Dynamic stress field around the mode III crack tip in an orthotropic functionally graded material

2000 ◽  
Vol 21 (6) ◽  
pp. 651-658 ◽  
Author(s):  
Li Chunyu ◽  
Zhou Zhenzhu ◽  
Duan Zhuping
Keyword(s):  
Stress Field ◽  
Functionally Graded Material ◽  
Dynamic Stress ◽  
Crack Tip ◽  
Functionally Graded ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Dynamic Stress Field ◽  
Graded Material

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.

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.

Mode III Yoffe Dynamic Crack in an Infinite Length Strip for Orthotropic Anisotropy Functionally Graded Material

2006 ◽  
Vol 324-325 ◽  
pp. 287-290 ◽  
Author(s):  
Cheng Jin ◽  
Xin Gang Li ◽  
Nian Chun Lü
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Functionally Graded Material ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Shear Loading ◽  
Functionally Graded ◽  
Infinite Strip ◽  
Graded Material

A moving crack in an infinite strip of orthotropic anisotropy functionally graded material (FGM) with free boundary subjected to anti-plane shear loading is considered. The shear moduli in two directions of FGM are assumed to be of exponential form. The dynamic stress intensity factor is obtained by utilizing integral transforms and dual-integral equations. The numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of the strip, gradient parameters and nonhomogeneous coefficients.

Computation of dynamic stress intensity factors for cracks in three-dimensional functionally graded solids

2017 ◽  
Vol 233 (5) ◽  
pp. 862-873
Author(s):  
Safa Peyman ◽  
Rahmatollah Ghajar ◽  
Saeed Irani
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Material ◽  
Stress Intensity Factors ◽  
Material Properties ◽  
Dynamic Stress ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Interaction Integral ◽  
Graded Material

Dynamic stress intensity factors are important parameters in the dynamic fracture behavior of a cracked body. In this paper, an interaction integral method is utilized to compute the mixed-mode dynamic stress intensity factors of three-dimensional functionally graded material solids. Using a proper definition of actual and auxiliary fields, a new formulation and application of the interaction integral is proposed, which is independent of the derivatives of the material properties. ABAQUS finite element package is applied to analyze the functionally graded material cracked bodies. Accordingly, a user material subroutine is written for implementing the continuous variation of the material properties. Temperature was used as an additional variable to consider the variation of density. A research code is developed to compute the interaction integral. This code is then validated by solving some homogeneous and functionally graded material problems. Furthermore, the effect of the material properties on the dynamic stress intensity factors of FGM bodies with elliptical crack is investigated by taking the sigmoidal model into account. Several important fracture behavior of functionally graded material cracked bodies under dynamic loadings for different material property profiles are explored in detail.

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