Experimental and theoretical evaluation of influence of hole size on deformation and fracture of elastic perforated plate

As an ideal benchmark problem for the researches of solid mechanics and fracture mechanics, the influence of the hole size on the deformation and the fracture behaviors of perforated plates has been studied for more than sixty years. However, the seemingly simple problem has not been thoroughly answered yet. To gain more understanding of the hole-size dependence of the strain/stress concentration, the present study measured the stress and the strain concentration factors by using tensile tests together with the digital image correlation analysis. A noticeable hole-size dependence was observed for both concentration factors. The experimental observations can be reasonably explained in terms of a new formulation of strain energy density which considers the contributions of both the conventional strain and the high-order strain. It is shown that the strain energy density gets more uniformly distributed when the hole gets smaller. Accordingly, the maximum strain decreases as well. Due to the positive contribution of the higher-order strain energy, the material around the hole hardens and results in a concentration factor lower than three. Because of the influence of the length scale parameter, the stress cannot be scaled by a reference strain and this may lead to a discrepancy between the stress and the strain concentration factors.