Stresses in a thin centrally cracked circular disk

Abstract

Full field solutions, based on small deformation three-dimensional finite element analysis of a center-cracked circular thin disk under mode I, and mixed mode I and II loadings have been performed. Under mode I loading, the solution for the stresses under small scale yielding has been compared with the HRR plane stress solution. The existence of a high triaxial state of stress at the near crack tip in the mid-plane of the disk has been possible due to the thickness effect. This is in contrast to the loss of triaxiality of stresses in the plane strain condition in the presence of a significant amount of compressive T-stress along the crack flanks [C. Betegon and J. W. Hancock, Two parameter characterization of elastic-plastic crack-tip fields. J. appl. Mech. 58, 104–110 (1991)]. The extent of the three-dimensional zone surrounding the crack front has been mapped and compared with the available experimental results of Chiang and Hareesh [Three dimensional crack tip deformation: an experimental study and comparison to HRR-field. Int. J. Fracture 36, 243–253 (1988)]. Under mixed mode I and II loading, the annular region surrounding the plastic zone in which the K-field dominates has been explored. This has been performed at a specific load level at which the fatigue crack extension experiment has been performed in the thin disk [T. K. Paul, Three-dimensional stress field near the crack front in a thin circular disk of elastic-plastic material (submitted for publication)]. The plastic zone shapes and sizes are quite different from the plane stress shape as obtained in the mode I analysis of a thin cracked sheet by Hom and McMeeking [Large crack tip opening in thin elastic-plastic sheet. Int. J. Fracture 103–122 (1990)] and plane stress mixed mode I and II by Shih [Elastic-plastic analysis of combined mode fracture problems, Ph.D. Dissertation, Harvard University (1973)].