Higher-Order Terms for the Mode-III Stationary Crack-Tip Fields in a Functionally Graded Material

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Linhui Zhang ◽  
Jeong-Ho Kim
Keyword(s):  
Functionally Graded Material ◽  
Crack Tip ◽  
Functionally Graded ◽  
Mode Iii ◽  
Stationary Crack ◽  
Crack Tip Field ◽  
Homogeneous Solutions ◽  
Variable Approach ◽  
Graded Material ◽  
Plane Displacement

This paper provides full asymptotic crack-tip field solutions for an antiplane (mode-III) stationary crack in a functionally graded material. We use the complex variable approach and an asymptotic scaling factor to provide an efficient procedure for solving standard and perturbed Laplace equations associated with antiplane fracture in a graded material. We present the out-of-plane displacement and the shear stress solutions for a crack in exponentially and linearly graded materials by considering the gradation of the shear modulus either parallel or perpendicular to the crack. We discuss the characteristics of the asymptotic solutions for a graded material in comparison with the homogeneous solutions. We address the effects of the mode-III stress intensity factor and the antiplane T-stress onto crack-tip field solutions. Finally, engineering significance of the present work is discussed.

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

2018 ◽  
Vol 53 (14) ◽  
pp. 1883-1896
Author(s):  
Ren Xiaohui ◽  
Wu Zhen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Normal Strain ◽  
Sinusoidal Model ◽  
Proposed Model ◽  
Graded Material ◽  
Plane Displacement ◽  
Stress Free Boundary ◽  
Transverse Normal Strain

A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

Predicting Speed of Crack Running in Functionally Graded Material

2005 ◽  
Author(s):  
Michihiko Nakagaki ◽  
Ryosuke Matsumoto
Keyword(s):  
Functionally Graded Material ◽  
Crack Tip ◽  
Functionally Graded ◽  
Constitutive Law ◽  
Nonlinear Material ◽  
Spherical Particles ◽  
Fracture Parameter ◽  
Crack Speed ◽  
Equivalent Inclusion Method ◽  
Graded Material

A theoretical and computational methodology for the analysis of the functionally graded material (FGM) is introduced, and its application is made to the problem of a dynamically propagating crack running transversely in the FGM, where the intensity of the estimated crack-tip severity is managed to keep in valance with the graded material toughness in the FGM during the propagation. To detect the crack-tip severity, an integral fracture parameter, T*, is used. The crack is propagated so that the value of T* is equated to the prescribed varying critical values of T* for the graded material. Emphasis is placed on the use of a fuzzy inference technique in order to control the crack speed, which is deduced from a few T* values immediately preceding the current crack position. As to describing the constitutive law for the FGM, micro-spherical particles of arbitrary size in mesoscale are considered to be randomly dispersed in the matrix medium. By assuming that the volume fraction of the inclusion is continuously varied from 0 to 100 percent in the material, the grading is modeled. For modeling the constitutive law for the FGM composite media of thermo-elastoplasticity, a closed form SCC-LRM constitutive model describing the nonlinear material mechanics of the particle-dispersed medium is used. The model is based on the self-consistent scheme and uses Eshelby’s equivalent inclusion method. Unprecedented analytical results of predicting the crack speed of a crack running transversely in the FGM plate are obtained. In some cases of material grading, apparent crack arresting is observed as the crack runs into the metal rich area of the FGM.

Behaviour of three parallel non-symmetric mode III cracks in a functionally graded material plane

2008 ◽  
Vol 222 (12) ◽  
pp. 2311-2330 ◽  
Author(s):  
P-W Zhang ◽  
Z-G Zhou ◽  
L-Z Wu
Keyword(s):  
Integral Equations ◽  
Functionally Graded Material ◽  
Jacobi Polynomials ◽  
Functionally Graded ◽  
Shielding Effect ◽  
Mode Iii ◽  
Dual Integral Equations ◽  
Plane Shear ◽  
Graded Material ◽  
Material Plane

In this article, the behaviour of three parallel non-symmetric finite-length cracks in an infinite functionally graded material plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier transform into three pairs of dual integral equations, in which unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors depend on the crack lengths, spacing of cracks, and the material parameters. It was also revealed that the crack shielding effect is present in functionally graded materials.

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