Stress intensity factors and T-stress in functionally graded materials

2003 ◽  
pp. 381-386
Author(s):  
Jeong-Ho Kim ◽  
Glaucio H. Paulino
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
T Stress

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.

scholarly journals A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3581 ◽  
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method

2020 ◽  
Vol 234 (10) ◽  
pp. 2012-2023
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

The numerical calculation of stress intensity factors of two-dimensional functionally graded materials is introduced by an enriched Petrov–Galerkin natural element method (enriched PG-NEM). The overall trial displacement field is basically approximated in terms of Laplace interpolation functions and it is enriched by the near-tip asymptotic displacement field. The overall strain and stress fields which were approximated by PG-NEM were smoothened and enhanced by the patch recovery. The modified interaction integral [Formula: see text] is used to evaluate the stress intensity factors of functionally graded materials with the spatially varying elastic modulus. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors of four numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with a remarkably improved accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

scholarly journals Numerical Analysis for Cracked Functionally Graded Materials by Finite Block Method

2017 ◽  
Vol 754 ◽  
pp. 145-148
Author(s):  
J. Li ◽  
C. Shi ◽  
Pi Hua Wen
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Stress Intensity Factors ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Block Method ◽  
Graded Materials ◽  
Linear Elastic ◽  
Derivative Matrix

The finite block method (FBM) is developed to determine stress intensity factors with orthotropic functionally graded materials under static and dynamic loads in this paper. The higher order derivative matrix for two and three dimensional problems can be constructed directly. For linear elastic fracture mechanics, the COD and J-integral techniques to determine the stress intensity factors are applied. Several examples are given and comparisons have been made with both analytical solutions and the finite element method in order to demonstrate the accuracy and convergence of the finite block method.

Sign in / Sign up

Export Citation Format

Share Document