The fracture mechanics of finite crack extension

This paper describes a modification to the traditional Griffith energy balance as used in linear elastic fracture mechanics (LEFM). The modification involves using a finite amount of crack extension (Δa) instead of an infinitesimal extension (da) when calculating the energy release rate. We propose to call this method finite fracture mechanics (FFM). This leads to a change in the Griffith equation for brittle fracture, introducing a new term Δa/2: we denote this length as L and assume that it is a material constant. This modification is extremely useful because it allows LEFM to be used to make predictions in two situations in which it is normally invalid: short cracks and notches. It is shown that accurate predictions can be made of both brittle fracture and fatigue behaviour for short cracks and notches in a range of different materials. The value of L can be expressed as a function of two other material constants: the fracture toughness K_c (or threshold ΔK_th in the case of fatigue) and an inherent strength parameter σ₀. For the particular cases of fatigue-limit prediction in metals and brittle fracture in ceramics, it is shown that σ₀ coincides directly with the ultimate tensile strength (or, in fatigue, the fatigue limit), as measured on plain, unnotched specimens. For brittle fracture in polymers and metals, in which larger amounts of plasticity precede fracture, the approach can still be used but σ₀ takes on a different value, higher than the plain-specimen strength, which can be found from experimental data. Predictions can be made very easily for any problem in which the stress intensity factor, K is known as a function of crack length. Furthermore, it is shown that the predictions of this method, FFM, are similar to those of a method known as the line method (LM) in which failure is predicted based on the average stress along a line drawn ahead of the crack or notch.