Torsion in Strain-Gradient Plasticity: Energetic Scale Effects

Abstract

Abstract. We study elasto-plastic torsion in a thin wire within the framework of the straingradient plasticity theory elaborated by Gurtin and Anand in 2005. The theory in question envisages two material scales: an energetic length-scale, which takes into account the so-called "geometricallynecessary dislocations" through a dependence of the free energy on the Burgers tensor, and a dissipative length-scale. For the rate-independent case with null dissipative length-scale, we construct and characterize a special class of solutions to the evolution problem. With the aid of such characterization, we estimate the dependence on the energetic scale of the ratio between the torque and the twist. Our analysis confirms that the energetic scale is responsible for size-dependent strain-hardening, with thinner wires being stronger. We also detect, and quantify in terms of the energetic length-scale, both a critical twist, after which the wire becomes fully plastified, and two boundary layers near the external boundary of the wire and near the boundary of the plastified region, respectively.

Modelling the torsion of thin metal wires by distortion gradient plasticity

“…Figs. 1 and 2 show the perfect agreement between the analytic results of Chiricotto et al (2012) and the numerical ones obtained by our FE implementation. Note that in Fig.…”

“…Eq. (31) can be easily particularised to the analogous equation obtained by Chiricotto et al (2012), who in fact applied the model of Gurtin and Anand (2005) to the torsion problem. Of course, in the case of irrotational plastic flow, Eqs.…”

“…In order to validate the FE model, we resort to the results of Chiricotto et al (2012), who have analytically solved the torsion problem governed by the Gurtin and Anand (2005) SGP, with quadratic defect energy in the form (5) and neglecting the higher-order dissipation. We can particularise our DGP to that case by imposing 0 p ϑ = at all the nodes of the FE model (irrotational plastic flow) and by setting 0 1 ℓ = and M 1 2 = in Eq.…”

“…(7), 0 χ = , and L¼ 0. Moreover, the analysis of Chiricotto et al (2012) is rate-independent, so that we choose appropriately small rate-sensitivity by setting N ¼ 5 Á EÀ 4 and 5 E 5 s 0 1 ε̇= · − − (see Eq. (17)).…”

Mass-constrained minimization of a one-homogeneous functional arising in strain-gradient plasticity

“…However, the only rigorous results we are aware of concerning scale effects are those in [6], where the role of L is analyzed in torsional symmetry.…”