Validation of a phenomenological strain-gradient plasticity theory

Abstract

Strain-gradient plasticity theories have been developed to account for the size effect in small-scale plasticity in metals. However, they remain of limited use in engineering, for example in standards for nanoindentation, because of their phenomenological nature. In particular, a key parameter, the characteristic length, can only be determined by fitting to experiment. Here, it is shown that the characteristic length in one such theory derives directly from known quantities through fundamental dislocation physics. This explains and validates the theory for use in engineering.

Keywords:

• Plasticity of metals
• strengthening mechanisms
• strained layers
• dislocations
• strain-gradient theory
• critical thickness theory

Acknowledgements

Undergraduate students, David Lewis and Viktor Jevdomikov assisted with strain-gradient theory. Discussions with the late Tony (A.G.) Evans, and with Dabiao Liu, Andy J. Bushby and Alan J. Drew are gratefully acknowledged.