A 50‐year retrospective review of three‐dimensional effects at cracks and sharp notches

Abstract

This review is a brief survey of three‐dimensional effects at cracks and sharp notches. The overall aim is to review developments over the past 50 years leading up to the current state of the art. The review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack or notch tip. It is also restricted to static loading and to constant amplitude fatigue loading. An enormous amount of theoretical and experimental information relevant to three‐dimensional effects has been published in the past five decades, so the review is, of necessity, highly selective. Theoretical topics covered are linear elastic fracture mechanics, including Volterra distorsioni, stress intensity factors, corner point singularities, crack front line tension, displacement analysis of cracks and notches, and through thickness distributions of stresses and stress intensity factors. Crack path topics covered are fatigue crack path constraints, determination of fatigue crack paths, oscillating crack fronts in thin sheets and the transition to slant crack propagation in thin sheets. Plane strain fracture toughness testing, including standards, is covered. Overall, it can be concluded that the existence of three‐dimensional effects at cracks and sharp notches has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three‐dimensional effects numerically in detail. Despite increased understanding, three‐dimensional effects are sometimes ignored in situations where they may be important.

A generalised approach to rapid finite element design of notched materials against static loading using the Theory of Critical Distances

“…In particular, in the vicinity of a stress concentrator the actual linearelastic stress distribution varies across the thickness, with this holding true both under normal [40,42,43] and shear loading [40,44,45]. Under these circumstances, the problem is that the maximum value of the local stress is away from the surface [40]. As far as real threedimensional components are concerned, this results in the fact that a safe design can be performed provided that the required FE models are done so that the adopted mesh is capable of capturing the through-thickness local effects.…”

“…When the proposed simplified approach is used to design real components, attention must be paid to correctly take into account three-dimensional effects and stress states near sharp and rounded notches [40,41]. In particular, in the vicinity of a stress concentrator the actual linearelastic stress distribution varies across the thickness, with this holding true both under normal [40,42,43] and shear loading [40,44,45].…”

Corner point singularities under in-plane and out-of-plane loading: a review of recent results

“…5 (Pook, 1968). Bažant and Estenssoro's analysis was not completely successful in that various paradoxes and inconsistencies appeared (Pook, 2013). For example, their analysis predicts that for a crack front intersection angle of 90 (Fig.…”

“…Application of Bažant and Estenssoro's analysis was successful in explaining some aspects of behavior in the vicinity of a corner point (Pook, 2013). For example, the parameter  is a function of Poisson's ratio, , and the crack front intersection angle, β (Fig.…”

“…The linear elastic analysis of homogeneous, isotropic cracked bodies is a Twentieth Century development (Pook, 2013(Pook, , 2015, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 (Williams, 1957) that widespread application of linear elastic fracture mechanics (LEFM) to practical engineering problems became possible. A stress intensity factor is the leading term of a series expansion of a crack tip stress field.…”