The correlation between indentation hardness and material properties with considering size effect
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sing a two-dimensional axisymmetric finite element model, the indentation hardness has been studied with different combinations of material properties at different indentation depths. As the forward problem, the testing hardness is not only a function of material properties (E, ry, and n), indenter geometry (half apex angle, indenter shape), and friction, but also relating to the indentation depth. Based on the previous research on size effect, a model of correlation between several indentation experiment parameters (hardness H, maximum load Pm, and loading curvature C) and material properties has been derived. From simulation results, a better fitting result is obtained by the established model. Furthermore, the characteristic length h∗ in Nix/Gao model has been rewritten and discussed with material properties accordingly.
I. INTRODUCTION
As a powerful technique, the depth-sensing instrumented indentation has long been used to study the fundamental mechanical properties of materials including Young’s modulus and hardness, based on the experimentally determined load–unload curves (P–h).1–5 Many aspects such as indentation size effect theory,6–9 material mechanical studies as forward and reverse problem,2,4,10–12 the correlation between testing hardness and material properties, etc.1,13–19 have been focused nowadays in research widely. Since 1950s, Tabor20 proposed a model as Tabor’s relation between the hardness and the flow stress, i.e., H 5 krr, where the hardness H is related to a representative stress rr, which is the flow stress of a certain representative strain around 8%, and k is a constant value of 3. Later, Cheng and Cheng19 gave a relationship between the hardness and the basic mechanical properties of solids with Young’s modulus, initial yield strength, and work-hardening exponent for certain indenter shape. Wei and Hutchinson17 concluded that the hardness was a function of the most important variables in the indentation test, including the size of the indenter relative to the material length parameters, the strain hardening exponent, the ratio of initial yield stress to Young’s modulus, and the geometry of the indenter. Qu et al.9 studied the size effect via the conventional theory of mechanism-based strain gradient and established a indenta-ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tion model of indentation hardness H ¼ H0 þ 141a2 l2 Rb in terms of the spherical indenter radius R and original a Þ. indentation hardness H0 H0 ¼ 2:8rref f ep ¼ 5R a)
Address all correspondence to this author. e-mail: yuanyekingfl[email protected] DOI: 10.1557/jmr.2014.120 J. Mater. Res., Vol. 29, No. 12, Jun 28, 2014
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Huang et al.8 established an analytical model for nanoindentation hardness based on the maximum allowable geometrically necessary dislocation density. Recently, Cao et al.15 studied the sharp indentation in soft metals and found a simple relation between the nominal hardness, Hn, and the flow stress, rr, i.e., Hn 5 4.4rr. Based on the previous research, this study foc
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