Arbitrarily Oriented Cracks in a Layered Media

Abstract

Cracks occurring at arbitrary orientations in lamellar composites are studied. The associated boundary value problem is formulated in terms of dual integral equations in which the kernels are found in series form. This series representation of the kernels is shown to converge quite rapidly. Variation of the stress intensity factors with the constituent elastic moduli is presented, and a comparison of calculated values with a Mohr's circle approximation of the stress intensity factors at arbitrary orientations is made. This comparison results in the conclusion that the Mohr's circle approximation is accurate as long as the crack tip is far enough from the bimaterial interface.

Fracture initiation in a lamellar alloy

“…3 are assumed to be perfectly bonded. Perfect bonding requires continuity of displacements and tractions across the interfaces and allows the procedure developed in [16] to be utilized in order to determine the Airy stress function associated with a dislocation lying within a sandwiched layer. For a dislocation with Burgers vector of magnitude bx0 in the x 0 direction this Airy stress function is …”

“…In addition to each stress term having a 1/r character, with r measured from the referencing coordinate frame, the difference in material constants also positively effects convergence [16].…”

“…Numerically this work differs from these previous studies in that the Green's function K(x, 17;) was represented by a series. This series converges rapidly [16], thus allowing the integral equation to be solved readily.…”

“…Algebraically the relationship between the applied stress and the dislocation intensity factor ~d can be written as OyA=(2)(r+sq)d). (16) In this equation rn is given by (4), r is the ductile phase's flow stress, and s is the slope of a plot such as Fig. 5.…”

“…In (19)a is once again the order of the stress singularily present at the slip band's tips. When this expression for q~a is utilized in (16), it can be rewritten as…”