Special Session 15: 

The Dugdale criterion as generalized energy criterion

Maria Specovius-Neugebauer
University of Kassel
Germany
Co-Author(s):    Sergej Nazarov
Abstract:
We consider a plane elasticity problem in a domain $\Omega\subset \mathbb{R}^2$ with an internal straight crack. Dealing with small strains is an essential assumption while using the linear elasticity theory, however, the asymptotic behavior of the solution $u$ near the crack tips leads to unbounded strains (and stresses) which needs further physical interpretation. In the model of Dugdale it is assumed that the stress cannot overcome a certain yield stress $\sigma_c$. Therefore ahead of the crack $\Lambda$ a (one dimensional) plastic zone appears, where $\sigma_{22}=-\sigma_c$ and $\sigma_c$ is large in comparison with the external loading. Leonov and Panasyuk used the argument that in the crack mouth there exist strong adhesive forces which must be overcome to initiate the growth of the crack. Both models lead to the same nonlinear mathematical problem and the same fracture criterion for crack growth under Mode I loading. It can be generalized to the case of orthotropic media, like in the case of isotropic media it coincides with the classical energy criterion (and Irwin`s criterion, resp.) asymptotically. With asymptotic analysis it can be shown how the geometry of the problem influences the solution, this leads to a refined Dugdale-criterion. By introducing a generalized energy functional this refined criterion can be interpreted as an energy criterion as well.