图  1  (a) [001]、$ [01\overline{1}] $以及[111]晶向在准等熵加载下的应力-应变曲线，(b) 图1(a)中3条曲线的最大应力及对应的应变，(c) 3个晶向在最高应力时刻所对应的金属原子所在的FCC结构的位错密度以及均方根位移柱状图

Figure  1.  (a) Stress-strain curves of the [001], $ [01\overline{1}] $, and [111] crystallographic directions under quasi-isentropic loading; (b) maximum stress and the corresponding strains of the three curves in Fig.1(a); (c) dislocation density and root mean square displacement histograms of the FCC structure of metal atoms at the moment of maximum stress for the three crystallographic directions

图  2  (a) HEC、NbC和TiC充分弛豫后的径向分布函数，(b) 3种材料在图2(a)中的峰值以及半高全宽，(c) 3种材料在压缩程度不断增加时，仅包含金属原子的结构中不同原子结构所占比例随应变变化的关系曲线，(d) HEC中C、Ti、Nb原子以及NbC中C、Nb 原子和TiC中C、Ti原子的均方根位移随压缩应变的演化

Figure  2.  (a) Radial distribution functions of HEC, NbC, and TiC after full relaxation; (b) peaks and full width at half maximum (FWHM) of the three materials in Fig.2(a); (c) relationship curves of the proportions of different atomic structures in the structures containing only metal atoms as a function of strain for the three materials under increasing compression; (d) evolution of the RMSD with compressive strain for C, Ti, and Nb atoms in the HEC, for C and Nb atoms in NbC, and for C and Ti atoms in TiC

图  3  (a) 沿[001]晶向加载时HEC的剪应力/温度/局域化变形参数-应变曲线，其中灰色标记应变下的(b) 金属原子结构云图、(c) 剪应变云图、(d) 剪应变大于0.200的原子剪应变云图

Figure  3.  (a) Stress/temperature/localization deformation parameter-strain curves of HEC in the [001] crystallographic direction; correspond to (b) structural cloud maps of metal atoms, (c) shear strain cloud maps, and (d) shear strain cloud maps with atoms having shear strain larger than 0.200, respectively, at the strains marked by the gray lines in Fig. 3(a)

图  4  (a)～(c) 不同加载时刻下所有原子、金属原子以及碳原子的径向分布函数；(d)～(f) 对应时刻下的局部原子排列（左列为整个体系，右列仅金属原子的结构）

Figure  4.  (a)−(c) Radial distribution functions of all atoms, metal atoms, and carbon atoms at different loading times; (d)−(f) atomic arrangement diagrams for corresponding moments, with the left column showing the entire system and the right column showing the structure containing only metal atoms

图  5  (a) $ [01\overline{1}] $晶向下HEC的应力/温度/局域化变形参数-应变曲线，(b) 图5(a)中的灰色线所标记的4个应变下的剪应变云图，(c) 剪应变大于0.200时原子的剪应变云图

Figure  5.  (a) Stress, temperature, localization deformation parameter-strain curves of HEC in the $ [01\overline{1}] $ crystallographic direction; (b) and (c) correspond to the shear strain cloud maps, and shear strain cloud maps with atoms having shear strain larger than 0.200, respectively, at the four strains marked by the gray lines in Fig. 5(a)

图  6  (a)～(d) 不同压缩应变下沿y方向的位移云图（去除了剪应变小于0.150的原子），(e)～(h) 图6(a)～图6(d)中的局部放大云图，(i)～(l) 沿(111)平面的2层原子在与图图6(a)～图6(d)对应时刻沿y方向的位移云图

Figure  6.  (a)–(d) Displacement cloud maps along the y-direction under various compressive strains (with atoms having shear strain less than 0.150 removed); (e)–(h) zoomed-in cloud maps corresponding to Fig. 6(a)–Fig. 6(d); (i)–(l) displacement cloud maps of a pair of atomic layers along the (111) plane at the moments corresponding to Fig. 6(a)–Fig. 6(d)

