Research On Crack Problem Of Functionally Graded Materials With General Property

Functionally graded materials(FGMs)play an important part in many application fields with complex application circumstances and extreme temperature changes,such as aeronautics and astronautics,nuclear reactor and medical science.The extreme application environments may raise the risk of fracture failure of FGMs.Some inclusions and pores will be produced in manufacturing FGMs so that the safety of FGMs in application area has attracted much attention.And avoiding fracture failure is the key problem of designing and manufacturing FGMs.Thus the study on the fracture problem of FGMs has great significance in design and optimization of material structure and safety performance evaluation.Similar to classical study on fracture mechanics parameters of the homogeneous materials,the research on stress intensity factors(SIFs)of the inhomogeneous materials is of particular importance.In this paper,the effects of the material property distributions,geometric parameters of cracks and randomness of meso-particles used to manufacturing FGMs upon the mechanical properties of FGMs are discussed.And a few meaningful results are obtained.First of all,the fracture problem of the functionally graded strip with collinear cracks is investigated.With the typical properties of FGMs taken into consideration,the fracture problem on collinear cracks is modeled.Applied the inhomogeneous laying method of the piecewise exponential function,a set of singular integral equations is derived and then solved by numerical method and SIFs near crack-tips are obtained.The influences of the different distributions of material properties,geometric parameters of cracks and distance between the both cracks on the SIFs are discussed.By analyzing the numerical examples,it can be found that there are significant differences in SIFs for different property distribution forms of FGMs.Secondly,a functionally graded strip with typically thermomechanical properties and collinear cracks under thermal loadings is studied.The steady state fracture mechanics model is proposed.Based on the inhomogeneous layering method,the real property of the material is approximated using the piecewise exponential function.The temperature field is solved.And applying the superposition rule,equivalent thermal loadings on the both cracks surfaces are obtained.Then the thermal stress intensity factors(TSIFs)are obtained after solving the singular integral equations.The change characteristics of TSIFs are analyzed for the functionally graded strip with the two collinear cracks perpendicular to the free surfaces of the material under thermal stresses.The influences of the different thermomechanical property distributions and geometric parameters of cracks with temperature changes on TSIFs are analyzed efficiently.Afterwards some meaningful results have been obtained.In the end,stochastic features of the effective parameters on mechanics of FGMs are paid attention to.From the view of stochastic characteristics of the meso-scopic component of FGMs,the influences of stochastic characteristics of the meso-component of FGMs on the fracture mechanics behavior near crack-tips is studied for the FGMs with an arbitrarily oriented crack.Combining the layering model used to macro analysis on the fracture mechanics and the meso-scopic analysis used to on the composition of material components,probabilistic characteristics of the mixed-mode SIFs in FGMs with stochastic mechanical properties are analyzed.The stress intensity factors of FGMs with uncertain mechanical properties of are solved theoretically.The effects of the randomness of the meso-component of FGMs on macro material properties and probability characteristics of mix-mode SIFs are analyzed.The results in this paper may provide theoretical basis for designing FGMs,mechanics analysis on FGMs with general properties and security analysis of components on FGMs with cracks.