Discrete dislocation plasticity modeling of short cracks in single crystals

Scaling of discrete dislocation predictions for near-threshold fatigue crack growth

“…[23][24][25]. We emphasize that the irreversibility in the cohesive relation does not alter the cohesive strength.…”

“…The formulation is outlined here and further details and references are given in Refs. [23][24][25]. Geometry changes are neglected and symmetry about the crack plane is assumed.…”

“…All calculations presented here were carried out on a tensile bar 2H × W = 16 × 4 µm and at the imposed loading rate U / H = 100 / s. The discrete dislocation plasticity predictions of the tensile response are not sensitive to the specimen size [25]. The plane strain tensile response of materials (i)-(iv), with the source and obstacle strengths mentioned previously, is shown in Fig.…”

“…The dislocation density increases gradually with the number of loading cycles: as in Refs. [23][24][25], it is the evolving dislocation structure that gives rise to cycle-by-cycle crack growth. Furthermore, for approximately equal values of applied ⌬K I , the three materials in (Fig.…”

“…Here, we analyze the scaling of the fatigue crack growth rates with the yield strength, Young's modulus and cohesive strength and energy in the near-threshold regime using the discrete dislocation plasticity framework used in previous studies to analyze the fatigue threshold [23], the Parislaw behavior of long cracks [24] and the accelerated growth rate of short cracks [25]. A key feature of the approach is that the material model and fracture properties are independent, with the material model applicable whether or not there is a crack, see e.g.…”