多主元合金因其独特的成分构成以及形成优异性能合金的潜力，自2004年首次报道以来就受到广泛关注[1,2]。作为最早提出的高熵合金体系之一，等原子比CrMnFeCoNi合金 (Cantor合金)及其衍生物展现出高强度、良好的延展性和出色断裂韧性等特性，引起人们的极大兴趣[3~7]。相较于Cantor合金，三元衍生物CrCoNi中熵合金(medium-entropy alloy，MEA)在室温及低温条件下的力学性能更加优异。一方面，变形孪晶的形成提高了加工硬化率，并推迟了颈缩的发生、增加了延展性[8~11]；另一方面，CrCoNi MEA发生fcc→hcp马氏体相变[12,13]，进一步提高了应变硬化率，使其在承受更大应力/应变的同时仍能保持整体稳定。CrCoNi MEA通过传统加工方式能够获得优异的低温以及室温性能，其强度、韧性等性能也超过大多数高熵合金和多相合金[8,14]。由于结构材料在复杂的工作环境中长期承受循环载荷的作用，容易出现破坏性疲劳失效[15]。为确保CrCoNi合金在实际应用中长期稳定且安全使用，有必要充分探索其疲劳特性和损伤机理，这对于提高其应用潜力具有重要意义。
在循环载荷作用下，各种界面是裂纹形核和扩展的有利位置[16,17]。大角度晶界在循环变形中由于受到滑移带撞击导致应变局部化而萌生裂纹[18]，高的表面能量使其抵抗裂纹扩展的能力较低，进而容易发生疲劳开裂[16]。孪晶界(twin boundary，TB)具有稳定的共格界面特征以及独特的位错与孪晶界面的交互作用[19]，既能够作为阻碍位错运动的障碍，也能够作为滑移面容纳位错运动或穿过[20,21]。孪晶界被证明具有比大角度晶界更好的抵抗疲劳开裂的能力[22,23]。在低周疲劳过程中，孪晶界开裂的难易程度受到孪晶界-加载轴之间的角度[24]、晶粒尺寸[25]、堆垛层错能(stacking fault energy，SFE)以及基体-孪晶之间Schmid因子差(difference of Schmid factor，DSF)的影响[26~28]。随着DSF增加或SFE降低，孪晶界两侧因位错塞积程度增加促使孪晶界开裂更加容易[26]。CrCoNi MEA具有较低的SFE[9]，退火后易于形成大量退火孪晶，还可使位错交滑移困难而易塞积于孪晶界，可能导致孪晶界开裂倾向增大而成为薄弱环节，因此，迫切需要开展孪晶界疲劳开裂行为的研究。此外，细晶强化是单相CrCoNi MEA强化的关键途径之一[2]，位错塞积数量以及变形的均匀程度在一定程度上受到晶粒尺寸的影响。已有研究表明，随着晶粒尺寸降低，滑移带撞击孪晶界位点增加，导致孪晶界开裂更容易[25]，但考虑到位错塞积数量和变形均匀程度时，则晶粒尺寸越小，孪晶界开裂越困难[29]。也就是说，尽管fcc晶体中有关晶粒尺寸与疲劳寿命之间的关系已经得到充分认识[30,31]，但孪晶界开裂难易程度与晶粒尺寸之间的关系尚不明确。特别是对于平面滑移的CrCoNi MAE来说，明确大量退火孪晶的疲劳开裂倾向以及晶粒尺寸对孪晶界开裂行为的影响，对减少沿晶疲劳裂纹萌生位置、增强断裂韧性、提高材料抗疲劳能力具有重要意义。
本工作选取粗晶和细晶两种晶粒尺寸的CoCrNi MEA样品，研究了低周疲劳条件下晶粒尺寸、孪晶界两侧滑移系Schmid因子差与孪晶界开裂之间的关系，增强对中熵合金疲劳开裂和变形行为的理解，为设计具有优异疲劳性能的先进材料提供参考。
1 实验方法
采用纯度高于99.9%的Co、Cr、Ni纯金属为原料，在真空感应熔炼炉中制备具有单相fcc结构的等原子比CrCoNi中熵合金。合金在1000 ℃条件下进行热锻，锻造后尺寸为150 mm × 60 mm × 20 mm，然后进行压下量为70%~80%的冷轧，经过冷轧的样品分别在900和1100 ℃下退火1 h得到具有不同晶粒尺寸的完全再结晶组织。用电火花线切割法在再结晶材料上加工狗骨头状疲劳试样，样品尺寸如图1所示，标距段尺寸为12 mm × 4 mm × 4 mm。
图1
