Discrete Dislocation Studies On Several Topics Associated With The Micro-indentation Size Effects

In recent years, micro-electromechanical systems (MEMS) and micro/nano devices have been widely applied in more and more rising industries. Unlike traditional large-scale structures, the dominant dimension of components in MEMS is usually down to the micron or even below. As well known, with the decrease of the characteristic dimension, material's mechanical properties exhibit significantly size-dependent effect. Classical scale-independent continuum mechanics, due to lack of intrinsic size, fails to depict material mechanical behaviors in the micro-scale. With rapid development of micro-nano devices and apparatus, the knowledge about the mechanical behavior of materials at the micro- and nanoscale becomes increasingly important. It is vital to develop all sorts of micro-tests technologies and establish size-dependent plasticity theroy for safety design and reliability of the assessment.In the last decade, a series of micro-experiments, such as micro-bending, micro-torsion, the micro-tension/compression and micro-indentation, are repeatedly performed to measure the mechanical behavior of materials at the micron scale. Different from other experiments, the micro/ nano-indentation test is relatively simple, and thus has been extensively used to measure the mechanical properties of materials at the microscale or nanoscale, including the yield strength, modulus and stress-strain curve. A series of study has indicated that the factors influencing the indentation size effects are quite complex, including the indenter geometry (shape and size), the material property (micro-structure, non-uniform and module), the surface performance (roughness and energy) and so on. Although quantitative studies on indentation size effect and corresponding inherent mechanism have be widely addressed, some deep-seated problems relating to the size dependence of indentation are still open.In this dissertation, based on the two-dimensional discrete dislocation framework by Van der Giessen and Needleman (1995) and the ANSYS(?) finite element software, we have developed the two-dimensional semi-infinite plane indentation computional program, and adopted it to investigate the indentation size effects of various materials and micro-structures, including polycrystal, particle-reinforced metal matrix composite, film/substrate system and micropillar. Some remarkable conclusions are shown as following:1. For polycrystalline materials, the grain size and indenter radius play a very important role in the indentation hardness. (1) At the same depth, the indentation force and hardness increase with decreasing grain size and indenter radius. (2) The indentation hardness of ploycrystals depends on indentation position relative to the grain boundary. For the impenetrable grain boundary, the indentation force increases with the indenter approaching to the grain boundary. (3) A simple relation about the indentation hardness to the grain size and the indenter radius is established, with satisfactory agreement with the computational results.2. The mechanical behavior of compressed uniform micropillar displays a strong size effect. Due to the strong constraint from the base and the indenter, the size effect of micro-pillar strongly depends on the pillar geometry (i.e. the pillar size, the ratio of pillar height to width and the taper), the slip plane orientation and so on. It is shown that there exist at least two dislocation mechanisms governing the size effect of micro-pillar attached to a huge base, i.e. the dislocation slip-out from the micro-pillar sidewalls and the dislocation pile-up at the top end and the base. Generally speaking, for slender micro-pillars, when slip planes intersect with the micro-pillar free sidewalls, the dislocation slip-out mechanism dominates and the hardening ratio of stress-strain curves is low; however, for podgy ones, as most slip planes intersect with the constrained micro-pillar ends, the dislocation pile-up dominates and the hardening ratio of stress-strain curves is high; If the two mechanisms synchronously govern the micro-pillar plasticity, the size effect becomes complex.3. For simply periodically distributed particle-reinforced metal matrix composites, the particle size and indenter location have strong and complex influences on the response of nano-indentation. In cases of higher particle area fractions, due to the inevitable strong blocking effect of particles on the dislocation gliding, the nominal hardness generally increases with the decrease of particle size regardless of the indentation location. However, in cases of lower particle area fractions, the influence of the particle size on the variation of nominal hardness with indentation depth becomes relatively complex. Generally, the nominal hardness decreases as soon as the particle distribution in PR-MMCs is in favor of formation and development of long free slip bands,, and vice versa, regardless of the particle size.4. For film/substrate system, the indentation hardness depends on the indentation depth, the indenter radius and the film thickness. (1) At the same indentation depth h, the indentation hardness increases with the decrease of the film thickness L due to strong constraint to dislocations from substrate. (2) The dislocation distribution below indenter is closely associated with the film thickness. As the film thickness is small, dislocations can be activated and glide on the slip planes far from the indenter. While the film thickness is large, nearly all dislocations distribute in the rectangular zone below the indenter, which is different from the general semi-spherical distribution assumption. (3) Finally, we establish an empirical relation of indentation hardness H to the indentation depth h, the indenter radius R and the film thickness L, which is in agreement with the computational results.