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基于球面触点接触模式的铜膜纳观变形探析∗

  • 陈晶晶1

    机 构：

    1. 宁德师范学院信息与机电工程学院 宁德 352100

    ×
  • ， 翁盛槟2

    机 构：

    2. 衢州学院工程实训中心 衢州 324000

    ×
  • ， 吴昊3

    机 构：

    3. 北京航天发射技术研究所 北京 100048

    ×

1. 宁德师范学院信息与机电工程学院 宁德 352100；
2. 衢州学院工程实训中心 衢州 324000；
3. 北京航天发射技术研究所 北京 100048；

Effects of Mechanism Analysis for Spherical Contact Pair on Contact Deformation in Copper Film from Nano-perspective∗

  • CHEN Jingjing1

    Affiliation：

    1. School of Information and Mechatronics Engineering,Ningde Normal University, Ningde 352100 , China

    ×
  • ， WENG Shengbin2

    Affiliation：

    2. Engineering Training Center, Quzhou University, Quzhou 324000 , China

    ×
  • ， WU Hao3

    Affiliation：

    3. Beijing Institute of Space Launch Technology, Beijing 100048 , China

    ×

1. School of Information and Mechatronics Engineering,Ningde Normal University, Ningde 352100 , China；
2. Engineering Training Center, Quzhou University, Quzhou 324000 , China；
3. Beijing Institute of Space Launch Technology, Beijing 100048 , China；

作者简介:

陈晶晶,男,1989年出生,硕士,讲师。主要研究方向为机械表/界面摩擦磨损与防护润滑。E-mail:chenjingjingfzu@126.com

中图分类号:TG156;TB114

DOI:10.11933/j.issn.1007-9289.20210318001

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目录contents

    摘要

    对微机电系统金属铜膜接触变形特征的了解和位错原子迁演的寻迹对改善工况接触质量极为重要。 基于分子动力学法,对球面触点与微器件铜膜的接触变形展开研究,分析铜膜力-位移曲线对应构型演变特征,用 WSDA 法描述接触变形特性,并比对触点轮廓对铜膜内、外表面的变形差异。 研究表明:弹性接触时,力-位移曲线的 Hertz 理论与 MD 结果吻合,而接触区铜膜两侧的位错环凸显是塑性变形始发源与侧面滑移带产生的萌芽端,也是弹性阶段后的 Hertz 理论与 MD 的力-位移曲线不吻合主因。 受载铜膜的位错原子会演化为位错环,位错环构型演变有 4 个动态阶段:位错环萌芽期、生长增大期、繁衍增殖期、维持稳定期。 随着触点轮廓增加,位错环构型也相应扩张,而位错环演化 4 个阶段不受外围轮廓影响。 另外,受载铜膜接触区两侧滑移带蔓延处的应力较集中,亚表层应力集中度强烈依赖于触点外围轮廓尺寸。 验证了 WSDA 法可有效描述铜膜受载时的变形特征,并随触点轮廓增加而迅速向两侧蔓延传播,与受载铜膜的应力、应变趋势获得一致。 研究结果将对微观金属弹塑性变形转化的微观临界态揭示中有着重要参鉴价值。

    Abstract

    To insight the underlying deformation for micro devices in micro / nano electrical mechanical system ( MEMS / NEMS) is extremely important. However, a few research was reported on the evolution of copper deformation and the explore of dislocation atomic migration rules at atomic level. Therefore, the correlated understand work for them behaviour and mechanism were studied. The configuration evolution for dislocation atoms, and the curve characteristic of force vs displacement were analyzed. Wigner-seitz defect analysis (WSDA) method was proposed to describe this effect of spherical contact pair with different contour on them deformation. It was showed that the force vs displacement curve obtained consistent by comparing Hertz theory with molecular dynamics (MD) result at elastic stage. Furthermore, the dislocation loop was found as the original source of plastic deformation, it was the main reason to lead the curve of force vs displacement is not inconsistency after elastic deformation. An interesting phenomena was demonstrated on dislocation loop evolution process, which experienced four stages during loading, namely formal stage, growth stage, reproduction stage, maintenance stage. This external configuration features for dislocation ring evolution shows expand as curvature contour increase. Nevertheless, all above four stages are not affected by them increase. In addition, it is serious than other places in subsurface deformation at loading. The WSDA method was applied to describe their defect characteristics, this result shows that the propagation route can spreads to sides rapidly as contour increase, which is consistent with changes of stress and strain trend. This research result plays a significance role in understanding the underlying mechanism on its elastic-plastic deformation.

