Enhanced gradient crystal-plasticity study of size effects in B.C.C. metal
2013-02-04T09:37:33Z (GMT) by
Owing to continuous miniaturization, many modern high-technology applications such as medical and optical devices, thermal barrier coatings, electronics, micro- and nano-electro mechanical systems (MEMS and NEMS), gems industry and semiconductors increasingly use components with sizes down to a few micrometers and even smaller. Understanding their deformation mechanisms and assessing their mechanical performance help to achieve new insights or design new material systems with superior properties through controlled microstructure at the appropriate scales. However, a fundamental understanding of mechanical response in surface-dominated structures, different than their bulk behaviours, is still elusive. In this thesis, the size effect in a single-crystal Ti alloy (Ti15V3Cr3Al3Sn) is investigated. To achieve this, nanoindentation and micropillar (with a square cross-section) compression tests were carried out in collaboration with Swiss Federal Laboratories for Materials Testing and Research (EMPA), Switzerland. Three-dimensional finite element models of compression and indentation with an implicit time-integration scheme incorporating a strain-gradient crystal-plasticity (SGCP) theory were developed to accurately represent deformation of the studied body-centered cubic metallic material. An appropriate hardening model was implemented to account for strain-hardening of the active slip systems, determined experimentally. The optimized set of parameters characterizing the deformation behaviour of Ti alloy was obtained based on a direct comparison of simulations and the experiments. An enhanced model based on the SGCP theory (EMSGCP), accounting for an initial microstructure of samples in terms of different types of dislocations (statistically stored and geometrically necessary dislocations), was suggested and used in the numerical analysis. This meso-scale continuum theory bridges the gap between the discrete-dislocation dynamics theory, where simulations are performed at strain rates several orders of magnitude higher than those in experiments, and the classical continuum-plasticity theory, which cannot explain the dependence of mechanical response on a specimen s size since there is no length scale in its constitutive description. A case study was performed using a cylindrical pillar to examine, on the one hand, accuracy of the proposed EMSGCP theory and, on the other hand, its universality for different pillar geometries. An extensive numerical study of the size effect in micron-size pillars was also implemented. On the other hand, an anisotropic character of surface topographies around indents along different crystallographic orientations of single crystals obtained in numerical simulations was compared to experimental findings. The size effect in nano-indentation was studied numerically. The differences in the observed hardness values for various indenter types were investigated using the developed EMSGCP theory.