Abstract
The strain energy density theory has successfully been used to address the problem of material damage and structural failure in problems of engineering interest. The theory makes use of the strain energy density function, dW/dV, and focuses attention in its stationary values. The directions of crack growth and yielding are determined from the minimum and maximum values of dW/dV, respectively, along the circumference of a circle centered at the point of failure initiation. Failure by crack growth or yielding takes place when these values of dW/dV become equal to their critical values which are material constants. In the present work the basic principles of the strain energy density theory were reviewed. Furthermore, this theory was used to study three problems of structural failure, namely the problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension, the problem of fracture instability of a plate with a central crack and two notches, and the problem of unstable crack growth in a circular disc subjected to two equal and opposite forces. The results of stress analysis were combined with the strain energy density theory to obtain the whole history of crack growth from initiation to instability. A length parameter was introduced to define the fracture instability of a mechanical system. Fracture trajectories were obtained for fast unstable crack propagation.
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Dedication The present article is dedicated to my good friend and colleague Anthony Kounadis on the occasion of his seventy fifth year anniversary. The article is a tribute to Anthony for his innovative contributions to the stability of structures that will remain indelibly imprinted in the history of the failure of structural problems. I wish him many more healthy and productive years ahead and further personal and professional successes.
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Gdoutos, E.E. Crack growth instability studied by the strain energy density theory. Arch Appl Mech 82, 1361–1376 (2012). https://doi.org/10.1007/s00419-012-0690-9
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DOI: https://doi.org/10.1007/s00419-012-0690-9