A Micromechanical Model for the Fiber Bridging of Macro-Cracks in Composite Plates

Abstract

Recent experimental studies on the propagation of transverse cracks in composites have shown that fiber bridging is frequently present, and can be considered as the cause of increased toughness. This paper presents a model that is capable of quantifying this effect and explaining the decrease in the crack growth rate in either a monotonic or a cyclic load profile. Both Modes I and II are considered. The model is based on the elastic loading of a fiber located on the macro-crack face close to the tip and under dominantly plane strain conditions. Two fundamental cases of fiber bridging configurations are distinguished, namely when the fiber-matrix interface is intact and when the fiber-matrix interface has partially failed. Following the single fiber analysis, the model is extended to the case of multiple fibers bridging the faces of the macro-crack. The analysis is for a generally anisotropic material and the fiber lines are at arbitrary angles. Results are presented for the case of an orthotropic material with unidirectional fibers perpendicular to the crack faces. Specifically, the reduction in the stress intensity factor (relative to the nominal value) is investigated for the glass fibers in a glass/epoxy composite system. The effects of fiber debonding and pullout with friction as well as fiber breaking are accounted for in the analysis, and results with respect to a parameter representing the fiber-matrix interface friction are presented. Results are also presented regarding the partial or full fracture of the fiber bridging zone. The model can also be used to analyze the phenomenon of fiber nesting, which is similar to fiber bridging, and occurs with growing delaminations.