Numerical and experimental analysis of the notch effect on fatigue behavior of polymethylmethacrylate metal based on strain energy density method and the extended finite element method

Abstract

This work investigates the effect of the notch on fatigue behavior by combining two methods: the extended finite element method (XFEM) and the averaged strain energy density (ASED) method, which considers the combined action of bending and shear loading. The ASED method has already been proven accurate for assessing the failure of components in the presence of sharp and blunt notches, and several results are available in the literature for different materials. These results were compared with those obtained from the experimental tests reported here. The main purpose of this study was twofold: The first part is an experimental study of fatigue in rotary bending of specimens weakened by U and V notches made of polymethyl-methacrylate (PMMA) material. Two values for the radius were used for the U-notches (0.2 and 2 mm) and two angles for the V-notches (20° and 140°). The second part of the study consisted of performing several simulation tests using the Cast3m software for different angles and radii. The local approach based on the mean value of the ASED acted over a finite-sized volume surrounding the highly stressed regions. The maximum principal stress located at the notch edge defined the center of the control volume. If the notch is blunt, the control volume assumes a crescent shape with its width measured along the notch bisector line. When the notch is considered pointed (V-notched) or is a crack, the control volume becomes a circle with its center at the notch tip. The presence of geometric discontinuities in structures affects their lifetime by reducing it, producing a high concentration of local energy around the notch tip. Good convergence was obtained between the numerical simulation and experimental results for the ASED in a finished zone surrounding the notch tip.