Development And Application Of Phase Field Method Towards Complex Fracture Behaviors

In modern society,fracture problem is one of the main issues that puzzle the safe use of advanced materials and structural systems,and therefore the study of fracture behavior of materials has great theoretical and practical value.Throughout the research status at home and abroad,the mechanical models for studying the fracture behavior of materials can be grouped into two categories: discrete crack models based on fracture mechanics and continuous damage models based on continuum mechanics.However,both types of methods have significant deficiencies.The phase field method has received extensive attention in the field of fracture mechanics because it does not require materials to contain initial cracks and does not need to introduce crack initiation criteria.It can continuously characterize the whole process from crack initiation to crack propagation to final failure.Although the phase field method has shown its superiority in more and more fracture mechanics problems,there are still obvious deficiencies due to short development history.This thesis will carry out a series of studies to improve phase field method aimed at overcoming its shortcomings.The first chapter mainly introduces the research background,purpose and significance of this thesis.The classical methods for studying the fracture behavior of materials,i.e.fracture mechanics and continuum damage mechanics and the corresponding computational fracture mechanics methods are reviewed.The inadequacies of these methods in studying the complex fracture mechanism are pointed out.Next,the origin of phase field method and its advantages and disadvantages are compared with the above two methods.The research status of phase field method is expounded from two aspects of crack resistance and crack driving force.Finally,the overall research framework of this paper is proposed.The second chapter firstly sorts out the phase field method governing equation and the corresponding finite element discrete format.Then,models with complex material properties and geometric configurations are often difficult to perform code verification due to lack of analytical solutions.In view of this situation,the second chapter introduces the code verification method-the Method of Manufactured Solutions in fluid mechanics to solid mechanics,and verifies the correctness of the phase field method finite element code.Finally,by comparing with the classical gradient damage model,the advantages ofthe phase field method in the field of fracture research are further highlighted.In the third chapter,the research on the deficiency of the traditional phase field method in the second chapter to characterize the hybrid fracture problem is carried out.The traditional phase field method only considers mode ? fracture energy.For the materials of which mode ? and mode ? fracture energy are of huge difference,and the standard phase field method cannot accurately characterize the crack propagation path under the mixed loading.Inspired by the linear fracture criterion based on the critical energy release rate in the fracture mechanics,a power-law based modified phase field method considering the critical energy release rates of mode ? and mode ? is proposed.Firstly,the method is able to predict the complex fracture phenomenon,that is secondary crack leads to final failure of rock with inclined crack under compression loading,which validates the effectiveness of the proposed method.Then,based on the shear plate test,the effects of material parameters and energy split methods on the mixed fracture behavior of the material are investigated.The results show that the current method has unique advantages for simulating the mixed crack propagation of different materials.The above chapters mainly focus on the study of elastic materials.The fourth chapter studies the accelerated fracture behavior of viscoelastic materials in complex environments by introducing viscous crack driving force within phase field method.In this paper,the governing equations of the viscoelastic phase field method are derived based on micro force balance equation.The corresponding residual vector and Jacobian matrix in the finite element analysis are given.Numerical analysis based on classical viscoelastic tests such as stress relaxation,creep,cyclic loading and different strain rates loading tests as well as mode ? and mixed crack propagation show that the proposed viscous crack driving force can effectively characterize the accelerated crack propagation of viscoelastic materials.The consistency between numerical crack path and experimental crack path for mixed mode fracture indicates that the current method can be very effective for studying the fracture behavior of viscoelastic materials.So far,all research has been conducted on homogeneous materials.In the fifth chapter,a micro damage model is proposed by combing the viscoelastic phase field method and the representative volume element.The complex fracture behavior of the polymer bonded particulate composite is studied from the microscopic view.Firstly,the effects of microstructural features such as particulate size and particulate volume fraction on the fracture behavior of composites were investigated.Next,the effects of strainrates loading and viscous crack driving force on the fracture behavior of the material were studied.Finally,the fracture mechanics behavior of these materials under triaxial compression load is analyzed.The numerical results obtained are consistent with the results in the literature.The sixth chapter studies the complex fracture behavior of the elastic inhomogeneous material-human proximal humerus from the macroscopic scale.Within the framework of traditional phase field theory,a power relationship between bone density and fracture energy is proposed.A mesh convergence analysis was first performed to determine a reasonable mesh size.Next,the effects of length scale and spatial variation of fracture energy on bone fracture behavior were studied.The obtained numerical results are quantitatively and qualitatively consistent with the experimental results,which proves that the phase field method considering non-uniform fracture energy can effectively predict the complex fracture behavior of the humerus bone.Moreover,the numerical study proved the inference in the experiment for the first time,that is,the crack initiates at the trabecular bone inside the human tibia and propagates towards cortical shell on the surface of bone.