@article{Liu2026, 
author = {Ming Liu and Zhitong Xu and Noraphat Yuktanan and Tang Gu and Guangan Zhang and Jinyang Jiang and Fuqian Yang and Rui Liang},
title = {Scratch-induced damage of doped DLC and MoS2 coatings—Deep symbolic analysis},
year = {2026},
journal = {Friction},
volume = {14},
number = {3},
pages = {9441166},
keywords = {microscratch, MoS2 coating, deep symbolic optimization (DSO) algorithm, diamond-like carbon coating (DLC)},
url = {https://www.sciopen.com/article/10.26599/FRICT.2025.9441166},
doi = {10.26599/FRICT.2025.9441166},
abstract = {Understanding contact-induced damage is of paramount importance in the analysis of the lifespan and performance of surface coatings. In this work, we investigate the effects of dopants and interlayers on the structural durability of diamond-like carbon coatings (DLCs) and molybdenum disulfide (MoS2) coatings on stainless steel via microscratch tests. The analysis of X-ray photoelectron spectroscopy (XPS) survey spectra and Raman spectra of the DLCs shows that the ratio of sp2/sp3 (i.e., the intensity ratio of sp2 to sp3 obtained via XPS) is proportional to ID/IG, where ID and IG are the intensities of the D and G bands of the Raman spectrum, respectively. The analysis of the scratch tests reveals that there are three critical loads for the scratch-induced damage of the DLCs and MoS2 coatings, corresponding, respectively, to the initiation of periodic V-cracking, the minimum load for periodic semicircle cracking or peel-off, and the minimum load for partial and periodic delamination. Dopants can reduce the friction coefficient of DLCs and have a negligible effect on Ti/MoS2 coatings. The Cr interlayer can better enhance the bonding strength between the DLCs and the steel substrate than the Si interlayer. Doping Cr and H can reduce the hardness of DLCs; doping Si can increase the hardness of DLCs; doping Ti, Pb, and PbTi can reduce the hardness of MoS2 coatings. The deep symbolic optimization (DSO) algorithm is used to establish nominal-mathematical formulations between the critical variables for the scratch test and the material parameters of the surface coating. The DSO analysis demonstrates the feasibility of using “deep learning” to establish “quantitative” relationships between the critical variables for mechanical deformation and material parameters.}
}