Adhesive wear law at the single asperity level

Abstract

Macroscopic wear experiments in mid 1950s suggested an empirical wear relation: wear volume is linearly proportional to load and sliding distance. Recent asperity-level wear experiments and simulations reported a breakdown of this law at the nanoscale, posing the fundamental question: Is the macroscopic wear relation recoverable at the asperity level? Here we show that discrepant observations of wear relations can be reconciled into a unified framework. Using systematic long-timescale coarse-grained molecular dynamic wear simulations, we show that a linear adhesive wear law can be recovered at the single-asperity level only if the material removal is dominated by plastic deformation, confirming the longstanding Archard's theoretical hypothesis. Alternatively, the relation breaks down when cleavage fracture or thermally activated atomic detachment governs the loss of material at the asperity level.

Introduction

Decades of engineering-scale wear experiments (Burwell and Strang, 1952a, b; Vakis et al., 2018) affirmed the existence of a simple empirical wear law: the wear volume (i.e. the total volume of wear debris) linearly scales with the macroscopic load acting normally to the interface and sliding distance. To rationalize this relation at the asperity level, (Archard, 1953) argued that the only possible mechanism to recover this relation at the asperity level is the removal of lumps from contact areas formed by plastic deformation. He accordingly developed an adhesive wear model by considering that adhesive sliding between two asperities of size a results in the removal of volume ~a³ over an effective sliding distance ~a, resulting in the wear rate ~a². The model recovered a linear correlation between the wear rate (i.e. wear volume per unit of sliding distance) and the load carried by the junction, assuming fully plastic deformation at the asperity tip. Recent atomic force microscope (AFM) wear experiments (Bhaskaran et al., 2010; Gotsmann and Lantz, 2008; Jacobs and Carpick, 2013; Liu et al., 2017; Maw et al., 2002; Schirmeisen, 2013; Shao et al., 2017) and atomistic simulations (Chandross et al., 2008; Sha et al., 2013; Sorensen et al., 1996; Yang et al., 2016) have questioned this picture by reporting breakdown of the linear wear relation at the asperity level (Bhaskaran et al., 2010; Liu et al., 2010; Vahdat et al., 2013). This discrepancy poses the fundamental question whether the linearity between the wear volume and the applied load is a collective result of wear events at the multi-asperity contact or a phenomenon that can be recovered at the single asperity level.

Contrary to Archard's assumption (i.e. material detachment by fully plastic deformation), microscopic analysis of wear at small scales (Jacobs and Carpick, 2013) showed that the breakdown of linear wear relation is associated with the existence of other wear mechanisms at the asperity level such as atom-by-atom removal (i.e. atomic attrition mechanism) (Bhaskaran et al., 2010; Gotsmann and Lantz, 2008; Jacobs and Carpick, 2013) and asperity cleavage fracture (Chung et al., 2005; Liu et al., 2010). Nanoscale wear experiments (Bhaskaran et al., 2010; Gotsmann and Lantz, 2008; Jacobs and Carpick, 2013) revealed that the atomic attrition mechanism is favored within the very low applied force and adhesion regime. However, it is diminished for larger applied loads and adhesion (Gotsmann and Lantz, 2008). A recent in-situ nanoscale wear experiment (Bernal and Carpick, 2019) showed that all aforementioned wear mechanisms coexist during an AFM wear test, but a longstanding question is how and to what extent each individual mechanism controls the overall wear relation.

In our recent study (Aghababaei et al., 2017), we confirmed Archard's hypothesis that the size of debris and the effective sliding distance (i.e. sliding distance to form a debris from an asperity collision) are both proportional to the size of the junction, formed between colliding asperities. This leads to a linear relation between the wear rate and junction area for a single isolated wear particle. A linear correlation between the applied normal force and the debris volume, however, was not recovered as the applied normal force at the asperity level cannot accurately represent the contact area where a high degree of adhesion and plastic shearing is present. Alternatively, it was shown (Aghababaei et al., 2017) that the wear relation at the debris level can be accurately described as a linear correlation between the debris volume and the work done by frictional (tangential) force, a correlation which was first hypothesized at the macroscopic level by Reye in 1860 (Reye, 1860) and intermittently discussed and observed experimentally (Agrawal et al., 2009; Burwell and Strang, 1952b; Rabinowicz, 1995; Reye, 1860; Uetz and Fohl, 1978; Whittaker, 1947). We refer to this correlation (i.e. V_wear ~ ∫FdS) as Reye's wear relation in this study.

This study aims to examine the wear law at the asperity level in the presence of sequential wear events. We perform systematic large-scale atomistic simulations and conduct in-situ tracking of wear mechanisms at the asperity tip during adhesive sliding. Our simulations reveal that the wear mechanism dictates the validity or breakdown of the linear wear relation at the asperity level. Our results confirm Archard's longstanding theoretical hypothesis that the only possible mechanism to recover a linear wear relation at the asperity level is the removal of material from contact areas formed by plastic deformation. Additionally, it is shown that while Archard's representation of the wear law, which is based on the applied normal force, cannot accurately present wear at the asperity level, Reye's representation well characterizes plasticity-driven wear at the single asperity level. Considering that contact occurs at tiny asperity junctions where the local pressure is extremely high and a high degree of ductility is expected, this finding suggests that the linear wear relation at the macroscopic length scales is a direct result of plasticity-dominated removal of material at the asperity level. This finding also highlights the importance of wear characterization methodology on examining wear relations at the asperity level in atomistic simulations and AFM wear experiments.