Fig. 1 Models for the MD simulations of wear on NbMoTaW surface. a Section view of the indentation and scratching processes, b grain distribution for the NG-5, c NG-10, d NG-20, and e single-crystalline model. Atoms belonging to different crystal structures are distinguished by the common neighbor analysis (CNA) [28] module of OVITO. Atoms belonging to the BCC phase are colored as dark purple, while GB atoms are colored as gray

Fig. 2 Evolution of the indentation and scratching force in the normal (y) and tangential (x) directions of the three nanograined models and the single-crystalline model. a and b Variations in Fy and Fx during the indentation process, c and d variations in Fy and Fx during the scratching process

Fig. 3 Average friction force of each model during the scratching process

Fig. 4 Nano-scratching process of the single-crystalline model. a-d Atomic structure evolution of the single-crystalline at different stages during the scratching process, e-h the nucleation and growth of deformation twins during the scratching process

Fig. 5 Nano-scratching process of the NG-5 model. a-d Atomic structure evolution of the NG-5 model during the scratching process, e-h enlarged view of the area enclosed by the yellow frame in a-d

Fig. 6 Nano-scratching process of the NG-10 model. a-d Atomic structure evolution of the NG-10 model during the scratching process, e-h enlarged view of the area enclosed by the yellow frame in a-d

Fig. 7 Nano-scratching process of the NG-20 model. a-d Atomic structure evolution of the NG-20 model during the scratching process, e-h enlarged view of the area enclosed by the yellow frame in a-d

Fig. 8 Atomic structure evolution of three nanograined models a NG-5, b NG-10, c NG-20, during the scratching process

Fig. 9 Dislocation density of four models with different grain sizes

Fig. 10 Evolution of the indentation and scratching force in the normal (y) and tangential (x) directions of the NG-20 models at 300 K, 700 K, and 1100 K. a and b Variations in Fy and Fx of the NG-20 models during the indentation process, c and d variations in Fy and Fx of the NG-20 models during the scratching process

Fig. 11 Averaged friction force of the NG-20 model during the scratching process at different temperatures

Fig. 12 Atomic structure evolution of the NG-20 models a at 300 K, b at 700 K, c at 1100 K, during the scratching process

Fig. 13 Dislocation density evolution of the NG-20 models at different temperatures

Fig. 14 Stress distribution plots for models with different grain sizes during the scratching simulation: a NG-5 model, b NG-10 model, and c NG-20 model