Effect of temperature and small-scale defects on the strength of solids

Abstract

Using a statistical-thermodynamic formulation, we investigate the failure of ideal and almost-ideal solids at finite temperature. We propose that the onset of failure in a defect-free crystal is associated with the loss of a metastable minimum in the free energy at a critical value of the applied tensile force. Using a mean-field approximation, we estimate the free energy of the two-dimensional Lennard-Jones crystal under stress and derive the temperature dependence of its ideal strength and other properties. These results are compared to Monte Carlo simulations of this system, and the mean-field estimate of the ideal strength is shown to be an upper bound to the values observed via simulation. We also show that atomic-scale defects such as vacancies and substitutional impurities significantly reduce the crystal’s strength as a result of stress enhancement effects. While the overall strength of a defective crystal depends strongly on both temperature and the nature of the defects, the maximum local stress that the crystal can sustain without failure is essentially independent of these factors.

Quantized fracture mechanics

“…0 the ideal strength is approached, if vacancies are assumed as the defect. The detailed statistical mechanics treatment (Selinger et al 1991) of the influence of defects on strength thus agrees with QFM. Note that by simply assuming 2 % a, as in the section on quantized strength levels, the predicted strength scaling factors are, respectively, 0.79, 0.65 and 0.56 (and so on, see figure 2).…”

“…6.3. Two-dimensional spring lattices The influence of one-, two-and three-adjacent vacancies in a two-dimensional triangular Lennard-Jones crystal was investigated by using a statistical-mechanics formulation (Selinger et al 1991); the results for the strength at 0 K were 0.78, 0.69 and 0.62 of the defect-free strength, respectively. The authors noted that they expected these values to become somewhat larger with increasing temperature.…”

Dynamics and instabilities of defects in two-dimensional crystals on curved backgrounds

“…The three dislocations whose dynamics are analyzed in this paper are displayed within the blue box. a result of stress enhancement effects [15]. Jain and Nelson [16] performed an extensive investigation of interstitials and vacancies in two-dimensional planar crystals and identified three different interstitials and vacancies, depending on their symmetry, as the prevalent structures.…”

What determines static friction and controls the transition to sliding?

“…The relation between n and d is also time dependent (n = n(d, t)) as indicated by the observed relaxations after increasing the applied stress by one step. One may ascribe a fracture-probability to each link (see fiber-bundle models [22]) which depends on the acting stress (which may fluctuate due to thermal motion), the environment of each link (how many neighboring links are already broken) and the redistribution of stress, as well as the rate of reformation of links [22][23][24]. We want to emphasize that we are mainly concerned with the stick behavior at a given frequency and we have neglected any dissipative aspects.…”