Elastic recovery in the unloading process of pyramidal microindentation
- PDF / 494,353 Bytes
- 10 Pages / 612 x 792 pts (letter) Page_size
- 86 Downloads / 237 Views
It is confirmed on the basis of extensive test results for various ceramic and metallic materials that the indentation load P versus penetration depth h curves (P–h curves) both in loading and unloading processes are well approximated with the quadratic formulas of P ⳱ k1h2 and P ⳱ k2(h − hr)2, respectively, and unloading parameter k2 is quantitatively related to the elastic modulus E⬘ of the material indented, where hr is the residual penetration depth after a complete unload. The unloading/reloading indentation processes for a locally deformed conical/pyramidal impression are well represented by the equivalent mechanical process of a conical/pyramidal indenter with the effective face angle of eff ⳱ ( − r) on a flat elastic half-space, in terms of the inclined face angles  and r of the indenter used and of the residual impression formed, respectively. With utilization of the unloading parameter k2 and the relative residual depth of penetration r, a novel method is proposed for estimating E⬘. Theoretical considerations for a nonquadratic P–h unloading behavior are also made.
I. INTRODUCTION
Stilwell and Tabor conducted the very first quantitative study for the elastic recovery in indentation unloading.1 They used two tungsten carbide cones with inclined face angle  of 22° and 45°, having shown there is little change in the diameter of the impression during unloading but a significant elastic recovery in its penetration depth. Furthermore, they demonstrated that the indentation load P versus penetration depth h unloading curve is approximately expressed by a quadratic form of P ⬀ (h − hr)2 in terms of the residual penetration depth hr of impression after a complete unload. Lawn and Howes examined the elastic recovery at Vickers hardness indentations of various types of brittle ceramics and two steels (soft and hard steels).2 They also reported that the in-surface elastic recovery is negligibly small, compared with the recovery in the penetration depth, in addition to that the unloading occurs elastically, and essentially reversible in unloading/reloading processes. However, their elastic considerations on the unloading/reloading processes lead to a somewhat different quadratic P–h unloading formula of P ⬀ h2 − hr2. Extensive microindentation test results in the literature confirmed that (i) the in-surface recovery during unloading can be neglected and so the projected area Ar of residual impression after unloading is well approximated to the projected contact area Ac of impression at the peak a)
e-mail: [email protected] J. Mater. Res., Vol. 18, No. 7, Jul 2003
http://journals.cambridge.org
Downloaded: 04 Feb 2015
load Pmax and (ii) both the loading and the unloading P–h curves of pyramidal indentation are well approximated by P ⳱ k1h2 and P ⳱ k2(h − hr)2, respectively, in the regime of microindentation.3–6 In contrast to the quadratic unloading P–h relationship in microindentation, it has been well recognized that the relation for pyramidal nanoindentation can be described in its general form by P
Data Loading...
