Small scale, grain size and substrate effects in nano-indentation experiment of film–substrate systems

Abstract

The mechanical properties of film-substrate systems have been investigated through nano-indentation experiments in our former paper (Chen, S.H., Liu, L., Wang, T.C., 2005. Investigation of the mechanical properties of thin films by nano-indentation, considering the effects of thickness and different coating-substrate combinations. Surf. Coat. Technol., 191,[25][26][27][28][29][30][31][32], in which Al-Glass with three different film thicknesses are adopted and it is found that the relation between the hardness H and normalized indentation depth h/t, where t denotes the film thickness, exhibits three different regimes: (i) the hardness decreases obviously with increasing indentation depth; (ii) then, the hardness keeps an almost constant value in the range of 0.1-0.7 of the normalized indentation depth h/t; (iii) after that, the hardness increases with increasing indentation depth. In this paper, the indentation image is further investigated and finite element method is used to analyze the nano-indentation phenomena with both classical plasticity and strain gradient plasticity theories. Not only the case with an ideal sharp indenter tip but also that with a round one is considered in both theories. Finally, we find that the classical plasticity theory can not predict the experimental results, even considering the indenter tip curvature. However, the strain gradient plasticity theory can describe the experimental data very well not only at a shallow indentation depth but also at a deep depth. Strain gradient and substrate effects are proved to coexist in film-substrate nano-indentation experiments.

The coupling effect of size and damage in micro-scale metallic materials

“…Relevant works include Acharya and Bassani (1995), Wang (2000, 2002a), Gao and Huang (2001), Abu Al-Rub and Voyiadjis (2006) and Askari et al (2015). With the strain gradient plasticity theories, size effect found in various micro-tests can be effectively predicted, such as the thin wire torsion and ultrathin beam bending (Fleck et al, 1994;Wang, 2000, 2002a;Huang et al, 2000;Gao and Huang, 2001;Mao et al, 2013;Bardella and Panteghini, 2015), the micro-and nano-indentation (Nix and Gao, 1998;Abu AlRub and Voyiadjis, 2006;Chen et al, 2007;Ouyang et al, 2010;Ma et al, 2012), compression of micropillars (Kiener et al, 2011;Zhang et al, 2014;Lin et al, 2016) as well as uniaxial compression and tension of particle-reinforced metal matrix composites (PMMC) (Fleck and Hutchinson, 1997;Chen and Wang, 2002b;Aghababaei and Joshi, 2011;Azizi et al, 2013;Legarth, 2015). The strain gradient theories have also been successfully applied to study some other interesting issues at micro-scales.…”

“…The strain gradient theories have also been successfully applied to study some other interesting issues at micro-scales. For instances, finite element method (FEM) combining strain gradient plasticity theories have been implemented to explain the cleavage fracture near the crack tip (Xia and Hutchinson, 1996;Chen and Wang, 2002c;Huang et al, 2014;. Strain gradient theories were also used to analyze void size effect on the stress distribution and void growth in porous solids (Liu et al, 2003;Wen et al, 2005;Monchiet and Bonnet, 2013).…”

Cylindrical nano-indentation on metal film/elastic substrate system with discrete dislocation plasticity analysis: A simple model for nano-indentation size effect

“…However, a series of studies indicated that the factors influencing the indentation size effects are quite complex, not only depending on the indenter geometry (shape and size) (Swadener et al, 2001(Swadener et al, , 2002Xue et al, 2002) but also on the film material properties (soft or hard) (Saha et al, 2001;Saha and Nix, 2002). In particular, when measuring the nano/micro-indentation hardness of thin films with the thickness of only several microns or dozens of nanometers, strong constraint to the dislocation glide in thin film from elastic substrate must be considered (Joslin and Oliver, 1990;Saha et al, 2001;Saha and Nix, 2002;Chen et al, 2007). The indentation of thin films usually displays very different behaviors from bulk metals; as a result, it is extremely difficult to measure the mechanical properties of film materials (Chen et al, 2005.…”

“…Some people argued that influences from the substrate can be ignored when the indentation depth is less than one tenth of the thin film thickness (Buckle, 1973); however, others claimed that this empirical rule is not always valid even for a hard film on a soft substrate (Pelletier et al, 2006). In fact, it is very difficult to insure that the indentation depth is always less than one tenth of the film thickness especially when the thickness of the thin film is on the sub-micron or nanometer order (Xu and Rowcliffe, 2004;Chen et al, 2005Chen et al, , 2007. Therefore, when employing nano/micro-indentation experiments to measure the mechanical properties of thin films with micron or nanometer thickness, many problems are still open for solutions (Oliver and Pharr, 2004).…”

Strain gradient plasticity analysis of transformation induced plasticity in multiphase steels

“…The focus has been primarily placed on measuring and modeling size effects in the response of small structures loaded homogeneously such as thin films (Nicola et al, 2003;Fredriksson and Gudmundson, 2005;Siska et al, 2007;Huang, 2007;André et al, 2007;Keralavarma and Benzerga, 2007), micropillars (Uchic et al, 2004;Tang et al, 2007) or to the response under large plastic strain gradients as promoted by nanoindentation (Delincé et al, 2006;Kizler and Schmauder, 2007;Chen et al, 2007;Abu Al-Rub, 2007), microbending (Stölken and Evans, 1998), wire torsion (Fleck et al, 1994), or the presence of 0020-7683/$ -see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2008.05.025 grain boundaries or phase boundaries (Evers et al, 2004;Balint et al, 2006;Janssen et al, 2006;Yang and Vehoff, 2007;Aifantis and Ngan, 2007;Liu et al, 2007;Ekh et al, 2007).…”