Size effects in yield and plasticity under uniaxial and non-uniform loading: experiment and theory

Abstract

The size of microstructural features has long been known to determine the strength of materials, as in the Hall–Petch effect of grain size. More recently, the importance of the size of the structure itself (thin foil, wire or pillar) or of the loaded volume (indentation) has been recognised. Many phenomenological theories have been proposed to account for the size effect. Here, experimental data of very high accuracy are reported on copper wire in torsion which distinguish the size effects of grain size and structure size on the elastic limit and on the flow stress at low plastic strain. The data are compared with less accurate data from similar wires in tension. The size effects are shown to arise by first-principles analysis of dislocation behaviour, exploiting the slip-distance theory of Conrad together with forest (Taylor) work-hardening theory, but with modifications to both theories to account for finite structure size. The resulting theory is compatible with the concepts of dislocation starvation and of strain-gradient plasticity. The size effect in the elastic limit is due to the constraint the size puts on dislocation curvature, while the size effect on the flow stress is due to the constraint size puts on dislocation mean free path and to the fate of a dislocation after it has moved.

Keywords:

• strengthening mechanisms
• plasticity
• size effect
• stress–strain measurement
• copper wire
• torsion
• tensile testing

Acknowledgements

The late Professor Tony Evans brought the Conrad slip-distance theory to our attention when he was a Distinguished Visiting Professor at Queen Mary in 2007. Herr Bruno Ehrler explained the coupling of grain size and structure size in Equation (1) when he was an ERASMUS exchange student from Aachen University at Queen Mary in 2007. We acknowledge very useful discussions at the ECI Barga 2009 conference, particularly with Professor Bill Nix, Professor Bill Gerberich, Dr Nigel Jennett and Dr Karsten Durst. EPSRC provided financial support for this programme under grant EP/C518004/1.