Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples

Indentation studies in b.c.c. crystals with enhanced model of strain-gradient crystal plasticity

“…Up to now, different modelling approaches have been proposed to characterise phenomena observed in compression of nano-and micron-sized pillars, such as a source-truncation model [19], a source-exhaustion hardening model [20], multiplication via a single-arm source operation [19,21], a weakest-link theory [22] and a dislocation-starvation/dislocation-nucleation theory [23]. The general premise of these theories is to represent dislocation-source operations in a discrete fashion, where strength of samples is linked to the source lengths.…”

Flow Stress in Submicron BCC Iron Single Crystals: Sample-size-dependent Strain-rate Sensitivity and Rate-dependent Size Strengthening

“…In contrast, σ bowout is due to dislocation-obstacle interactions, where the obstacles may be other dislocations (forest dislocation hardening), free surfaces (source truncation hardening [28]), etc. that impede dislocation line length growth.…”

“…σ bowout , as exemplified by the Orowan equation σ bowout ∝ μb/L, is on the other hand microstructural length scale sensitive but less sensitive toε, because of its usually much larger activation volume involved in bowing out through a critical curvature. [29] According to the source truncation hardening [28] interpretation of 'smaller is stronger'…”

“…and L is the mobile free-arm length [28] between an internal pinning point and the surface. From Equation (1), then, we can deduce that when L is large, for example when a large single crystal of BCC metal is undergoing stage-1 easy glide, σ friction σ bowout dominates the flow stress, so σ ≈ σ friction .…”

Finite element investigation of size effects on the mechanical behavior of nickel single crystals

“…For polycrystals, this phenomenon is linked to the low number of grains inside the cross section which leads to strong stress gradients [2][3][4][5]. starvation model or the troncature model [22,23]. In this case, only few dislocations are available to carry the plastic deformation due to their strong interactions with free surfaces leading to the famous "smaller is stronger" effect.…”