  • 0 前言

  • 由于微/纳机电系统的微器件尺度锐意缩减,其表面效应和尺度效应常会影响微器件复杂工况的接触性能改变和服役寿命期的缩短。 XU等[1] 指出, 接触界面在频繁往复碰磨时,会诱导界面接触质量发生黏着咬聚,触发工况中的微器件接触故障与失效产生。由于界面黏着与磨损两态是互存相联,对磨时会驱使材料因塑性变形而去除形成磨粒,在界面产生局部磨损,从而加剧黏着效应。因此,为延长器件服役寿命期,并改善界面接触质量,非常有必要知晓界面接触变形的特征与规律。而目前对此探究尚有几点不明晰。比如:金属受载时的微观变形特征与机制有哪些,金属滑移带产生的萌芽源是否有可循微观迹象凸显,接触体弹塑性变形转化的临界微观迹象是什么。对上述相关基础问题研究和洞悉金属材质内的微观演化特征,将对优化金属力学性能提升和改善界面接触质量有着重要意义。由于精仪直接探测接触体微观变形演化所需的技术不仅要求严苛,而且受试验表征手段的限制与成本昂贵等约束,对金属器件局部接触区的微观变形特征的理解与弹塑性变形临界转化的微观迹象揭示仍是尚待解决的关键基础性科学问题。

  • 目前,对接触变形研究主要用纳米压痕/划痕法、连续介质有限元法、全原子分子动力学( MD) 法。其中,MD法成为了解微观接触变形演化过程的有效研究工具[2-6],能弥补试验法和有限元法的不足。最近相关文献[4-7] 表明,金属位错构型演变是诱导宏观材料力学性能改变的内因。 SUBIN等[5]结合试验与MD模拟,对冲击载荷诱导金属位错环的形核展开研究,指出材料微观弹塑性变形行为与位错环演化紧密性强。 XIAO等[6] 比较了单晶铜动态犁削过程的变形与静态犁削差异性,表明动态犁削时几乎没有屑片形成,而静态犁削时,观察到大量屑片形成。 ZHANG等[8] 用MD法分析单晶锗不同晶面的相变路径差异,指出卸载时的锗膜变形层深度和形状受晶体取向影响较大,而相变转化是单晶锗薄膜变形主要机制。黄健萌等[9] 指出半球形探针较针尖形探针更有利于加剧铜膜塑性变形, 且半球形探针刻化基底易产生位错环构型演变,但该研究尚未对单晶铜受压接触时的位错环迁演规律展开详细研究。陈晶晶等[10-11]用MD模拟了铜膜黏着接触的失效,发现了黏着突跳与滞后的纳观现象, 指出黏着效应是诱导微机械装置失效主因,其敏感性受触点轮廓影响显著。 XIANG等[12] 对单晶氮化铝和氮化镓的棱柱形位错环演变展开原子尺度模拟,指出套索状机制和嵌套环机制是引起B4陶瓷棱柱形环形成的两种机理,表明两种不同剪切环的螺段会发生吸引,棱柱型位错环受载脱落时会释放内应力集中。 SHI等[13] 用MD研究了超薄水膜对铜变形影响,指出磨粒刻化铜基底时,随着滑动距离增加,水膜不断被挤出,导致铜表面产生沟槽和脊线,并诱导Cu衬底发生位错迁变。

