Line-spring analysis of surface flawed plates and shells using deformation theory

The line-spring model is an efficient tool introduced by Rice and Levy [1] for the approximate analysis of surface flaws in plates and shells. A finite element implementation of the linear elastic line-spring was reported by Parks et al. [2]. The stress intensity factors obtained using this model were in close agreement to those calculated through three-dimensional continuum finite element solutions. Extensions of the model to elastic-plastic crack analysis have been undertaken by Parks and co-workers [3, 6, 7] using the incremental theory of plasticity. The deformation theory of plasticity is employed in the current formulation, and a Ramberg-Osgood description of the material is assumed. Further, we make use of the asymptotic results obtained by Shih and Hutchinson [4] for a small ligament subject to an arbitrary combination of tension and bending. An effective crack depth is taken into account in the elastic part of the current line-spring model. Numerical solutions are presented for a number of 3-D structural problems with surface cracks. Comparisons of the model's predictions with relevant continuum solutions are presented. Finally, we report observations regarding the shift of the loading axis with increasing loads. This phenomenon plays an important role in the discussion of HRR-dominance and the possible use of the J-integral as the single parameter for the characterization of crack tip fields.