The elastic threshold for strain-gradient plasticity, and comparison of theoretical results with experiments

Abstract

This work continues an earlier study, aimed at determining the threshold of elastic behaviour for specimens at the microscale. Given the size-dependent nature of the response the theory makes use of a model of rate-independent strain-gradient plasticity to establish conditions for lower and upper bounds to the threshold. The model is based on a family of yield or dissipation functions. In the earlier work bounds were established for one member of the family, in which the dissipation depends on the root mean square of the magnitude of plastic strain and its gradient. In this work bounds are derived based on a second alternative, in which the dependence is linear. These two alternatives are most relevant in determining length scales through fits to experimental results. The second aim of this work is to carry out comparisons between the bounds obtained theoretically, with experimental data on initial yielding for torsion tests. The correlations are in some cases reasonable, while in others there are discrepancies. Generally they illustrate the complexities – for example in accurate experimental determination of the elastic threshold, and of the length scale – in predicting aspects of behaviour at the microscale.