Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks

The framework of fracture mechanics analysis for interface cracks as outlined by Willis (1971) is recast into a form resembling the customary framework for cracks in homogeneous materials. Based on the complex-valued “stress concentration vector” introduced by Willis, a new definition of real-valued stress intensity factors is introduced. The definition is an extension to that for cracks in homogeneous materials and reduces to the one given recently by Rice for isotropic interface cracks. In terms of the new stress intensity factors, tractions ahead of the crack and the relative crack face displacements given by Willis are rewritten into real-form expressions. The energy release rate obtained by Willis is also expressed into a real form in terms of the stress intensity factors. The validity of using the stress intensity factors as parameters controlling fracture is discussed along the line advanced by Rice (1988).

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Energy-Release Rate and Crack Kinking Under Combined Loading

Journal of Applied Mechanics ◽

10.1115/1.3157666 ◽

1981 ◽

Vol 48 (3) ◽

pp. 520-524 ◽

Cited By ~ 109

Author(s):

K. Hayashi ◽

S. Nemat-Nasser

Keyword(s):

Stress Intensity ◽

Quadratic Form ◽

Energy Release Rate ◽

Energy Release ◽

Release Rate ◽

Stress Intensity Factors ◽

Continuous Distribution ◽

Combined Loading ◽

Intensity Factors ◽

Kink Angle

Based on the maximum energy-release-rate criterion, kinking from a straight crack is investigated under the plane strain condition. Solutions are obtained by the method that models a kink as a continuous distribution of edge dislocations. The energy-release rate is expressed as a quadratic form of the stress-intensity factors that exist prior to the onset of kinking, and the coefficients of this quadratic form are tabulated for various values of the kink angle. The examination of the results shows that Irwin’s formula for the energy-release rate remains valid for any kink angle provided that the stress-intensity factors in the formula are taken equal to those existing at the tip of a vanishingly small kink.

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Kinking of a Crack Out of an Interface

Journal of Applied Mechanics ◽

10.1115/1.3176078 ◽

1989 ◽

Vol 56 (2) ◽

pp. 270-278 ◽

Cited By ~ 496

Author(s):

Ming-Yuan He ◽

John W. Hutchinson

Keyword(s):

Stress Intensity ◽

Energy Release Rate ◽

Energy Release ◽

Release Rate ◽

Intensity Factors ◽

Elastic Solids ◽

Kinked Crack ◽

Compliant Material ◽

Stiff Material ◽

Plane Strain Crack

Kinking of a plane strain crack out of the interface between two dissimilar isotropic elastic solids is analyzed. The focus is on the initiation of kinking and thus the segment of the crack leaving the interface is imagined to be short compared to the segment in the interface. Accordingly, the analysis provides the stress intensity factors and energy release rate of the kinked crack in terms of the corresponding quantities for the interface crack prior to kinking. Roughly speaking, the energy release rate is enhanced if the crack heads into the more compliant material and is diminished if it kinks into the stiff material. The results suggest a tendency for a crack to be trapped in the interface irrespective of the loading when the compliant material is tough and the stiff material is at least as tough as the interface.

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