Crack In Functionally Graded Materials Study Of The Theory Of The Stress Intensity Factor

The functionally gradient material is a new material of various components.It is available in order to meet the performance requirements of parts in variousspecial environment。Now，application of functional gradient materials hasbeen extended to aerospace, energy, transport, optical, chemical, biomedicalengineering and other fields. However, functionally gradient material will havesome defects in manufacturing process due to the influence of processconditions. It is inevitably that these defects will produce crack under the stressand the expansion of crack will affect the entire materials component. So, it isvery important to study on crack and its extension of functionally gradientmaterials.In this paper, double parameters even exponential function and doubleparameters any power function model were used as the material parametersmodel to study the problems of dynamic and static crack tip stress intensityfactor in the infinite strip of functionally gradient materials and infinitefunctionally gradient materials respectively. The effects of gradient parameter,crack length, strip height, crack movement speed and inhomogenous coefficienton the dynamic and static crack tip stress intensity factor in the infinite strip offunctionally gradient materials and infinite functionally gradient materials havebeen obtained by mathematical software.The control equation of infinite strip of functionally gradient materials istranslated into Euler equation by using of Fourier cosine transform in thespecified parameters of even exponential function model, then a set of dualintegral equations are got in using of the solution of Euler equation. The controlequation of infinite functionally gradient materials is translated into modifiedBessel equation by using of Fourier cosine transform in the specified parametersof double parameters any power function model, then a set of dual integralequations are got in using of the solution of modified Bessel equation. And thenthe expressions of stress intensity factor in the infinite strip of functionally gradient materials and infinite functionally gradient materials have beenobtained through solving the dual integral equations by the Copson method. Inthis paper, the expressions of dimensionless stress intensity factor have beenanalyzed in using of some mathematical software, also. Some important resultswhich provide important theoretical value on the fracture analysis offunctionally graded material have been obtained.