Fracture Analysis For Heterogeneous Materials By Boundary Element Method

In order to improve specific strength and modulus of traditional materials,more and more researchers pay attention to added reinforced materials into traditional materials.The formed heterogeneous materials have been applied in aviation,automobile,bridge fields,etc.Heterogeneous materials are considered to be one of the advanced materials,whose physical properties change along a specific direction.Composite materials,one of the heterogeneous materials,including carbon fiber-reinforced composite materials and silicon carbide particle-reinforced copper matrix composite materials,have been widely used in industrial field.It should be noted that mechanical properties of composite structures are closely dependent on their fabrication process.In addition,poor service environments,including fatigue,corrosion,high temperature,etc.will greatly reduce their service life.To improve their mechanical properties,reduce the accidents,more and more scholars have payed attention to analyze fracture problem by employing numerical methods,which will lay a solid foundation for their structural optimization design.Numerical methods commonly used in engineering fields include finite element method(FEM),boundary element method(BEM),etc.For the crack problem,BEM will reduce the dimension of unsolved equations by establishing the integral equation at the boundary surfaces.Compared with FEM,BEM will solve the structural crack with fewer elements,and improve the calculation efficiency to a great extent.In this paper,crack propagations in homogeneous and heterogeneous materials were both considered by employing BEM.The main research work was as follows:The formula of direct boundary element theory was deduced.The unknown quantities on boundary were obtained by discretization of the established boundary integral equations.Boundary element model,which was respectively discretized by constant elements,linear elements or secondary elements,were established.Furthermore,elastic plane problem of the heterogeneous materials were also discussed.Stress distribution of the plate with a central hole was acquired.To validate the proposed method,numerical results by FEM were also indicated for a comparison.On this basis,stress intensity factors of a 3D model with central crack and the unilateral crack were both analyzed.In addition,the service life of a fixture was predicted by using the BEM.For composite materials,the interfacial damage between inclusions and matrix materials should be pay more attentions.Therefore,interfacial surface extrapolation method was proposed to explore fracture problem of two-phase heterogeneous materials.Stress intensity factor of heterogeneous materials with full consideration of crack length and elastic constants were considered,and the numerical results shown good consistency to T.M.results.Microscopic modeling of continuous fiber-reinforced composites was executed by subdomain boundary element theory based on the representative volume element.Elastic modulus and Poisson's ratio with respective to fiber volume fraction were also investigated and compared with numerical results acquired by Mori-Tanaka theory and FEM.It can be found that with the increase of fiber content,the elastic modulus of fiber-reinforced composites is also increasing.Poissonis is the opposite.It is verified that the BEM coupled with homogenization theory can be effectively to predict effective properties of composites.On this basis,microscopic stress distributions with consideration of crack at interface between inclusion and matrix materials were fully analyzed.It is found that with the increase of weekly crack,the anti-pull performance of the material is decreasing.The stress concentration coefficient of the first main stress near the crack tip increases and decreases.