The ASTM standard test method based on linear elastic fracture mechanics (standard E-399, 1974) for plane strain fracture toughness of metallic materials requires that the characteristic specimen dimensions (such as the crack size, the size of the uncracked ligament and specimen thickness) be greater than 2.5 x (KIc/σy)2 , where Kic is the mode I fracture toughness in plane strain and ay is the yield strength of the material. Similarly, the standard test method for the elastic-plastic fracture toughness jIc (standard E-813, 1981) requires that the size of the uncracked ligament and the specimen thickness be greater than 25JIC/σy, where JIc is the critical value of the J-integral for fracture initiation.

(a) Noting the relationship between J and K, Eqs. 9.57 and 9.8, derive an expression for the ratio bK/bj for a linear elastic material, where bK /bJ is the uncracked ligament length for bK test specimen and bj is that for a JIC test specimen. σy, E and v, respectively, are yield strength, Young's modulus and Poisson's ratio for the material.

(b) Calculate the ratio bK/bj for a steel for which Kic = 250 MPa ,

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