使用Instron 8801疲劳试验机进行总应变控制的对称拉-压疲劳实验，总应变幅范围为0.4%~0.6%，应变速率为8 × 10-3 s-1，控制波形为三角波。疲劳过程中使用标距长度为10 mm的Instron 2620-603夹持式引伸计测量并控制应变幅。为了观察疲劳后样品表面形貌特征，疲劳前对样品进行机械研磨和电解抛光处理，以获得光滑且无应力的表面。抛光电压20 V，抛光时间15~30 s，抛光液为10%HClO4 + 90%C2H6O (体积分数)混合溶液。采用Sigma 500扫描电子显微镜(SEM)及电子背散射衍射(EBSD)系统、New ViewTM 9000白光干涉显微镜、VL3000DX-SVF18SP超高温激光共聚焦显微镜(CLSM)和Tecnai F20透射电子显微镜(TEM)对疲劳实验前后试样的微观组织进行表征。疲劳断裂后，在二次电子(SE)成像模式下检测表面变形形貌和孪晶界开裂行为。
2 实验结果
图2a和b为CoCrNi中熵合金在不同温度退火后的微观组织反极图(IPF)。所有样品均呈现出完全再结晶的微观组织，具有均匀的等轴晶粒，没有明显的织构。所有经过退火处理的样品中均出现大量退火孪晶，如图2a和b中红色实线所示。经统计，900和1100 ℃退火1 h后孪晶界体积分数分别为63.5%和62.1%。图2c和d为退火后晶粒尺寸分布图(包括孪晶界)。经900和1100 ℃再结晶退火得到的平均晶粒尺寸分别约为5.0和33.5 μm，随着退火温度升高，晶粒从细晶(fine grain，FG)长大为粗晶(coarse grain，CG)。随着晶粒尺寸增加，材料的强度降低，延展性增加，低周疲劳寿命降低，如表1所示。
图2
图2
不同晶粒尺寸的CoCrNi中熵合金(MEA)的微观组织与晶粒尺寸分布
Fig.2
Inverse pole figures (IPFs) and twin boundaries maps (a, b) and the corresponding grain size distributions (c, d) of the CrCoNi medium-entropy alloy (MEA) specimens annealed at 900 oC (a, c) and 1100 oC (b, d) for 1 h (The twin boundaries were shown by red lines in Figs.2a and b)
表1 不同晶粒尺寸CrCoNi MEA样品在室温下的力学性能
Table 1
| T / oC | d / μm | YS / MPa | UTS / MPa | UE / % | TE / % | Nf / cyc |
|---|---|---|---|---|---|---|
| 900 | 5.0 | 395.6 | 862.4 | 58.6 | 84.5 | 57883 |
| 1100 | 33.5 | 231.3 | 686.1 | 83.5 | 107.7 | 23208 |
总应变幅为0.4%时，不同晶粒尺寸CrCoNi MEA疲劳断裂后断口附近的表面形貌如图3所示。图3a和d表明，两组晶粒尺寸的样品疲劳后裂纹主要沿晶界(grain bodoundary，GB)、滑移带和孪晶界处萌生。图3b、c和3e、f分别为粗晶和细晶样品中疲劳裂纹在滑移带处萌生，同时沿着滑移带扩展，甚至穿透孪晶界的形貌。在循环变形过程中，由于位错的滑移和湮灭，材料表面形成了具有侵入、挤出特征的滑移带，由此产生了应力集中和组织不均匀等，滑移带疲劳开裂正是由于侵入、挤出产生的应力集中所导致。相较于细晶材料，粗晶材料表面损伤严重，侵入、挤出程度大。这是因为随着晶粒尺寸的减小，循环变形能分散到更多的滑移带，因此在细晶材料中的滑移带疲劳裂纹较短，并且扩展路径更加曲折。这些滑移带还会循环往复撞击大角度晶界，引起缺陷累积和应力集中使其开裂，如图3a和d所示。在细晶样品中，分散的滑移带带给大角度晶界的撞击作用相对较弱；而粗晶样品中，变形集中的滑移带产生的更强撞击作用导致大角度晶界更容易开裂。
图3
图3
CrCoNi MEA样品在0.4%总应变幅下的晶界开裂和滑移带开裂表面形貌
Fig.3
