Chapter 3 - Strain Gradient Plasticity Theory at the Microscale

Abstract

Many experiments have shown that materials have a strong size effect when the characteristic length scale is on the order of micrometers: The smaller, the stronger. Conventional plasticity theories cannot predict this size dependence of material behavior at the microscale because their constitutive models possess no internal length scale. In contrast, at the microscale, stress at a material point depends not only on the strain at the same point but also on the strain gradient at nearby points. Therefore, it is important to establish a micron-level or nonlocal continuum theory. In this chapter, three strain gradient plasticity theories are described: couple stress, stretch and rotation gradient, and mechanism-based strain gradient deformation.