图  7  (a) [111]晶向下HEC的应力/温度/局域化变形参数-应变曲线，(b) 图7(a)中灰色线所标记的4个应变下的剪应变云图，(c) 剪应变大于0.200的原子剪应变云图以及仅金属原子的位错云图

Figure  7.  (a) Stress/temperature/localization deformation parameter-strain curves of HEC in the [111] crystallographic direction; (b) shear strain cloud maps, and (c) shear strain cloud maps with atoms having shear strain larger than 0.200 and dislocation clouds with analyzing only metal atoms, respectively, at the four strains marked by the gray lines in Fig. 7(a)

图  8  (a)～(c) (100)平面上不同压缩应变下去除剪应变小于0.100后材料的原子剪应变云图，(d)～(f) 与图8(a)～图 8(c)相对应的平面以该平面原子位移着色的轨迹云图

Figure  8.  (a)−(c) Atomic shear strain cloud maps of the material on the (100) plane under different compressive strains after removing atoms with shear strain less than 0.100; (d)−(f) trajectory cloud maps of the corresponding planes in Fig. 8(a)−Fig. 8(c), colored by the displacement of the atoms in those planes

图  9  (a) HEC、(b) NbC和(c) TiC在[111]晶向下的压缩变形模式(第1行和第2行分别对应塑性变形前期和后期)

Figure  9.  Evolution of compressive deformation in (a) HEC, (b) NbC, and (c) TiC along the [111] orientation, showing the early (top row) and late (bottom row) stages of plasticity

图  10  原子位移云图

Figure  10.  Atomic displacement maps

图  11  (a) 7.9～8.5 ps内金属（TM）与碳（C）空位数量的演化及分布云图，(b) HEC及其单组分碳化物在富碳和富金属环境下的C空位形成能

Figure  11.  (a) Evolution of the number of metal (TM) and carbon (C) vacancies and their distribution cloud maps within the time range of 7.9−8.5 ps; (b) C-vacancy formation energies of HEC and its monocarbides under both carbon-rich (C-rich) and metal-rich (TM-rich) conditions

图  12  (a) HEC在压缩应变ε=0.200时，原子沿<110>{100}、<110>{110}以及<110>{111}滑移系下的每个原子的分解剪应力（RSS）分布；(b)～(g) 不同滑移系下的分解剪应力云图

Figure  12.  (a) Distribution of resolved shear stress (RSS) for each atom of HEC under ε=0.200, along the <110>{100}, <110>{110} and <110>{111} slip systems; (b)−(g) RSS distribution maps for different slip systems

图  13  沿(a) [001]、(b) $ [01\overline{1}] $ 和(c) [111]晶向斜波加载下，t=10 ps时剪应变云图以及正应力-剪应力-剪应变波剖面曲线

Figure  13.  Shear strain snapshots and normal stress-shear stress-shear strain wave profiles under ramp wave loading along the (a) [001], (b) $ [01\overline{1}] $, and (c) [111] directions at t=10 ps, respectively

图  14  t=10 ps时(a) [001]、$ [01\overline{1}] $以及[111] 3个晶向的粒子速度以及密度波剖面曲线，(b) 3个晶向下切片内的平均剪应变以及局域变形参数随时间的演化曲线

Figure  14.  (a) Profiles of particle velocity and density waves at t=10 ps for the [001], $ [01\overline{1}] $, and [111] crystallographic directions; (b) evolution of average shear strain and local deformation parameters over time for the three crystallographic directions

图  15  斜波加载和准等熵压缩加载下(a) 剪应变、剪应变率以及粒子速度随时间的演化曲线，(b) 应力-应变和温度-应变曲线

Figure  15.  (a) Evolution curves of shear strain, shear strain rate, and particle velocity over time, and (b) stress-strain and temperature-strain curves under ramp wave impact and quasi-isentropic compression loading conditions