Three-dimensional elastic stress fields ahead of blunt V-notches in finitethickness plates

Based on detailed three-dimensional (3D) finite element analyses, elastic f ields in front of blunt V-notches in finite thickness plates subjected to u niaxial far-end tensile stress have been investigated. By comparison with t he corresponding planar V-notch fields and 3D through-thickness sharp crack fields, various aspects of the 3D fields of the blunt V-notches in finite thickness plates are revealed: (1) The plate thickness and notch angle have obvious effects on the stress concentration factor (SCF) K-t, which is hig her in finite thickness plates than in the plane stress and plane strain ca ses. When the notch angle is smaller than 90 degrees, the SCF is insensitiv e to the notch angle, but has close relation with the dimensionless plate t hickness. With the notch angle increasing further, the SCF decreases and th e effect of dimensionless plate thickness on it becomes weaker. (2) For any notch angle considered, the variation of the opening stress sigma (yy) nor malized by its value sigma (yy0) at the notch-root with the distance x from the root normalized by the root-radius rho, is insensitive to the plate th ickness and coincides well with the two-dimensional (2D) planar solution. ( 3) The 3D distribution of the out-of-plane constraint factor T-z = sigma (z z)/(sigma (yy) + sigma (xx)) is controlled by the plate thickness (B), the notch-radius (rho) as well as the notch angle (beta), but for deeper V-notc hes with beta less than or equal to 90 degrees, the distribution of T-z coi ncides well with that of a U-notch as well as a sharp 3D through-thickness crack and an explicit empirical expression of T-z is presented. (4) The dis tribution of the in-plane stress ratio T-x = sigma (yy)/sigma (xx) in front of the 3D V-notch is nearly independent of the plate thickness and coincid es well with the corresponding 2D solutions when the opening angle beta is smaller than 120 degrees. (5) The gradient of the out-of-plane strain epsil on (zz) is significant near the free surface in finite thickness plates. On the free surface, the epsilon (zz) can be 3.5 times the value on the mid-p lane, and the through-thickness gradient of the epsilon (zz) increases with decreasing notch angle. It is of interest to note that most of the field q uantities ahead of V-notches are insensitive to the notch angles when the n otch angle is smaller than 90 degrees.