Delayed fracture in glass

An important delayed-fracture effect is found for mineral glass. A likely cause might be the gradual spread of Griffith cracks, but a theorem due to Griffith states that cracks do not spread below a certain average stress, and that at this stress they spread catastrophically. In the present paper, Griffith's theorem is re-examined and it is shown that in materials having atomic constitution, fracture does not occur catastrophically at the Griffith stress; the Griffith stress is the least at which a crack may start to spread by a process of splitting, and the rate of spread is controlled by the rate at which thermal motions overcome energy barriers. Catastrophic fracture does not occur until the stress at the end of the crack equals the maximum a material can withstand. An improved method of estimating this stress from thermal data is given. The best estimate is that the maximum stress is equal to the intensity of the given stress system which makes the latent heat of evaporation zero. The rate of spread of cracks by Griffith's process is considered to be too slow to account for much of the delayed-fracture effect in glass. Other processes are considered under the headings of approach to homogeneous and heterogeneous equilibrium. The attainment of homogeneous equilibrium under stress in materials in equilibrium when stress-free involves, in the absence of phase changes, but a small entropy change, and is not likely to cause an appreciable time effect. Glass, however, is not in thermal equilibrium when stress-free, the high temperature phase persisting at temperatures below the transition point. On account of the high internal viscosity of glass, approach to equilibrium effectively ceases soon after manufacture. Stress reduces the internal viscosity and enables approach to equilibrium to continue. Because of the concentration of stress at the ends of the cracks, the approach to equilibrium made possible by stress is much faster in the material at the ends of the cracks than elsewhere, and as attainment of equilibrium involves volume shrinkage, the stress at the end of the crack is increased and the crack spreads. This effect would be expected to cause an appreciable delayed fracture effect. Two effects are considered under the heading of approach to heterogeneous equilibrium. The first is evaporation of the material at the end of the crack. An estimate of delayed fracture due to this cause suggests that it is unimportant. A much more important cause of delayed fracture is atmospheric attack of the glass. Due to concentration of strain energy, the material at the end of the crack has a much higher free energy than normal unstressed glass, and is therefore much more chemically active. Atmospheric attack will result in the formation of a complex of glass and atmospheric constituents. The crack will extend continually if the strength of this complex, during or after its formation, is less than the load imposed on it. Changes due to stress in the stable phase at room temperature are considered, but these are not likely to be important for glass, as in this material the high-temperature phase persists at room temperature. Phase changes under stress may have important effects on the behaviour of other materials. Included in the paper are formulae for the stress coefficients of vapour pressure, entropy and phase-transition temperature, of material subjected to a generalized stress system.