Elastic Limit and Strain Hardening of Thin Wires in Torsion

Abstract

A theory for the size effect in the strength of wires under torsion is reported and compared with data from thin copper wires. Critical thickness theory is solved rigorously and used to validate a useful approximation which is combined with slip-distance theory modified for a finite structure size. Experimental data with high accuracy around and above the elastic limit show excellent agreement with the theory. The results strongly imply that the physical principle is the constraint that size, whether grain size or structure size, puts on allowed dislocation curvature.

Torsion in Strain-Gradient Plasticity: Energetic Scale Effects

“…Our analysis confirms that the normalized energetic length-scale λ results in size-dependent strain-hardening: for thinner wires, a higher torque is needed to attain the same twist in the plastic range; that is, the torque-twist curves increase with λ. However, the experiments reported [9] show an additional size effect: thinner wires can withstand a higher torque without undergoing plastic flow; that is, the torque needed to induce a nonzero plastic shear increases as R decreases. This effect, which goes by the name of size-dependent strengthening, is not displayed by the solutions we construct (regardless of λ, plastic flow starts at θ = 1 and q(1) = 3/4).…”

Critical thickness phenomenon in single-crystalline wires under torsion

“…Generally, the size effect associated to 14 the non-uniform plastic deformation is attributed to the presence of geometrically necessary 15 dislocations (GNDs [11,12], sometimes they are called misfit dislocations [13], excess 16 dislocations [14,15], or non-redundant dislocations [16]). The size effect in the torsion of 17 thin metal wires has been analyzed by using various theories, for examples, strain gradient 18 plasticity (SGP) theories [1,2,[17][18][19][20][21][22][23][24][25][26][27], stress gradient plasticity theory [28,29], critical 19 thickness theory (CTT) [3,30,31], continuum dislocation theory (CDT) [15,16,32,33], and 20 by molecular dynamics (MD) and discrete dislocation dynamics (DDD) simulations [34][35][36][37][38][39][40]. 21…”

Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size

“…Ehrler et al, 2008), thin wires in torsion (e.g. Dunstan et al, 2009;Liu et al, 2013) and perhaps in tension (e.g. Bushby and Dunstan, 2011), micropillars in compression (see Korte and Clegg, 2010, for a compilation of much data), in foams (e.g.…”