Theoretical and Experimental Determination of Variable Length Scales

Professor Voyiadjis has dedicated tremendous effort in pioneering the establishment of a consistent formulation and experimental verification of length scales in metals and soils. The definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects. However, the full utility of the gradient-type theories hinges on one’s ability to determine the intrinsic material length that scales with strain gradients, and this study aims at addressing and remedying this situation. Based on the Taylor’s hardening law, a micromechanical model that assesses a nonlinear coupling between the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) is used here in order to derive an analytical form for the deformation-gradient-related intrinsic length-scale parameter in terms of measurable microstructural physical parameters. This work also presents a method for identifying the length-scale parameter from micro- and nano-indentation experiments using both spherical and pyramidal indenters. The deviation of the Nix and Gao (1998) and Swadener et al. (2002) indentation size effect (ISE) models’ predictions from hardness results at small depths for the case of conical indenters and at small diameters for the case of spherical indenters, respectively, is largely corrected by incorporating an interaction coefficient that compensates for the proper coupling between the SSDs and GNDs during indentation. Experimental results are also show that the ISE for pyramidal and spherical indenters can be correlated successfully by using the proposed model.

However, a fixed value of the material length-scale is not always realistic and different problems could require different values. Moreover, a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. This work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem. It is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro-bending and micro-torsion tests if a definite and fixed length scale parameter is used. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed by Voyiadjis and his group. This model assesses the sensitivity of predictions in the way in which the local and nonlocal parts are coupled. In addition a physically-based relation for the length scale parameter as a function of the course of deformation and microstructural features is proposed. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.