  • 综上所述,目前虽有报道面心金属受载接触变形与力学性能的关联性研究,但对受载诱导的位错环演化特征与规律探究,及弹性变形向塑性变形转化的微观临界态揭示却鲜有报道。因此,本文用分子动力学法对铜膜接触变形微结构演化展开研究, 着重观察力-位移曲线对应阶段的铜膜位错环演化形态,并比对触点外围轮廓对铜膜位错环演变的差异。本研究将对受载的面心立方金属轨迹迁变过程的知悉,及其弹塑性变形的临界转折点的微观迹象理解有着重要学术参鉴价值。

  • 1 分子动力学计算

  • 1.1 条件设置

  • 图1 为球面触点接触模式的物理模型与示意图,将刚性金刚石压头抽象为微观多粗糙表面的单粗糙峰触点,将触点视为具有球面轮廓特征,以此研究球面触点模式的铜膜微观变形行为。铜膜 X、Y、 Z 轴晶向依次为[100]、[010]、[001],对应尺寸分别为18.07nm×18.07nm×14.46nm。铜膜晶格常数为0.361 5nm,金刚石晶格常数为0.356 7nm,刚性触点半径 R=4nm。模拟时,金刚石球面触点底部距铜膜上表面距离为1nm。图1a铜膜基底被划分固定层、恒温层、牛顿层。其中,恒温层和牛顿层统称为运动层。图1物理模型 Z 轴用非周期性边界( 简称FBC), X 和 Y 轴用周期性边界 ( 简称PBC),并固定铜膜 Z 轴底部五层原子,防止固定层原子位移变化,引起计算精度降低[9-14]。模型搭建后,用共轭梯度算法优化模型,为后续计算可靠性提供保障。为保证微观原子热运动符合室温条件,对运动层原子赋予298K初始温度,并用随机种子数产生初始速度。采用朗之万控温法控制运动层温度于298K,基于NVE系综完成牛顿方程计算。时间步长取1fs,体系经2ns充分弛豫平衡后。刚性触点以40m/s匀速沿 Z 轴负方向加载铜膜。本文计算采用开源LAMMPS软件和OVITO软件可视化[15]。

  • 图1 球面触点接触模式的铜膜模型图与示意图

  • Fig.1 3D physical model and schematic diagram constructed for copper film based on spherical contact mode at loading process

  • 1.2 势函数描述

  • 基于Verlet算法[16] 求解牛顿运动方程。由于势函数对计算结果准确性起决定作用, 相关文献[9,17]表明,嵌入原子势(简称EAM) [18-19]在研究单晶铜变形有显著优势,可很好反映铜膜Cu-Cu间相互作用,势函数EAM公式如式(1):

  • Etot=12∑i≠j φijrij+∑j Eiρi
    (1)

  • 式中, E tot 为总能量,右式中第一项为原子 i,j 之间对势, 第二项为嵌入势。

  • 球面触点与铜膜间C-Cu相互作用基于Morse势函数[20],其表达如式(2):

  • E(r)=Dexp⁡-2αr-ro-2exp⁡-αr-ro
    (2)

  • 式中,D 为结合能系数,α 为势能曲线梯度系数,r o为原子间作用力等于零的平衡间距,其关键参数依据文献[9]、[10],相应取值为 D=0.087eV, α=51.4nm-1, r o=0.205nm。

  • 1.3 位错类型描述

  • 采用共域邻列(CNA) 法[20-22] 对局部接触区位错类型识别。其中,面心立方结构(FCC)用绿色原子表示,密排六方结构(HCP) 用红色原子显示,体心立方结构 ( BCC) 用蓝色原子展示, 灰色原子 (Other)表示其他原子类型,即非晶态。

  • 1.4 应力与应变描述

  • 材料结构变形往往是应力超过一临界值,而结构变形破坏与von Mises stress有紧密联系。因此, 用von Mises stress表征材料受载集中度[23-24],其应力公式见式(3)。另采用剪切应变公式表示接触区变形程度[25],其表达式如式(4):

