晶界取向差对双晶高温合金常温和高温拉伸性能的影响

图1 双晶板样品的籽晶方位和定向凝固示意图

Fig.1 Schematic diagram of two crystal seeds method (a) orientations of seeds crystals, (b) directional solidification

按照图2a所示的方法从DD6双晶板上切取含有晶界的板状拉伸样品和观察组织的块状样品。拉伸样品的尺寸如图2b所示。晶界位于样品平行段中央并垂直于应力加载方向。将块状样品腐蚀后用扫描电镜观察其组织形貌，腐蚀剂的成分为80 mL HCl + 20 g CuSO₄ + 100 mL H₂O。用4组晶界取向差为0°、4°、8°、12°的双晶样品进行拉伸实验。每组样品在同一温度做3次拉伸实验，取其结果的平均值。拉伸实验机的型号为Instron5982，引伸计为人工装卡类型，标距为12.5 mm，应变加载速率为5 $\times$ 10^-4/s，实验温度为常温与760 ℃。拉伸实验后用超声波清洗样品断口，用扫描电镜观察断口的形貌。

图2

图2 板状拉伸样品和块状金相样品切取过程的示意图和拉伸样品的尺寸

Fig.2 Schematic diagram of tensile sample and metallographic sample (a) sample cutting process, (b) shape and dimension of tensile sample (unit: mm)

2 实验结果

2.1 不同晶界取向差样品的组织结构

图3给出了不同晶界取向差样品的组织结构，图中的白色区域为 $γ$ 基体相，黑色区域为 $γ^{'}$ 沉淀强化相^[15,16]。由图3a可以看出，DD6单晶高温合金具有由 $γ$ 相基体和 $γ^{'}$ 沉淀强化相组成的双相结构。 $γ^{'}$ 相呈规则立方状，与 $γ$ 相保持共格关系，4种晶界取向差样品中 $γ^{'}$ 相的平均尺寸均约为0.5 μm。

图3

图3 双晶样品的晶界组织结构

Fig.3 Microstructure of GBs of bicrystal samples (a) 0°, (b) 4°, (c) 8°, (d) 12°

如图3所示，4°晶界为一条白色折线，几乎完全由 $γ$ 相基体构成，晶界两侧为被晶界切过的不完整的 $γ'$ 相。随着晶界取向差的增大，晶界处 $γ$ 相基体的含量逐渐降低。晶界取向差增大到8°时(图3c)，在晶界出现连续条状形态的 $γ'$ 相。这表明，随着取向差的增大晶界处 $γ$ 相的比例降低。取向差达到12°时(图3d)，晶界在黑色条状形态 $γ'$ 相的基础上出现间断的平均长度为1 μm的白色析出相。扫描电镜能谱仪(EDS)分析确定，12°双晶晶界析出相富含Ni、W、Mo、Co，且过渡族元素与VI族元素的原子比为7∶6。由此可以推断，该析出相是 $μ$ 相或M₆C^[17]。Huang等^[11]研究DD6晶界组织与取向差的关系时发现，晶界取向差为10.5°和12.2°时晶界析出相为 $μ$ 相；随着晶界取向差的增大在晶界处同时析出 $μ$ 相或M₆C，因此12°双晶晶界的析出相为 $μ$ 相。

同时，如图4所示，在双晶组织中铸造微孔均匀分布，其尺寸约为80 μm。由于制备工艺完全相同，4组样品的基体组织相同，因此其中铸造微孔的密度和尺寸也大致相同。

图4

图4 双晶样品中铸造缩孔的金相照片和 SEM照片

Fig.4 Metallographic images (a) and SEM images (b) of cast micropores in bicrystal samples

2.2 不同晶界取向差样品的拉伸性能

图5给出了DD6高温合金双晶样品的常温和760 ℃抗拉强度、断后伸长率与晶界取向差的关系。从图5可见，晶界取向差增大到12°时，除了常温断后延伸率，其余的力学性能均有所降低；随着拉伸温度的升高高温合金力学性能降低的幅度提高，表明晶界的影响更为显著。

图5

图5 在不同温度下抗拉强度和伸长率与晶界取向差的关系

Fig.5 Tensile strength (a) and elongation to fracture (b) vs. the misorientation at different temperatures

如图5所示，0°样品的常温抗拉强度为1000 MPa，断后伸长率为5.5%。晶界取向差从0°增大到12°，双晶样品的常温抗拉强度连续降低了173 MPa，而断后伸长率几乎不变。

