Mechanism of Fracture of Glass and Similar 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=λ0E/f, where E is Young's modulus and λ0 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 on glass, and moisture plus oxygen on certain metals, are important catalytic or fatigue-promoting factors because they reduce the unit activation energy, α. The theory leads to the equations t=(1/k0)eEα/fkTand logt=−logk0+(Eα/2.3kT)/f,where t is the time for fracture (duration of the stress), k is the Boltzmann constant, T the absolute temperature, and α and k0 are experimentally determined constants. The logarithmic expression has the same form as the Glathart-Preston [J. App. Phys. 17, 189 (1946)] empirical relation logt= −a/m+1/fm, which, in the case of glass, appears to be valid over a time factor of 107. 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. An equation, Eλ0=2γ, is proposed which connects Young's modulus and the critical fracture distance with the surface tension, γ, of the solid. Some examples are given.

Analysis of plastic deformation according to Von Mises' theory, with application to the South Silverton area, San Juan County, Colorado

“…Among the better known is that of Griffith (see Nadai, 1950, p. 196-198;and Ode, 1956), who investigated the effect of small cracks, flaws, or foreign bodies upon the strength of amorphous materials. N. W. Taylor (1947) has also proposed a criterion that relates the stress required to break a brittle material under simple tension to the duration of application of stress. It should be emphasized that the laws governing fracture and flow of solids are still imperfectly understood.…”

Investigation of PVC life at sinusoidal loading

“…As is shown in Figure 1, the results obtained from the tests coincide with the results calculated as per Eq. (1).…”

“…(1) for PVC, when testing its tensile strength: When testing cyclic durability, stresses at which life is within the range of several seconds to several days have b b n used. The Bailey integral13 should be valid for the ideal case of variable loads.…”

Mechanical failure of solid polymers

“…Тей-лор 138 считает, что при любой нагрузке в теле существуют связи, деформа-ции которых близки к предельным. Кинетика разрушения заключается в процессе сосредоточения таких связей в одном сечении за счет тепловых флуктуации.…”