Grain boundary (GB) cracking and slip band (SB) cracking morphologies for CrCoNi MEA specimens fatigued under a total strain amplitude of 0.4% (a, d) GB cracking in fine-grained (FG) (a) and coarse-grained (CG) (d) specimens, respectively (b, c) SB cracking in FG specimen under low (b) and high (c) magnifications (e, f) SB cracking in CG specimen under low (e) and high (f) magnifications
不同晶粒尺寸样品表面疲劳形貌和起伏程度的CLSM表征结果如图4所示。无论在细晶样品(图4a)还是粗晶样品(图4b)中，样品表面都出现了许多跨过孪晶界的“Z”字形滑移带，滑移带可以连续贯穿一个或几个孪晶界，最后终止在大角度晶界处。与图3描述相一致，当孪晶界两侧的滑移带对应性和连续性较好时，孪晶界不容易开裂。表面起伏程度检测结果显示，细晶样品中有大量细小且低起伏的滑移带穿过孪晶界，仅有少量几个不相邻的滑移带表面轮廓高度较大，对孪晶界造成的损伤较小；而粗晶样品中穿过孪晶界的滑移带数量少且相邻滑移带表面轮廓高度较大，对孪晶界产生的损伤较大。细晶材料表面滑移带平均起伏高度约为0.15 μm，远低于粗晶材料(约为0.90 μm)，如图4c和d所示，再次说明减小晶粒尺寸有助于将循环变形分散到更多的滑移带。其中粗晶样品中孪晶界附近滑移带高度最大约为1.52 μm，高于细晶样品孪晶界附近的滑移带高度。
图4
图4
不同晶粒尺寸CrCoNi MEA样品在0.4%总应变幅下的表面疲劳形貌及高低起伏特征
Fig.4
Surface deformation features in FG (a) and CG (b) CrCoNi MEA specimens fatigued at a total strain amplitude of 0.4%; and height fluctuations of slip bands for FG (c) and CG (d) specimens along the arrows in Figs.4a and b, res-pectively
图5
图5
不同晶粒尺寸CrCoNi MEA样品在0.4%应变幅下疲劳后孪晶界开裂表面形貌
Fig.5
Low (a, c) and high (b, d) magnified post-fatigue surface morphologies for CrCoNi MEA specimens at a total strain amplitude of 0.4% (TB—twin boundary) (a, b) TB cracking in FG specimen (c, d) TB cracking in CG specimen
图6
图6
不同晶粒尺寸CrCoNi MEA样品在0.4%总应变幅下疲劳后孪晶界两侧疲劳形貌特征
Fig.6
Surface deformation features in FG (a) and CG (b) CrCoNi MEA specimens fatigued at a total strain amplitude of 0.4%; and height (h) fluctuations of slip bands for FG (c) and CG (d) specimens along the arrows in Figs.6a and b, respectively
图7
图7
总应变幅0.4%条件下不同晶粒尺寸CoCrNi MEA样品疲劳位错结构的明场TEM像
Fig.7
