Charles Edward Inglis's 1913 Stress Concentration Paradox and Stop-Drilling Technique

A seemingly counterintuitive engineering practice—drilling a hole into a critical structure like a bridge beam or airplane wing to address cracks—is actually rooted in fundamental mathematics. The method's rationale traces back to Charles Edward Inglis's influential 1913 paper, where he modeled cracks as squished ellipses to understand why ship hulls fracture. Inglis's equation showed that local stress at the crack tip equals the remote stress multiplied by '1 + 2A/B', where A is crack length and B is the tip radius; if B nears zero (as in a razor-sharp crack), the local stress climbs toward infinity. This 'stress concentration' creates conditions where the atomic bonds at the tip unzip instantly, with the crack accelerating through the metal at sonic speed. By drilling a circular hole at the crack's end, engineers replace the effectively zero-radius tip with a large, round surface, causing B to skyrocket and stress to plummet by orders of magnitude. This principle visibly manifests: a pristine sheet of paper is hard to rip (force distributed evenly), but a small cut focuses stress, ripping the sheet dramatically faster. Introducing a round hole at the tip redistributes the force, halting crack propagation—a process called 'stop drilling'. This technique is widely used as a temporary repair for cracks in aircraft, ships, and machinery. Ultimately, changing the geometry of a structural flaw can mean the difference between catastrophic failure and survival.