Quasi-static crack propagation

TLDR

Irreversible deformation during crack propagation in brittle materials or large cracks in ductile structures is confined to a small volume adjacent to the crack surfaces. The authors formulate a general theory of quasi‑static crack propagation, establish stability criteria under monotonically increasing load and displacement, propose a principle governing crack paths with experimental confirmation, and interpret crack spreading under cyclic loading. Quasi‑static crack experiments record load and displacement to deduce fracture toughness without stress calculations, vary crack speed to examine toughness dependence on front velocity, and present a theoretical framework and stability criteria. When fracture toughness is scale‑independent, stress intensity for geometrically similar cracks varies inversely with the square root of size, supporting the proposed crack‑path principle and providing insights into cyclic loading behavior.

Abstract

When cracks of any size spread in brittle materials and when large cracks spread in large structures of ductile materials, irreversible deformation is confined to a small volume of material contiguous with the crack surfaces. A general theory of quasi-static crack propagation under such conditions is formulated. The stability of crack propagation is subject to chosen constraints, and general stability criteria under monotonically increasing load and displacement are presented. Experiments in which cracks are spread quasi-statically are described, and by recording both load and corresponding displacement of load, the local specific work of crack spreading, or fracture toughness ( R ) may be deduced without calculation of the elastic stress distribution or even measuring the shape of the test piece. By causing the crack to spread at a range of speeds, variation of R with speed of crack front may be found. When R is independent of scale, it is shown that the stress intensity to propagate geometrically similar cracks in geometrically similar structures varies inversely as the square root of the size. A principle controlling the path of a quasi-static crack is proposed and some experimental confirmation is offered. An interpretation of crack spreading under cyclic loading is given.