Theoretical Transient Analysis of the Interaction Between a Dynamically Propagating In-Plane Crack and Traction-Free Boundaries

[+] Author and Article Information
Chwan-Huei Tsai

Department of Mechanical Engineering, Huafan University, Taipei Hsien, Taiwan 223, Republic of China

Chien-Ching Ma

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, Republic of China

J. Appl. Mech 64(4), 819-827 (Dec 01, 1997) (9 pages) doi:10.1115/1.2788987 History: Received July 26, 1996; Revised March 14, 1997; Online October 25, 2007


In this study, the transient response of a propagating in-plane crack interacting with half-plane boundaries is investigated in detail. The reflected waves which are generated from traction-free boundaries will interact with the propagating crack and make the problem extremely difficult to analyze. The complete transient solutions are constructed by superimposing fundamental solutions in the Laplace transform domain. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or the propagating crack faces. We focus our attention on the determination of the dynamic stress intensity factor. The dynamic stress intensity factors of a propagating crack in a configuration with boundaries and subjected to dynamic loadings are obtained in an explicit closed form. The transient solutions obtained in this study are in agreement with the experimental results from the literature. Some interesting phenomena observed in the published experimental works are also identified and discussed. It is concluded that the reflected waves generated from the boundary parallel to the crack have much stronger influence on the propagating crack than those generated from the boundary perpendicular to the crack. When the reflected waves generated from the boundary parallel to the crack return to the moving crack tip, the stress intensity factor will increase rapidly.

Copyright © 1997 by The American Society of Mechanical Engineers
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