A theoretical bound for the modulus of the generalized stress intensity factor at an interface crack tip related to the method of caustics
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Date
1989-09
Authors
Ioakimidis, Nikolaos
Journal Title
Journal ISSN
Volume Title
Publisher
Kluwer Academic Publishers
Abstract
A theoretical bound is derived for the modulus (or absolute value) of the complex generalized stress intensity factor at a crack tip of an interface crack lying between two isotropic elastic half-planes in plane isotropic elasticity. This bound can be experimentally computed by employing the experimental method of caustics, which is a popular and efficient method for the computation of stress intensity factors at crack tips, but in the present case concerning an interface crack two experiments with appropriately selected overall mechanical–optical constants in the method of caustics are required. The derivation of the formula for the present bound is based on the use of the first complex potential of Kolosov–Muskhelishvili (in its expressions for both half-planes) together with the use of the classical maximum modulus principle in complex analysis. Moreover, the same formula for the bound includes two bielastic constants depending on four elastic constants, more explicitly, on the shear moduli and on the Muskhelishvili constants of the two isotropic elastic half-planes. Evidently, in the special case of just one isotropic elastic medium with a straight crack, the present bound reduces to the simpler bound valid in this special case.