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jfmolinari's picture

Journal club for December 2023 : Recent trends in modeling of asperity-level wear

Ernest Rabinowicz’s words, spoken two decades ago in his groundbreaking textbook on the friction and wear of materials [1], continue to resonate today: ’Although wear is an important topic, it has never received the attention it deserves.’ Rabinowicz’s work laid the foundation for contemporary tribology research [2]. Wear, characterized as the removal and deformation of material on a surface due to the mechanical action of another surface, carries significant consequences for the economy, sustainability, and poses health hazards through the emission of small particles. According to some estimates [1, 3], the economic impact is substantial, accounting for approximately 5% of the Gross National Product (GNP).

Despite its paramount importance, scientists and engineers often shy away from wear analysis due to the intricate nature of the underlying processes. Wear is often perceived as a ”dirty” topic, and with good reason. It manifests in various forms, each with its own intricacies, arising from complex chemical and physical processes. These processes unfold at different stages, creating a time-dependent phenomenon influenced by key parameters such as sliding velocity, ambient or local temperature, mechanical loads, and chemical reactions in the presence of foreign atoms or humidity.

The review paper by Vakis et al. [5] provides a broad perspective on the complexity of tribology problems. This complexity has led to numerous isolated studies focusing on specific wear mechanisms or processes. The proliferation of empirical wear models in engineering has resulted in an abundance of model variables and fit coefficients [6], attempting to capture the intricacies of experimental data.

Tribology faces a fundamental challenge due to the multitude of interconnected scales. Surfaces exhibit roughness with asperities occurring at various wavelengths. Only a small fraction of these asperities come into contact, and an even smaller fraction produces wear debris. The reasons behind why, how, and when this occurs are not fully understood. The debris gradually alter the surface profile and interacts with one another, either being evacuated from the contact interface or gripping it, leading to severe wear. Due to this challenge of scales, contributions of numerical studies in wear research over the past decades sum up to less than 1% (see Fig. 1). Yet, exciting opportunities exist for modeling, which we attempt to discuss here.

While analyzing a single asperity contact may not unveil the entire story, it arguably represents the most fundamental level to comprehend wear processes. This blog entry seeks to encapsulate the authors’ perspective on this rapidly evolving topic. Acknowledging its inherent bias, the aim is to spark controversies and discussions that contribute to a vibrant blogosphere on the mechanics of the process.

The subsequent section delves into the authors’ endeavors in modeling adhesive wear at the asperity level. Section 3 navigates the transition to abrasive wear, while Section 4 explores opportunities for upscaling asperity-level mechanisms to the meso-scale, with the aspiration of constructing predictive models. Lastly, although the primary focus of this blog entry is on modeling efforts, it would be remiss not to mention a few recent advances on the experimental front.

Scholarship Support for Attending NSF Workshop on the BEM: Bridging Education and Industrial Applications

Sponsored by the National Science Foundation and the NSF Institute for Mathematics and its Applications, the University of Minnesota (Minneapolis, Minnesota, USA) is hosting a workshop on the boundary element method (BEM) April 23-26, 2012. This workshop consists of a two-day short course and a two-day colloquium on advances in the BEM with educational and industrial applications. Researchers and engineers from around the world, as well as students (both graduate and undergraduate) are invited to participate in this workshop.

A Workshop on the Recent Developments in the Boundary Element Method

Do you want to learn the boundary element method (BEM) and the latest fast solution methods from the experts around the world? If yes, come and attend the workshop on the BEM in September.

ahmed.hussein's picture

A boundary element formulation problem

I am working on some boundary integral equation formulation and I am currently stuck with some mathematics. I wish anyone can help me out with this. 

 

I have an anisotropic (sometimes called generalized) biharmonic differential operator which  takes the form

L = k11 D1^4 +  k12 D1^2 D2^2 + k22 D2^4 

where D1 = d/dx, D2 = d/dy, my problem is two dimensional.

I need to find a fundamental solution (Green's function) for this operator, that is 

L(u) = -delta

where delta is Dirac delta function.

Honghui Yu's picture

Integral Formulations for 2D Elasticity: 1. Anisotropic Materials

Might also be useful for simulating dislocation motion in a finite body.

Several sets of boundary integral equations for two dimensional elasticity are derived from Cauchy integral theorem.These equations reveal the relations between displacements and resultant forces, between displacements and tractions, and between the tangential derivatives of displacements and tractions on solid boundary.Special attention is given to the formulation that is based on tractions and the tangential derivatives of displacements on boundary, because its integral kernels have the weakest singularities.The formulation is further extended to include singular points, such as dislocations and line forces, in a finite body, so that the singular stress field can be directly obtained from solving the integral equations on the external boundary without involving the linear superposition technique often used in the literature. Body forces and thermal effect are subsequently included. The general framework of setting up a boundary value problem is discussed and continuity conditions at a non-singular corner are derived.  The general procedure in obtaining the elastic field around a circular hole is described, and the stress fields with first and second order singularities are obtained. Some other analytical solutions are also derived by using the formulation. 

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