  • σMises =σxx-σyy2+σyy-σzz2+σzz-σxx2+6τxy2+τyz2+τzx22
    (3)
  • ηiMises =6ηxy2+6ηyz2+6ηxz2+ηxy-ηyy2+ηyy-ηzz2+ηzz-ηxx26
    (4)

  • 式中, σxx、σyy、σzz、τxy、τyz、τzx 分别表示应力张量分量,ηxx、ηyy、ηzz、ηxz、ηxy、ηyz 分别表示剪切应变分量。

  • 1.5 晶格点缺陷统计原理

  • 为描述受载铜膜的晶格动力学点缺陷的迁移行为,基于Wigner-Seitz Defect Analysis( WSDA) 法描述接触变形过程,其原理如图2。图2圆圈表示原子,1或2的数字表示新位置占据该区域的原子总数。

  • 图2 晶格点缺陷中占据原子数统计原理图

  • Fig.2 Statistical schematic diagram for occupied atomic number on lattice point defects

  • 1.6 Hertz理论描述

  • Hertz理论[26]给出弹性阶段的球面接触副的载荷与位移关系表达式,即载荷 F、探头半径 a、接触位移 δ 之间函数关系如式(5),依据文献[27]计算复合弹性模量见式(6):

  • F=43E*a12δ32
    (5)
  • E*=1-vs2Es+1-vi2Ei-1
    (6)

  • 式中,E ∗为复合弹性模量,E s 和E i 表示基底和触点弹性模量,v s 和v i 为其对应的泊松比,参数依据文献[27]。对Hertz曲线拟合时,选取压头与铜膜间接触力为0,代表压头接触位移(δ)开始时刻。从图3a知,压头下压位移 D=0.88nm时,力为零,其拟合曲线见图3a所示。

  • 2 结果与分析

  • 2.1 微结构分析

  • 图3 示出触点半径 R=4nm的力-位移曲线和对应阶段的铜膜构型, 运用球面Hertz接触理论[26]对MD的力-位移曲线拟合(见图3a)。从图3b知,在阶段A前,力-位移曲线呈线性递增,表明该接触近似弹性变形。图3a在弹性阶段A前,MD的力-位移曲线同Hertz理论吻合。在弹性接触时,受载基底正下方会积累弹性能,该变形能会驱动紧密接触区原子点阵产生挪移,导致受压区原子堆垛累积,其形态呈“V” 字型( 见图3c字母A)。而超过阶段A后(见图3b),Hertz理论力曲线远大于MD结果,说明此阶段后的铜基质由先前弹性变形为主,向后期塑性变形为主发生过渡,为观察此弹塑性变形转折点所对应的微观迹象。观察图3c字母A~C阶段的构型知,紧密接触区两侧会渐近式的出现位错环,且构型演化呈生长增大态势,表明受载铜膜弹性变形向塑性变形转折的临界微观迹象为位错环出现,也说明紧密接触区通过形成位错环,并以繁衍与滑移形式释放过渡积累的应变能,该应变能释放有效促进塑性阶段的位错构型发生具有时变性特征的演化。图3b接触阶段C~E间,力-位移曲线斜率增涨较A~C阶段慢,其原因可观察图3c的C~E阶段所对应构型,C~E阶段增殖繁衍出新位错环,及部分位错环会形核脱落。整个接触中,位错环构型演变对力-位移曲线的波动与基底弹性变形向塑性变形转变的临界微观迹象有重要影响,表明铜膜受载时位错环出现是塑性变形始发讯号,也是铜膜缺陷萌芽处(见图4~6)。

  • 图3 力-位移曲线中对应构型的动态演化过程

  • Fig.3 Dynamic configuration evolution described correspondingly according to force vs displacement curve

  • 图4 球面触点R=2.5nm时的铜膜位错环演化 XZ 截面图

  • Fig.4 Plastic loop evolution represented for copper film based on spherical contact mode with R=2.5nm from XZ plane observe

