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In-Plane Bending Fracture of a Large Beam Containing a Circular-Arc Crack

Published online by Cambridge University Press:  05 May 2011

Y. C. Shiah ,
Jiunn Fang ,
Chin-Yi Wei  and
Y.C. Liang
Y. C. Shiah*
Affiliation:
Department of Aeronautical Engineering, Feng Chia University, Taichung, Taiwan 40724, R.O.C.
Jiunn Fang*
Affiliation:
Department of Aeronautical Engineering, Feng Chia University, Taichung, Taiwan 40724, R.O.C.
Chin-Yi Wei*
Affiliation:
Department of Aeronautical and Astronautical Engineering, Republic of China Air Force Academy, P.O. BOX 90277–4, Kangshan, Kaohsiung, Taiwan 820, R.O.C.
Y.C. Liang*
Affiliation:
Department of Aeronautical and Astronautical Engineering, Republic of China Air Force Academy, P.O. BOX 90277–4, Kangshan, Kaohsiung, Taiwan 820, R.O.C.
*
* Assistant Professor
** Associate Professor
** Associate Professor
* Assistant Professor
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Abstract

In this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

Keywords

Circular-arc crackbendingBeamMapping functionStress intensity factors
Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 3 , September 2002 , pp. 145 - 151
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

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