Indentation of a hard film on a soft substrate: Strain gradient hardening effects

The equivalent axisymmetric model for Berkovich indenters in power-law hardening materials

“…1), Burgers vector b, shear modulus l, empirical coefficient a around 0.3, and M = 3.06 for fcc metals. The linear relation between the square of micro-indentation hardness H 2 and the reciprocal of indentation depth 1/h agrees with the experimental data for single crystal and polycrystalline copper (McElhaney et al, 1998) and single crystal silver (Ma and Clarke, 1995 micro-indentation of conical indenters has been extended to spherical indenters (Swadener et al, 2002;Qu et al, 2006) or conical indenters with spherical tips (Xue et al, 2002;Qu et al, 2004) or different indenter angles (Qin et al, 2007), to nanoindentation , and to bcc metals (Qiu et al, 2001) and thin films on substrates (Saha et al, 2001;Zhang et al, 2007). There are other studies of indentation size effect (e.g., Begley and Hutchinson, 1998;Niordson and Hutchinson, 2003; Abu Al-Rub and Voyiadjis, 2004) based on strain gradient plasticity theories (e.g., Hutchinson, 1993, 1997;Chen et al, 1999;Huang et al, 1999).…”

“…The above flow stress then becomes (i) triangular pyramid indenter (ii) conical indenter is the intrinsic material length in strain gradient plasticity, which represents a natural combination of elasticity (shear modulus l), plasticity (reference stress r ref ) and atomic spacing (Burgers vector b). Zhang et al, 2007) …”

The strength of friction stir welded and friction stir processed aluminium alloys

“…As a starting point for modelling, we may consider the density of geometrically necessary dislocations (GNDs) related to the deformation predicted by flow models. Detailed treatments of GNDs are available (see e.g., [18,28,29]), and in a simplified form the density of GNDs (ρ GND ) is related to the effective plastic strain gradient η p by [18,30]:…”

The Nano-Jackhammer effect in probing near-surface mechanical properties

“…A microstructurally-based strain gradient plasticity model, first introduced by Nix and Gao (1998) is commonly used to explain the effect. Strain gradient plasticity has been applied by several others to help understand microbend tests (Shi et al, 2008), plasticity (Abu-Al-Rub, 2008;Abu-Al-Rub and Voyiadjis, 2006;Qu et al, 2006;Volokh and Trapper, 2007;Wang et al, 2007), hardening effects (Abu-Al-Rub, 2008;Zhang et al, 2007), interface fracture and plasticity (Abu-Al-Rub, 2008;Siddiq et al, 2007) and the Taylor dislocation model (Hwang et al, 2004;Liu et al, 2005). The main concern is that the dissipative energy associated with even small oscillatory displacements of sharp tips could result in different properties (Cordill, 2007;Cordill et al, 2008), particularly with regard to dislocation nucleation and theoretical shear stress determinations.…”