  • 图5 球面触点R=3.25nm的铜膜位错环演化 XZ 截面图

  • Fig.5 Plastic loop evolution represented for copper film based on spherical contact mode with R=3.25nm from XZ plane observe

  • 图6 球面触点R=4nm的铜膜位错环演化 XZ 截面图

  • Fig.6 Plastic loop evolution represented for copper film based on spherical contact mode with R=4nm form XZ plane observe

  • 2.2 位错环演化

  • 为体现受载铜膜变形的演变过程,采用CNA法[17,19]描述位错迁移演变动态进程。观察图4~6可知,位错原子会演化成位错环,该构型受触点轮廓影响显著。同时,位错原子数随触点下降位移增加而逐渐增多。观察图4a知,在 h=0.76nm,接触区左侧的位错环出现最早,随后位错环动态演变历经4个进程:第一进程为开始受载的位错堆积期(见图4a的h=0.68nm),此期间是蕴育位错环的萌芽期, 也是铜膜发生塑性变形讯号期;第二进程为位错环生长增大期,观察图4a知,在 h=0.76nm时,位错环于铜膜左侧出现,铜膜继续受载时,做功产生的热量易被缺陷原子吸收而发生迁移,随着压深增加,构型也相应扩张(见图4b)。另外,文献[5,19]指出: 面心金属位错环出现与演变是金属产生滑移的主要形式,也是受载时缺陷产生的信号源[9];第三进程为位错环增殖繁衍期,观察图4c黑色箭头知,接触区右侧会繁衍出其它位错环数;最后第四阶段为位错环维稳期(见图4c的 h=1.24nm)。铜膜出现非晶态(见灰色原子),该非晶数目随压深h增加而逐渐增多。为排除位错环演变不是偶然现象,另补算了球面触点轮廓对其演化特征影响(见图5和图6)。观察图5和图6知:位错环演化仍有4个进程。此外,我们还观察到图5c位错环在接触区右侧出现是在 h=1.08nm时(见图5黑色箭头),而图6c位错环右侧成型在 h=0.72nm时出现(见图6黑色箭头)。由此说明位错环演变受触点轮廓尺寸影响显著,外围轮廓越大,接触两侧位错环出现也更早。对比图4~图6知,触点轮廓增加会驱动位错环构型出现相应扩张,而位错环演变4个阶段不受触点轮廓影响。可见,位错环轨迹演变可间接表明铜膜内塑性变形强烈度,且位错环出现是金属发生塑性变形的始发讯号源,而增殖繁衍可表现为塑性变形程度剧烈。

  • 2.3 铜膜缺陷识别分析

  • 观察图4~6知,铜膜局部接触区会堆积大量HCP结构和BCC结构,且HCP结构会堆垛成核,形成新稳定构型(见图4c~6c位错环)。对比图7c与图7d知:接触区HCP结构远多于BCC结构,并随触点轮廓增加而近似呈类抛物线上升规律。另外, HCP数额随触点位移增加的变化规律(见图7c)与位错线长度曲线变化规律一致(见图7b),表明局部接触的铜膜相变以HCP结构为主。从图7a知,触点轮廓越大,局部接触区面积也增大,导致铜膜内变形更剧烈,局部接触区相变数额也随之增多( 见图7c~7d)。图7e为受载铜膜原子迁移矢量图,从该图可知,受载铜膜原子运动方位为竖直向下(见图7e箭头),接触区两侧原子在载荷作用下被向上挤出,运动趋势为弯曲向上(见图7e箭头)。为进一步描述铜膜变形,图8示出WSDA法刻化铜膜原子缺陷演化过程,有利分析铜膜受载破坏形式和轨迹迁移,该方法原理见图2示。从图8知,铜膜原子缺陷演化随压深和触点轮廓改变有明显差异。压深 h 增加,导致缺陷原子占据数相应增加,并向铜膜底部蔓延范围更广。同等压深时,缺陷原子传播轨迹也随触点轮廓增加而迅速蔓开,与图4~6位错环演变趋势一致。此结果也与铜膜受载的应力、应变规律相呼应。

