Applied Mathematics and Mechanics >
Higher-order crack tip fields for functionally graded material plate with transverse shear deformation
Received date: 2015-09-02
Revised date: 2015-10-19
Online published: 2016-06-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 90305023 and 11172332)
The crack tip fields are investigated for a cracked functionally graded material (FGM) plate by Reissner's linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson's ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner's plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner's effect when the in-homogeneity parameter approaches zero.
Dianhui HOU, Xiao CHONG, Guixiang HAO, Yao DAI . Higher-order crack tip fields for functionally graded material plate with transverse shear deformation[J]. Applied Mathematics and Mechanics, 2016 , 37(6) : 695 -706 . DOI: 10.1007/s10483-016-2083-6
[1] Timoshenko, S. and Woinowsky-Kriege, S. Theory of Plates and Shells, McGraw-Hill Book Com-pany, New York, 1-81 (1959)
[2] Williams, M. L. The bending stress distribution at the base of a stationary crack. Journal of Applied Mechanics, 28, 78-82 (1976)
[3] Reissner, E. On bending of elastic plates. Quarterly of Applied Mathematics, 5, 55-68 (1947)
[4] Knowles, J. K. and Wang, N. M. On the bending of an elastic plate containing a crack. Journal of Mathematics and Physics, 39, 223-236 (1960)
[5] Hartranft, R. J. and Sih, G. C. Effect of plate thickness on the bending stress distribution around through cracks. Journal of Mathematical Physics, 47, 276-291 (1968)
[6] Murthy, M. V. V., Raju, K. N., and Viswanath, S. On the bending stress distribution at the tip of a stationary crack from Reissner's theory. International Journal of Fracture, 17, 537-552 (1981)
[7] Liu, C. T. Stresses and deformations near the crack tip for bending plate. Acta Mechanica Solid Sinica, 3, 441-448 (1983)
[8] Liu, C. T. and Jiang, C. P. Fracture Mechanics for Plates and Shells, Defense Industry Press, Beijing, 139-163 (2000)
[9] Qian, J. and Long, Y. Q. The expression of stress and strain at the tip of notch in Reiss-ner's plate. Applied Mathematics and Mechanics (English Edition), 13(4), 297-306 (1992) DOI 10.1007/BF02451417
[10] Xu, Y. J. Eigen-problem in fracture mechanics for a Reissner's plate. Acta Mechanica Solid Sinica, 25, 225-228 (2004)
[11] Reddy, J. N. A simple higher order theory for laminated composite plates. Journal of Applied Mechanics, 51, 745-752 (1984)
[12] Reddy, J. N. Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 47, 663-684 (2000)
[13] Reddy, J. N. and Khdeir, A. A. Buckling and vibration of laminated composite plates using various plate theories. AIAA Journal, 27, 1808-1817 (1989)
[14] Erdogan, F. and Wu, B. H. The surface crack problem for a plate with functionally graded properties. Journal of Applied Mechanics, 64, 449-456 (1997)
[15] Li, Y. D., Jia, B., Zhang, N., Dai, Y., and Tang, L. Q. Anti-plane fracture analysis of a functionally gradient materials infinite strip with finite width. Applied Mathematics and Mechanics (English Edition), 27(6), 683-689 (2006) DOI 10.1007/s10483-006-0608-z
[16] Huang, G. Y., Wang, Y. S., and Yu, S.W. A new multi-layered model for in-plane fracture analysis of functionally graded materials. Acta Mechanica Sinica, 37, 1-8 (2005)
[17] Cheng, Z. Q. and Zhong, Z. Fracture Analysis of a functionally graded strip. Chinese Quarterly of Mechanics, 19, 114-121 (2006)
[18] Butcher, R. J., Rousseau, C. E., and Tippur, H. V. A functionally graded particulate composite: preparation, measurements and failure analysis. Acta Materialia, 47, 259-268 (1999)
[19] Delale, F. and Erdogan, F. The crack problem for a nonhomogeneous plane. Journal of Applied Mechanics, 50, 609-614 (1983)
[20] Jin, Z. H. and Noda, N. Crack-tip singular fields in nonhomogeneous materials. Journal of Applied Mechanics, 61, 738-740 (1994)
[21] Dai, Y., Zhang, L., Zhang, P., Li, S. M., Liu, J. F., and Chong, X. The eigen-functions of anti-plane crack problems in non-homogeneous materials. Science China: Physica, Mechanica & Astronomica, 8, 852-860 (2012)
[22] Liu, C. T. and Li, Y. Z. Stress strainfields at crack tip and stress intensity factors in Reissner's plate. Acta Mechanica Sinica, 16, 351-362 (1984)
/
| 〈 |
|
〉 |
Email Alert
RSS