Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T11:14:44.476Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Chaker, C. and Barquins, M., “On the Crack Compression in PMMA Plates,” Proceedings of the Second International Symposium on Thermal Stresses and Related Topics, pp. 275–278 (1997).Google Scholar
2Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Netherlands, pp. 358–361 (1953).Google Scholar
3Sih, G. C., Paris, P. C. and Erdogan, F., “Crack-Tip, Stress-Intensity Factors for Plane Extension and Plate Bending Problems,” J. Appl. Mech., 29, pp. 306–312 (1962).CrossRefGoogle Scholar
4Cotterell, B. and Rice, J. R., “Slightly Curved or Kinked Cracks,” Int. J. Fract., 16(2), pp. 155–169 (1980).CrossRefGoogle Scholar
5Ioakimidis, N. I. and Theocaris, P. S., “A System of Curvilinear Cracks in an Isotropic Elastic Half-Plane,” Int. J. Fract., 15(4), p. 299 (1979).CrossRefGoogle Scholar
6Chen, Y. Z. and Hasebe, N., “Fredholm Integral Equation for the Multiple Circular Arc Crack Problem in Plane Elasticity,” Archive of Applied Mechanics, 67, pp. 433–446 (1997).CrossRefGoogle Scholar
7Vroonhoven, J. C. W. van, “Stress Intensity Factors for Curvilinear Cracks Loaded by Bending and Torsional Moments,” Int. J. Fract., 68, pp. 193–218 (1994).CrossRefGoogle Scholar
8Shiah, Y. C., “Transverse Flexural Fracture of a Plate Containing an Arc Crack,” J. Chin. Inst. Eng., 25(2), pp. 189–198 (2002).CrossRefGoogle Scholar