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金属学报, 2025, 61(10): 1567-1578 DOI: 10.11900/0412.1961.2023.00499

研究论文

纳米压痕下VCoNi 中熵合金的塑性变形行为

王方圆1, 张玉龙2, 王章维,1, 熊志平3, 王辉4, 宋旼1, 夏文真,2

1 中南大学 粉末冶金国家重点实验室 长沙 410083

2 安徽工业大学 冶金工程学院 微纳组织与力学研究所 马鞍山 243032

3 北京理工大学 冲击环境材料技术国家级重点实验室 北京 100081

4 北京科技大学 新金属材料国家重点实验室 北京 100083

Plastic Deformation Behaviors of VCoNi Medium-Entropy Alloy Under Nanoindentation

WANG Fangyuan1, ZHANG Yulong2, WANG Zhangwei,1, XIONG Zhiping3, WANG Hui4, SONG Min1, XIA Wenzhen,2

1 State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China

2 Institute of Microstructure and Micro/nano-mechanics, School of Metallurgical Engineering, Anhui University of Technology, Ma'anshan 243032, China

3 National Key Laboratory of Science and Technology on Materials Under Shock and Impact, Beijing Institute of Technology, Beijing 100081, China

4 State Key Laboratory for Advance Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China

通讯作者: 王章维，z.wang@csu.edu.cn，主要从事高熵合金研究;夏文真，w.xia@ahut.edu.cn，主要从事微纳力学研究

责任编辑: 梁烨

收稿日期: 2023-12-29   修回日期: 2024-01-27  

基金资助: 国家重点研发计划项目(2022YFE0134400)
国家自然科学基金青年科学基金项目(52201057)
冲击环境材料技术重点实验室基金项目(6142902220101)
新金属材料国家重点实验室开放基金项目(2023-Z05)

Corresponding authors: WANG Zhangwei, professor, Tel: 19158163789, E-mail:z.wang@csu.edu.cn;XIA Wenzhen, professor, Tel: 18255544320, E-mail:w.xia@ahut.edu.cn

Received: 2023-12-29   Revised: 2024-01-27  

Fund supported: National Key Research and Development Program of China(2022YFE0134400)
Young Scientists Fund of National Natural Science Foundation of China(52201057)
National Key Laboratory Foundation of Science and Technology on Materials under Shock and Impact(6142902220101)
State Key Laboratory for Advanced Metals and Materials(2023-Z05)

作者简介 About authors

王方圆，女，1999年生，硕士

张玉龙，男，1998年生，硕士，共同第一作者

摘要

fcc等原子比VCoNi中熵合金因优异的力学性能受到广泛关注，而探究其塑性变形机制对于力学性能调控至关重要。为了探究晶粒取向对位错运动过程和位错间相互作用的影响机理，本工作利用纳米压痕实验探讨了VCoNi中熵合金{101}、{111}和{001}晶粒的塑性变形行为。通过滑移台阶演变和载荷-位移曲线的分析，重点研究了晶体取向对其塑性变形行为的影响，以及位错间相互作用、载荷-位移变化行为与位错运动之间的关系。结果表明，VCoNi中熵合金中晶粒取向决定纳米压痕诱导滑移系的激活与开动顺序，以及位错反应过程，进而显著影响压痕压坑和其周边滑移台阶的形貌，以及载荷-位移变化行为。位错相互作用的分析结果表明，位错反应易在{101}晶粒中形成Lomer-Cottrell位错锁和Glissile结，在{111}晶粒中易形成Collinear结和Lomer-Cottrell位错锁，而在{001}晶粒中易形成Glissile结，这决定不同晶粒压痕载荷-位移曲线中的后续位移突变行为。

关键词： 中熵合金; 纳米压痕; 滑移台阶; 塑性变形; 位错反应

Abstract

High- and medium-entropy alloys have attracted considerable attention because of their innovative design concepts. The VCoNi medium-entropy alloy with equiatomic ratio, a distinctive type of medium-entropy alloy, is characterized by a fcc structure. As it exhibits remarkable mechanical properties such as strength and plasticity across a broad temperature spectrum, it is suitable for versatile applications. Current research on VCoNi medium-entropy alloys predominantly focuses on the alloy design and the manipulation of heat treatment technologies to enhance mechanical properties with relatively less emphasis on elucidating plastic deformation mechanisms. A profound understanding of these mechanisms is imperative for controlling their properties. Although previous studies have revealed plastic deformation mechanisms mediated by dislocations in VCoNi medium-entropy alloys, the impact of grain orientation on dislocation movement and interaction mechanisms remains elusive. Nanoindentation technology has been widely used to assess plastic deformation behavior and dislocation evolution in materials. Grain orientation profoundly influences the mechanical properties and plastic deformation behavior of materials at the microscale. Therefore, investigating the influence of grain orientation on the plastic deformation mechanism in the VCoNi medium-entropy alloy is of great importance. A comprehensive understanding of plastic deformation and dislocation interactions can be achieved by analyzing slip steps generated by nanoindentation. This study delves into the plastic deformation behavior of VCoNi medium-entropy alloy in {101}, {111}, and {001} grains using nanoindentation. By analyzing the evolution of slip steps and load-displacement curves, it concentrates on the influence of crystal orientation on plastic deformation behavior and explores the intricate relationship among dislocation interactions, load-displacement behavior, and dislocation motion. The grain orientation in the VCoNi medium-entropy alloy dictates the activation and sequence of slip systems induced by nanoindentation, thereby substantially influencing the morphology of indentations, surrounding slip steps, and load-displacement behavior. The slip steps on the same slip plane in each grain preferentially appear on a positively inclined slip plane. On {101} grains, the slip steps appear on the (111) and (111¯) slip planes initially, and then on the (11¯1¯) and (11¯1) slip planes. In {111} grains, the slip steps appear on the (111¯), (11¯1¯), and (11¯1) slip planes. On {001} grains, the slip steps appear on the four {111} slip planes. {101}, {111}, and {001} grains exhibit butterfly-shaped, nested triangle-shaped, and cross-shaped overall indentation morphologies, respectively. Additionally, only a limited occurrence of double cross-slip is observed at the edges of the slip steps in {101} and {001} grains. The analysis of dislocation interactions revealed that on {101} grains, dislocation reactions tended to form Lomer-Cottrell locks and Glissile junctions, in {111} grains they tended to form Collinear junctions and Lomer-Cottrell locks, and in {001} grains they tended to form Glissile junctions. This determination influences the subsequent pop-in behavior in the load-displacement curves of different grains.

