The role of crystalline anisotropy in mechanical property extractions through Berkovich indentation

Abstract

This work uses crystal plasticity finite element simulations to elucidate the role of elastoplastic anisotropy in instrumented indentation P-h s curve measurements in face-centered cubic (fcc) crystals. It is shown that although the experimental fluctuations in the loading stage of the P-h s curves can be attributed to anisotropy, the variability in the unloading stage of the experiments is much greater than that resulting from anisotropy alone. Moreover, it is found that the conventional procedure used to evaluate the contact variables ruling the unloading P-h s curve introduces an uncertainty that approximates to the more fundamental influence of anisotropy. In view of these results, a robust procedure is proposed that uses contact area measurements in addition to the P-h s curves to extract homogenized J 2 -plasticity-equivalent mechanical properties from single crystals.

Nanomechanical behaviour of open-cell nanoporous metals: Homogeneous versus thickness-dependent porosity

“…For the extraction of mechanical properties, the hardness and the reduced Young's modulus values were evaluated at the beginning of the unloading segment by means of the method of Oliver and Pharr, 1992. In order to estimate the yield stress, σ ys , we used the methodology described in Alcalá et al, 2009;Casals and Alcalá, 2005. It is well known that during sharp indentation of a homogeneous material, the relation between the applied load and the displacement of the indenter can be expressed through (Cheng and Cheng, 1999;Giannakopoulos et al, 1994;Lawn and Howes, 1981):…”

“…being E eff the effective Young's modulus, η is assumed to vary with the indenter's shape (Cao et al, 2007;Meza et al, 2008;Xu and Li, 2008) and it is equal to 0.793 for a Berkovich indenter (Alcalá et al, 2009), and A max is the projected contact area between the material and the indenter at (h max , P max ). E eff can be written as:…”

Continuum crystal plasticity analyses of the plastic flow features underneath single-crystal indentations

“…These are referred to as the original and modified Bassani and Wu (BW) models for pure crystals [32,40] and the Peirce, Asaro and Needleman (PAN) model for alloyed counterparts [41,42]. These models have been extensively tested under uniaxial and indentation loading conditions in our prior investigations [30,32,34]. A clear difference between them concerns the value of the critical shear strength for dislocation gliding, 0 , which is $1.5 MPa and 60 MPa for copper and aluminum-copper, respectively.…”

“…By comparing these figures, one can readily discern that, although the more heterogeneous dislocation interactions assumed for the modified BW model lead to stronger variations in the uniaxial stress-strain curves in different crystallographic orientations as compared to those in the original BW model [32], this difference does not appear to influence the plastic zone shape beyond computational fluctuations. The two models, however, predict a somewhat different plastic zone size which, as discussed next, can be explained by reinterpreting the single-crystal indentation behavior in the context of a homogenized (J 2 -plasticity equivalent) response [30,34]. According to these investigations, it is noticed that the indentation behavior from the original BW model can be assimilated into that of an isotropic polycrystalline aggregate with a somewhat milder strain hardening response than the J 2 -plasticity equivalent polycrystalline copper from the modified BW model.…”

“…Based on three-dimensional continuum crystal plasticity finite element simulations of spherical and pyramidal (Berkovich) indentations performed in fcc metals with a defined set of slip systems [27][28][29][30][31][32][33][34], this paper seeks to (i) provide a fundamental mechanistic rationale into the influence of the spatial distribution of slip systems and the indentation-induced stress field upon the development of lobe and rosette formations in (001), (011) and (111) indentations; (ii) evaluate the activity of the individual slip systems and their role in the above morphologies; (iii) gain an insight into the plastic flow patterns developing directly underneath the imprint; and (iv) evaluate the role of the strain hardening response, including the heterogeneity in the strengthening brought by different types of dislocation interactions ( junctions), upon the indentation-induced plastic flow patterns.…”