Research On Fracture Behaviors Of Piezoelectric Solids Via The Phase Field Method

With the development of science and technology,various smart and advanced materials have emerged to satisfy the requirement in the information technology industry.Piezoelectric materials are widely used in various fields such as energy harvesters,sensors and memories owing to their desirable electro-mechanical coupling effect.Piezoelectric materials are brittle and have poor fracture toughness,and some defects are generated during production and processing.Due to the existence of these characteristics,piezoelectric materials are prone to fail,when they are subjected to the thermal,electrical and mechanical loadings during the service process.Therefore,it is of significance to investigate the fracture behaviors of piezoelectric materials,and it is also one of the hot spots in the community of smart materials.Over the past decades,researches on fracture behaviors of piezoelectric materials have drawn considerable attentions,and fruitful achievements have been achieved by scholars.However,the studies on crack extension of piezoelectric materials are limited,and there are still various unsolved problems.Within the framework of the phase field approach,crack propagations of the piezoelectric solids are systematically investigated with the help of the finite element method and isogeometric analysis in this dissertation,and the following studies have been carried out:(1)The fatigue fracture problems of piezoelectric materials are investigated by the phase field approach.A cumulative history variable is introduced to quantify the degradation of the fracture toughness under cyclic loadings.The proposed model accounts for three representative electrical boundary conditions on crack surfaces describing the fatigue fracture behaviors in different physical situations.The staggered scheme is extended to address the fatigue fracture problems in the context of electro-elasticity.The present algorithm overcomes the convergence problems inherited to the monolithic approach and shows higher accuracy with lower computational effort in comparison to the single-pass staggered scheme.Systematic numerical simulations are carried out to discuss the effect of the electrical boundary condition,external electrical field,and the geometry of the crack tip on the fatigue fracture behaviors.The relationship between the fatigue lifetimes and the amplitude of the displacement load has been presented.(2)By the phase field method,the fracture behaviors of transversely isotropic piezoelectric materials with an anisotropic fracture toughness have been investigated.A robust and efficient staggered scheme,which is implemented in the finite element software ABAQUS,is adopted to deal with the corresponding fracture problems.Numerical simulations are carried out to discuss the validity of the present algorithm and investigate the effects of the anisotropic fracture toughness,poling direction and external electrical field on the fracture behaviors of the piezoelectric materials.The differences in characterizing the fracture behaviors between the transversely isotropic electro-elastic model and the isotropic counterpart have been systematically discussed.By means of the nonlinear regression method,a phenomenological model is developed to predict the fracture load.(3)The fracture behaviors of piezoelectric materials with the thermal effect have been investigated within the framework of thermo-electro-elasticity.A residual controlled staggered algorithm,which is employed to deal with the corresponding multi-physics problems,is proposed.Numerical calculations are performed to model the mode-I and mixed-mode fractures,and the variations of the electrical field,temperature evolution and mechanical deformation during the fracture process are quantificationally characterized.The thermal effect on the fracture behavior of piezoelectric materials has been also discussed.(4)Based on the fourth-order phase field theory,a higher-order fracture phase field model for piezoelectric materials is developed to study the fracture mechanics behaviors of piezoelectric materials.A more accurate description of the phase field evolution is achieved by introducing a high-order term of the phase field variable into the fracture energy functional.The governing equations with high-order gradient terms are solved within the framework of the isogeometric analysis,and the differences in fracture behaviors between the fourth-order fracture model and the second-order one are compared.In addition,the effects of the electric boundary conditions and external electric fields on the fracture behaviors of piezoelectric materials are systematically investigated.In this dissertation,some phase field models for the brittle fracture and fatigue fracture of piezoelectric materials are developed to clarify the fracture behaviors of piezoelectric materials within the framework of electro-elasticity.This dissertation is of significance to fracture mechanics of piezoelectric solids and may be helpful in practical engineering.