Keywords： medium-entropy alloy; nanoindentation; slip step; plasticity; dislocation interaction

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本文引用格式

王方圆, 张玉龙, 王章维, 熊志平, 王辉, 宋旼, 夏文真. 纳米压痕下VCoNi 中熵合金的塑性变形行为[J]. 金属学报, 2025, 61(10): 1567-1578 DOI:10.11900/0412.1961.2023.00499

WANG Fangyuan, ZHANG Yulong, WANG Zhangwei, XIONG Zhiping, WANG Hui, SONG Min, XIA Wenzhen. Plastic Deformation Behaviors of VCoNi Medium-Entropy Alloy Under Nanoindentation[J]. Acta Metallurgica Sinica, 2025, 61(10): 1567-1578 DOI:10.11900/0412.1961.2023.00499

高熵和中熵合金因其新颖的合金设计理念而受到广泛关注[1~6]。与其他各类高熵和中熵合金相比，具有fcc结构的等原子比VCoNi中熵合金在较宽温度范围内综合力学性能更优异，被视为极具应用潜力的结构材料[7~10]。研究[7,11]表明，VCoNi中熵合金在室温下屈服强度和延伸率分别可达到1 GPa和38%，且在低温下力学性能更为优异，屈服强度和延伸率分别为1.2 GPa和42%，此外其耐腐蚀和抗氢脆等性能更优异[12]。VCoNi中熵合金优异的强度-塑性匹配归因于塑性变形过程中形成的高密度且均匀分布的滑移带。随着应变的不断增加，平面滑移带的间距会不断细化，这个过程可以产生非常高的应变硬化率，稳定塑性变形[7]。然而，关于VCoNi中熵合金在塑性变形过程中的位错运动过程以及位错间相互作用的机理，目前仍然不甚清楚。因此，深入探究VCoNi中熵合金的位错行为和强韧化机制，对于进一步优化其力学性能具有重要意义。

纳米压痕技术，作为研究材料塑性变形行为和位错演变机制的常用方法[13,14]，已被广泛应用于揭示高熵和中熵合金的变形机制[15,16]。例如，Ye等[15]研究了TiZrHfNb高熵合金在纳米压痕过程中的位错形核，发现其机理为多个原子的协同迁移；Hua等[16]通过对CoCrNi中熵合金进行纳米压痕实验，发现Cr团簇处更倾向于发生非均匀位错形核。此外，晶粒取向在微观尺度下显著影响材料的力学性能和塑性变形行为[17,18]，而纳米压痕技术能够揭示晶粒取向对塑性变形机制的影响。晶粒取向通过影响不同变形机制的激活，进而影响材料塑性变形行为[19,20]。Kang等[21]利用纳米压痕技术研究了晶粒取向对高锰孪生诱导塑性(TWIP)钢压痕模量和最大剪切应力的影响，发现其值均随(001)、(101)和(111)晶粒顺序增加，并且仅在(001)晶粒中观察到变形孪晶。Sarvesha等[22]利用纳米压痕技术研究了晶粒取向对单晶Zn塑性变形的影响，发现压痕形貌、孪晶载荷和堆积/下沉程度随晶粒取向发生显著变化，这与孪生和激活的滑移系有关。上述研究均表明，纳米压痕技术适用于研究VCoNi中熵合金中的塑性变形机制。

在纳米压痕加载过程中，当压头作用于金属材料表面引发塑性变形时，位错开始形核并沿滑移面运动，当位错运动到材料表面后，会在材料表面形成滑移台阶，并伴随着表面形貌变化。而滑移台阶的形貌特征可提供与位错滑移相关的信息，并可定性描述塑性变形的过程。McInteer等[23]于1980年通过光学显微镜(OM)观察滑移台阶并研究H对Ni变形机制的影响。随着表征技术的发展，Tromas等[24]通过纳米压痕和原子力显微镜(AFM)研究了单晶MgO在(001)晶面上的滑移台阶以及单个位错初始塑性变形。之后，研究者们[25~28]开始通过研究不同晶粒取向下滑移台阶的演变规律揭示晶粒取向对位错的影响。例如，Nibur等[25,26]通过电子背散射衍射(EBSD)系统和AFM识别{001}、{011}和{111}晶粒压痕周围的滑移台阶并分析其差异性，建立了压痕下方塑性变形机制与滑移台阶之间的关联。此外，Nibur和Bahr[25]提出了正/负倾斜滑移面概念，即位错从压头正下方移动到样品表面，远离压头的面为正倾斜滑移面，而从外部靠近压头的为负倾斜滑移面。Xia等[27,28]在此基础上提出3种判断正/负倾斜滑移面的方式，即EBSD、EBSD + 电子通道衬度成像(ECCI)、EBSD + AFM，并通过分析{001}、{011}和{111}晶粒中滑移台阶的演变研究位错相互作用和塑性流动。综上所述，通过分析纳米压痕产生的滑移台阶，可以深入了解不同晶粒取向下的塑性变形及位错间相互作用。

