**1. Introduction**

Surface wear of metals is very important to many industries such as automobile and aerospace etc. The wear rate often limits the lifetime and the durability of machinery parts, and thus leads to major economic losses. Wear phenomenon often involves the contacts between two or among more asperities on material surfaces, resulting in breaking old and forming new atomic bonds and plastic deformation in the contact areas. At the atomic scale, if only a few asperities come into contacts, the actual contact areas are very small when comparing with the macroscopic contact size. Thus local stresses in these areas can be exceptionally high, leading to high degrees of localized plastic deformation and heat generation, and even possibly local melting among asperities. In adhesive wear, aluminum (Al) wear is especially important because the Al is a relatively soft metal which is highly reactive with oxygen. Generally, a fresh (newly-formed) aluminum surface has little or no protection from oxides, and is less stable than the alumina (Al2O3). Therefore, excessive stresses and temperatures in the Al contact areas can provide an activation energy to initiate extremely exothermic reactions of fresh Al surfaces with oxides.

**298**

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

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For example, during the rolling of an aluminum sheet by a steel roller, if excessive stresses are applied onto the sheet surface without lubricant coverings, the newlyformed (fresh) Al surface may easily react with oxides on the steel roller, resulting in the local melting of aluminum to bond onto the roller surface, a so-called severely adhesive wear which causes the catastrophic breakage of the steel roller.

Moreover, different L-J potentials from weak to strong values may describe the bonding strength between the Al- and the hard-asperities, which may reveal an effect of the inter-asperity interactions on the severely adhesive wear. In Section 2, we describe our methodology. In Section 3, we list the simulation procedures. In Section 4, we assess the results of our MD simulations. Finally, in Section 5, we

*Atomistic Simulation of Severely Adhesive Wear on a Rough Aluminum Substrate*

Molecular dynamics (MD) is a methodology which depicts motions of a manyparticle system using classical Newton's equations. It has been over 40 years since the first MD's application to a hard sphere system by Alder and Wainwright

[21, 22]. The MD method is particularly useful for studying dynamical properties of materials, and help researchers extract physical-insights from the modeling works. In the MD simulations, for a finite size system, classical trajectories of particles

*mi*€**r***<sup>i</sup>* <sup>¼</sup> **<sup>F</sup>***<sup>i</sup>* <sup>¼</sup> **<sup>P</sup>**\_ *<sup>i</sup>* ¼ � *<sup>∂</sup>Vtot*

A standard way to solve Eq. (1) was the finite-difference method: given a configuration of a system (positions and velocities of all particles) and other dynamical information at time *t*, the numerical integration would determine the new configuration of the system at a later time *t* + *Δt* (*Δt* is the time step). Commonly used methods in the MD simulations were *the Verlet algorithm* [23], *the Leapfrog algorithm* [24], and *the Gear predictor–corrector* (*GPC*) *algorithm* [25]. An ideal algorithm should be simple, run fast, require little memory and permit using a long time step *Δt* to hold the whole system trajectories as true as possible, and preserve conservation laws of momentum and energy. According to these, *the Verlet algorithm* can be regarded as the most widely used algorithm. *The leapfrog algorithm* was essentially identical to *the Verlet algorithm*. *The GPC* method was

usually more accurate as well as more complicated than others.

Commonly used statistical ensembles in the MD simulations were *the*

*microcanonical ensemble* (*NVE*), *the canonical ensemble* (*NVT*), *the isothermal-isobaric ensemble* (*NPT*) and *the grand canonical ensemble* (*μVT*). Please note, thermodynamic variables in parenthesis for each ensemble were fixed during the MD simulations. Usually, the (*NVE*) ensemble was most convenient to realize since all equations of motion conserve the total energy *E* and the particle number *N*, and the constant volume *V* was fixed by using periodic boundary conditions. The (*NVT*) ensemble was very commonly used for practical calculations. However, it needed to

where *Vtot* is the total potential energy of the system, *mi* is the mass of particle *i*, *P<sup>i</sup>* is the momentum of particle *i*, and *F<sup>i</sup>* is the total inter-particle force acting on particle *i*, and the "**∙**" denotes the first order of the time derivative. In practice, the convenience of using the MD simulation would mainly depend upon some particu-

*∂***r***i*

, (1)

in real space are traced by solving the Lagrange equations numerically: when choosing the Cartesian coordinates, these equations would become Newton's

summarize the results.

