Modes of deformation and weak boundary conditions in wedge indentation
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esearch Letters
Modes of deformation and weak boundary conditions in wedge indentation Narayan Sundaram, Yang Guo, and Srinivasan Chandrasekar, Center for Materials Processing and Tribology, Purdue University, West Lafayette, Indiana 47907-2023 Address all correspondence to Narayan Sundaram at [email protected] (Received 6 December 2011; accepted 5 April 2012)
Abstract We study strain fields and deformation patterns produced by wedge indentation of metals using high-resolution imaging, image correlation and simulation. A long-standing problem associated with simulation of narrow angle wedge indentation is overcome by introducing a weak form of the symmetry boundary conditions. The simulated deformation fields show good agreement with experiment. Based on strain localization, three distinct modes of deformation largely cover the range of wedge angles. Importantly, narrow angle wedge indentation is characterized by intense strain localization at points close to the free surface and thus offers a possible new tool to probe strain gradient effects.
The physics of indentation of metals by wedges, fundamental to hardness tests and assessment of mechanical behavior,[1–4] has a long history of theoretical and experimental investigation.[5–9] Theoretical tools for studying wedge indentation include slip-line fields[5] and cavity models.[10] Experimentally, deformation patterns have been obtained by studying changes in the shape of an inscribed rectangular grid[5] or using microstructural features as markers.[11,12] These experimental techniques are, however, limited in one or more of the following aspects: spatial resolution, temporal resolution and field of view. More recently, electron microscopy (electron backscatter diffraction, EBSD) has been used to determine lattice rotations in indentation of single crystals,[13] but not plastic strain or other measures of deformation. Further, given the complexity of indentation, slip-line fields, while useful, provide an over-simplified view of the deformation field. With these motivating factors, we use a combination of high-resolution imaging, particle image velocimetry (PIV) and finite-element analysis (FEA) to study wedge indentation strain fields with enhanced spatial and temporal resolution. Noteworthy prior studies of wedge indentation using FEA and related simulation include conventional elastic–plastic FEA,[14,15] discrete dislocation plasticity for films[16] and polycrystalline aggregates,[17] FEA using strain-gradient plasticity[18] and crystal-plasticity-based FEA for face-centered cubic single crystals.[19] Importantly, however, the application of FEA to indentation by narrow angle wedges (and cones) has been problematic and largely ignored. A recent attempt to resolve problems in simulating narrow angle indentation (cone) is noteworthy; it uses a needle-like protrusion from the indenter tip and removes a thin layer of material adjoining the symmetry axis from the specimen.[20] In fact, the aforementioned problem in FEA arises due to an unrealistic constraint generated by th
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