Wear modeling and the third body concept
Introduction
During the second part of the 20th century, much effort was employed to model wear. In particular, Archard proposed in 1953 [1] one of the first wear laws that proved to be a major contribution. It shows that dW/dt the mass of detached matter from the solids in contact, per unit time, is directly proportional to the applied pressure P multiplied by the sliding speed V. Equality is obtained by the “wear coefficient” K:
According to case, scientists have tried to apply Archard's law to their own experiments, changing the coefficient by several orders of magnitude and many have attempted to complete the law by adding new parameters. Today, 50 years later, hundreds of wear laws can be found in the literature, using more than 100 parameters [2] and most of them are derived from Archard's law. Unfortunately, very few can be chosen with confidence to predict the wear of a contact in a general way, since most are only valid for the range of experiments for which they have been established.
Our goal here is not to invent new laws for each type of experiment, material, etc. but to try to understand process of wear from a global standpoint. Definitions of wear rates, wear mechanisms and wear maps (as in [3] or [4]) that can be found in the literature are, most of the time, related to Archard's conception of wear, i.e. “how some particles are detached from the solids in contact”. This leads to the definition: wear is the process in which two materials are pressed together and displaced, such that they degrade to finally liberate particles, usually called “wear particles” (see Fig. 1).
However, in many applications, such particles can only be found by opening the contact after its operation. This suggests that these particles, trapped inside the contact, can play a role in accommodating differences of velocity between the two solids [5].
In the 1970s, Godet proposed the concept of third body to identify the medium at the interface between two solids in contact [6]. This medium is sometimes injected artificially, as in the case of oil and other types of lubricant. However, in the case of dry contacts, this third body is often composed of particles detached from the rubbing surfaces.
With the presence of such a layer of particles at the interface, the “wear mechanisms” should be very different. Godet highlighted several functions of the third body:
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it supports the load,
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it can participate in accommodation velocity,
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it separates the surfaces in contact, avoiding direct interactions.
The materials are no longer subjected to all the stresses and displacements imposed by the mechanism on the contact: the third body at the interface is able to shear without serious degradation, whereas this is not so for the two solid bodies (see Fig. 2).
The third body produced is thus able to protect the materials rubbing against each other from further degradation. For Godet [7] the list of “wear mechanisms” (abrasion, adhesion, fatigue, etc.) does not represent wear but merely “particle detachments mechanisms”.
So what is wear? For engineers in industry, wear may be defined as the way a contact looses its function. Classically, the loss of function is assimilated to a loss of mass by particles being detached from materials rubbing together. However, it has been shown that these particles prevent further degradation, thus wear should be considered as the loss of these third body particles for the whole contact. Consequently, wear is not only a particle detachment mechanism, but the process in which particles are detached from solids in contact, how they act inside the contact as the third body and, finally, how they are ejected from the contact.
Berthier [8] has synthesized this cycle into a Tribological Circuit (Fig. 3).
At the interface between the two “first bodies” in contact is a certain mass of third body (Mi). The detachment of particles is represented by source flow (Qs) of third body, while the ejection of the particles is represented by wear flow (Qw). It is therefore possible to write the equilibrium of the mass inside the contact as:
It can be seen that the wear process constitutes a form of competition between the source flow and the wear flow. These two flows do not act directly on each other; rather they both modify mass Mi of the third body particles at the interface. As shown in Fig. 4, the main consequence of particle detachment is an increase of the mass of third body (I). However, with the creation of an adequate interfacial layer (which supports the load and accommodates the difference of velocity), less particle detachment is expected (II). On the other hand, a particularly thick layer of third body will probably give rise to the activation of the particle ejection process (III), while the ejection of particles themselves obviously decreases the mass of the third body (IV).
In Section 2 we propose analyzing wear by dissociating the process of particle detachment from that of particle ejection. In particular, our aim will be to find two relations:
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one between Qs and Mi,
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and another between Qw and Mi.
Then, the whole process of wear will be described via the mass equilibrium (Eq. (2)). Using only simple analytical reasoning, an analytical wear model will be given that includes the concept of the third body. Its aim is not to give quantitative results for the prediction of any real wear problem, but to set new qualitative bases from which better comprehension of wear can be achieved.
This model was first suggested by a numerical approach [9] in which it is easy to control the input parameters and measure the flows of third body precisely. The following is a theoretical demonstration that explains the need to take into account the third body in order to understand the phenomenon of wear (Section 2). Like any theoretical model, it must be confronted with reality. In addition to encouraging numerical results, real experiments have been performed and are presented in Section 3. Finally, Section 4 describes how our model can be considered to widen classical approaches, by including the fate of the detached particles in the wear process.
Section snippets
Construction of an analytical model for wear that includes the concept of third body
As explained above, wear has often been understood as the process of particle detachment only. However, we also propose to study the effect of particles inside the contact and their ejection from it.
Since only one equation (i.e. (1), the mass equilibrium) is available, which involves three quantities (Mi, Qs and Qw) to characterize wear, our goal is to find a relationship:
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on the one hand, between source flow Qs and mass Mi of the third body trapped in the contact
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and on the other hand,
Experimental validation of the analytical model
The experimental results confirming the analytical wear model are presented after a short description of the experimental device.
Assessment: how this model repositions classical wear laws such as that of Archard
As stated in the introduction, Archard's law forms the basis for almost all the other law relating to wear [14]. The variety of these laws highlights the lack of understanding regarding the wear process. Consequently, our goal was not to improve any pre-existing law, but to start thinking along new lines.
One thing Archard's law (and as a consequence the majority of the other derived laws) does not take into account is the crucial lubricant role that can be played by an interfacial film (which
Conclusion and prospects
The wear model proposed above by numerical simulations [9] is justified analytically and validated experimentally.
In a general way, we show that the wear problem has to take into account the particle detachment process, and the flow of particles inside the contact until their ejection, as proposed in the analytical model. Although many studies of particle detachment mechanisms (often called “wear mechanisms”) can be found in the literature, very few studies have been carried out in order to
Acknowledgements
The authors wish to thank Anca-Iulia Biolan and Claude Godeau for the major role they have played in performing the experimental tests.
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