本工作从VCoNi中熵合金中选取{101}、{111}和{001}取向的晶粒进行纳米压痕实验，通过分析滑移台阶和载荷-位移(P-h)曲线研究晶粒取向对VCoNi中熵合金塑性变形机制的影响。旨在探究不同取向晶粒滑移台阶整体形貌以及演变过程的差异性；位错间相互作用及P-h曲线与滑移台阶、位错运动之间的关联，以期深化对VCoNi中熵合金塑性变形机制的认识。本工作揭示了VCoNi中熵合金沿不同晶向的塑性变形行为机理，为优化此类合金的力学性能提供了理论依据。

1 实验方法

选取纯度为99.9% (质量分数)的V、Co和Ni作为原料，通过真空电弧熔炼制备VCoNi铸锭。将铸态合金样品在1200 ℃进行均质化热处理，保温24 h后立即水淬。将均质化后的样品进行多道次冷轧，总压下量为50%。将冷轧态合金样品在1200 ℃进行再结晶退火，保温48 h后立即水淬。热处理后样品表面经砂纸打磨，金刚石抛光膏抛光，以及0.02 μm的胶体SiO2悬浮液精细抛光，以确保去除表面的应力层。经过表面处理后，采用配备EBSD探头的Helio NanoLab G3 UC扫描电子显微镜(SEM)表征样品的显微组织及晶粒取向，选取取向接近{101}、{111}和{001}的晶粒进行纳米压痕实验。

采用KLA G200X纳米压痕仪进行压痕实验，压头选用半径为5 μm的球形金刚石压头，应变速率恒定为0.1 s-1。当热漂移小于0.5 nm/s时开始实验。在选取的3个晶粒中分别施加5、10、20、40和80 mN的法向力，每个压坑之间根据不同压痕载荷间隔10~30 μm的距离，并且压痕位置远离晶界，确保各压痕间具有足够的间距以避免相互干扰。压痕实验完成后，采用Helio NanoLab G3 UC SEM中的二次电子(SE)和ECCI模式分别观察样品表面滑移台阶的形貌和位错。SE模式下工作参数为：加速电压2.00 kV，电流25 pA，工作距离4.0 mm。ECCI模式下工作参数为：加速电压30.00 kV，电流1.6 nA，工作距离4.0 mm。

2 实验结果

2.1 滑移台阶的形貌及演变

图1为80 mN压痕载荷下不同取向晶粒的SE像、反极图(IPF)、相应滑移面示意图及ECCI像和示意图，IPF中晶界被加粗的晶粒为本工作选取的取向接近{101}、{111}和{001}的晶粒。晶粒的精确取向分别为{1¯10}、{12 13 15}和{2 18 1}。根据图1d~f所示的滑移面示意图，并结合正/负倾斜(P/N)滑移面的定义，标定了图1a~c中的正/负倾斜滑移面及滑移面指数。由于{101}晶粒内(11¯1¯)和(11¯1)滑移面所对应的滑移台阶，以及{001}晶粒中(11¯1)和(111)滑移面所对应的滑移台阶基本平行，因此难以通过表面滑移台阶的SE像进行区分。由于滑移台阶线上的位错均与压头同侧，因此位错向远离压头的方向移动，即滑移台阶所对应的滑移面均为正倾斜滑移面[28]。故图1g所示区域为(11¯1)正倾斜滑移面，图1h所示区域为(111)正倾斜滑移面。

图1

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图1   80 mN压痕载荷下不同取向晶粒的二次电子(SE像)、反极图、相应滑移面示意图及电子通道衬度成像(ECCI)和示意图

Fig.1   Secondary electron (SE) images and inverse pore figures (insets) (a-c), corresponding schematics of slip planes (d-f), and electron channeling contrast imaging (ECCI) images and corresponding schematics (insets) (g, h) of grains with different orientations under 80 mN indentation load (P represents positive inclined, N represents negative inclined. Boxes 1, 2, and 3 in Figs.1a and c represent regions where double cross-slip exists. In Figs.1d-f, white lines represent the intersection line between the slip planes and the surface, which are the slip steps; bolded portions at the edges of the slip planes represent the angles closer to the sample surface, indicating the inclination angles between the slip planes and the surface)

(a, d, g) {101} grain (b, e) {111} grain (c, f, h) {001} grain


如图1a所示，{101}晶粒中存在沿4个{111}滑移面滑移所形成的滑移台阶。(111¯)和(111)滑移面与表面的倾斜角接近90°，Schmid因子较大，位错易滑移，故(111¯)和(111)滑移面上的滑移台阶数量高于(11¯1¯)和(11¯1)滑移面，{101}晶粒的滑移台阶整体形状为蝴蝶状。如图1b所示，{111}晶粒中存在沿3个{111}滑移面滑移所形成的滑移台阶，即(11¯1)、(111¯)和(11¯1¯)滑移面，且它们与表面的倾斜角接近70°；而(111)滑移面与表面的倾斜角接近0°，Schmid因子较小，位错难滑移，故不存在沿(111)滑移面滑移所形成的滑移台阶，{111}晶粒的滑移台阶整体形状为嵌套三角形，内部三角形由正倾斜滑移面上的滑移台阶构成，外部三角形由负倾斜滑移面上的滑移台阶构成。如图1c所示，{001}晶粒中存在沿4个{111}滑移面滑移所形成的滑移台阶，{001}晶粒的滑移台阶整体形状为十字形。3个晶粒中的滑移台阶均为直线，表明位错为平面滑移[25]。这与VCoNi中熵合金在变形阶段为平面滑移的实验结果[7]一致。

