THE ROLE OF STRAIN GRADIENTS IN THE GRAIN-SIZE EFFECT FOR POLYCRYSTALS

The role of grain size on the overall behaviour of polycrystals is inv estigated by using a strain gradient constitutive law for each slip sy stem for a reference single crystal. Variational principles of Hashin- Shtrikman type are formulated for the rase where the strain energy den sity is a convex function of both strain and strain gradient. The vari ational principles are specialized to polycrystals with a general mult i-slip strain gradient constitutive law. An extension of the Hashin-Sh trikman bounding methodology to general strain gradient composites is discussed in detail and then applied to derive bounds for arbitrary li near strain gradient composites or polycrystals. This is achieved by a n extensive study of kernel operators related to the Green's function for a general ''strain-gradient'' linear isotropic incompressible comp arison medium. As a simple illustrative example, upper and lower bound s are computed for linear face-centred cubic polycrystals: a size effe ct is noted whereby smaller grains are stiffer than large grains. The relation between the assumed form of the constitutive law for each sli p system and the overall response is explored.