Statistical Kinetics of Fracture of Heterogeneous Solids

Abstract

Up to the middle of the 50’s, in the physics of strength the agreed-upon notion was that the fracture of solids occurs when stress or deformation reaches their limiting values. The kinetic concept of the strength of solids opened up an essentially new approach to the problems of the physics of fracture [1]. From basing on extensive experimental material it was proved that the macroscopic fracture takes place not only when the stress limit is reached, but also at lower loading in case of the duration of their action is long. For a uniaxial tension, an empirical expression for lifetime (τ) of a specimen was obtained:

$$\tau = {\tau _0}\exp (\frac{{{U_0} - \gamma \times \sigma }}{{kT}})$$

(1)

where U ₀ is the activation energy of fracture whose value is close to the energy of sublimation; σ is the applied stress; T is the absolute temperature; k is the Boltzmann constant; γ is the structure-sensitive parameter which can be equal to 10–10³ of atomic volumes. The pre-exponential factor τ ₀ coincides with the period of thermal vibrations of atoms in a solid. Relation (1) is valid for a wide range of materials: metals and alloys, halide and semiconductor crystals, glasses, polymers, composites, and rocks [2]. It was established that exponential relations similar to (1) describe different processes: chemical reactions, diffusion, phase transitions. As the rate of these processes increase with temperature, they are called as thermoactivation processes.