×

Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique. (English) Zbl 1197.74088

Summary: We review, unify and extend work pertaining to evaluating mode mixity of interfacial fracture utilizing the virtual crack closure technique (VCCT). From the VCCT, components of the strain energy release rate (SERR) are obtained using the forces and displacements near the crack tip corresponding to the opening and sliding contributions. Unfortunately, these components depend on the crack extension size, \(\Delta \), used in the VCCT. It follows that a mode mixity based upon these components also will depend on the crack extension size. However, the components of the strain energy release rate can be used for determining the complex stress intensity factors (SIFs) and the associated mode mixity. In this study, we show that several-seemingly different-suggested methods presented in the literature used to obtain mode mixity based on the stress intensity factors are indeed identical. We also present an alternative, simpler quadratic equation to this end. Moreover, a \(\Delta \)-independent strain energy release based mode mixity can be defined by introducing a “normalizing length parameter.” We show that when the reference length (used for the SIF-based mode mixity) and the normalizing length (used for \(\Delta \)-independent SERR-based mode mixity) are equal, the two mode mixities are only shifted by a phase angle, depending on the bimaterial parameter \(\varepsilon \).

MSC:

74R10 Brittle fracture
74G70 Stress concentrations, singularities in solid mechanics

Software:

ABAQUS

References:

[1] ABAQUS (2003) Version 6.4, Hibbit, Karlsson, & Sorenson Inc
[7] Cherepanov GP (1979) Mechanics of brittle fracture, Mc-Graw Hill
[30] Rice JR, Suo Z, Wang J-S (1990) Mechanics and thermodynamics of brittle interfacial failure in bimaterial systems, metal-ceramic interfaces. Ruhle M, Evans AG, Ashby MF, Hirth JP (eds). Acta-Scripta Metallurgica Proceedings Series 4, pp 269–294
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.