Castigliano’s Second Theorem for Deformation Determination of a Cracked Body
Publication: Journal of Aerospace Engineering
Volume 28, Issue 5
Abstract
In this paper, a continuum theory capable of describing the deformation of a cracked body based on Castigliano’s second theorem is presented. The additional deformation due to the crack presence is described by the concept of stress intensity factor (SIF) of linear elastic fracture mechanics. Both the crack opening distance and the body deformation can be easily computed for any arbitrary loading on any boundary. As a demonstration, the proposed theory is applied to cases of edge-cracked infinite plane and edge-cracked beam, and the results show high accuracy when compared to those predicted by the numerical finite-element method.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was partially supported by the Natural Science Foundation of China (11172170, 10932007) and the National Basic Research Program of China (2010CB613003/5).
References
Broek, D. (1982). Elementary engineering fracture mechanics, Springer, New York.
Dym, C. L. (2010). “Extending Castigliano’s theorems to model the behavior of coupled systems.” J. Appl. Mech., 77(6), 061005.
Griffith, A. A. (1921). “The phenomena of rupture and flow in solids.” Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 221, Royal Society of London, 163–198.
Li, Z. (1990). “A method for calculating elastic deformations of crack body and its application prospects.” Int. J. Fract., 44(1), R7–R13.
Murakami, Y. (1987). Stress intensity factors handbook, Vol. 2, Pergamon Press, New York.
Potirniche, G. P., et al. (2008). “A two-dimensional damaged finite element for fracture applications.” Eng. Fract. Mech., 75(13), 3895–3908.
Qin, Q. H., and Yu, S. W. (1997). “Fracture and damage analysis of a cracked body by a new boundary element model.” Commun. Numer. Methods Eng., 13(5), 327–336.
Tada, H., Paris, P. C., andIrwin, G. R. (2000). The stress analysis of cracks handbook, 3rd Ed., ASME, New York.
Timoshenko, S. T., and Gere, J. M. (1972). Mechanics of materials, Van Nostrand Reinhold, New York.
Williams, T. N., Newman, J. J. C., and Gullett, P. M. (2011). “Crack–surface displacements for cracks emanating from a circular hole under various loading conditions.” Fatigue Fract. Eng. Mater. Struct., 34, 250–259.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 28 • Issue 5 • September 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jul 23, 2014
Accepted: Sep 23, 2014
Published online: Oct 27, 2014
Discussion open until: Mar 27, 2015
Published in print: Sep 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.