Numerical investigation of stress concentration at the tip of the V-notch partially filled with material

Abstract

One of the ways to reduce the stress level in the vicinity of V-shaped notches is to fill them with material. The effectiveness of achieving this result is largely determined by the mechanical characteristics of the filling material. The study of the stress state in the vicinity of the tip of a V-shaped notch is generally related to consideration of the composite wedge problem, which in the framework of the classical theory of elasticity, can have singular solutions with infinite values of stresses at the wedge vertex. The paper presents solutions for a composite closed wedge, which allows us to determine the range of mechanical characteristics and angles of the composite wedge, at which there is no stress singularity at the vertex. The proposed variant of the computational procedure, which is based on the finite element method, makes it possible to find a relationship for stresses in the vicinity of the wedge vertex, providing the evaluation of the stress singularity indices and constants known as stress singularity intensity factors. In real industrial technologies currently used for filling notches with another material, a small region (cavity) generally remains unfilled in the vicinity of the notch tip. This defect becomes more pronounced at small notch angles. In the presence of a cavity at the notch tip, a singular solution exists at any mechanical characteristics of the filling material. The developed algorithm has been used to calculate the values of the intensity factor of singularity for a V-shaped notch partially filled with materials, which either eliminate or preserve the stress singularity in the case of complete filling. The results obtained demonstrate that at the tip of the notch partially filled with another material the singularity intensity factor can be significantly reduced.