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Pergamon J. Mech. Phys. Solids, Vol. 44, No. 8, pp. 1353-1370, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved PI1 SOO22-5096(%)00043-9 0022-5096/96 $15.00+0.00 ON A DYNAMICALLY ACCELERATING DUGDALE-ZONE IN ELASTIC AND VISCOELASTIC MATERIAL JAY R. WALTON Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A. (Received 8 November 1995) ABSTRACT A closed form solution and numerical simulation arepresented for a dynamically accelerating, semi-infinite, anti-plane shear crack with a Dugdale-zone in an Achenbach-Chao linear viscoelastic solid in the limiting case of a vanishing equilibrium shear modulus. The solution is valid for arbitrary forward crack motion at speeds below the glassy shear wave speed. Motivated by previous experimental observations, special attention in the numerical simulation is given to the case of constant speed for the material crack-tip, which is defined to be the trailing edge of the Dugdale-zone. Even for this special case, the motion of the mathematical crack-tip, defined to be the leading edge of the Dugdale-zone at which the stress intensity factor cancellation condition is applied, is non-steady, necessitating the full generality of previously developed dynamically accelerating crack solutions. Comparison with results for elastic material is made and implications are drawn on the use of a critical crack opening displacement fracture criterion. Copyright 0 1996 Elsevier Science Ltd Keywords : A. dynamic fracture, A. cohesive zone, B. elastic material, B. viscoelastic material. 1. INTRODUCTION It is now generally accepted [See, e.g., Schapery, (1975) and Walton, (1987)] that for cracks in viscoelastic material, a fracture criterion that is based upon the singular stress solution will not fully reflect the viscoelastic properties of the material. This is true both for quasi-static as well as dynamic crack analyses. The most common method of eliminating the stress singularity is through the introduction of a cohesive zone behind the crack-tip, which is usually modeled either as a Dugdale-zone or Barenblatt-zone. &tlund and Nilsson (1993) give an excellent account of these issues in the context of elastic material. Dynamic, anti-plane shear, accelerating, semi-infinite crack analyses incorporating a Dugdale-zone for elastic material have been given by Achenbach (1970) and Glennie and Willis (1971). In both of these papers, certain approximations within the Dugdale- zone were introduced in order to simplify the mathematical complications. In this paper, an exact analysis is carried out for the corresponding crack problem in the context of a linear viscoelastic material, the Achenbach-Chao approximation to a Maxwell fluid. This model is chosen out of mathematical convenience, since it permits the use of the dynamic, accelerating crack solution recently derived for this material model by Bourne and Walton (1993). Nevertheless, it is reasonable to expect that 1353