Research Of Several Typical Fracture Mechanics Parameter Analysis Methods At Macro And Micro Scales

Fracture mechanics is a new subject of solid mechanics,which was constructed and developed based on the summary of catastrophic fracture accidents in real life.Among them,the continuum fracture mechanics based on macro scale has a very rigorous and complete theoretical system,including various fracture criteria and methods,such as stress intensity factor,strain energy release rate,J-integral,cohesive zone model and so on.In these fracture studies,the solution of criterion parameters plays an important role.For the linear elastic fracture problem,the complex factors such as thermal load,material interface and interface crack make it difficult to solve the stress intensity factor,so it is necessary to carry out in-depth theoretical research.With the gradual reduction of the research scale,the nonlinear effect caused by the internal structural defects will become more and more obvious.Thus,the study of nonlinear fracture behavior is particularly important.When the size of the material is further reduced to tens of nanometers,the material nonlinearity will lead to the complete failure of the linear elastic hypothesis,and the atomic dispersion near the end of the crack or notch will make the macro continuum hypothesis no longer effective.Therefore,it is significant to study the lower limit of continuum fracture theory on the nano scale.Based on the above background,this paper has carried out a series of studies from the following four perspectives:Firstly,a domian independent interaction integral method is established for the thermal fracture problem of interface cracks in inhomogeneous linear elastic bodies with complex material interfaces.Through theoretical derivation,a new auxiliary field of interfacial thermal fracture problem is obtained,and the mathematical relationship between the interaction integral and stress intensity factor is given.This method realizes the separation and extraction of mixed mode stress intensity factors in the thermal fracture problem of interfacial cracks,and simplifies the domain integral solution with complex interfaces.In this paper,the numerical calculation of the interaction integral is realized through the extended finite element method,and the effectiveness and region independence of this method are verified.Then,combined with molecular statics simulation,the J-integral is extended to the nanoscale.Through the mesh reconstruction of the atomic model,this paper solves the problem that it is difficult to calculate the atomic displacement gradient.Considering the influence of the long-range force between atoms on both sides of the crack surface at the nanoscale,the line integral along the crack surface is calculated in this paper.Then,taking the cracked graphene nanoribbon as an example,this paper verifies the effectiveness and conservation of the atomic J-integral through a series of numerical examples.The influence of the geometric nonlinearity of the crack tip on the integral conservation at the nano scale is discussesd by introducing the Green strain.The results show that the atomic J-integral is effective at all scales,which breaks through the lower limit of the scale of nonlinear fracture theory.Thirdly,this paper studies the parameter determination and scale effect of the cohesive zone model at the nano scale.Taking the bilinear cohesive zone model as an example,the parameters of the cohesive zone model for nonlinear fracture problem are determined by introducing the uniaxial tensile molecular simulation results of graphene nanoribbons with cracks.Then,the scale effect of cohesive zone model parameters at the nano scale is studied.The results show that the parameter based on the larger size model may no longer be applicable to the smaller size model.By considering the nano scale material nonlinear effect and brittle fracture mechanism,this paper proposes a microscopic method to determine the cohesive zone model parameters,and proves that this method has better applicability at the nanoscale.Further,this paper studies the failure of the cohesive zone model itself at the nanoscale and explores its lower limit of dimension.Finally,based on the previous three chapters about the fracture of macro and micro cracked bodies,this paper further studies the strength failure of non-cracked bodies under the nonlinear assumption.By introducing the molecular statics experiment of single-layer graphene nanoribbons,the lower limit of the strength criterion and J-integral criterion under the continuum assumption at the nanoscale is determined.This paper defines the characteristic length scale parametersΛ_S,Λ_NL andΛ_J to describe the breakdown of continuum fracture mechanics criteria at the nanoscale,and to reveal the failure causes,which provides a clear idea for studying the applicability of the continuum fracture criteria at the nanoscale.By using the energy release rate method based on atomic mechanics,this paper calculates the change of the potential energy caused by the fracture of the first atomic bond at the end of the material defect,so as to describe the nonlinear elastic fracture controlled by the atomic bond.The results show that the atomic energy release rate method can characterize the nonlinear fracture behavior of cracked and non-cracked bodies at the same time.This is a unified fracture criterion suitable for all sizes and types of defects.