Functional Graded Material Crack Propagation Simulation Based On Adaptive Finite Element Method

In this paper,the adaptive finite element numerical method AFEM-QPE is developed to solve the crack propagation problem of functionally graded materials.By calculating the stress intensity factor,the correctness and effectiveness of AFEM-QPE method are verified.Aiming at the problem of crack propagation in functionally graded materials with arbitrary Angle central crack,the effects of crack Angle and direction of functional graded on crack stress intensity factor were analyzed and the crack propagation path was simulated.The main contents are as follows:1.An AFEM-QPE method for simulating crack propagation in functionally gradient materials was developed and programmed using Python language.The ide a of AFEM-QPE method is as follows:based on the governing equation of linear elasticity theory,the finite element method equation is established;The graded reconstruction error estimator is introduced to realize the non-uniform automatic mesh encryption.The Laplacian smoothing technique is used to improve the mesh quality at a lower cost.The contact condition of crack interface is considered.The maximum circumferential stress criterion is adopted as the crack initiation condition.QPE element is introduced to simulate the singularity of crack tip element.The stress intensity factor was obtained by displacement extrapolation method.2.The correctness and effectiveness of AFEM-QPE method was verified through the calculation of stress intensity factor.The effects of the crack Angle and the graded direction on the stress intensity factor were analyzed.3.The crack propagation path in the functionally graded disk and functionally graded plate was simulated.The effects of graded direction and crack Angle on crack growth path were analyzed.