Three-dimensional elastic stress fields near notches in finite thickness plates

Abstract

Based on detailed three-dimensional finite element (3D FE) analyses, elastic notch-root fields in plates with different thicknesses and notch configurations subjected to uniaxial tension have been investigated. By comparing with the planar notch-root fields and crack-tip fields, the following characteristics of the 3D stress–strain fields near the notch front are revealed: (1) The plate thickness and notch configuration have obvious effects on the stress concentration factor (SCF) K t , which is higher in finite thickness plates than in plane stress and plane strain cases. (2) The variation of the opening stress normalized by its value at the notch root with a distance x from the root normalized by the root radius ρ is insensitive to the notch configuration and the plate thickness and coincides well with the two-dimensional (2D) planar solution when x/ ρ<0.75. (3) Strong 3D effects exist within a radius of about three-eighth the plate thickness from the notch root. Further away from the root, the through-thickness variation of field quantities decreases and, at the radial distance of approximately 1.25 times the plate thickness, all of the through-thickness changes disappear completely. At least for notches with opening angles less than 90°, these “2D–3D” transition distances and the variations of the out-of-plane constraint normalized by its value at the notch root with a distance x from the root normalized by the plate thickness B are essentially independent of the notch configuration and plate thickness. (4) In the 3D-effect zone, the gradient of the out-of-plane strain ε zz in the thickness direction is significant near the free surface in thick plates. On the free surface, ε zz can be 3.5 times as high as the value on the mid-plane. It is also found that the in-plane stress ratio in an arbitrary thickness plate coincides very well with the 2D solutions within a distance of about three-tenth of the root radius from the notch root.