Study Of Material Fracture Behavior Based On J-integral And Configurational Forces Theory

The traditional continuum mechanics which is rooted on deformational forces system mainly deals with the problems of the spacial movement and deformation of continuum. Recently, a new branch of continuum mechanics, configurational force which is also called material space mechanics, is developed to represent the evolution of material structures and the motion of defects. The present thesis primarily aims at carrying out the study of configurational forces theory in the framework of thermodynamics, and on this basis the fracture problems are investigated by combining configurational forces approach and the deformational forces system. This not only provides a fresh look and method onto the classical fracture mechanics, but also deepens the understanding on fracture problems. The main ideas, methods and conclusions are summarized as following:In Chapter 1, the methods dealing with fracture problems are reviewed, including the classical fracture mechanics theory characterized by singular field theory and contour integrals, configurational forces approach to fracture mechanics and cohesive zone model.In Chapter 2, starting from the deformational forces system, the fracture problem of materials with the incremental plasticity response is investigated with emphasis on the calculation of the energy dissipation and the evaluation of crack growth resistance during crack propagation. For the elastic-plastic body containing sharp crack, the total energy dissipation consists of the energy dissipation in plastic zone and that concentrated at the crack tip. Using local steady-state condition of crack propagation, crack tip dissipation can be reformulated as the form of J teipp-integral which is the value of J ep-integral evaluated along the infinite small contour circling the crack tip. Compared with Rice's J -integral, J ep-integral has the following particularities: the energy-momentum tensor in J ep-integral is defined by the free energy density rather than stress working density; J^ep-integral is path-dependent no matter incremental plasticity or deformation plasticity; J_farss^ep -integral,the value of J^ep-integral evaluated along the far boundary contour under the global steady-state condition of crack propagation, can be rewritten as the sum of J^tipep-integral and the plastic dissipation, which indicates that J_far^ep-integral can be taken as a candidate to evaluate crack growth resistance due to the reasonable physical meaning. Both the J_far^ep-integral crack growth resistance and energy dissipation rate resistance are evaluated theoretically and numerically. Simulation results show that J_far^ep-integral resistance increases with the crack growth, whereas energy dissipation rate resistance decreases. When the steady-state condition is reached approximately the two resistances lie in the same level. At last, the crack propagation is simulated by using Gurson model. The effects of material hardening level, the void volume fraction and the yield strain on fracture energy and crack growth resistances are discussed and the numerical results demonstrate that fracture energy is stress-triaxiality-dependent instead of a material constant.In Chapter 3, the concepts of configurational forces and migrating control volume are introduced and the basic equations of configurational forces are established for thermomechanical and electro-mechanical loading using Gurtin's ideas. The working expended on migrating control volume consists of not only deformation working but also configurational working which accounts for the addition and deletion of material particles through the boundary of the migrating control volume. The exchange of material observer is given. The balance equations of configurational forces and moment of multi-physical fields are established by using the basic principle that the total working on migrating control volume holds invariant under arbitrary translation and rigid rotation of material observer. Eshelby relation relating deformational forces and configurational forces is identified by combining the first thermodynamic law and the requirement that configurational working is independent of the tangential component of evolution velocity of the boundary of the migrating control volume. The configurational heating of thermomechanical process can be determined from the second thermodynamic law.In Chapter 4, the configurational forces are used to investigate the fracture problems of thermoelastic and electroelastic materials. Energy dissipation concentrated at the crack tip is derived from the generalized mechanical version of the second law of thermodynamics applicable to migrating control volume. Theoretical derivation shows that the negative projection of the internal configurational force concentrated at the crack tip along the direction of crack propagation plays the role of energy release rate no matter thermomechanical process or electro-mechanical processe. This indicates that the internal concentrated configurational force acts to govern crack propagation and its working is converted into irreversible energy dissipation. Furthermore, the inertia part of the concentrated configurational force at the crack tip is determined from the generalized kinetic energy theorem. Further, the internal configurational force concentrated at the crack tip can be obtained by substituting the inertia part of the configurational force into the configurational force balance.In addition to singular field theory, cohesive zone model is also widely used to study the fracture problems of materials and components. In Chapter 5, the concept of interfacial deformation gradient is introduced and the traction and separation displacement vectors of material space are constructed by using the basic ideas of configurational forces. On this basis, the irreversible cohesive zone model of material space is developed. The cohesive law not only meets the requirement of objectivity principle but also predicts the path-dependent cohesive energy. The discrete form of balance equation of the continuum containing cohesive zone are derived using variational principle and the finite element solution is implemented by coding user element subroutine (UEL) of the cohesive zone model in the commercial software ABAQUS. At last, the interfacial crack propagation of double cantilever beam (DCB) is simulated, and the effects of interfacial parameters and loading configuration on the loading capacity of DCB specimen are discussed.