scholarly journals Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials

2015 ◽  
Vol 65 (1) ◽  
pp. 57-76
Author(s):  
M. Repka ◽  
J. Sládek ◽  
V. Sládek ◽  
M. Wünsche
Keyword(s):  
Asymptotic Expression ◽  
Crack Tip ◽  
Weak Form ◽  
Functionally Graded ◽  
Single Fracture ◽  
Fracture Parameter ◽  
Fracture Parameters ◽  
Crack Problems ◽  
T Stress ◽  
Graded Material

Abstract The finite element method (FEM) is developed for coupled thermoelastic crack problems if material properties are continuously varying. The weak form is utilized to derive the FEM equations. In conventional fracture theories the state of stress and strain at the crack tip vicinity is characterized by a single fracture parameter, namely the stress intensity factor or its equivalent, J-integral. In the present paper it is considered also the second fracture parameter called as the T-stress. For evaluation of both fracture parameters the quarter-point crack tip element is developed. Simple formulas for both fracture parameters are derived comparing the variation of displacements in the quarter-point element with asymptotic expression of displacement at the crack tip vicinity. The leading terms of the asymptotic expansions of fields in the crack-tip vicinity in a functionally graded material (FGM) are the same as in a homogeneous one with material coefficients taken at the crack tip.

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.

Delamination of Compressively Stressed Orthotropic Functionally Graded Material Coatings Under Thermal Loading

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
Bora Yıldırım ◽  
Suphi Yılmaz ◽  
Suat Kadıoğlu
Keyword(s):  
Functionally Graded Material ◽  
Bond Coat ◽  
Thermal Loading ◽  
Layer Structure ◽  
Crack Problem ◽  
Functionally Graded ◽  
Internal Crack ◽  
Correlation Technique ◽  
Fracture Parameters ◽  
Graded Material

The objective of this study is to investigate a particular type of crack problem in a layered structure consisting of a substrate, a bond coat, and an orthotropic functionally graded material coating. There is an internal crack in the orthotropic coating layer. It is parallel to the coating bond-coat interface and perpendicular to the material gradation of the coating. The position of the crack inside the coating is kept as a variable. Hence, the case of interface crack is also addressed. The top and bottom surfaces of the three layer structure are subjected to different temperatures and a two-dimensional steady-state temperature distribution develops. The case of compressively stressed coating is considered. Under this condition, buckling can occur, the crack can propagate, and the coating is prone to delamination. To predict the onset of delamination, one needs to know the fracture mechanics parameters, namely, Mode I and Mode II stress intensity factors and energy release rates. Hence, temperature distributions and fracture parameters are calculated by using finite element method and displacement correlation technique. Results of this study present the effects of boundary conditions, geometric parameters (crack length and crack position), and the type of gradation on fracture parameters.

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.

The Higher Order Crack Tip Fields for Physical Weak-- Discontinuous Crack of FGM Plate with Reissner’s Effect

2013 ◽  
Vol 664 ◽  
pp. 841-845
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Engineering Application ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Graded Materials ◽  
Crack Problems ◽  
Asymptotic Expansion Method

The physical weak-discontinuous problem of an interfacial crack between homogeneous material and functionally graded materials (FGMs) is studied based on Reissner’s plates considering transverse shear deformation effect. The crack-tip higher order asymptotic fields of homogeneous materials and FGMs regions are obtained by the asymptotic expansion method, respectively. Finally, the whole crack tip high order fields are assembled and given. The results provide a theoretical basis for solving interfacial crack problems of FGMs plates and their engineering application.

The Higher Order Crack-Tip Field for Reissner's Bidirectional FGMs Spherical Shell

2013 ◽  
Vol 748 ◽  
pp. 341-344
Author(s):  
Yao Dai ◽  
Zhang Lei ◽  
Xiao Chong
Keyword(s):  
Spherical Shell ◽  
Functionally Graded Materials ◽  
Superposition Principle ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Crack Tip Field ◽  
Graded Materials ◽  
Crack Problems

The crack tip fields for a cracked functionally graded materials spherical shell considering Reissners effect are obtained. Similar to Williams solution for homogeneous material, the eigen-solution of the crack tip field for bi-directional FGMs spherical shell is obtained by stress superposition principle. This result can be used to deal with the crack problems for FGMs shell.

On Accurate Numerical Evaluation of Stress Intensity Factors and T-Stress in Functionally Graded Materials

2005 ◽  
Vol 492-493 ◽  
pp. 403-408 ◽  
Author(s):  
Jeong Ho Kim ◽  
Glaucio H. Paulino
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Stress Intensity Factors ◽  
Integral Form ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Center Crack ◽  
T Stress ◽  
Graded Material

This paper revisits the interaction integral method to evaluate both the mixed-mode stress intensity factors and the T-stress in functionally graded materials under mechanical loading. A nonequilibrium formulation is developed in an equivalent domain integral form, which is naturally suitable to the finite element method. Graded material properties are integrated into the element stiffness matrix using the generalized isoparametric formulation. The type of material gradation considered includes continuum functions, such as an exponential function, but the present formulation can be readily extended to micromechanical models. This paper presents a fracture problem with an inclined center crack in a plate and assesses the accuracy of the present method compared with available semi-analytical solutions.

Sign in / Sign up

Export Citation Format

Share Document