It is proposed that the difficulties encountered with the meaning of subcritical crack growth arose from a misunderstanding of the Griffith equation. This equation is G=2γ for an equilibrium crack (stable or unstable) where γ is the intrinsic surface energy. When G>2γ the crack has a velocity v depending on the crack extension force G−2γ, even in a vacuum, and the following equation, well verified for adherence of elastomers, G−2γ=2γφT(v) where φT(v) is related to viscoelastic losses or internal friction at the crack tip, is generalized to other materials. At a critical speed vc, dφ/dv becomes negative; as a negative branch cannot be observed the velocity jumps to high values on a second positive branch, so that G=Gc is a criterion for crack speed discontinuity, not the Griffith criterion. The multiplicative factor 2γ on the right-hand side accounts for the shift of the v-K curves with environment. No stress corrosion is needed to explain subcritical crack growth. Subcritical crack growth in glasses and ceramics and velocity jump in brittle polymers are shown to agree with this proposal. This model can also explain stick-slip motion when a mean velocity is imposed in the negative branch. Occurrence of velocity jump or stick-slip depends on the geometry tested and the stiffness of the apparatus. A second kind of stick-slip associated with cavitation in liquid-filled cracks is discussed. When the surrounding medium can reach the crack tip and reduce the surface energy, even at the critical speed vc, the critical strain energy release rate Gc is reduced in the same proportion as γ, and a loading which would have given subcritical growth will give a catastrophic failure. Reduction of surface energy in the Rehbinder effect and in embrittlement by segregation is discussed. Finally, the evolution of ideas concerning the Irwin-Orowan formula and fracture toughness is examined.

Subcritical crack growth, surface energy, fracture toughness, stick-slip and embrittlement

The mechanics of crack initiation and propagation beneath an axisymmetric flat punch are investigated. The stress tensor given by Sneddon in 1946 is described. Numerical integration along stress trajectories gives the strain energy release rate as a function of both the crack length and its position relative to the indenter. Comparison with Hertzian fracture is made. The initiation of crack outside the circle of contact is shown to be due to the steepest gradient of stresses along the flaws near the circle of contact. The meaning of Auerbach's law is discussed. The Auerbach range is shown to correspond to the relatively flat maximum of the envelope of theG againstc/a curves for various starting radii. The influence of subcritical crack growth is also discussed. The model proposed in 1978 by Maugis and Barquins for kinetics of crack propagation between punches and viscoelastic solids is used. It is assumed that the static fatigue limit corresponds to the true Griffith criterion with intrinsic surface energy γ, and that the critical strain energy release rateG
c corresponds to a criterion for crack speed instability and velocity jump, so that no stress corrosion is needed to explain subcritical crack growth for 2γ<G<G
c. The 1971 experimental results of Mikosza and Lawn are easily interpreted by this model. Finally, experiments performed on a borosilicate glass give results that agree satisfactorily with the theory. Due to kinetic effects, an apparent surface energy of about 4.5 J m−2 is obtained, larger than the intrinsic surface energy and slightly lower than the fracture energy derived from high-speed experiments.

Fracture indentation beneath flat and spherical punches

The fatigue process in ceramic materials is reviewed It is shown that there are few cases where fatigue effects have been unequivocally demonstrated Mechanisms pertinent to the substantiated fatigue conditions are presented and discussed The need for further definitive experimentation to deduce the realm of fatigue, and its dependence on microstructure, vis-a-vis the fatigue models, is emphasized

Fatigue in ceramics

Double torsion tests in ambient air and liquid water have been used to establish critical stress intensity factors (KIc) and stress intensity factor (KI)‐crack velocity (v) diagrams for propagation of single tensile cracks in Whin Sill dolerite and Ralston Intrusive. KIcfor Whin Sill dolerite was 3.28 MN m‐3/2and for Ralston Intrusive was 2.58 MN m=3/2. No stress corrosion limit was encountered. Acoustic response was monitored during experiments on Whin Sill dolerite which spanned a velocity range from 5 × 10‐4to 5 × 10‐9m s‐1. The rate of acoustic emission was an indirect measure of crack velocity. The slopes of KI‐v diagrams and KI‐acoustic emission rate diagrams had similar slopes of c. 30 in double logarithmic coordinate frames. Slopes of the KI‐v curves for Ralston Intrusive fell from 43.4 in air to 23.3 in water, during tests which spanned a crack velocity range from 5 × 10‐4to 10‐8m s‐1. The activation enthalpy for dolerite between 20° and 75°C was determined by two complementary methods to be 30.4 × 1.9 and 33‐46 kJ mol‐1. Amplitude distributions of acoustic emission events depend strongly on KIand the ‘humidity’ at the crack tip. As KIcis approached, b‐values for dolerite in air decrease from 1.8 to 1.25, and for dolerite in water a decrease occurs in b‐value from 3.5 to 1.25. At KIgreater than 0.8 KIcthe b‐values for tests in water and in air are virtually identical. A discussion is given of these results in terms of their implications for earthquake mechanics. Copyright © 1983, Wiley Blackwell. All rights reserved

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A.G. Evans

Papers

Acoustic emission and crack propagation in polycrystalline alumina

Proof testing — the effects of slow crack growth