*DOI: http://dx.doi.org/10.5772/intechopen.94025*

**2.1 Molecular dynamics**

larly arithmetic algorithms to solve Eq. (1).

**2.2 Algorithms and statistical ensembles**

**2. Methodology**

equations

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During past six decades, studies on the Al wear under a dry-sliding (no lubricants) constraint have revealed that the large plastic strain would occur near subsurfaces on the Al-substrate when the wear process took place. Some experimental observations suggested that the Al wear rate be inversely proportional to the Al hardness because the higher Al hardness usually led to less plastic deformation on the Al-substrate [1]. Therefore, the understandings of the wear process may provide some valuable information for mechanisms of friction, lubrication and adhesion at the nano-scale [2–7]. Even if, during asperity contacts at the atomic-scale, it was still difficult to observe wear mechanisms in nano-seconds.

In theoretical study, molecular dynamics (MD) may simulate the nano-scale phenomena in a very short time. Thus during past four decades, advances in the MD simulations have helped researchers understand atomic mechanisms which brought two kinds of materials into contact. For examples, Landman *et al* used the MD simulations to observe the hard-tip (Ni) jump-to-contact, the plastic yielding, the adhesion to induce the atomic flow and the slip generation in the Au-substrate [8, 9]. Plimpton *et al* used the MD simulations to observe the nucleation of partial dislocation loops occurring within the contact areas where a displacementcontrolled hard sphere indented into a gold (Au) substrate surface. They found that the dislocation loops would grow rapidly into the substrate, but emerge at the surface edges, and then dislocation slips may produce complicated structures in the substrate [10–12]. Tanaka *et al* ran the MD simulations to observe that, during the two/three-body sliding contacts, an amorphous phase transformation would take place on the silicon substrate, i.e., the deformation on the silicon substrate would fall into adhering and plowing, but no wear regimes [13, 14]. Mendelev *et al* employed the MD simulations to observe that, during a flat ruthenium (Ru) slab downward into a gold (Au) substrate with a single asperity, the Au was very ductile at 150 and 300 K, while the Ru showed the considerably less plasticity at 300 and 600 K [15]. In our former works, we have ran several MD simulations on the Al deformation at the nano-scale, including the wear [16] and the nano-indentation on the Al-substrates [17]. However, our these studies adopted a very low strength of inter-asperity bonding between the Al-substrate and a hard-tip, in which we found that, even if there was a large plastic deformation on the Al-substrate, no Al atoms were removed from the Al-substrate if the inter-asperity bonding was below a critical value.

To summarize, although many interesting MD simulations for deformation and wear on metal surfaces have been discussed at the atomic scale, there have not yet any MD simulations to focus on investigating a severely adhesive wear between two sliding surfaces. In the actual manufacturing, this kind of wear would occur during the rolling of aluminum sheet and many other forming processes. So in this chapter, such the wear will be discussed by the MD simulations to find out what may occur when a soft Al-asperity on an Al slab is contacted by another asperity on a hard tool surface when these two surfaces are sliding relative to another. In our MD investigation, multiple MD simulations were conducted by varying some constraint factors: the inter-asperity bonding, the geometry overlap between two asperities, the relative impact velocity between two asperities and the starting temperature of the Al-substrate etc. In details, the Al-substrate was simulated by an EAM potential [18–20], while the hard-asperity was simulated by a strong Lennard-Jones (L-J) potential which may serve as a model for hard tool surfaces (with their oxides).

*Atomistic Simulation of Severely Adhesive Wear on a Rough Aluminum Substrate DOI: http://dx.doi.org/10.5772/intechopen.94025*

Moreover, different L-J potentials from weak to strong values may describe the bonding strength between the Al- and the hard-asperities, which may reveal an effect of the inter-asperity interactions on the severely adhesive wear. In Section 2, we describe our methodology. In Section 3, we list the simulation procedures. In Section 4, we assess the results of our MD simulations. Finally, in Section 5, we summarize the results.
