Study Of The Fracture Behavior Of Functionally Graded Materials With Phase Field Method

Taking great advantages of relieving thermal stress and improving bonding strength,FGMs which realizes smooth transition between materials with different properties has been widely used in aerospace,biomedicine,nuclear reactor and many other fields.However,most of the existing researches on FGMs are limited to the analysis of material distribution function or stress intensity factor at the crack tip,and the related fracture tests are rare,which leads to the failure law not fully discussed.Therefore,it is of great significance to study the fracture mechanism and fracture characteristics of FGMs by numerical simulations for improving the overall mechanical properties of structures.In this paper,static and dynamic phase field models are founded to simulate the fracture behaviors of FGMs under mechanical and thermal loading conditions.The derivation of the coupling equations and the completion of finite element method are given as well.The accuracy of phase field model is verified by four point bending test,shear test and quenching test.On these bases,the fracture response of FGMs under multiple loading conditions is further discussed.The main contents and relevant conclusions are as follows:1.The quasi-static fracture model is used to study the crack growth path under mode I,II and biaxial loads.The effects of gradient,material structure and crack inclination on the initial crack deflection angle are discussed.The results show that the crack always tends to deflect to the side with smaller elastic modulus,and the larger material gradient and loading ratio usually correspond to the larger initial crack deflection angle.2.The crack growth path and crack growth velocity under dynamic load are studied by dynamic fracture model.The results show that the crack growth velocity in FGMs will not increase indefinitely,but will be limited by the bifurcation of the main crack,and its upper limit is about 0.6 times of Rayleigh wave velocity.In addition,the branch crack has no symmetry as well as the crack growth velocity,and the region with higher elastic modulus has higher velocity.3.The evolution of microcrack and the path of crack growth under thermal shock are studied by the thermo-mechanical coupled fracture model.The effects of material distribution,thermal loading conditions,temperature difference and preset crack density on the thermal crack morphology are discussed.On the whole,the fracture of FGMs and the quenching test of ceramic have similar characteristics,that is,there is a transition from uniform damage to periodic damage in the early stage of thermal shock.After that,the crack generates vertically to the material surface and distributes alternately in length.Generally speaking,the crack is the result of temperature gradient and structural deformation.