Anti-plane Yoffe Moving Crack Problem in Isotropic Functionally Graded Materials

2007 ◽  
Vol 26 (2) ◽  
pp. 127-137 ◽  
Author(s):  
Hong Min Xu ◽  
Xue Feng Yao ◽  
Xi Qiao Feng ◽  
Hsien Yang Yeh
Keyword(s):  
Functionally Graded Materials ◽  
Crack Problem ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials

SINGULAR INTEGRAL EQUATION METHOD FOR A MOVING CRACK PROBLEM IN ANTIPLANE ELASTICITY OF FUNCTIONALLY GRADED MATERIALS

2007 ◽  
Vol 04 (03) ◽  
pp. 475-492 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Functionally Graded Materials ◽  
Material Property ◽  
Singular Integral ◽  
Crack Problem ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials ◽  
Antiplane Elasticity

In this paper, elastic analysis for a Yoffe moving crack problem in antiplane elasticity of the functionally graded materials (FGMs) is presented. The crack is assumed to move with a constant velocity V. The traction applied on the crack face is arbitrary. The Fourier transform method is used to derive an elementary solution. Furthermore, using the obtained elementary solution a singular integral equation for the problem is obtained. After the singular integral equation is solved, the stress intensity factor (SIF) can be evaluated immediately. In the case of evaluating the SIFs at the leading crack tip and the trailing crack tip, the difference between the two cases is investigated. From the numerical solution of the SIFs, the influence caused by the velocity V and the FGM material property β1 are addressed. It is found that when the FGM material property β1 = 0, i.e. the homogeneous case, the SIFs at the crack tips do not depend on the moving velocity of the crack. Finally, numerical examples are given.

Thermoelastic Fracture Mechanics for Nonhomogeneous Material Subjected to Unsteady Thermal Load

1999 ◽  
Vol 67 (1) ◽  
pp. 87-95 ◽  
Author(s):  
B. L. Wang ◽  
J. C. Han ◽  
S. Y. Du
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Crack Problem ◽  
Laminated Composite ◽  
Functionally Graded ◽  
Comprehensive Treatment ◽  
Numerical Illustration ◽  
Graded Materials ◽  
Nonhomogeneous Material ◽  
Crack Problems

This article provides a comprehensive treatment of cracks in nonhomogeneous structural materials such as functionally graded materials. It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using a laminated composite plate model to simulate the material nonhomogeneity, we present an algorithm for solving the system based on the Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problems in the functionally graded materials with arbitrarily varying material properties. The algorithm can be applied to steady state or transient thermoelastic fracture problem with the inertial terms taken into account. As a numerical illustration, transient thermal stress intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of nonhomogeneous material with properties varying in the thickness direction. [S0021-8936(00)01601-9]

Implementation of Crack Problem of Functionally Graded Materials with ABAQUSTM

2011 ◽  
Vol 284-286 ◽  
pp. 297-300 ◽  
Author(s):  
Hong Liang Zhou
Keyword(s):  
Functionally Graded Materials ◽  
Interface Crack ◽  
Crack Problem ◽  
Functionally Graded ◽  
Closure Technique ◽  
Graded Materials ◽  
Finite Element Software ◽  
User Subroutine ◽  
Implementation Method ◽  
Crack Element

An implementation method of the virtual crack closure technique (VCCT) for fracture problems of non-homogeneous materials such as functionally graded materials (FGMs) with commercial finite element software ABAQUSTMis introduced in this paper. In order to avoid the complex post proceeding to extract fracture parameters, the interface crack element based on the VCCT is developed. The heterogeneity of FGMs is characterized though user subroutine UMAT and the interface crack element is implemented by user subroutine UEL. Several examples are analyzed to demonstrate the accuracy of the present method.

Higher Order Crack-Tip Fields of Reissner’s Linear Functionally Graded Materials Plates

2012 ◽  
Vol 549 ◽  
pp. 914-917
Author(s):  
Yao Dai ◽  
Jun Feng Liu ◽  
Lei Zhang ◽  
Xiao Chong ◽  
Hong Qian Chen
Keyword(s):  
Functionally Graded Materials ◽  
Crack Problem ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Graded Materials ◽  
Fracture Theory ◽  
Bending Fracture ◽  
Asymptotic Expansion Method

Reissner’s plate bending fracture theory with consideration of transverse shear deformation effects is adopted for the crack problem of functionally graded materials (FGMs) plates. Assume that the crack is perpendicular to the material property gradient. By applying the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to Williams’ solutions of homogeneous materials are obtained.

scholarly journals Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

2020 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Youn-Sha Chan ◽  
Edward Athaide ◽  
Kathryn Belcher ◽  
Ryan Kelly
Keyword(s):  
Integral Equations ◽  
Functionally Graded Materials ◽  
Singular Integral ◽  
Mixed Mode ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Functionally Graded ◽  
Fredholm Integral Equations ◽  
Mixed Mode Fracture ◽  
Graded Materials

A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

Fracture Dynamics of a Mode III Moving Crack Impacted by Elastic Wave in Functionally Graded Materials

2010 ◽  
Vol 105-106 ◽  
pp. 683-686
Author(s):  
Xin Gang Li ◽  
Zhen Qing Wang ◽  
Nian Chun Lü
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Functionally Graded Materials ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Functionally Graded ◽  
Moving Crack ◽  
Graded Materials ◽  
Sh Waves

The dynamic stress field under the SH-waves at the moving crack tip of functionally graded materials is analyzed, and the influences of parameters such as graded parameter, crack velocity, the angle of the incidence and the number of the waves on dynamic stress intensity factor are also studied. Due to the same time factor of scattering wave and incident wave, the scattering model of the crack tip can be constructed by making use of the displacement function of harmonic load in the infinite plane. The dual integral equation of moving crack problem subjected to SH-waves is obtained through Fourier transform with the help of the exponent model of the shear modulus and density, then have some process on the even and odd term of the integral kernel. The displacement is expanded into series form using Jacobi Polynomial, and then the semi-analytic and numerical solutions of dynamic stress intensity factor are derived with Schmidt method.

Dynamic Analysis with Stress Recovery for Functionally Graded Materials: Numerical Simulation and Experimental Benchmarking

2014 ◽  
Vol 2 (1) ◽  
pp. 21
Author(s):  
Carlos Alberto Dutra Fraga Filho ◽  
Fernando César Meira Menandro ◽  
Rivânia Hermógenes Paulino de Romero ◽  
Juan Sérgio Romero Saenz
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Stress Recovery ◽  
Graded Materials
Sign in / Sign up

Export Citation Format

Share Document