Nanoindentation with a Knoop indenter tip can reveal the plastic response of brittle materials, which is contained in the measured Knoop hardness anisotropy and force–displacement curves. Due to short length scales, details of the local dislocation distribution and dislocation stresses cannot be ignored in the analysis of experimental measurements. Inclusion of such effects leads to a non-local theory of plasticity, where gradients of strain fields are present in the expressions for stress. In this work, a non-local plasticity model is developed and implemented in the Abaqus finite element software. The geometrically necessary dislocations (GND) are quantified via the Nye tensor, and the backstress tensor is found from gradients of the Nye tensor by summation of dislocation stresses. Micro- and nanoindentation experiments on pentaerythritol tetranitrate (PETN) are simulated with the developed model. The average errors between simulated and measured micro- and nanohardness are around 13% and 25%, respectively, while the maximum errors are around 20% and 30%, respectively. The set of active slip systems for PETN that can match the experimental hardness anisotropy trends is {110}⟨11¯1⟩, {100}⟨011⟩, and {101}⟨101¯⟩. The GND hardening, the backstress, and the indenter shape are investigated in relation to the indentation size effects. The model predicts a weak effect of backstress on hardness, while the coupled effects of indenter shape and GND hardening are predominantly responsible for predicted size effects.
Milovan Zečević, Morgan C. Chamberlain, Alexandra C. Burch et al.· Modelling and Simulation in...· 0 citations
The deformation behavior of solders based on β-Sn is influenced by a high homologous operating temperature and microstructural heterogeneity. In this study, the deformation mechanisms of single-crystal and polycrystalline Sn were investigated using high-temperature nanoindentation combined with post-indentation microscopy. Constant strain-rate and dynamic mechanical analysis tests were conducted between 30℃ and 180℃ (0.6–0.9 T
m
) to quantify hardness, pop-in, and creep constitutive parameters. Hardness decreases with increasing temperatures (as expected), while pop-in loads shift to lower values at higher temperatures, indicating thermally assisted activation of plastic deformation. Indentations into polycrystalline Sn regions exhibit higher stress exponents (
n
≈ 6.8–7.4) and activation energies at moderate temperatures than indentations in single grains remote from any boundaries, reflecting the influence of grain boundary constraints in accommodating plasticity. At higher temperatures, both microstructures converge toward lower stress exponents and activation energies, suggesting a transition toward deformation mechanisms increasingly governed solely by thermally activated processes. Microstructural characterization reveals slip band formation, dislocation localization, and grain boundary sliding, demonstrating that deformation in polycrystalline Sn at these temperatures results from the combined effects of intragranular dislocation activity and intergranular strain accommodation.
J. Tien, D. Bahr· JOM· 0 citations
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