A bi-linear cohesive law-based model for Mode II fracture analysis: Application to ENF test for unidirectional fibrous composites

Abstract The complicated toughening mechanism of Mode II cracking in end notch flexure (ENF) test for fibrous composites prevents the existence of clear crack-tip. Hence the concept of equivalent linear crack length was proposed to avoid detecting the crack-tip in ENF test, which assumes that the increase of compliance due to the development of fracture process zone (FPZ) or crack propagation is attributed to the equivalent elastic crack length giving the same compliance as the one of the actual crack with its FPZ; thus the equivalent crack length can be estimated according to the associated compliance obtained from experiment. The objective of the presented work was to develop an analytical model for the analysis of ENF test specimen without need for crack-tip identification and complicated data reduction. Bilinear cohesive law was employed to model the cohesive force across the potential crack interfaces. Analytical solutions for the governing equation were derived. Furthermore, methods to determine the cohesive parameters, the length of fracture process zone (FPZ), and the energy release rate were developed. The critical loads corresponding to the damage and crack onset can also be estimated by the model. Experimental validation was implemented and a good agreement was achieved between the test results and model predictions. It can be concluded that bilinear cohesive law may achieve a good approximation for the tangential traction-separation constitutive relationship in Mode II fracture; the shear strength of the material can be taken as the critical stress of cracking onset; the energy release rate depends on the initial crack length to some extent, and this effect could be reduced as the length of initial crack increases.