The title problem is studied by using the explicit asymptotic analysis presented in the accompanying paper. The asymptotic analysis indicates that the very basic problem is a semi-infinite L-shaped crack governed by a single integral equation. This equation is discretized to a system of complex algebraic equations and solved by a standard HARWELL subroutine. It is found that the maximum-energyrelease-rate criterion has two branches, one for tensile loads and one for compressive loads. Our numerical results indicate that the maximum energy-release rate is always associated with maximum K 1 and K 2 = 0, where K1 and K 2 are the stress-intensity factors at the fractured tip. Thus, the well-known K-G relation valid for crack-parallel propagation also holds for non-crack-parallel propagations. This conclusion is, however, purely numerical.
IntroductionThe fracture of a straight crack under nonsymmetric loading conditions was first studied by Erdogan and Sih [1]. Their analysis is now commonly referred to as the maximum-stress criterion. In a discussion of [1], McClintock [2] applied the criterion to an elliptical model and showed that the slit and elliptical models do not agree. This discrepancy was later discussed by Cotterell [3]. The implication of including more terms in the near-tip solution on the maximum-stress criterion was discussed by Williams and Ewing [4], Finnie and Saith [5], and Ewing and Williams [6]. Sih (cf.[7]) recently proposed a new approach called the strain-energy-density criterion. This criterion is often referred to as the S-criterion.Both the maximum-stress and S-criteria base their predictions on the near-tip behavior that exists prior to the onset of crack propagation. An alternative approach, consistent with Griffith's energy-release-rate concept [8,9], would be to determine the energy-release rate as a function of the direction of propagation, and then determine the critical direction by maximizing the energy-release rate. This approach shall be referred to as the maximum-energy-release-rate criterion and was, * Supported by U.S. Army Research Office-Durham under Grant DAAG-29-76-G-0272. Journal of Elasticity 8 (1978) 235-257 236 Chien H. Wu in fact, first mentioned by Erdogan and Sih in [1]. To carry out the required calculations, the elasticity solution of a branched crack must first be obtained. In addition to the analytic difficulties inherent in a branched-crack problem, the energy-release-rate calculation further requires that the branch-crack ratio must tend to zero. This limiting process, while can be worked toward our advantage, has been the origin of various difficulties in a number of recent attempts.The first attempt appears to have been given by Hussian, Pu and Underwood [10].* The limiting process was improperly applied and their "exact" solution is incorrect. Palaniswamy and Knauss [11] introduced a modified (non-singular) problem to represent the true (singular) problem, and a Fourier-expansion procedure was then applied. The general validity of their modification, howeve...