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J-shaped stress/strain curves and crack resistance of biological materials

The influence of the stress/strain curve shape on the cracking of a brittle elastic material is analysed in terms of the energy balance theory of fracture mechanics. Both r-shaped and J-shaped elastic curves are investigated. For some cracking tests, for example the trouser tear and lubricated cutting tests, the shape of the stress/strain curve is found to have little effect on the crack extension force; this is determined mainly by the fracture surface energy of the material. However, in other tests such as tension, the shape of the stress/strain curve does influence the fracture stress, but not by a large amount when compared with the effect of reinforcement. Whether an r-shaped or J-shaped curve leads to a higher fracture stress depends on such factors as the fracture energy and the size of the pre-existing crack. It thus appears that no general statement can be made about the effect of the shape of the stress/strain curve upon the crack resistance of materials, contrary to views expressed previously in the literature.