Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip

FENG Wen-jie; LI Xiang-guo; WANG Shou-dong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(12): 1278-1284

FENG Wen-jie, LI Xiang-guo, WANG Shou-dong. Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1278-1284.

Citation:

FENG Wen-jie, LI Xiang-guo, WANG Shou-dong. Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1278-1284.

Citation:

FENG Wen-jie, LI Xiang-guo, WANG Shou-dong. Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1278-1284.

PDF( 293 KB)

Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip

1.
Department of Mechanics and Engineering Science, Shijiazhuang Railway Institute, Shijiazhuang 050043, P. R. China;

Received Date: 2003-01-19
Rev Recd Date: 2004-07-06
Publish Date: 2004-12-15

Abstract

Abstract

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered.The shear modulus is assumed to be functionally graded such that the mathematics is tractable.Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation.The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function.Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that,as crack driving force,they are equivalent for the present crack problem.Investigated are the effects of material nonhomogeneity and strip's highness on the dynamic fracture behavior.Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus,and that the dynamic behavior varies little with the adjusting of the strip's highness.
- dynamic stress intensity factor,
- torsional impact,
- penny-shaped crack,
- functionally graded strip,
- integral transform,
- energy density factor

FullText(HTML)

References(7)

References

[1]	Erdogan F. The crack problem for bonded nonhomogeneous materials under antiplane shear loading[J].ASME Journal of Applied Mechanics,1985,52(4):823—828. doi: 10.1115/1.3169153
[2]	Gerasoulis A, Srivastav R P. A Griffith crack problem for a nonhomogeneous medium[J].Internat J Engrg Sci,1980,18(2):239—247. doi: 10.1016/0020-7225(80)90023-3
[3]	Konda N, Erdogan F. The mixed-mode crack problem in a nonhomogeneous elastic medium[J].Engineering Fracture Mechanics,1994,47(4):533—545. doi: 10.1016/0013-7944(94)90253-4
[4]	Li C Y, Zou Z Z. Local stress field for torsion of a penny-shaped crack in a functionally graded material[J].Internat J Fracture,1998,91(2):L17—L22.
[5]	李春雨, 邹振祝, 段祝平. 功能梯度材料裂纹尖端动态应力场[J]. 力学学报,2001,33(2):270—274.
[6]	Copson E P. On certain dual integral equations[J].Proceedings Glasgow Mathematical Association,1961,5:19—24.
[7]	Zuo J Z, Sih G C. Energy density theory formulation and interpretation of cracking behavior for piezoelectric ceramics[J].J Theoret Appl Fracture Mech,2000,34(1):17—33. doi: 10.1016/S0167-8442(00)00021-5