Bright-field TEM images of post-fatigued CoCrNi MEA specimens tested with a total strain amplitude of 0.4% (a, b) dislocation arrays composing planar slip bands in CG specimen (c, d) stacking faults (SFs) and dislocation arrays composing planar slip bands in FG specimen
以上结果表明，有些孪晶界由于滑移带撞击萌生裂纹后发生疲劳开裂，有些没有萌生裂纹的孪晶界被开裂的滑移带贯穿。在疲劳过程中，孪晶界可与两侧不同取向的晶粒发生不同的位错-孪晶界交互作用，从而承受不同程度的损伤[33,19]。图8a为fcc晶体孪生取向关系对应的双Thompson四面体，取中间片层{111}TB为孪晶界面，那么孪晶界面两侧镜面对称的晶体学面分别是基体中的{111}M和孪晶中的{111}T (下标M和T分别代表基体和孪晶)。当孪晶界两侧滑移系具有对称滑移面和相同滑移矢量时，例如图8a中，基体内(111)M滑移面上的 b1滑移矢量与孪晶内(111)T滑移面上的 b2滑移矢量，孪晶界处产生的损伤程度最小[19]。此时，两侧晶内的Schmid因子分别为ΩM和ΩT，二者差值定义为Schmid因子差(ΔΩ)，即，ΔΩ = ΩM - ΩT，默认前者大于后者，保证ΔΩ为正值[26]。随着∆Ω的增加，一方面，位错塞积程度变大，另一方面，位错与孪晶界倾向于发生除图8a以外的交互作用[19.26.29]，最终都导致位错与孪晶界交互作用偏离该最小损伤情况的程度变大[26,29]。因此，该参数的提出能统一衡量所有孪晶界承受不同取向晶粒带来的位错塞积损伤程度，这在前人的研究工作[19,26,27]中得到了很好的验证。
图8
图8
利用滑移形貌法确定取向的原理示意图
Fig.8
Mechanism schematics of the slip morphology method for determining the crystallographic orientation
(a) crystallographic relationship of twinning in fcc metals (ΩM—Schmid factor of slip systems in the matrix, ΩT—Schmid factor of slip systems in the twin, b1—Burgers vector of dislocations in the matrix, b2—Burgers vector of dislocations in the twin)
(b) a typical surface morphology showing slip bands interacting with a twin boundary (RD—rolling direction)
为了进一步明确ΔΩ对不同晶粒尺寸中孪晶界抵抗裂纹萌生能力的差别，统计了所有应变幅下的疲劳样品表面形貌，对孪晶界开裂和滑移带开裂对应的ΔΩ进行计算。在一定ΔΩ范围内，不同晶粒尺寸材料中孪晶界开裂/滑移带开裂的数量统计结果如表2所示，其中第1个数值表示ΔΩ在一定范围内孪晶界开裂的晶粒数量，第2个数值表示ΔΩ在一定范围内滑移带开裂的数量。可知：(1) 对于不同晶粒尺寸的材料，随着ΔΩ的降低，孪晶界开裂可能性降低；(2) 由滑移带开裂到孪晶界开裂的转变过程存在一个过渡区，在此区域内孪晶界开裂和滑移带开裂同时存在；(3) 粗晶材料中孪晶界开裂所需ΔΩ范围小于细晶材料，粗晶样品即使在很小的ΔΩ范围内孪晶界也会发生开裂。随着晶粒尺寸增加，发生孪晶界开裂的ΔΩ降低，孪晶界开裂更容易。以上结果表明，对于同一种材料，晶体取向和晶粒尺寸共同影响了孪晶界对疲劳裂纹萌生抗力。
表2 晶粒尺寸与晶体取向对孪晶界/滑移带疲劳开裂行为影响统计数据
Table 2
| Grain type | ΔΩ | |||
|---|---|---|---|---|
| 0-0.05 | 0.05-0.10 | 0.10-0.15 | 0.15-0.30 | |
