**1. Introduction**

Probably the most recognized property associated with abrasitvity, i.e., "the ability of a material or substance to cause abrasive wear" [1], is hardness. An unambiguous proof of this relation is the possibility to define hardness by employing the wear that a particle can promote on a surface, as postulated former by Tonn [2].

The relation between hardness and wear depends on the level of severity imposed by the tribological system. In this sense, the mild and severe regimes of abrasion [3] can be associated with the abrasive particle/worn material hardness ratio [4]. For a better understanding, here, this tribological pair will be called 'indenter/worn material' because some examples will be associated with the scratching process. For this reason, the hardness ratio will be referred to as *Hi/Hw*.

For rescuing the historical information, one could ask when the effect of the *Hi/Hw* ratio on the abrasive wear was first experimentally determined. For that reason, five manuscripts were consulted to check the cited references on the topic. A summary of these experimental investigations can be shown in **Table 1**.

Based on data presented in **Table 1**, one can note that the investigations performed by Nathan and Jones [6] and Richardson [7] were most cited, but the former one can be considered that conducted by Wahl in 1951 [12].

For exemplifying the effect of the *Hi/Hw* ratio on friction, it is fashionable to mention the findings of Tabor [15]. He conducted an unusual experiment using a scratch device for investigating the existence of a critical value of the *Hi/Hw* ratio. The experiment consisted of a metal with a sharp point at this end (indenter role)


#### **Table 1.**

*References cited on the experimental values of the Hi/Hw ratio.*

scratching a sheet with variable hardness along its length, obtained by suitable heat treatment. The measurement of tangential force was able to define the mode of contact during the scratching, i.e., if the sharp point was able to scratch the metallic surface or not.

The indenter hardness indicated in **Figure 1** allows concluding that it will scratch the sheet's surface only if *Hi/Hw* ≥ 1.2. Here this value is referred to as critical hardness ratio (*Hi/Hw*)CRIT. Magnee [13], in his model formulation, called it a lethal abrasion coefficient.

The relation between the (*Hi/Hw*)CRIT and the abrasion regime - mild or severe wear - only makes sense if the wear mechanisms and observed damages on bodies' surfaces are well related. This task was done by Pintaude et al. [4], and it is summarized in **Figure 2**. Besides the findings described in [4], the detailed description of wear mechanisms could be found in Piazzetta et al. [16], who performed a Cherchar abrasivity test, sliding on nine rocks.

Considering the previous overview published [17], this review intends to incorporate experimental results to understand the concept of critical hardness ratio. The manuscript will be divided into three sections: i) the scratchability of materials, ii) the fragmentation of abrasive particles and size effects, and iii) the description of abrasion severity.

**Figure 1.** *Friction force determined between a metal point and a metal sheet of varying hardness [15].*

*Remarks on Wear Transitions Related to Hardness and Size of Abrasive Particles DOI: http://dx.doi.org/10.5772/intechopen.99324*

#### **Figure 2.**

*Summary of wear mechanisms and surface damages on surfaces associated with each wear regime of abrasion, separated by the hardness ratio* Hi/Hw, *following [4].*
