Explaining the competition between strength and toughness in perforated plates using computational finite fracture mechanics

Abstract

We present a computational implementation of mode I finite fracture mechanics (FFM) that allows us to explore how hole shape and size affects the strength of linear elastic perforated plates. We compute the FFM predicted strength of a plate with centre crack, circle, diamond, and hexagon perforations of different sizes, as well as filleted (rounded) diamond perforations. Of the studied hole shapes, the diamond has the lowest predicted failure stress. By varying the toughness and strength material parameters, we elucidate how energy (toughness) and stress (strength) considerations compete for dominance in the coupled FFM failure criterion. We find that as the perforation radius goes to zero, failure is strength-dominated, while at small non-zero perforation sizes both strength and toughness play a role in determining failure. For perforation shapes with stress singularities (diamond, hexagon, centre crack), toughness dominates at larger perforation sizes, while strength strongly dominates at larger radii for circle perforations. The filleted diamond computations indicate that failure stress increases continuously as the hole shape deforms from a diamond into a circle, and so does the balance between toughness and strength in the coupled criterion. The presented results suggest new avenues for experimental work to further validate and explore the FFM coupled failure criterion. Our FFM implementation that uses Matlab and Ansys is provided as supplementary material.