图2为80 mN压痕载荷下滑移台阶的局部放大SE像，其中图2a为图1a中方框1的局部放大图({101}晶粒)，图2b和c分别为图1c中方框2和3的局部放大图({001}晶粒)。位错在2个不同滑移面上发生位错反应所形成的位错结会阻碍后续位错的滑移。此现象在SE像中表现为不同滑移面滑移台阶相交并且不再延伸。而图2中的情况则与上述情况不同，以图2a为例，P(11¯1)滑移面(图2a中实线方框)上的滑移台阶比附近正常沿P(11¯1)滑移面形成的滑移台阶要短很多。这表明沿P(11¯1)滑移面形成的滑移台阶不是直接形成的。此外，图2a中2个P(11¯1)滑移面上的滑移台阶通过一条短的P(111)滑移面上的滑移台阶相连，同样这条P(111)滑移面上的滑移台阶比其附近沿P(111)滑移面的滑移台阶要短得多。因此推测，图2a中标注的滑移台阶存在双交滑移，图2b和c中也存在类似情况。据此，结合Thompson四面体确定了发生双交滑移的位错的Burgers矢量：在{101}晶粒中，P(11¯1)滑移面(图2a中虚线方框)上的位错交滑移到P(111)滑移面上，滑移一段距离后交滑移到新的P(11¯1)滑移面(图2a中实线方框)，Burgers矢量为1/2[1¯01]。在{001}晶粒中，P(111¯)滑移面(图2b中虚线方框)上的位错先交滑移到P(111)滑移面，随后交滑移到新的P(111¯)滑移面(图2b中实线方框)，Burgers矢量为1/2[1¯10]；此外，P(11¯1¯)滑移面(图2c中虚线方框)上的位错先交滑移到P(111)滑移面上，再交滑移到新的P(11¯1¯)滑移面(图2c中实线方框)，Burgers矢量为1/2[011¯]。VCoNi中熵合金的塑性变形研究[7]表明，在高应变下VCoNi中熵合金缺乏频繁的交滑移，这与本工作观察到的现象一致，即在较高载荷作用下VCoNi中熵合金出现少量的双交滑移，说明VCoNi中熵合金的层错能较高。此外，压痕实验后VCoNi中熵合金滑移台阶的整体形貌与Fe-25Cr-20Ni奥氏体不锈钢较为一致。Fe-25Cr-20Ni奥氏体不锈钢的层错能为45 mJ/m2，塑性变形由位错主导，结果的相似性也进一步说明了VCoNi中熵合金的层错能较高[28]。

图2

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图2   80 mN压痕载荷下滑移台阶局部放大SE像

Fig.2   Partially enlarged SE images of slip steps in {101} grain (a) and {001} grain (b, c) under 80 mN indentation load (Dotted rectangles represent the slip steps formed by dislocations sliding along the slip plane before double cross-slip, solid rectangles represent the slip steps formed by dislocations sliding along the slip plane after double cross-slip.b—Burgers vector)

(a) box 1 in Fig.1a (b) box 2 in Fig.1c (c) box 3 in Fig.1c


图3为不同压痕载荷下不同取向晶粒的SE像。当压痕载荷为5 mN时，{101}晶粒中只存在沿(111¯)和(111)滑移面滑移所形成的滑移台阶，这是因为(111¯)和(111)滑移面与表面的倾斜角接近90°，Schmid因子较大，位错易滑移，所以位错优先沿这2个滑移面形核增殖并滑移，滑移台阶形貌为平行四边形，如图3a所示。随着压痕载荷的增大，滑移台阶数目增加且长度增长，这归因于位错密度的增大和位错滑移距离的增加，如图3b所示。继续增大压痕载荷，(111)和(111¯)滑移面上的滑移台阶相互突破。(11¯1¯)和(11¯1)滑移面上沿滑移方向上的分切应力达到临界分切应力，此时出现沿(11¯1¯)和(11¯1)滑移面滑移所形成的滑移台阶，并且均在正倾斜滑移面上，逐渐形成蝴蝶状图案，如图3c所示。而对于{111}晶粒，当压痕载荷为5 mN时，未观察到沿(111)滑移面的滑移台阶，这是因为(111)滑移面与表面的倾斜角为5°，Schmid因子较小，位错难滑移。另外3个滑移面的滑移台阶形成了嵌套三角形的形貌，内部三角形由正倾斜滑移面上的滑移台阶组成，外部三角形由负倾斜滑移面上的滑移台阶组成，如图3d所示。并且正倾斜滑移面上滑移台阶的数量远高于负倾斜滑移面，故滑移台阶优先在正倾斜滑移面上产生。随着压痕载荷的增大，滑移台阶的长度和数量不断增加，如图3e所示。进一步增大压痕载荷至20 mN，滑移台阶的整体形貌以几何相似性增长，保持嵌套三角形的形状，如图3f所示。对于{001}晶粒，当压痕载荷为5 mN时，由于(111¯)和(11¯1¯)滑移面与表面倾斜角大于(111)滑移面，故优先沿(111¯)和(11¯1¯)滑移面形成滑移台阶，而后在(111)滑移面上形成滑移台阶并对其他滑移面上的滑移台阶产生阻碍，滑移台阶形貌为四边形，如图3g所示。此外，(111)和(11¯1)滑移面上的滑移台阶均出现在正倾斜滑移面上，进一步说明滑移台阶优先出现在正倾斜滑移面上。随着压痕载荷增加，滑移台阶的长度和数量不断增加，滑移台阶的整体形貌仍保持四边形的形貌，如图3h所示。当继续增加压痕载荷至20 mN时，(11¯1)滑移面上的滑移台阶突破(111¯)滑移面上滑移台阶的阻碍，滑移台阶逐渐向外扩展，逐渐形成十字形，如图3i所示。图3a、d和g中方框标记的区域中存在2个滑移台阶同时相交于一点的情况。

