Crack-bridging in a unidirectionally fibre-reinforced plate

Abstract

The mechanics of a matrix crack situated in a unidirectional fibre-reinforced elastic plate where the fibres have experienced debonding over an identifiable zone is examined. This results in a condition referred to as crack-bridging or flaw-bridging; the mechanics of the matrix crack is influenced by the kinematic constraints exerted by the bridging actions of the fibres. The problem is of interest when examining the role of delaminations in ideal fibre-reinforced solids in the presence of fibre continuity. The boundary-integral equation is applied to determine the influence of the elastic stiffness of the bridging fibres on the stress-intensity factor at the tip of the crack, which governs the energy release for the extension of the crack. The paper presents the computational approach and provides examples that clearly demonstrate the significant role of the bridging action and the fibre elasticity in suppressing crack extension in a self-similar fashion.

Bridged defects in continuously and discretely reinforced solids

“…Analogous results for the case of the bridged plane crack are also presented in [28]. The assumption of a constant length of a ligament zone is a limitation of the above modelling approach.…”

“…Note that the parameter V f appearing in (28) accounts for the fact that effective fibre elasticity in the fibrous spheroidal inclusion region is volume averaged. The absence of the factor V f would imply that the entire fibrous inclusion region is composed of material with elasticity E f .…”

“…The absence of the factor V f would imply that the entire fibrous inclusion region is composed of material with elasticity E f . In (28), n z is the direction cosine of the normal to the spheroidal interface ∂B or q = ρ, with…”

“…The problem of a bridged penny-shaped crack in a transversely isotropic elastic solid [8,9] is relevant to examining the bridging action across penny-shaped flaws in unidirectionally fibre-reinforced solids. The general approach can also be used to examine bridged Griffith cracks and edge cracks in composite plates [28] and locally loaded bridged external cracks in composite solids [29]. The bridging action across defects located in composite materials is amenable to mathematical modelling only in special situations where the external loading of the unidirectionally reinforced composite does not induce a state of compression in the bridging fibre region.…”

Stress analysis of composites with interfacial bridged cracks and damaged zones

“…In all these papers interaction between crack faces was not assumed nor considered. Only few papers have been directed to analysis of bridged cracks in finite size structures, two-dimensional problems were considered in [13][14][15], IOP Publishing doi:10.1088/1742-6596/2231/1/012021 2 axisymmetric problems were considered for bridged penny-shaped cracks in homogeneous [16] and transversely isotropic [17] elastic materials. The main objective of this paper is the stress analysis of composite structures with bridged interfacial cracks by the direct boundary integral equations method in axisymmetric formulation.…”