Fracture Analysis Of Functionally Graded Piezoelectric Materials With Arbitrary Properties

Functionally graded piezoelectric materials(FGPM)as a new inhomogeneous composite material,materials properties continuously change in the gradient direction.Existing experiments show that cracks or defects will occur in the manufacturing and use of FGPM,making them produce stress and electric field concentration phenomenon,and may lead to material damage or even failure.Therefore,it is of great significance to analyze the fracture of FGPM.In this paper,the fracture problems of FGPM with arbitrary properties are studied.The paper first studies the static fracture mechanics of FGPM with mode I crack and arbitrary properties.A piecewise exponential model is proposed,in the piecewise exponential model,the FGPM is divided into several layers along the thickness direction,it is assumed that the material properties of each layer change in the form of an exponential function.Then,using the methods of integral transformation and residue theorem,the singular integral equations are derived to obtain the stress intensity factor at the crack tip,and the effects of the number of layers,crack length and distribution form of material properties on the stress intensity factor are analyzed.The results show that the convergent solution of the stress intensity factor can be obtained when the number of layers is large enough;it is limited to solve the fracture problem of FGPM by assuming to assume the material properties as a special function.Secondly,the static fracture of FGPM with arbitrary direction crack and arbitrary properties is studied.Firstly,the crack problem is divided into two parts by the superposition principle.Secondly,using the piecewise exponential model to solve the two solutions respectively.Finally,the singular integral equations are derived according to the boundary conditions,the stress intensity factor at the crack tip is obtained,and the correctness of piecewise exponential model to solve this fracture problem is verified,the influence of crack angle and other parameters on the stress intensity factor at the crack tip is analyzed.The results show that the crack angle is an important factor influencing the stress intensity factor.Finally,the dynamic fracture mechanics of FGPM with mode I crack and arbitrary properties is analyzed.Firstly,this dynamic fracture problem is transformed into a static fracture problem in the Laplace domain by using Laplace transform.Then,the piecewise exponential model is used to solve the problem and the stress intensity factor is obtained.Finally,the stress intensity factor in the time domain is obtained by Laplace inversion technique,the effects of inhomogeneous parameters and crack length on the stress intensity factor were analyzed.The results show that the influence of inhomogeneous parameters on the stress intensity factor is obvious.