图3

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图3   不同压痕载荷下各晶粒的SE像

Fig.3   SE images of {101} (a-c), {111} (d-f), and {001} (g-i) grains under indentation loads of 5 mN (a, d, g), 10 mN (b, e, h), and 20 mN (c, f, i) (Boxes 1-6 represent regions where dislocation interactions exist)


综上，VCoNi中熵合金中晶粒取向决定了纳米压痕诱导滑移系激活与开动的顺序，从而显著影响压坑周边滑移台阶的形貌。同一滑移面上的滑移台阶优先出现在正倾斜滑移面上。在{101}、{111}和{001}晶粒中，滑移台阶的整体形貌分别为蝴蝶状、嵌套三角形和十字形。

2.2 P-h 曲线

根据Hertz接触理论给出的载荷(P)与深度之间的关系[29]，P的表达式如下：

P=43ErRh32

式中，Er为折减模量，R为有效半径，h为对应载荷下的深度。因本工作使用的是球形压头，所以R≈Ri (下角标i代表压头)。因此可由P-h的关系得到Er，利用Er可进一步得到弹性模量(Es)[29]：

1Er=1-νi2Ei+1-νs2Es

式中，ν为Poisson比；E为弹性模量(下角标s代表材料)。本工作使用的是金刚石球形压头，故Ei = 1141 GPa，νi = 0.07，νs = 0.334[7]。初始塑性变形时，P-h曲线上出现第1个不连续的小台阶，即位移突变现象(pop-in)，此时压头下方最大剪切应力(τmax)可通过下计算[29]：

τmax=0.316π3PEr2R213

根据Tuck等[30]的理论，塑性功(Wp)为：

Wp=(Pmax·hf) / 3

式中，Pmax为最大载荷；hf为残余深度。

图4为不同压痕载荷下不同取向晶粒的P-h曲线和塑性功分布。如图4a~c所示，VCoNi中熵合金中各晶粒均经历弹性和初始塑性阶段。每个晶粒在不同压痕载荷下的弹性阶段均符合Hertz弹性接触理论曲线。同一晶粒在5和10 mN时的曲线较为吻合，说明其在5和10 mN压痕载荷下的原始位错状态相同。但当压痕载荷为20 mN时，P-h曲线存在差异，所需载荷较小，弹性阶段持续深度较浅；不同晶粒的P-h曲线中第1个pop-in对应的载荷取决于晶粒取向[31]。{101}、{111}和{001}晶粒在5 mN压痕载荷下，第1个pop-in对应的载荷分别为4.56、4.50和2.76 mN；在10 mN压痕载荷下，第1个pop-in对应的载荷分别为5.08、4.25和2.52 mN。第1个pop-in的出现表明材料发生了弹塑性转变，此时应力已达到位错形核的临界值或预先存在的位错发生滑移的临界剪切应力[32]。VCoNi的剪切模量为72 GPa[7]，通过 式(3)计算得出{101}和{111}晶粒在5和10 mN压痕载荷下的τmax为G / 30 (其中G为剪切模量)，而其他计算值均低于G / 30[33]。故载荷为20 mN时，P-h曲线的差异可能是由于该区域下方存在少量位错所致，位错激活所需的剪切应力低于位错形核的剪切应力，因此降低了第1个pop-in所对应的载荷[34]。在20 mN载荷下，不同晶粒的P-h曲线中间歇性出现较小的pop-in，如图4a~c中红色箭头所示。图4a中1号标记处和图4b中3号标记处因与其他载荷下的P-h曲线有重叠，因此在图中插入了局部放大图。后续的pop-in可能与不同滑移系统的激活和位错反应相关[35]。

图4

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图4   不同压痕载荷下各晶粒的载荷-深度(P-h)曲线和塑性功分布

Fig.4   Load-displacement (P-h) curves of {101} (a), {111} (b), and {001} (c) grains and plastic work distributions (d) under different indentation loads (Insets in Figs.4a and b are enlarged images of pop-in. Red arrows and numbers together indicate the location of the subsequent pop-in. Wp—plastic work)


不同取向晶粒的P-h曲线存在差异。利用 式(1)和(2)可计算出{101}、{111}和{001}晶粒的弹性模量依次为126、123和117 GPa。在相同压痕载荷下，不同取向晶粒的弹性阶段持续深度存在差异。在弹性变形阶段，曲线均呈指数状增长。当压痕载荷继续增大时，晶粒中位错发生增殖，位错运动加剧，塑性变形程度不断增大。位错的相互作用导致P-h曲线出现一定的波动[36]，但整体呈近直线增长。塑性功越大表明材料的塑性越好。如图4d所示，不同取向晶粒的塑性变形能力存在差异。综上，VCoNi中熵合金的弹性模量和塑性变形具有晶体取向相关性。

3 分析与讨论

VCoNi中熵合金中的滑移台阶和P-h曲线上后续出现的pop-in可归因于晶粒内部滑移系统的激活与位错运动。在运动过程中，不同滑移面的位错相遇时发生相互作用，即位错反应。由于晶粒取向、局部应力状态及滑移面的不同，参与反应的位错和位错反应的类型均存在显著差异。位错的相互作用会进一步影响塑性变形的过程，进而导致P-h曲线产生变化。因此，本节在明确不同晶粒内部位错间相互作用的基础上，进一步分析了后续pop-in与位错运动之间的关系。

