A centrally cracked thin circular disk, Part I: 3D Elastic–plastic finite element analysis

Abstract

Abstract A full field solution, based on small deformation, three-dimensional elastic–plastic finite element analysis of the centrally cracked thin disk under mode I loading has been performed. The solution for the stresses under small-scale yielding and lo!cally fully plastic state has been compared with the HRR plane stress solution. At the outside of the 3D zone, within a distance of rσ o / J =18, HRR dominance is maintained in the presence of a significant amount of compressive stress along the crack flanks. Ahead of this region, the HRR field overestimate the stresses. These results demonstrate a completely reversed state of stress in the near crack front compared to that in the plane strain case. The combined effect of geometry and finite thickness of the specimen on elastic–plastic crack tip stress field has been explored. To the best of our knowledge, such an attempt in the published literature has not been made yet. For the qualitative assessment of the results some of the field parameters have been compared to the available experimental results of Chiang and Hareesh (1988) . Under mixed mode loading, the dominance of the elastic K-field outside the elastic–plastic region h!as been demonstrated at the load level at which the crack extension experiment has been performed in the thin disk. At this load level the extents of yielding are about four sheet thickness under mode I loading and about five to seven sheet thicknesses under mixed mode I and II. These extents of plastic zones are smaller than the crack length but not much smaller. In the mode I analysis, it has been demonstrated that in the elastic–plastic region, the elastic stress intensity factor, K , gives a fair estimate of the crack opening stress near the crack front at a distance of order 10 −2 in. On the basis of this analysis, the Linear Elastic Fracture Mechanics approach has been adopted in analyzing the fatigue crack extension experiments performed in the disk (Part II).