A multiscale model of friction considering the influence of third-body wear particles

TL;DR

This study develops a hierarchical multiscale framework to predict friction in sliding interfaces contaminated by third-body wear particles. A 1D macroscale FEM bar couples to a mesoscale BEM–DEM solver that resolves particle–surface interactions and yields a local friction coefficient μ that depends on normal pressure, sliding velocity, surface roughness, and particle density β; β evolves via Archard wear-generated particle production. The mesoscale results feed back into the macroscale through a Bowden–Tabor–type friction law modified by active particle area A_p, enabling prediction of macroscopic friction μ̄ that agrees with strip-draw experiments and captures the observed dependence on normal load and tool size. The work demonstrates how debri-induced lubrication and inertial effects control friction in practical tribosystems and provides a pathway for scaling laboratory tests to industrial settings.

Abstract

Accurately predicting friction in sliding interfaces that contain third body wear particles is critical for engineering applications such as sliding movement in pistons, bearings, or metal forming. We present a hierarchical multiscale framework that links particle scale mechanics to macroscopic friction in a strip draw friction test. At the macroscale, a one dimensional finite element model reproduces the global stress state of the strip draw setup and updates the local wear particle density via Archard's law. The local friction force at each node is then computed from mesoscale simulation results. At the mesoscale, a coupled discrete element boundary element approach resolves load sharing between rough surfaces and rigid oblate spheroidal wear particles. The mesoscale solution returns to the macroscale solver a friction coefficient that depends on normal pressure, sliding velocity, surface geometry, and particle density, thereby closing the loop between scales. The simulated friction coefficient matches strip draw experiments, capturing both the observed decrease in friction with increasing normal pressure and the influence of tool pad size.

Figures (21)

• Figure 1: (a) Schematic of the flat strip-draw experimental test, where the tools are subjected to a normal load, and the aluminum sheet is pulled horizontally with a force $F_{\text{Pull}}$ at a prescribed velocity $V_0$. (b) Schematic of the macroscale simulation setup representing the experiment, in which a rigid tool is subjected to a normal pressure $P_N$ (resulting from the normal load $F_N$) and applied to an elastic one-dimensional bar that is pulled at a prescribed velocity $V_0$. The red points represent nodes on the bar that are in contact, while the black points indicate nodes that are either not yet in contact or have moved out of the contact zone. The number of nodes in the actual simulation is significantly higher than shown in the schematic. Due to geometric symmetry, only half of the domain is modeled in the numerical simulations.
• Figure 2: Evolution of the average friction coefficient, denoted $\bar{\mu}$, over the converged portion of $\mu(t)$, as a function of applied normal pressure $P_N$: (a) for different tool-pad lengths (the influence of tool-pad width was minimal and is shown in Appendix \ref{['sec:pad-width']}); (b) for multi-pass strip-draw tests using a tool 35 mm long and 35 mm wide.
• Figure 3: SEM image of wear debris generated during the strip-draw friction test. The particles exhibit a flake-like morphology, characterized by large lateral dimensions relative to their thickness.
• Figure 4: Average particle size distribution of flake-like particles, measured by laser diffraction (Mastersizer 3000, Malvern Panalytical) in toluene dispersion mode. The curve shows the mean volume percentage as a function of particle diameter, expressed as the volume-equivalent spherical diameter. The shaded region represents the variation across all measured samples under applied normal pressures from 1 to 13 MPa (±1 standard deviation). Each test was repeated twice to confirm reproducibility. No clear trend indicating a dependence of particle size on applied normal pressure was observed. The x-axis is shown on a logarithmic scale to capture the full size range.
• Figure 5: Surface topography measured by confocal microscopy. (a) Confocal image of the aluminum sheet surface before strip-draw testing. (b) Aluminum surface after the application of 10 MPa normal pressure and 90 mm of sliding, at the exact same location as (a). (c) Surface profile of the cast-iron tool used in the strip-draw friction test.