Fracture Mechanics of Periodic Multilayers With Different Microstructural Scales and Moduli Contrast

Abstract

In a recent investigation of microstructural effects in finite periodic multilayers, we have shown that under Mode I loading, the crack-opening displacement approaches that of the same crack in an equivalent homogenized material as the microstructure comprised of alternating stiff and soft layers becomes increasingly finer. In contrast, Mode I stress intensity factor asymptotically converges to values that depend on the stiffness of the cracked layer. Preliminary calculation of Mode I strain energy release rate as a function of the microstructural refinement suggested that this may be a better fracture mechanics parameter for assessing fracture toughness of periodic layered media. Herein, we extend the above investigation by considering both Mode I and II loading to study the effect of layer modulus ratio on fracture mechanics parameters as a function of microstructural refinement. The previously introduced concept of partial homogenization of the microstructure sufficiently far from the crack is also pursued in order to gauge its efficiency in correctly capturing fracture mechanics parameters with a minimum of computational effort. The fracture mechanics parameters are shown to be influenced by the local microstructure to an extent that depends on the layer modulus mismatch. An accurate calculation of these parameters requires the retention of several layers adjacent to the affected cracked layer whose number depends on the modulus mismatch and loading mode.