256 Prakt. Met. Sonderband 52 (2018) 
analysed, and therefore limited the model domain to a total scratch length of I =d + A. 
Finally, the law of variation of the depth between phases was assumed to be exponential. 
a 0 wm N d ; N2 .b) a= 45° a=11.3° 
E 0.01 ee A= 11.3% 0 
tome = 57° | -0.04 
z we 00 = 2.86% N . 
- -0.02 0.2 J ? LZ y 
; -0.2°% 0.2 4 
! 0.03| n= k7° a= 2.86° In 
: Wow 
io ify 
OÖ -0.04 0 ot 
Bh Ch 0.04 . 
i L002 2 ve 
Scratch distance in ym 0 ied 
Figure 2 — Height model for four different attack angles a) Height function 2D view, b) Full Ti. 
3D visualization of the selected scratch model, all axes display distances in pm. wr 
fie. 
Figure 2 shows the conceptual difference between these depths, the model domain and the 
behaviour of the selected function for different values of the effective attack angle a. {Rest 
Considering an wedge-shaped indenter of flank angle 26, Equation (3) can be rewritten in 
integral form: il 
2 d+ Foe: 
V, 2 je 
g = —_—— . 2 4 he 
Is = 5 tan8 J fan (%) + hy(x)?dx (4) N UM 
be r= 
After performing the integration in Equation (4) with the selected exponential function, 
simplifying, linearizing the exponential and logarithmic terms and rearranging the result, we 
arrive to: N 
V tan @ (hy — hg)? 
9s = Az fava + v(Aafav,a — Arfaba) + tana 2(d + AZ (dfaba + Afav,2) (5) 5 
Thus, it can be concluded that Equation (5) is an extension of the model presented in [8], = 
being reduced to the simpler form when the effective attack angle takes the value a = 90°. 
3. Disc: 
3. Experimental campaign Te 
To showcase the relevance of the aforementioned microstructural parameters in abrasive Er = 
wear settings, and also to complement the information already provided in the introduction oe 
and in the References [3-8], single nano-scratch tests were performed on three PM steels. i 
Wes, 
3.1. Materials is 
Three PM steels were chosen with different carbide composition, volume content, and Sh 
morphology. All steels were quenched and tempered. Table 1 summarises the main Wicuz 
features, steel type and chemical composition of each steel. The final polishing was SC 
performed with a diamond suspension containing an average grain size of 0.04 um. crs: 
fl