Crack deflection in laminates with graded stiffness—lessons from biology

Abstract

A crack propagating through a laminate can cause severe structural failure, which may be avoided by deflecting or arresting the crack before it deepens. Inspired by the biology of the scorpion exoskeleton, this study shows how crack deflection can be achieved by gradually varying the stiffness and thickness of the laminate layers. A new generalized multi-layer, multi-material analytical model is proposed, using linear elastic fracture mechanics. The condition for deflection is modeled by comparing the applied stress causing a cohesive failure, resulting in crack propagation, to that causing an adhesive failure, resulting in delamination between layers. We show that a crack propagating in a direction of progressively decreasing elastic moduli is likely to deflect sooner than when the moduli are uniform or increasing. The model is applied to the scorpion cuticle, the laminated structure of which is composed of layers of helical units (Bouligands) with inward decreasing moduli and thickness, interleaved with stiff unidirectional fibrous layers (interlayers). The decreasing moduli act to deflect cracks, whereas the stiff interlayers serve as crack arrestors, making the cuticle less vulnerable to external defects induced by its exposure to harsh living conditions. These concepts may be applied in the design of synthetic laminated structures to improve their damage tolerance and resilience.