Influence of Size and Shape of Defects on Deformation Concentration and Brittle Fracture of Perforated Plates

The study investigates how different shapes and sizes of defects affect the fracture of a typical brittle material. The strain distribution and the fracture strength of perforated polymethyl methacrylate (PMMA) plates with three types of defects, namely, circular holes, rounded square holes, and blunt cracks, are measured. A noticeable size effect on the strain/stress concentration and the fracture strength has been observed, but it fails to be explained by the classical theory of solid mechanics. It is found that as the defect gets smaller, the material around the defect gets hardened and the deformation concentration becomes weaker regardless of the shape of the defect. When the defect is small enough, the deformation concentration nearly disappears. The unconventional mechanical behavior can be quantitatively described by a novel formulation of the strain energy density. And it is found that when the high-order deformation is properly treated, either the maximum principal stress or the equivalent fracture stress still can be used as an effective strength index.