A SEMI ANALYTICAL METHOD TO SOLVE J-INTEGRAL FOR MODE-I CRACK COMPONENTS

The J-integral to characterize the singular level of the stress and strain field at the crack tip is definite and rigorous and is a basic parameter of elastoplastic fracture mechanics. The calculation of J-integral mainly depends on the plastic factor method and the finite element method at present. For theoretical predicting and testing of material fracture toughness, it is important and difficult to obtain analytical expressions about J-integral-load and load-displacement relations of cracked components. The most widely used test for structure integrity evaluation with J-integral is the ductile fracture toughness of type-I cracked specimens. Here, based on the Chen-Cai energy equivalence hypothesis, a unified characterization method of J-integral-load and load-displacement relation is proposed for six Mode-I cracked components which are commonly used in fracture toughness test under the plane strain condition. Then, the undetermined parameters of the engineering semi-analytical formulas of the J-integral-load and the load-displacement relations are obtained by a small amount of finite element analysis. The results show that the J-integral-load and load-displacement relation predicted by the unified semi-analytical formulas are in good agreement with those from finite element method. The engineering semi-analytical J-integral-load formula, which contains the elastic modulus, stress strength coefficient and strain hardening exponent of materials, can be widely adapted for different materials. And the J-integral value corresponding to arbitrary load points can be easily obtained by the formula. The presented novel method is convenient to establish the engineering semi-analytical formulas of J-integral-load and load-displacement relations for various type-I cracked components or specimens.