Adhesive Wear Modelling Methods

TriboNet

January, 28 2025
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Introduction

Wear in dynamic systems significantly impacts performance, efficiency, operational costs, and safety. Predicting wear using computer simulations, empirical data, or theoretical frameworks is crucial for determining system reliability and durability. Haibo et al. [1] Reviewed wear modelling methods and depicted that wear modelling could be on macro, micro, or atomic scales. In light of this, wear modelling could be divided into a phenomenological approach or real contact conditions; the former utilizes physical understanding and experimental observation, i.e., macroscale level.

In phenomenological technique, assumptions must be made, and empirical coefficients must be determined. Those models are constrained by their assumptions and lack generality, even though they provide accurate predictions for a specific range of operations and rely on the constraints of the empirical coefficients. Archard’s theory [2] and Rabinowicz’s criterion [3] These are examples of such models. The second method, such as asperities contact models, implements advanced numerical techniques to find the wear at micro- or atomic levels under relaxed assumptions and more realistic conditions; however, analytical models have been utilized for material and fracture estimation, and the actual surface characteristics may need to produce specific and accurate results. In the next section, microscale modelling techniques have been introduced.

Wear Models

Phenomenological approach

An example of this approach is Archard’s wear model which is a famous model to evaluate adhesive wear. Theoretically, the Archard wear model estimates the adhesive wear volume of softer material. The model is named after Archard publicizes his work [2]; He said that the wear volume depends on the normal load and sliding distance and is inversely proportional to the hardness of the softer material.

The wear volume (W) is defined as [4]:

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W = (K*P*S)/H – Equation-1

Where P is the normal force, S is the sliding distance, H is the softer material hardness, and is the dimensionless wear coefficient, and commonly used is the dimensional wear coefficient which is found experimentally and its value depending on lubricity condition and wear severity 1e-2 to 1e-9 [4] depending on the type of surface and lubricity condition.

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It’s commonly explained the wear rate is wearing volume per sliding distance (w) which is defined by [4]:

w = (K * P) – Equation-2

Asperity Level Approach

Asperity-level models for wear prediction offer valuable insights into wear phenomena, allowing for the estimation of wear volume and particle morphology.

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A prominent model developed by A. Greenwood and J. Williamson (GW model) [5], describes contact between rough, deformable surfaces, assuming that each asperity is loaded independently as shown in Figure 1. In this model, all asperities are hemispherical, with a constant radius of curvature distributed at different heights above mean surfaces.

Figure-1 : GW model, contact of two rough surfaces [5]

Numerical methods such as the Finite Element Method (FEM) and Boundary Element Method (BEM) are frequently employed to analyze complex dynamic systems. These methods transform model geometries into finite elements, making them particularly useful for studying rough surface contact—for example, Hu et al. [6] used asperity-level models to evaluate contact responses in such systems, and his FEM model is shown in Figure 2 which the rough surface has meshed with fine gird to capture the asperities contact.

Figure-2 : Finite element mesh required for asperity level models as illustrated by Hu et al. [6]

Rough surface

Smooth surface Surface

One of the critical advantages of asperity modelling is its ability to predict wear particle formation. H. Zhang and I. Etsion [7] utilized FEM to study spherical contact and the initiation of wear particles due to adhesive wear, finding the friction coefficient and wear volume for both elastic and plastic deformations. They also formulated wear particles resulting from these deformations as illustrated in Figure 3.

Figure-3 : Wear particle formulation as different sliding instants as predicted by H. Zhang and I. Etsion model [7]

At a smaller scale, atomic-level contact models have gained attention for providing detailed insights into contact phenomena. However, these models are limited to primary cases due to the need for extremely fine discretization.

For instance, J. François et al. [8], using similar principles of asperity contact as depicted in Figure 4 and implemented the BEM mode, shown in Figure 5, to study asperity contact at the atomic scale and identified junction growth as a critical factor in wear particle formation. Despite the depth of understanding these models provide, they are constrained by the need for highly dense finite element models, which limit their broader application.

Figure-4 : Schematic for atomistic simulations. (a) single-asperity surface (b) Interlocking asperities surface, J. François et al [8]

Figure-5 : BEM model results which determined two wear mechanisms at the microscale level. (a) the plastic deformation without wear particle formulation. (b) the plastic deformation with wear particle formulation, J. François et al .BEM model [8]

Moreover, asperity contact models require a failure criterion to simulate crack initiation and propagation for surface fracture. They also necessitate material models for plastic flow.

Author: Shenouda Adel

MSc in machine design

References

1. Zhang, H., R. Goltsberg, and I. Etsion, Modeling Adhesive Wear in Asperity and Rough Surface Contacts: A Review. Materials (Basel), 2022. 15(19).

2. Archard, J.F., Contact and Rubbing of Flat Surfaces. Journal of Applied Physics, 1953. 24(8): p. 981-988.

3. Rabinowicz, E., The effect of size on the looseness of wear fragments. Wear, 1958. 2(1): p. 4-8.

4. Bhushan, B., Principles of Tribology. Modern Tribology Handbook. Vol. 1. 2001: CRC Press LLC.

5. Greenwood, J.A. and J.H. Tripp. The Contact of Two Nominally Flat Rough Surfaces. in Proceedings of the Institution of Mechanical Engineers. 1967.

6. Hu, G.-D., et al., Adaptive finite element analysis of fractal interfaces in contact problems. Computer methods in applied mechanics and engineering, 2000. 182(1-2): p. 17-37.

7. Li, M., G. Xiang, and R. Goltsberg, Efficient Sub-Modeling for Adhesive Wear in Elastic–Plastic Spherical Contacts. Lubricants, 2023. 11(5).

8. Molinari, J.-F., et al., Adhesive wear mechanisms uncovered by atomistic simulations. Friction, 2018. 6(3): p. 245-259.

 

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