3.1 位错间的相互作用

如图1所示，根据对应晶粒的Thompson四面体确定了位错所在滑移面，可结合fcc金属的塑性流动方向判断位错运动的方向，塑性流动方向分为垂直于滑移台阶的正向流动和平行于滑移台阶的侧向流动。塑性流动方向取决于滑移面的倾斜角，随着倾斜角的增加，塑性流动方向从正向转变为侧向，且过渡角为55°~58° [27]。本工作同样存在一个过渡角范围(53°~57°)，当倾斜角大于57°时，塑性流动方向为侧向流动；当倾斜角小于53°时，塑性流动方向为正向流动。表1是fcc金属中全位错反应类型。全位错反应类型共有5种，其中4种可形成位错结，即Lomer、Hirth、Collinear和Glissile结[37]。根据位错所在滑移面和位错运动的方向，结合表1可进一步判断全位错反应的类型。

表1   fcc金属中全位错反应类型

Table 1  Types of perfect dislocation reactions in fcc metal

Slipb(11¯1¯)(111)(111¯)(11¯1)
plane1/2[110]1/2[011¯]1/2[101]1/2[1¯01]1/2[1¯10]1/2[011¯]1/2[011]1/2[1¯10]1/2[101]1/2[1¯01]1/2[011]1/2[110]
(11¯1¯)1/2[110]-CoplCoplLomHirthGlissLomHirthGlissGlissGlissColl
1/2[011¯]Copl-CoplGlissGlissCollHirthLomGlissLomHirthGliss
1/2[101]CoplCopl-HirthLomGlissGlissGlissCollHirthLomGliss
(111)1/2[1¯01]LomGlissHirth-CoplCoplLomGlissHirthCollGlissGliss
1/2[1¯10]HirthGlissLomCopl-CoplGlissCollGlissGlissLomHirth
1/2[011¯]GlissCollGlissCoplCopl-HirthGlissLomGlissHirthLom
(111¯)1/2[011]LomHirthGlissLomGlissHirth-CoplCoplGlissCollGliss
1/2[1¯10]HirthLomGlissGlissCollGlissCopl-CoplLomGlissHirth
1/2[101]GlissGlissCollHirthGlissLomCoplCopl-HirthGlissLom
(11¯1)1/2[1¯01]GlissLomHirthCollGlissGlissGlissLomHirth-CoplCopl
1/2[011]GlissHirthLomGlissLomHirthCollGlissGlissCopl-Copl
1/2[110]CollGlissGlissGlissHirthLomGlissHirthLomCoplCopl-

Note: Copl—coplanar reaction, Lom—Lomer reaction, Hirth—Hirth reaction, Gliss—glissile reaction, Coll—collinear reaction

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图5为图3中方框区域的局部放大图和相应滑移面示意图。当压痕载荷为5 mN时，{101}晶粒中的位错先在(111¯)和(111)滑移面上形核、增殖并运动。由于(111¯)和(111)滑移面与表面的倾斜角均为89°，因此塑性流动的方向均为侧向流动。如图5a和b所示，(111)滑移面上的位错均向斜上方运动，结合左下方的滑移面示意图可推测，位错的Burgers矢量为1/2[1¯01]或1/2[011¯]。由于(111)滑移面的塑性流动方向为侧向流动，因此(111)滑移面上位错的Burgers矢量倾向于是1/2[1¯01]。图5a中(111¯)滑移面上的位错向斜上方运动，图5b中(111¯)滑移面上的位错向斜下方运动，并且(111¯)滑移面塑性流动的方向为侧向流动，故图5a中(111¯)滑移面上位错的Burgers矢量倾向于是1/2[011]，图5b中(111¯)滑移面上位错的Burgers矢量可能为1/2[1¯10]。因此，结合表1可知，当P(111)滑移面上的1/2[1¯01]全位错和N(111¯)滑移面上的1/2[011]全位错同时相交于图5a中1号位置时，反应形成Lomer-Cottrell位错锁；当N(111)滑移面上的1/2[1¯01]全位错和N(111¯)滑移面上的1/2[1¯01]全位错同时相交于2号位置时，反应形成Glissile结。反应形成Lomer-Cottrell位错锁和Glissile结可阻碍位错运动，最终形成平行四边形的滑移台阶形貌。

图5

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图5   5 mN压痕载荷下各晶粒滑移台阶的局部放大SE像和相应滑移面示意图

Fig.5   Partially enlarged SE images of slip steps and schematics of slip planes (insets) of {101} grain in Fig.3a (a, b), {111} grain in Fig.3d (c, d), and {001}grain in Fig.3g (e, f) (Red arrows in boxes indicate the direction of dislocation movement; 1-6 represent the junctions of dislocation interactions)


当压痕载荷为5 mN时，{111}晶粒上的位错在(11¯1)、(111¯)和(11¯1¯)滑移面上形核、增殖并运动，滑移台阶整体形貌为嵌套三角形。因(11¯1)、(111¯)和(11¯1¯)滑移面与表面的倾斜角均大于57°，故塑性流动的方向均为侧向流动。如图5c和d所示，位错在(111¯)滑移面上均向斜上方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[1¯01¯]或1/2[1¯01]。因为在{111}晶粒中，负倾斜滑移面上的位错沿滑移面运动形成的滑移台阶在外部组成三角形，此时负倾斜滑移面上的塑性流动控制整体塑性流动速率，因此负倾斜滑移面上塑性流动比正倾斜滑移面上塑性流动更快。此外，由于(111¯)滑移面塑性流动方向为侧向，因此可判断图5c中P(111¯)滑移面上位错的Burgers矢量倾向于是1/2[1¯01¯]，图5d中N(111¯)滑移面上位错的Burgers矢量倾向于是1/2[1¯10]。如图5c所示，位错在(11¯1¯)滑移面上向斜上方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[1¯01¯]或1/2[011¯]。因P(11¯1)滑移面的塑性流动方向为侧向流动，且正倾斜滑移面的塑性流动速率小于负倾斜滑移面，故P(11¯1¯)滑移面上位错的Burgers矢量倾向于是1/2[1¯01¯]。如图5d所示，位错在N(11¯1)滑移面上向斜上方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[1¯1¯0]或1/2[101¯]。由于N(11¯1)滑移面的塑性流动方向为侧向流动，且负倾斜滑移面塑性流动速率大于正倾斜滑移面，因此N(11¯1)滑移面上位错的Burgers矢量倾向于是1/2[101¯]。结合表1可知，当P(111¯)滑移面上的1/2[1¯01¯]全位错和P(11¯1¯)滑移面上的1/2[1¯01¯]全位错同时相交于图5中3号位置时，反应形成Collinear结；当N(111¯)滑移面上的1/2[1¯10]全位错和N(11¯1)滑移面上的1/2[101¯]全位错同时相交于图5中4号位置时，反应形成Lomer-Cottrell位错锁。

