The effect of interfaces on the plastic behavior of periodic composites

Abstract

A theoretical framework is given for predicting the effect of microstructural size on the strength of N-phase periodic composites. It is assumed that the strength is elevated by plastic strain gradients in the bulk and by the resistance to plastic slip at internal material interfaces. Calculations are given for a two-phase, power-law material with a cubic array of spherical reinforcement particles. The macroscopic stress–strain relations are found to exhibit Hall–Petch behavior, and the size effect becomes more pronounced with increasing interface strength. Moreover, size effects are predicted for both yield strength and plastic hardening rate of the composite. The relative magnitude of these two effects is sensitive to the choice of constitutive description of the interface.

Keywords:

• elastic-plastic materials
• composites
• material interfaces
• strain-gradient
• plasticity

Acknowledgements

This research is based upon work supported by the European Community through the Sixth Framework Programme Integrated Project IP 026467-2 MANUDIRECT, and by the Engineering and Physical Sciences Research Council (EPSRC), UK, through a Materials Modelling Programme.

Notes

Notes

1. Sharper bounds could obviously be obtained by using a field t(x) which is uniform within each phase, but at the expense of more complicated computations.

2. In granular composites, all phases play the role of ‘grains’, as in a polycrystal, and there is no clearly defined matrix phase.