  • 图7 球面触点触点轮廓对铜膜变形影响

  • Fig.7 Influence of spherical contact mode with different curvature contour on copper deformation

  • 图8 球面触点外围轮廓对晶格点阵破坏影响的 XZ 平面图

  • Fig.8 Influence of spherical contact mode with different curvature contour on lattice damage from XZ plane observe

  • 2.4 铜膜变形分析

  • 为理解铜膜变形与触点轮廓的紧密性,分别用原子剪切应变和von Mises应力表征铜膜变形度与应力集中度。完整晶格铜膜上表面被视为表层,而亚表层表示距离完整晶格铜膜有一定距离,即受载铜膜紧密接触区被视为亚表层。从图9知,铜膜破坏程度随压深h增加而剧烈,接触应力主要集中亚表层,而表层应力集中不明显;接触区两侧的应力集中易诱导两侧应变加剧和滑移带蔓延(见图10)。此外,触点触点轮廓越大,亚表层应力越集中,更易驱使金属铜产生不同程度的变形与缺陷萌芽(见图10和图11)。

  • 图9 球面触点外围轮廓对铜膜应力分布影响的XZ平面图

  • Fig.9 Influence of spherical contact mode with curvature contour on stress distribution

  • 图10 示出铜膜接触区受载时剪切应变与触点轮廓关联性。由图10知,随压深 h 增加,受载区的应变程度逐渐加剧,且接触区两侧有滑移带伸长,同文献[10] 的滑移带扩展获得一致。接触区边缘两侧和亚表层应变最剧烈,其余区域较低,该结果与图9应力图趋势一致,表明载荷会诱使接触边缘滑移带产生与传播,而滑移是应力集中诱导的微观塑性变形迹象。此外,触点轮廓越大,接触区应变程度加剧,滑移带产生增多,波及范围也相应扩张,原因是触点轮廓越大,局部接触区受载更大,导致亚表层应力会驱动接触区的晶格发生畸变,以致受迫高能原子会向低能处迁移,以蔓延拓张方式来释放应力集中,该结果与图8应力获得对应。图11示出接触区边缘应变度最高,且上表面变形传播路径受加载深度、触点轮廓影响明显。加载深度越大,接触边缘破坏越激烈,相应铜膜上表面的变形也更突出。然而,上表面滑移方向随触点轮廓增加表现出无序化形式,说明铜膜上表面变形程度与触点外围轮廓增加尚无明显线性加剧关系。

  • 图10 球面触点外围轮廓对铜膜内变形影响的 XZ 平面图

  • Fig.10 Influence of spherical contact mode with curvature contour on copper deformation from XZ plane observe

  • 图11 球面触点对铜膜上表面变形影响的 XY 平面图

  • Fig.11 Influence of spherical contact mode with curvature contour on copper surface deformation from XY plane observe

  • 3 结论

  • 采用分子动力学法研究了球面触点模式对金属铜膜接触变形行为与机理,并分析比较了触点外围轮廓对受载纳米铜膜内表面和外表面的微观变形现象差异性机制,得出以下重要结论:

  • (1) 弹性变形阶段,力与位移曲线中的Hertz理论与MD结果吻合。而Hertz理论与MD结果不吻合表现在铜膜位错环的出现,位错环是铜膜发生弹塑性变形转化的临界微观现象。

  • (2) 铜膜缺陷原子数随触点下降位移增加,位错环构型有明显变化。位错环演变历经4个进程, 位错环萌芽期→位错环生长期→位错环增殖期→位错环稳定期,外围轮廓增加会使位错环外部构型也相应增大,而位错环演变4个阶段不受外围轮廓影响。

