Modelling the cyclic torsion of polycrystalline micron-sized copper wires by distortion gradient plasticity

ABSTRACT

In this contribution, we show that the distortion gradient plasticity recently proposed by our group, characterised by a higher-order plastic potential leading to reliable predictions under non-proportional loading, can predict experimental data of literature on the cyclic torsion of copper wires of diameter ranging from 18 to 42 $\mu \mathrm{m}$. To reach our goal, we plug our recent constitutive proposal in a framework that we have previously developed for the torsion problem, which is based on the pivotal theory established in 2004 by Gurtin, relying on Nye's dislocation density tensor to describe size effects in micron-scale metal plasticity. We implement the new model in a finite element code and identify its parameters by resorting to the Coliny evolutionary algorithm within the software Dakota.

KEYWORDS:

• Plasticity of metals
• cyclic deformation
• strain gradient plasticity
• size effect
• dislocation density tensor
• torsion

Acknowledgments

Dr Dabiao Liu is gratefully acknowledged for the provision of the experimental data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In order to avoid misunderstanding, we remark that in former contributions on conventional anisotropic plasticity within the finite deformation framework, different definitions of plastic spin have been introduced (see, e.g. [37] and references therein).

2 One should resort to a three-dimensional description of the torsion problem in order to explicitly model the grain boundaries. On the one hand, this would lead to a computationally almost impossible task, given the need for running several thousands of FE analyses to identify the material parameters. On the other hand, such sophisticated model would, in principle, allow a much more accurate description of the problem and the possibility of a much deeper discussion on the reliability of the length scale parameters entering the model.

3 We note that, by assuming a gauge length of 20 mm [38], in order to attain the (relatively small) maximum surface strain $\kappa a\approx 0.05$ reported in Figure 1, several tens of complete rotations between the wire ends have to be applied. In the light of the experimental set-up of Liu et al. [20], we infer that the extension to the finite deformation framework should not be relevant within our phenomenological theory, while such an extension might be significant in a three-dimensional model explicitly accounting for grain boundaries.

Additional information

Funding

This work was financed by the Italian Ministry of Education, University, and Research (MIUR).