Document Type : Research Paper
Authors
Mechanical Engineering Department, Basrah University, Basrah, Iraq,
Abstract
An extended meshless method that relying upon Galerkin formulation is applied on the crack analysis of orthotropic functionally graded Brazilian disc. Weak form is involved to solve the governing equation in the numerical method. In addition, enrichment terms and sub-triangle techniques are applied to improve the accuracy of relevant results. This paper depicts the influence of variation in the crack stretch and non-homogeneity parameters on the values of stress intensity factors using a developed MATLAB program. In the isotropic case, it is clear that when the length of crack increases, SIF increases. Graduation in has more effect in increasing the values of SIF in corresponding increased crack length. The verification has been checked by changing the range of the J-integral domain and variation of the support domain
Keywords
[3] J. E. Dolbow and M. Gosz, “On the computation of mixed-mode stress intensity factors in integral and micromechanics models,” International Journal for Numerical Methods in Engineering, Vol. 58, pp.1457–1497, 2003.
[4] B. N. Rao and S. Rahman, “Mesh-free analysis of cracks in isotropic functionally graded materials,” Engineering Fracture Mechanics, Vol.70, pp.1–27, 2003.
[5] J. H. Kim and G. H. Paulino, “An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction of the Interaction Integral Method for Fracture of Functionally Graded Materials,” Journal of Applied Mechanics, ASME, Vol. 72, pp 351-364, May, 2005.
[6] J. H. Kim and G. H. Paulino, “Consistent Formulations functionally graded materials,” International Journal of Solids and Structures, Vol. 39, pp.2557–2574, 2002.
[7] K. Y. Dai, G. R. Liu, K. M. Lim, X. Han and S. Y. Du, “A meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates,” Computational Mechanics, Vol.34, Springer-Verlag, pp.213–223, 2004.
[8] J. Sladek, V. Sladek and C. Zhang, “A meshless local boundary integral equation method for dynamic anti-plane shear crack problem in functionally graded materials,” Engineering Analysis with Boundary Elements, Vol.29, pp.334–342, 2005.
[9] H. Khazal, H. Bayesteh, S. Mohammadi, S. S. Ghorashi, and A. Ahmed, "An extended element free Galerkin method for fracture analysis of functionally graded material,” Mech. Adv. Mater. Struct., Vol.23, pp.513–528, 2016.
[10] H. Khazal, and N. Saleh, “XEFGM for crack propagation analysis of functionally graded materials under mixed-mode and non-proportional loading,” Mech. Adv. Mater. Struct. Vol.11, No.11, pp.975–983, 2019.
[11] H. Ibraheem, H. Khazal, and A. Ahmed, ''Steady State Thermo XFEM Fracture Analysis of Isotropic and an Isotropic FG Plate with Inclined Center Crack,” Basrah Journal for Engineering Sciences, Vol. 18, No.1, 201
[12] R. J. Butcher, C.-E. Rousseau and H. V. Tippur, “A functionally Graded Composite: Preparation, Measurements and Failure Analysis,” Acta mater. Vol. 47, No. 1, pp. 259-268, 1999.
[13] L. Lambros, A. Narayanaswamy, M. H. Santare, G. Anlas, “Manufacture and Testing of a Functionally Graded Material,” ASME, Vol.121, Oct., 1999.
[14] C. E. Rousseau and H. V. Tippur, “Compositionally Graded Materials with cracks normal to the elastic gradient,” Department of Mechanical Engineering, 202 Ross Hall, Auburn University, Auburn, AL 36849, USA, Acta Metallurgica , Elsevier Science, 2000.
[15] W. Farouq, H. Khazal, and A. K. F. Hassan, ''Fracture analysis of functionally graded material using digital image correlation technique and extended element-free Galerkin method,” Optics and Lasers in Engineering, Vol. 121, pp.307-322, October, 2019.
[16] H. Khazal, A. Hassan, W. Farouq, and H. Bayesteh, "Computation of Fracture Parameters in Stepwise Functionally Graded Materials Using Digital Image Correlation Technique,” Materials Performance and Characterization", Vol.8, No. 1, pp.344-354, 2019.
[17] G. R. Liu, “Meshfree methods moving beyond the finite element method,” second edition- by Taylor and Francis Group, LLC, 2010.
[18] P. Lancaster and K. Salkauskas, "Surfaces generated by moving least squares methods,” Mathematics of Computation, Vol. 37, pp. 141-158, 1981
[19] J. H. Kim and G. H. Paulino, “Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method,” Engineering Fracture Mechanics, Vol.69, pp.1557–1586, 2002.
[20] J. H. Kim and G. H. Paulino, “The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors,” Int. J. Solids Struct., Vol. 40, pp. 3967–4001, 2003.
)