当压痕载荷为5 mN时，{001}晶粒中位错在4个滑移面上形核、增殖并运动，滑移台阶整体形貌为四边形。如图5e所示，(111)滑移面与表面的倾斜角小于53°，塑性流动的方向为正向流动，而(111¯)滑移面与表面的倾斜角为53°，塑性流动的方向既包括正向流动也包括侧向流动，但正向流动占主导。如图5e所示，位错在(111)滑移面向斜上方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[011¯]或1/2[101¯]。由于(111)滑移面的塑性流动方向为正向流动，因此(111)滑移面上位错的Burgers矢量倾向于是1/2[011¯]。如图5e所示，位错在(111¯)滑移面向斜上方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[1¯10]或1/2[101]。由于(111¯)滑移面的塑性流动方向中正向流动占主导，因此(111¯)滑移面上位错的Burgers矢量倾向于是1/2[1¯10]。如图5f所示，(11¯1)滑移面与表面的倾斜角大于57°，塑性流动的方向为侧向流动。位错在(11¯1)滑移面上向斜上方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[110]或1/2[101¯]。由于塑性流动方向为侧向流动，因此(11¯1)滑移面上位错的Burgers矢量倾向于是1/2[101¯]。如图5f所示，位错在(111¯)滑移面上向斜下方运动，结合左下方的滑移面示意图可推测位错的Burgers矢量为1/2[101]或1/2[011]。正向流动占主导，因此(111¯)滑移面上位错的Burgers矢量倾向于是1/2[011]。结合表1可知，当P(111)滑移面上的1/2[011¯]全位错和N(111¯)滑移面上的1/2[1¯10]全位错同时相交于图5中5号位置时，反应形成Glissile结；P(11¯1)滑移面上的1/2[101¯]全位错和N(111¯)滑移面上的1/2[011]全位错同时相交于图5中6号位置时，反应形成Glissile结。

除了位错反应外，在图3中还可观察到不同滑移面的滑移台阶相互突破的现象。在{101}晶粒中，(111¯)和(111)滑移面上的滑移台阶相互突破。(111¯)和(111)滑移面的塑性流动方向均为侧向流动。随着载荷增大，位错锁倾向于解锁，位错在(111¯)和(111)滑移面上沿着滑移台阶的方向运动，相互突破阻碍。在{001}晶粒中，(11¯1)滑移面上的滑移台阶突破(111¯)滑移面上滑移台阶的阻碍。(11¯1)滑移面上塑性流动的方向为侧向流动，而(111¯)滑移面上塑性流动的方向为正向流动，因此，位错在(11¯1)滑移面上沿滑移台阶的方向继续向外扩展，突破(111¯)滑移面上滑移台阶的阻碍。

综上，不同取向晶粒在纳米压痕下激活的滑移系统不同，这也导致不同取向晶粒内的位错反应存在差异。{101}晶粒上位错反应形成Lomer-Cottrell位错锁和Glissile结；{111}晶粒上位错反应形成Collinear结和Lomer-Cottrell位错锁；{001}晶粒上位错反应形成Glissile结。此外，滑移台阶突破的现象与塑性流动有关，即与滑移面和表面之间的倾斜角有关。

3.2 P-h 曲线后续pop-in和位错运动之间的关联

位错运动和位错相互作用会导致P-h曲线产生变化。根据后续pop-in出现时所对应的载荷，并与不同载荷下滑移台阶形貌相结合，探究位错运动与其之间的关联。此外，在3.1节中讨论了位错间的相互作用，根据位错反应结果可进一步探讨其与后续pop-in之间的关联。

在20 mN压痕载荷下，各晶粒的P-h曲线中间歇性地出现较小的pop-in，与位错运动和相互作用存在关联。{101}晶粒在图4a中1号标记处出现的pop-in倾向于与(111¯)和111滑移面上的位错反应及位错锁解锁相关。位错反应形成Glissile结，Glissile结能够产生新的位错并在新的滑移系统上运动，促进塑性变形，增大塑性变形区，压痕深度因此增加[37]。Lomer-Cottrell位错锁的形成对位错运动起到一定阻碍作用，导致穿透阻力增加，大量位错集聚在压头下方。随着载荷增加，连接的可移动位错所受力达到临界分切应力，Lomer-Cottrell位错锁会解锁[38]。当载荷足够大时，位错会突破阻碍，大量位错开始运动，促进塑性变形，压痕深度会逐渐增大。{101}晶粒在图4a中2号标记处出现pop-in时压痕载荷接近20 mN。如图3c所示，20 mN压痕形貌图中沿(11¯1¯)和(11¯1)滑移面的滑移台阶在载荷较小时未出现。此外，该滑移面上的滑移台阶出现在边缘，与中心的滑移台阶之间距离较远，据此判断2号标记处出现的pop-in与(11¯1¯)和(11¯1)滑移面上位错被激活有关。随着(11¯1¯)和(11¯1)滑移面上位错被激活，部分位错发生滑移，由于位错滑移所需的驱动力小于新形核位错所需的驱动力，此时优先发生位错滑移而不是形成新的位错，压头下方阻力减小，压入深度会短暂的急剧增大，并且由于加载速率恒定，所以P-h曲线呈现出压痕载荷不变，而压入深度增加的现象，即出现新的pop-in。

