| Fracture is one of the most common failure modes in engineering materials and structures.A deep understanding of the fracture mechanism of the materials can provide theoretical guidance for the design of engineering materials and structures.In recent years,the phase field fracture method has developed into a powerful numerical tool for simulating crack nucleation,propagation,branching and convergence of cracks.Most of the previous phase field models are based on the classical continuum mechanics theory,which cannot characterize the size effect of fracture behavior.In view of this,phase field models for fracture based on the non-classical continuum mechanics theory(strain gradient elasticity theory and flexoelectric theory)are developed,and the fracture behavior of strain gradient elastic solids and flexoelectric solids under multiphysics loads such as mechanical,electric and themal loads are studied.The main content and conclusions of this thesis are as follows:(1)A novel phase field model for fracture based on the strain gradient elasticity theory is developed.In order to properly characterize the tensile/compressive asymmetric fracture behavior of strain gradient elastic solids,a spectral decomposition method of the strain energy density is proposed.The proposed phase field model can well describe the complex fracture behavior in strain gradient elastic solids and reproduce the toughening effect induced by strain gradient elasticity.(2)A phase field model for electro-mechanical fracture based on the flexoelectric theory is developed,and the permeable and impermeable crack surface boundary conditions are considered.According to Clausius-Duhem inequality,the damage driving force is derived,and a non-associative dissipative frame is introduced to assume the mechanical driving force as the driving force for the crack propagation.In order to properly characterize the asymmetric fracture behavior in flexoelectric solids,the driving force for crack propagation is decomposed.The numerical results reveal that the variation of the fracture loads with the electric fields is influenced by the flexoelectric effect near the crack tip.Specifically,when the flexoelectric effect is relatively small or does not exist,a negative electric field hinders the crack propagation,while a positive electric field promotes the crack propagation;when the flexoelectric effect is significant,both positive and negative electric fields promote the crack propagation,which can explain two inconsistent experimental phenomena.Moreover,the proposed phase field model can also capture the influence of electric field on crack deflection.(3)Applying the proposed phase field model for electro-mechanical fracture,the asymmetric fracture behavior induced by the flexoelectric effect in different poling directions is investigated.The physical mechanism of the asymmetric fracture behavior induced by flexoelectric effect is revealed.When the crack propagation direction is parallel or antiparallel to the poling direction,the flexoelectric effect will induce asymmetric fracture behavior,while when the crack propagation direction is perpendicular to the poling direction,the flexoelectric effect will not cause asymmetric fracture behavior.In addition,the size dependent asymmetric fracture behavior induced by flexoelectric effect is influenced by flexoelectric coefficients and specimen size.(4)A phase field model for thermo-electro-mechanical fracture in flexoeletric solids is developed,in which the crack surface is assumed to be impermeable and adiabatic.According to the Clausius-Duhem inequality,the constitutive relationships and the damage driving force are derived.A non-associative dissipative framework is introduced to assume the mechanical driving force as the driving force for the crack propagation.The numerical results show that the fracture loads under different electric fields are influenced by the temperature near the crack tip.When the temperature near the crack tip is relatively low,the fracture load monotonically decreases with the electric field;when the temperature near the crack tip is relatively high,the frature load varies non-monotonically with the electric field.In addition,the phase field model can well describe the influences of multi-physical field interactions on the crack propagation in flexoelectric solids. |
