Mixed-Mode Crack-Tip Fields in an Anisotropic Functionally Graded Material

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Linhui Zhang ◽  
Jeong-Ho Kim
Keyword(s):  
Functionally Graded Material ◽  
Mixed Mode ◽  
Crack Tip ◽  
Anisotropic Materials ◽  
Functionally Graded ◽  
Stress Fields ◽  
Order Partial Differential Equation ◽  
Graded Material ◽  
Exponentially Graded ◽  
Crack Tip Stress

This paper provides asymptotic full crack-tip stress field solutions for an in-plane mixed-mode stationary crack in an anisotropic functionally graded material. A monoclinic graded material that has a material symmetry plane is considered. The complex variable approach and the asymptotic scaling factor are used to solve the governing fourth-order partial differential equation for exponentially graded anisotropic materials with gradation either parallel or perpendicular to the crack. Full crack-tip stress fields under mode-I and mode-II loading are visualized and discussed for homogeneous and exponentially graded anisotropic materials. We observe that higher-order terms are affected by material gradation and play an important role on crack-tip stress fields in functionally graded materials.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

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.

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.

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

A Parallel Domain Decomposition BEM Algorithm for Three-Dimensional Exponentially Graded Elasticity

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
J. E. Ortiz ◽  
W. A. Shelton ◽  
V. Mantič ◽  
R. Criado ◽  
L. J. Gray ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Domain Decomposition ◽  
Functionally Graded Material ◽  
Computational Cost ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Graded Material ◽  
High Computational Cost ◽  
Exponentially Graded

A parallel domain decomposition boundary integral algorithm for three-dimensional exponentially graded elasticity has been developed. As this subdomain algorithm allows the grading direction to vary in the structure, geometries arising from practical functionally graded material applications can be handled. Moreover, the boundary integral algorithm scales well with the number of processors, also helping to alleviate the high computational cost of evaluating the Green’s functions. For axisymmetric plane strain states in a radially graded material, the numerical results for cylindrical geometries are in excellent agreement with the analytical solution deduced herein.

Sign in / Sign up

Export Citation Format

Share Document