{111}晶粒在图4b中3号标记处出现pop-in，这倾向于与(111¯)和(11¯1¯)滑移面上的位错反应相关。参与Collinear反应的位错具有共线关系，因Burgers矢量等大且反向，位错反应后会湮灭。位错湮灭和自由位错的运动对压头的阻力降低，在同等载荷下，压痕深度会增加[36,39]。此外，Collinear反应会形成边缘偶极子，进一步形成位错墙，对塑性变形起到促进作用，使得压痕塑性变形区扩大，压痕深度增加[40]。{111}晶粒在图4b中4号标记处出现pop-in，这倾向于与(111¯)和(11¯1)滑移面上的位错反应和位错锁解锁相关。Lomer-Cottrell位错锁解锁，大量位错开始运动，促进塑性变形，压痕深度会逐渐增大。

{001}晶粒在图4c中5号标记处出现pop-in，这倾向于与(111¯)、(111)和(11¯1)滑移面上的位错反应相关。位错反应形成Glissile结，Glissile结能够产生新的位错并在新的滑移系统上运动，促进塑性变形，增大塑性变形区，压痕深度因此增加[37]。{001}晶粒在图4c中6号标记处的pop-in倾向于与位错突破阻碍开始运动相关。在图3i中观察到(11¯1)滑移面上的滑移台阶突破(111¯)滑移面上滑移台阶的阻碍。因位错反应形成的位错结对位错有阻碍作用，大量位错聚集，当载荷达到某一值时，位错突破阻碍，大量位错开始运动，促进塑性变形，压痕深度增加。

综上，{101}晶粒后续pop-in与位错发生Glissile反应和Lomer-Cottrell位错锁解锁以及(11¯1¯)和(11¯1)滑移面上位错激活有关；{111}晶粒后续pop-in与位错发生Collinear反应和Lomer-Cottrell位错锁解锁有关；{001}晶粒后续pop-in与Glissile反应和位错突破Glissile结的阻碍有关。

4 结论

(1) VCoNi中熵合金中不同取向晶粒内部激活的滑移系不同，导致压痕形貌和演变过程存在差异。各晶粒中同一滑移面上的滑移台阶优先出现在正倾斜滑移面。{101}晶粒中(111)和(111¯)滑移面上先出现滑移台阶，(11¯1¯)和(11¯1)滑移面上后出现滑移台阶；{111}晶粒中(111¯)、(11¯1¯)和(11¯1)滑移面上出现滑移台阶；{001}晶粒中4个{111}滑移面上均出现滑移台阶。

(2) 仅在{101}和{001}晶粒滑移台阶的边缘处观察到少量双交滑移的现象。{101}晶粒中位错先沿P(11¯1)滑移面滑移，{001}晶粒中位错线先沿P(111¯)和P(11¯1¯)滑移面滑移，随后发生交滑移，沿P(111)滑移面滑移，最后位错分别回到P(11¯1)、P(111¯)和P(11¯1¯)滑移面滑移。

(3) 不同取向晶粒激活的滑移系不同，导致位错反应类型不同并决定不同晶粒压痕的载荷-位移曲线中后续pop-in行为。{101}晶粒后续pop-in与(11¯1¯)和(11¯1)滑移面上位错激活，以及与Glissile反应和Lomer-Cottrell位错锁解锁有关；{111}晶粒后续pop-in与Collinear反应和Lomer-Cottrell锁解锁有关；{001}晶粒后续pop-in与Glissile反应和位错突破Glissile结的阻碍有关。

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The elastic-to-plastic transition during the deformation of a dislocation-free nanoscale volume is accompanied by displacement bursts associated with dislocation nucleation. The dislocations that nucleate during the so-called "pop-in" burst take the form of prismatic dislocation loops (PDLs) and exhibit characteristic burst-like emission and plastic recovery. Here, we report the in-situ transmission electron microscopy (TEM) observation of the initial plasticity ensued by burst-like emission of PDLs on nanoindentation of dislocation-free Au nanowires. The in-situ TEM nanoindentation showed that the nucleation and subsequent cross slip of shear loop(s) are the rate-limiting steps. As the indentation size increases, the cross slip of shear loop becomes favored, resulting in a transition from PDLs to open half-loops to helical dislocations. In the present case of nanoindentation of dislocation-free volumes, the PDLs glide out of the indentation stress field while spreading the plastic zone, as opposed to the underlying assumption of the Nix-Gao model.

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This study analyzes the elastic-to-plastic transition during nanoindentation of polycrystalline iron. We conduct nanoindentation (Berkovich indenter) experiments and electron backscatter diffraction analysis to investigate the initiation of plasticity by the appearance of the pop-in phenomenon in the loading curves. Numerous load-displacement curves are statistically analyzed to identify the occurrence of pop-ins. A first pop-in can result from plasticity initiation caused by homogeneous dislocation nucleation and requires shear stresses in the range of the theoretical strength of a defect-free iron crystal. The results also show that plasticity initiation in volumes with preexisting dislocations is significantly affected by small amounts of interstitially dissolved atoms (such as carbon) that are segregated into the stress fields of dislocations, impeding their mobility. Another strong influence on the pop-in behavior is grain boundaries, which can lead to large pop-ins at relatively high indentation loads. The pop-in behavior appears to be a statistical process affected by interstitial atoms, dislocation density, grain boundaries, and surface roughness. No effect of the crystallographic orientation on the pop-in behavior can be observed.

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