Micro-to-Nano Indentation and Scratch Hardness in the Ni–Co System: Depth Dependence and Implications for Tribological Behavior

Abstract

Although size effects in hardness have been extensively reported and analyzed for the static (indentation) case, much less attention has been given to these effects in non-static (scratch) hardness measurements. In the present work, size effects in the indentation and scratch hardness response of the Ni–Co system are evaluated by performing tests at several penetration depths, from the micro to the nanometer range. It is shown that, for all the range of compositions, the hardness response of these materials is strongly affected by the depth of penetration of the indenter: when the depth decreases, both the indentation and scratch hardness increase several times. This result denotes that, when studying the wear behavior of materials, special care must be taken concerning the scale one is dealing with, since the tribo-mechanical response of the material may change significantly from the micrometric to the nanometric contact scale.

Appendix: Geometrical Characterization of Nanoindentation and Nanoscratch Hardness Tests

The Veeco DNISP diamond AFM tip used in this work is an equilateral triangular base pyramid (Fig. A1a) with tip apex angle of ~93° (Fig. A1b). Assuming that the tip is infinitely sharp (Fig. A2), the angle between the back face and the axis of the pyramid (β) is ~47.5°, while the angle between the front edge and the axis of the pyramid (α) is ~45.5°. By using simple trigonometric relations, the following equations can be obtained:

$$ a = h\tan \alpha , $$

(A1)

$$ b = h\tan \beta , $$

(A2)

$$ w = \frac{a + b}{\cos 30}, $$

(A3)

Fig. A1

SEM micrographs of Veeco DNISP probe viewed from bottom (a) and side (b). The side view shows that the top part of the diamond mounted on the cantilever is pyramidal, with the axis of the pyramid perpendicular to the cantilever, whereas the bottom part, where most of the glue is located, has irregular geometry

Fig. A2

Scheme of Veeco DNISP tip viewed from bottom (top) and side (bottom)

with a, b, w, and h, defined in Fig. A2. Combining Eqs. A1–A3, the area function of the tip, A _p(h), can be obtained:

$$ A_{\text{p}} = \frac{{w\left( {a + b} \right)}}{2} = \frac{1}{\sqrt 3 }\left( {\tan \alpha + \tan \beta } \right)^{2} h^{2} . $$

(A4)

Replacing the apex semi-angles α and β by the values retrieved from the SEM micrograph of Fig. A1b, an approximated value of the area function of the DNISP tip can be obtained:

$$ A_{\text{p}} \approx 2.568h^{2} . $$

(A5)

A 2-D scheme of the DNISP tip scratching the surface of a material can be seen in Fig. A3. During the scratching process it is assumed that the perimeter of the contact is located at the surface mean line and, consequently, pile-up or sink-in effects do not contribute to the contact area. In this case w corresponds exactly to the width of the groove. Moreover, the contact between indenter and material only occurs at the two frontal faces of the pyramid (dark areas at the bottom part of Fig. A3). By introducing the values of a and b (given by Eqs. A1 and A2, respectively) in Eq. A3, and solving this equation in relation to h, the following relation is obtained:

$$ h = \frac{\sqrt 3 w}{{2\left( {\tan \alpha + \tan \beta } \right)}}. $$

(A6)

Fig. A3

Scheme of scratching process using the Veeco DNISP tip. The lateral view of the process and the bottom view of the indenter are shown, respectively, in the top and bottom parts of the figure

From Fig. A3 results:

$$ c = a\sin 30. $$

(A7)

Combining Eqs. A1, A6, and A7, c can be written as function of w:

$$ c = \frac{\sqrt 3 w}{{4\left( {1 + \frac{\tan \beta }{\tan \alpha }} \right)}}. $$

(A8)

The projected area of contact between indenter and material during the scratch test, A _s, is then given by:

$$ A_{\text{s}} = 2\left( {\frac{wc}{2}} \right) = \frac{{\sqrt 3 w^{2} }}{{4\left( {1 + \frac{\tan \beta }{\tan \alpha }} \right)}}, $$

(A9)

and, finally, the scratch hardness (H _s) can be determined:

$$ H_{\text{s}} = \frac{{F_{\text{N}} }}{{A_{\text{s}} }} = \eta \frac{{F_{\text{N}} }}{{w^{2} }}, $$

(A10)

with

$$ \eta = \frac{4}{\sqrt 3 }\left( {1 + \frac{\tan \beta }{\tan \alpha }} \right). $$

(A11)

Replacing the apex semi-angles α and β by the values retrieved from the SEM micrograph of Fig. A1b leads to η = 4.786 for the DNISP tip.

The depth of the nanoindentations, h _i, can be estimated by combining Eqs. 1 and A5:

$$ h_{\text{i}} \approx 0.624\sqrt {\frac{{F_{\text{N}} }}{{H_{\text{i}} }}} , $$

(A12)

where H _i is the indentation hardness measured from the AFM images of nanoindentations. The depth of the nanoscratches can be determined by combining Eqs. A6, A10, and A11 and replacing the apex semi-angles α and β by the values retrieved from the SEM micrograph of Fig. A1b:

$$ h_{\text{s}} \approx 0.898\sqrt {\frac{{F_{\text{N}} }}{{H_{\text{s}} }}} , $$

(A13)

where H _s is the scratch hardness measured from the AFM images of nanoscratches.