Semi-analytical Method To Solve Elastoplastic Problems Of Mode-? Crack Based On Energy Equivalence Principle

The failure modes of engineering structures can be classified into three types: wear,corrosion and fracture.In general,most of the occurrence of fracture is sudden.For large engineering structures,once fracture occurs,the consequences are often disastrous.So,how to prevent fracture accidents economically and efficiently has become an important subject about equipment stability and personal safety.Therefore,the in-depth study of fracture mechanics has an important practical value for engineering application and social economy.Due to the complexity of engineering structure in geometry,material properties and stress state,the fracture analysis of engineering structures must rely on the corresponding specimen configuration.So far,the most widely used fracture test is the fracture toughness test of typeI crack components.Stress intensity factor K is an important parameter of linear elastic fracture mechanics and it has been widely applied to test fatigue-crack-propagation law and fracture toughness of materials and to evaluate structural integrity in the past half-century.Important task of fracture mechanics is to present the expressions of stress intensity factor K and the relationships between the compliance C and crack length for all kinds of cracked components,so as to facilitate structural integrity evaluation and fracture toughness tests.However,the expressions of K factor and compliance C of general cracked specimens are very different from each other,and the number of formula parameters of K factor and the compliance C for some specimens are much more than six,which is not convenient for application.The acquisition of K factor and the compliance C expressions for nonstandard samples mainly adopts the regression and fitting methods,which is quite complicated.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.In view of the existing problems and deficiencies in fracture toughness test,herein,the stress intensity factor,compliance and J-integral formula of different type-I cracks are studied.(1)In this paper,a unified model with only 2 or 3 parameters to predict K factor and compliance C for nine components with Mode-? crack is proposed based on the Chen-Cai energy equivalence method.Verifications show that the unified model of K factor and compliance C is in good agreement with the formulas in references and the results from finite element analysis.The establishment of the unified model is simple and effective,and it is convenient for engineering application.Therefore,the novel method is convenient to obtain the semi-analytical expressions of K factor and C for cracked specimens.(2)In this article,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-? 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 relations 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.(3)Herein,based on Chen-Cai energy equivalence principle,the derivation of stress intensity factor,compliance and J-integral formula of a thin-walled circular tube three-dimensional specimen is completed by using the PLT experimental device,and the undetermined parameters in the formula are determined by finite element method.