Building on an analogy to ductile fracture mechanics, we investigate the energetic cost of debris particle creation during adhesive wear . Macroscopically, Reye proposed in 1860 that there is a linear relation between frictional work and wear volume at the macroscopic scale. Earlier work suggested a linear relation between tangential work and wear debris volume also exists at the scale of a single asperity, assuming that the debris size is proportional to the micro contact size multiplied by the junction shear strength. However, the present study reveals deviations from linearity at the microscopic scale. These deviations can be rationalized with fracture mechanics and imply that less work is necessary to generate debris than what was assumed. Here, we postulate that the work needed to detach a wear particle is made of the surface energy expended to create new fracture surfaces, and also of plastic work within a fracture process zone of a given width around the cracks. Our theoretical model, validated by molecular dynamics simulations, reveals a super-linear scaling relation between debris volume ($V_d$) and tangential work ($W_t$): $V_d\sim W_t^{3/2}$ in 3D and $V_d\sim W_t^2$ in 2D. This study provides a theoretical foundation to estimate the statistical distribution of sizes of fine particles emitted due to adhesive wear processes.

基于与延性断裂力学的类比，我们研究了粘附磨损过程中碎片颗粒产生的能量成本。宏观上，Reye于1860年提出在宏观尺度上摩擦功与磨损量之间存在线性关系。早期的研究表明，切向功和磨屑体积之间的线性关系也存在于单个粗糙度的尺度上，假设碎屑尺寸与微接触尺寸乘以连接剪切强度成正比。然而，本研究揭示了微观尺度上的线性偏差。这些偏差可以用断裂力学合理化，并且意味着产生碎片所需的工作比假设的要少。这里，我们假设分离磨损颗粒所需的功是由产生新断裂表面所消耗的表面能以及裂纹周围给定宽度的断裂过程区域内的塑性功组成的。我们的理论模型通过分子动力学模拟验证，揭示了碎片体积之间的超线性比例关系（$V_d$) 和切向功 ($W_{吨}$):$V_d～W_{吨}^{\mathrm{3个}/\mathrm{2个}}$在 3D 和$V_d～W_{吨}^{\mathrm{2个}}$在二维中。本研究为估计由于粘着磨损过程排放的细颗粒尺寸的统计分布提供了理论基础。