Study On Fracture Mechanism Of Brittle Material Based On Peridynamics

The fracture of brittle material under loading with a small deformation,and accompany by crack initiation and propagation,the stress-strain curve shows nonlinear segment after the linear,this kind of brittle material is the main object of this research.The facture process of brittle material which is a change from continuous to discontinuous,so this paper will introduce Peridynamics(PD)to research it.Peridynamics is a new type of solid mechanics theory which based on the idea of non-local.PD has an integral form of motion equation,which can be solve the continuous and discontinuous problem without material continuity hypothesis;the PD numerical method has an advantages of meshless without meshing and remeshing like traditional numerical method.The main contents and achievements of this paper are as follows:(1)Construction of the peridynamics model of brittle material,which was composed of basical theory,the constitutive force function and numerical method.The bond-based peridynamics was the basical theory of the peridynamics model,which used “bond” to describe the constitutive relations within the material.According to the linear and nonlinear mechanical behavior of brittle material,introduced a nonlinear damage variable,which divided the break process of bond into three stages: linear elastic deformation,nonlinear damage deformation and break,into the linear constitutive force function of Prototype Microelastic Brittle Material(PMB)to construct a linear and nonlinear form of the constitutive force function of brittle material and its related parameters in the peridynamics model.The cubic-cell integration method(CCI)was the numerical method of this peridynamics model.Through the comparison between the numerical simulation results and experimental results on the facture of rock-like material with defect,the results show that the peridynamics model is feasible.(2)The analysis of microcrack and macrocrack propagation laws in the fracture process of brittle material.The microcrack propagation described a bond deformation process with a large number of potential microcracks initiation and propagation within it,finally the bond broken,and these microcracks formed a macro-defect.Therefore,put forward the microcrack propagation energy criterion by bond’s deformation energy density and damage release energy density to describ the microcrack propagation state of initiation,stable propagation,critical unstable propagation,unstable propagation,healing and macro-defect formation.Though the analysis of the microcrack propagation of a plate with defect,the results show that the microcrack propagation energy criterion sufficiently describe the microcrack propagation.The macrocrack propagation described the process of a number of broken bonds(macro-defects)get to together.The propagation conditions of the mode-I and mixed-mode macrocrack were proposed based on the curve of energy release speed-time,which could be judge the macrocrack propagation state of nucleation,branching and arrest in brittle material.By the analysis of the macrocrack propagation of a plate with defect and sphere,the results show that the macrocrack propagation conditions can be accurately judge for the propagation state of macrocrack.(3)Development and application of fracture simulation software for the brittle material.Based on the peridynamics model and the crack propagation laws,the fracture simulation software for the brittle material was developed.This software was composed of modeling part and solver part,which could build different kinds of structure model,and solve problems under multiple conditions.It was applied to research the laws and characteristics of facture of complex structure,composite material structure and defect structure.In this paper,the peridynamics model,the crack propagation laws and the software can provide a new theoretical analysis method and tool for the fracture analysis and structural optimization design of brittle material.