid both for subsonic and intersonic/supersonic motion, is focused on the instant in which the dislocation accelerates through the shear-wave speed barrier. Mathematically, the roots (of the argument of the step function f x ðÞ¼ t  hx ðÞ rb that defines the intervals of the path of the motion that contribute to the field point) change from a pair of complex conjugate to a double real, splitting into two real ones, and, at the instant of the transition to intersonic motion, the stress analysis is performed at this double root maximum of f x ðÞ. The stress at the forming Mach front contains a log ξξ* j j ξξ* j j 1 2 singularity in the coefficient of the delta function, which can be removed by a ramp-core (delta sequence rather than delta function) model of the core displacement. Keywords Dislocation dynamics . Supersonic motion . Intersonic motion . Edge Volterra dislocation . Accelerating motion Introduction The question of whether supersonic/intersonic dislocation motion is possible has not been totally resolved since it was posed in the 1940’ s and 50’ s. Eshelby [4] stated that supersonic motion is a “formal possibility”, and without giving complete references to the subject, we refer to the next major work by Weertman [18, 19] who provided analysis for supersonic velocities and gave expressions for the energy needed to sustain such motion. By computing the energy release rate for a motion jumping from rest to supersonic speed Clifton and Markenscoff [3] argued that supersonic motion cannot be sustained for too long, since the stress would exceed the strength of the material bonds. From the lattice dynamics approach, dislocation motion has been studied extensively and the review article of Weert- man and Weertman [20] contains over 150 references. The discrete lattice is a dispersive medium and the full spectrum of phase velocities exists, so that the velocity of the dislocation is always supersonic relatively to some lattice phase velocity at some particular wave-length, and subsonic relatively to others. Our analysis is based on an elastic continuum, which is not dispersive, and follows the work of Markenscoff and Clifton [14] for a generally accelerating edge dislocation. Atomistic simulations have shown that supersonic motion is possible if generated as such [7], while atomistic simulation results by Olmsted et al. [17] showed that a dislocation can accelerate through the shear- wave speed barrier, but splits into partials afterwards. In the analysis presented here we study the stress at the formation of the Mach cone as the Volterra edge dislocation accelerates through the shear-wave speed barrier into the intersonic region. The analysis is based on the solution for the stress given by Markenscoff and Clifton [14] for an arbitrarily moving edge dislocation. This solution is valid both for subsonic and intersonic/supersonic motion, but the physical difference arises due to the difference of the roots of the function that defines the intervals of the emitted wavelets that contribute to the front. This analysis follows the one due to a screw dislocation motion (Markenscoff and Huang submitted for publication) as it crosses the shear- Experimental Mechanics (2009) 49:219–224 DOI 10.1007/s11340-008-9122-8 S. Huang : X. Markenscoff (*) Department of Mechanical and Aerospace Engineering, University of California, La Jolla, San Diego, CA 92093-0411, USA e-mail: xmarkens@ucsd.edu