Indentation size effects in crystalline materials: A law for strain gradient plasticity

Discrete dislocation plasticity analysis of the wedge indentation of films

“…14a. The Nix and Gao (1998) relation fits the discrete dislocation predictions reasonably well. However, the bestfit parameters for the o ¼ 10 indenter have a value of p 0 much lower than the value given by a continuum plasticity calculation.…”

“…8a and b, respectively. These dislocation distributions differ from what is assumed in an idealized model such as that of Nix and Gao (1998). One contribution to this difference is that the discrete dislocation calculations give rise to both statistically stored and geometrically necessary dislocations, but there is also a difference in the number and orientation of the slip systems.…”

“…(9) will not provide a good fit to the discrete dislocation predictions of the actual indentation pressure versus d relation. However, we proceed to demonstrate that the discrete dislocation predictions of the nominal indentation pressure versus indentation depth are reasonably well represented by the Nix and Gao (1998) relation. The nominal indentation pressure versus indentation depth predictions for the o ¼ 5 and 10 wedge indentation of the h ¼ 50 mm films of the reference material are plotted in Fig.…”

“…For the 10 and 50 mm thick films sink-in occurs around the indenter, while pile-up occurs in the 2 mm film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact sizeindependent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998 …”

“…Begley and Hutchinson (1998), Wei and Hutchinson (2003) and Qu et al (2006). Nix and Gao (1998) presented a simple analytical formula for the indentation size effect based on the idea of geometrically necessary dislocations. With the characteristic length scale in the model used as a fitting parameter, experimental data have been fit reasonably well, see, for example, Lou et al (2003).…”