Research On Fracture Behavior Of Functionally Graded Materials Under Stress Coupling

The functionally graded material studied in this paper is a solid oxide electrolyte.The solid oxide electrolyte is the core component of the solid oxide fuel cell.It conducts oxygen ions by transporting oxygen vacancies.Under the action of the difference in oxygen concentration between the two poles,the oxygen vacancies are distributed in the electrolyte gradient,and the diffusion of the oxygen vacancies will be affected by the stress-induced potential function.Especially when the material has microcracks,the stress at the crack tip is at a higher level,which will attract oxygen vacancies to converge.The oxygen vacancy,as a kind of material defect,will affect the mechanical properties of the material.Therefore,the solid electrolyte under the coupling of force and chemical field can be equivalent to a functionally graded material whose modulus at the crack tip is affected by stress.The canonical perturbation method is used to prove that the stress at the crack tip of a functionally graded material with continuously differentiable Young’s modulus still has a square root singularity when the average stress has a small perturbation to the modulus.First,use the scale theory to non-dimensionally process physical quantities such as stress and strain to obtain the governing equation of the stress function of the functionally graded material with a coupling effect of stress on the modulus,and then expand the stress function with respect to the small parameter stress coupling factor as a power function expansion into the governing equation Approximate equations of all orders are obtained in.Solving the equations proves that the influence of stress on the modulus is embodied in higher-order terms,and has no influence on the singularity of the stress field.Finally,using the hierarchical E index model,the relationship between the linear change of the material modulus,the E index change and the homogenization of the crack length,the stress coupling factor and the stress coupling index and the stress intensity factor are calculated by the method of sequential iteration.This research provides reference value for the mechanical reliability design and fracture failure of solid oxide electrolyte under the coupling action of force and chemical field.