| To explain the size effect observed in experiments on micrometer-scale metallic structures, several theories of strain gradient plasticity have recently been developed. The scaling properties of four typical strain gradient theories, including Fleck and Hutchinson's CS and SG theories, Gao et al.'s MSG and TNT theory, are studied in Chapters 2 and 3. The small-size asymptotic scaling laws and load-deflection responses of all the four theories are obtained. After the scaling of the plastic hardening modulus for Acharya and Bassani's theory is determined in Chapter 4, the small-size asymptotic scaling laws obtained are then used to construct an asymptotic matching formula.; Recent tests of metal matrix nanocomposites show that the initial yield stress, at which the plastic strain vanishes, strongly increases when the particle size, D, decreases. This size effect is analyzed in Chapter 5 by considering the gradient of total strain, adopting BaZant's modification of MSG theory. The small-size asymptotic scaling of the initial yield stress is derived and an approximate size effect formula is obtained by asymptotic matching.; The size effect recently observed in pure tension tests of freestanding thin films can be explained by the existence of a boundary layer of a fixed thickness, located at the face that was attached during deposition to the substrate. The epitaxial boundary layer model proposed in Chapter 6 considers the effect of epitaxially influenced crystal growth on the dislocation density and texture, which cause significantly elevated yield strength. It is shown that this model may be combined with the strain gradient plasticity theories and the Hall-Petch relation for grain size effect.; In Chapter 7, a mathematically analogous size effect problem is studied for sea ice. The size effect on the nominal strength of a floating ice plate subjected to a vertical uniform line load is analyzed. The cracks produced by the load are treated as softening inelastic hinges. With only mild simplifications, an exact analytical solution can be obtained for this one-dimensional problem, which provides a good insight and understanding of the size effect of the floating sea ice plates. |