| FG | 0, 7 | 4, 3 | 4, 1 | 5, 0 |
| CG | 2, 4 | 7, 4 | 8, 0 | 9, 0 |
3 分析与讨论
疲劳裂纹萌生的主要原因是不可逆塑性变形引起的材料局部应变集中[34,35]。在多晶材料中，晶界是位错运动的障碍[16,35,36]。循环变形过程中位错在大角度晶界处堆积，导致晶界处应力集中而萌生裂纹[37,38]或形成驻留滑移带[39]。位错能够通过小角度晶界到相邻晶粒中运动，晶界两侧滑移带是连续的且保持良好的一一对应关系，小角度晶界开裂困难[40]。滑移带在大角度晶界处运动受阻，导致滑移带携带位错塞积在晶界处产生应力集中而萌生裂纹[41]。尽管孪晶界也可以像大角度晶界一样阻碍位错运动，但由于孪晶界与位错交互作用特殊，被证明具有比大角度晶界更强的可控的抵抗疲劳能力[40,42]。当孪晶界两侧晶粒存在一定取向差时，孪晶界阻碍位错穿过，位错塞积也会导致孪晶界像大角度晶界那样萌生疲劳裂纹。层错能以及晶粒的取向差共同作用并影响该位错的塞积程度以及孪晶界的开裂趋势[26,27]。晶粒尺寸不同也会引起界面前位错塞积数量[26]和疲劳开裂机制[43]的差异。
由Taylor理论和Orowan公式，塑性变形过程中切应力(τ)与位错密度(ρ)之间的关系为：
式中，K为常数；τ0为在没有其他位错影响的情况下开动位错所需要的起始剪切应力，类似于材料的屈服强度；G和b分别为剪切模量和位错Burgers矢量模。在塑性变形过程中，认为每个晶粒所受到的切应力与晶粒的晶体取向符合Schmid因子定律，即：
式中，σ为样品两端加载的流变正应力，与实验中材料的屈服强度相近。根据Zhang等[26]的推导，单位长度位错塞积的数目(n)与ρ、Ω之间的关系为：
式中，k为常数，表征晶界对强度影响的程度。
根据
位错塞积公式不但适用于大角度晶界，也适用于孪晶界(本工作中的孪晶界在晶粒尺寸统计时被当作大角度晶界考虑)。因此，简单认为在外加应力作用下，基体和孪晶都开动了单滑移系，其中，ΩMΩT。根据
孪晶晶粒一侧位错塞积数目(nT)为：
由取向差造成的孪晶界附近塞积位错密度(Δn)为：
在晶粒尺寸d范围内由于取向差导致的孪晶界位错塞积数量(
通过滑移形貌法对孪晶界开裂或滑移带开裂的SEM像进行分析，得到孪晶界是否开裂所对应的ΔΩ与d的关系，如图9所示。图中红色三角形表示孪晶界附近滑移带开裂对应的ΔΩ，黑色圆圈表示孪晶界开裂对应的ΔΩ。可以看出，ΔΩ与d-1/2成正比关系，图9中的实验结果与
图9
图9
晶体取向和晶粒尺寸对CrCoNi MEA孪晶界疲劳开裂趋势的影响
Fig.9
Influences of crystallographic orientation and grain size on the fatigue cracking tendency along TBs in the CrCoNi MEA
在不同晶粒尺寸材料中孪晶界两侧位错塞积作用导致的开裂过程如图10所示。在相同的疲劳变形条件下，粗晶材料的晶粒尺寸大，导致位错塞积数目高(
图10
图10
不同晶粒尺寸样品中孪晶界两侧位错塞积导致孪晶界开裂的示意图
Fig.10
Schematics of TB fatigue cracking under dislocation piling up in FG (a) and CG (b) specimens
4 结论
(1) 在循环载荷作用下，细晶样品表面滑移带起伏程度低于粗晶样品，变形均匀性更好，疲劳损伤分布在更多的区域。
(2) 随着孪晶界两侧晶粒内Schmid因子差的增加，位错塞积程度变大，孪晶界承受损伤的程度变大而易于疲劳开裂，孪晶界疲劳开裂存在一个临界Schmid因子差。
(3) 孪晶界开裂的临界Schmid因子差受晶粒尺寸影响，随晶粒尺寸增加，孪晶界处易于塞积较多位错，开裂所需临界Schmid因子差降低，孪晶界开裂更容易。
(4) 在孪晶界开裂的临界区内，Schmid因子差与d-1/2成正比关系，晶粒取向与晶粒尺寸共同影响孪晶界的疲劳开裂趋势。
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