Theoretical Investigation And Numerical Value Simulation Analysis Of Stress Field Near Crack Tip In Functionally Graded Materials

The material parameters of Functionally Graded Materials vary continuously in space because of it's special material structure, which can eliminate effectually the unmatching problem of convention complex material on interface and reduce or eliminate heat stress and remainder stress which can decrease stress concentration. And FGM has capacious applied prospect in field of aviation and spaceflight. It is especially important to study the crack development and expansion in FGM because kinds of cracks can be come into being which can lead to breakage of material in course of application. At present, the material parameters popularly adopt exponent function form and others function forms are seldom been seen in the study of FGM and the studies for dynamic problems are seldom been seen.In this paper, first the development and introduction of FGM are expounded, and then the static state and dynamic and motorial crack problems of mode III crack in infinity orthotropic FGM antiplane loaded are studied by using of integral transforms-dual integral equations method and material parameters are assumed to very in terms of power function form of two parameters of arbitrary times power. By virtue of numerical value solving and image simulation with Matlab soft ware a series of important results are obtained. Mode I,II crack of infinite strip orthotropic and anisotropic FGM plane loaded are studied respectively by using of complex function method. The main study process and production are as follows:1. Mode III crack antiplane fracture problem of static state of infinite FGM was studied. The results display that in orthotropic FGM the stress field remains the singular behavior of the inverse square root of r near the crack tip and the angle distributing function is the same as the uniformity material of orthotropic FGM. With the increasing of coefficient of inhomogenous material the value of stress intensity factor increases. So by increasing shear moduli's gradient of FGM can restrain the driving force of crack expanding.2. Mode III crack antiplane fracture dynamic problem of infinite FGM was studied. The results display that in orthotropic FGM the stress field remains the singular behavior of the inverse square root of r near the crack tip and the angle distributing function is the same as the uniformity material of orthotropic FGM. The dynamic stress intensity factor will decrease with the increase of graded parameters and rise with the increase of material inhomogenous coefficient.3. The dynamic problem of Yoffe type crack was studied subjected to antiplane shear impact in infinity orthotropic functionally graded materials. The dimensionless dynamic stress intensity factor will decrease with the increase of graded parameters and rise with the increase of material inhomogenous coefficient. And by increasing shear moduli's gradient of FGM can restrain the driving force of crack expanding.4. Mode I,II and I+II fixed crack problems in infinite strip of orthotropic and anisotropic FGMs were studied. The theory formulae of stress and strain fields and graded stress intensity factor near crack tip of Mode I,II and I+II fixed crack in orthotropic and anisotropic FGM with arbitrarily varying function parameter in the derection of thickness. were firstly introduced. The results shows that the stess remains the singular behavior of inverse square root of r near the crack tip. So those fracture mechanics methods which had been applied to homogeneous materials widely can be used to resolve problems of FGM.The productions mentioned above can provide important theory directions to preparation and performance optimizing of FGM and come into being important effects to more development and generalizing application of FGM.