  • (3) 铜膜内应力主要集中亚表层,其次是非接触区两侧滑移带应力容易集中,铜膜上表面应力集中最弱。触点轮廓越大,亚表层应力越易集中,接触两侧较集中的应力会诱导铜膜变形加剧。

  • (4) WSDA法可有效描述受载铜膜缺陷变形, 随压深h增加,变形逐渐向铜膜两侧和底部蔓延;随触点轮廓增加,迅速向两侧蔓延和分散;该方法与受载应力与应变趋势一致,而铜膜上表面变形与触点外围轮廓增加尚无明显线性加剧关系。

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  • 基本信息

    中图分类号: TG156;TB114
    DOI: 10.11933/j.issn.1007-9289.20210318001

    基金信息

    福建省自然科学基金(2017J01709, 2018J01509, 2018J01556)；
    宁德师范学院重大科研培育 (2017ZDK19)；
    2017 年福建省互联网+大学生创新创业省级教育(闽教学[2017] 52 号)资助项目；
    Supported by Natural Science Foundation of Fujian Province ( 2017J01709, 2018J01509, 2018J01556)；
    Major Project of Ningde Normal University (2017ZDK19)；
    Fujian University Students at Innovation and Entrepreneurship Education Project ([2017] 52).；

    引用信息

    稿件历史

    收稿日期: 2021-03-18

  • 参考文献

    • [1] XU H,KOMVOPOULOS K.Fracture mechanics analysis of asperity cracking due to adhesive normal contact [J].International Journal of Fracture,2013,181(2):273-283.

    • [2] SHIBUTANI Y,TSURU T,KOYAMA A.Nanoplastic deformation of nanoindentation:Crystallographic dependence of displacement bursts [J].Acta Materialia,2007,55(5):1813-1822.

    • [3] BEGAU C,HARTMAIER A,GEORGE E.Atomistic processes of dislocation generation and plastic deformation during nanoindentation[J].Acta Materialia,2011,59(3):934-942.

    • [4] CAO F H,WANG Y J,DAI L H.Novel atomic-scale mechanism of incipient plasticity in a chemically complex CrCoNi mediumentropy alloy associated with inhomogeneity in local chemical environment[J].Acta Materialia,2020,194(4):283-294.

    • [5] SUBIN L,AVIRAL V,JISEONG I M,et al.In-situ observation of the initiation of plasticity by nucleation of prismatic dislocation loops[J].Nature Communication,2020,11(1):2367-2378.

    • [6] XIAO G B,HE Y,GENG Y Q.Molecular dynamics and experimental study on comparison between static and dynamic ploughing lithography of single crystal copper [J].Applied Surface Science,2019,463(1):96-104.

    • [7] QIU C,ZHU P Z,FANG F Z.Study of nanoindentation behavior of amorphous alloy using molecular dynamics [J].Applied Surface Science,2014,305(30):101-110.

    • [8] LAI M,ZHANG X D,FANG F Z.Nanoindentation-induced phase transformation and structural deformation of monocrystalline germanium:a molecular dynamics simulation investigation [J].Nanoscale Research Letters,2013,8(12):353-362.

    • [9] 黄健萌,陈晶晶,李凝.两种不同形状压头与单晶铜基体间接触力和摩擦力的纳观分析 [J].摩擦学学报,2015,35(3):308-314.HUANG J M,CHEN J J,LI N.Analysis of the contact and friction force behaviour between different indenter shape and substrate on atomic scale [J].Tribology,2015,35(3):308-314.(in Chinese)

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    • [11] 陈晶晶,胡洪钧,李保震.纳观单晶铜表面黏着接触失效的分子动力学模拟[J].表面技术,2017,46(8):195-200.CHEN J J,HU H J,LI B Z.Molecular dynamics simulation of failure in adhesive contact with single crystal copper[J].Surface Technology,2017,46(8):195-200.(in Chinese)

    • [12] XIANG H G,LI H T,FU T.Formation of prismatic loops in AlN and GaN under nanoindentation [J].Acta Materialia,2017,138(1):131-139.

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