Maximum-energy-release-rate criterion applied to a tension-compression specimen with crack

Abstract

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...

Strength and Fracture Resistance of Amorphous Diamond‐Like Carbon Films for MEMS

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“…Figure 2.15 -Differences between crack growth in a specimen submitted to a compressive loading (a) and a tensile loading (b). (Whittaker, 1992) Figure 2.16 shows the crack initiation angle predicted by the c 0 -criterion, G-criterion and S-criterion (Wu, 1978), as well as experimental data obtained by Vallejo, 1987. As can be seen, both G 0 -criterion and G-criterion's results seem to be consistent with the experimental data for the cracks studied.…”

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