Mechanism of fracture of brittle solids

Abstract

A theory is proposed which connects the stress, f, required to break a brittle material in simple tension, with its duration of application, t. The slow process preceding fracture is shown to be the orientation of the atomic network contained in an elementary prism of length r = λ 0 E f , where E is Young's Modulus and λ 0 is the critical elongation required for fracture. The rate-controlling factor is the activation energy, Eα f , for the orientation or rearrangement of the atomic network under the stress, f. Moisture in glass, and oxygen in metals, are important catalytic or fatigue-promoting factors because they reduce the unit activation energy, α. The theory leads to the equations t = 1 k 0 e Eα fkT and log t = − log k 0 + 1 f ( Eα 2.3kT ) , where t is the time for fracture (duration of the stress), k is the Boltzmann constant, T the absolute temperature, and α and k 0 are experimentally determined constants. The logarithmic expression has the same form as the Glathart-Preston ( J. Applied Phys. 17, 180 (1046)) empirical relation log t = − a/ m + 1/ fm, which, in the ease of glass, appears to be valid over a time factor of 10 7. The theory shows why a solid object does not have a single characteristic breaking strength, and how it adjusts its fracture mechanism to whatever stress is applied. Quantitative tests of the theory are made, using fracture data on various glasses and on one glass at various temperatures. Applicability of the theory to certain aspects of fatigue of metals under stress-corrosion conditions, as well as to failure by fracture of the more rigid organic plastics, is indicated. (This abstract is a revision and correction of an earlier one which appeared in Rheology Bulletin, Nov. 1046.)