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

Based on detailed three-dimensional ®nite element (3D FE) analyses, elastic notch-root ®elds in plates with di€erent thicknesses and notch con®gurations subjected to uniaxial tension have been investigated. By comparing with the planar notch-root ®elds and crack-tip ®elds, the following characteristics of the 3D stress±strain ®elds near the notch front are revealed: (1) The plate thickness and notch con®guration have obvious e€ects on the stress concentration factor (SCF) Kt , which is higher in ®nite 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 q is insensitive to the notch con®guration and the plate thickness and coincides well with the two-dimensional (2D) planar solution when x=q < 0:75. (3) Strong 3D e€ects 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 ®eld 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±3Dʹʹ 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 con®guration and plate thickness. (4) In the 3D-e€ect zone, the gradient of the out-of-plane strain ezz in the thickness direction is signi®cant near the free surface in thick plates. On the free surface, ezz can be 3.5 times as high as the value on the mid-plane. It is also found that the inplane 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.