如图5所示，0°样品的760 ℃抗拉强度为1085 MPa，断后伸长率为14.5%。晶界取向差从0°增大到4°抗拉强度几乎不变，断后伸长率降低4%；晶界取向差从4°增大到8°，抗拉强度和断后伸长率都几乎不变；晶界取向差从8°增大到12°抗拉强度和断后伸长率均较速地降低：抗拉强度降低270 MPa，断后伸长率降低5.5%。

图6给出了DD6高温合金双晶的常温和760 ℃工程应力-应变曲线。可以看出，随着晶界取向差的增大屈服后的曲线变化趋势出现差异。晶界取向差小于8°的双晶样品其拉伸应力随着应变的增大持续增大，表现出明显的加工硬化趋势；而当晶界取向差达到12°时，随着应力的增大应变持续减小。

图6

图6 常温和760 ℃的工程应力-应变曲线

Fig.6 Tensile engineering stress-strain curves of tensile test of bicrystal samples with different misorientations tested at (a) ambient temperature, (b) 760 ^oC

图7给出了样品常温拉伸断口的形貌。可以看出，4种晶界取向差的样品其断口形貌极为相似。断口出现明显的塑性变形，在外加应力作用下样品的截面由正方形变为平行四边形。同时，拉伸断口出现明显的河流形貌，表明断裂方式为解理断裂^[18,19]。

图7

图7 不同晶界取向差样品的常温拉伸断口

Fig.7 Tensile fracture of samples of the different misorientations at ambient temperature (a) 0°, (b) 4°, (c) 8°, (d) 12°

760 ℃拉伸断口由单个或几个较大的平整倾斜面构成，因此用侧视观察断口，其形貌如图8所示。在760 ℃拉伸，4组样品的断口有所不同。其中晶界取向差为0°、4°、8°的样品其断口形貌相似，都由单个或几个较大的平面构成。其原因是，DD6单晶高温合金在760 ℃拉伸时主要滑移方式为八面体滑移。八面体滑移的滑移面为{111}，裂纹在{111}平面扩展，最终形成这种断口，断裂方式为沿 {111}晶面的类解理断口^[20]。随着晶界取向差的增大，断口显示出沿晶开裂特征。晶界取向差为8°的样品呈现沿晶开裂与类解理断裂的混合特征。晶界取向差增大到12°时拉伸样品完全沿晶界开裂，断口从侧面观察为锯齿形，与晶界取向差为0°、4°、8°样品的断口形貌完全不同。

图8

图8 不同晶界取向差样品的760 ℃拉伸断口

Fig.8 Tensile fracture of samples of the different misorientations at 760 ℃ (a) 0°, (b) 4°, (c) 8°, (d) 12°

熊新红等^[21]研究DD6单晶高温合金拉伸行为时也发现类似的现象：在常温和650 ℃拉伸试样表面出现滑移线，断裂方式为类解理断裂。在650 ℃拉伸出现类解离断裂特征，是动态应变时效与不均匀变形所致。随着拉伸温度进一步提高到1020 ℃，样品表现为韧窝断裂。

图9给出了在760 ℃拉伸时两种断裂方式的断口形貌俯视图。从图9a、b可见，晶界取向差为4°的样品其断裂方式为类解理断裂，断口由单个平整平面构成，裂纹从样品边缘萌生，表现出较为明显的河流花样特征。从图9c、d可见，晶界取向差为12°的样品其断裂方式为沿晶断裂，断口表现出明显的枝晶特征和出现了铸造微孔，表明这个样品内有缩孔。但是4组样品的制备工艺完全相同使其基体组织完全相同，双晶内铸造微孔的密度和尺寸也大致相同。因此可以推测，不同晶界取向差的双晶样品其晶界处缩孔的密度和尺寸大致相同。这表明，铸造微孔的存在不影响拉伸性能与晶界取向差的关系。

图9

图9 760 ℃不同断裂方式的拉伸断口

Fig.9 Tensile fracture at 760 ℃ (a, b) 4°, (c, d) 12°

3 讨论

3.1 晶界结构对拉伸性能的影响

晶界阻碍位错运动，使其在晶界处塞积^[22,23]。位错塞积于晶界，在晶界处产生的应力集中使材料的性能降低并使样品沿晶开裂^[9~12,24]。小角度晶界可看作一系列规则排列的位错。晶界取向差越大，则位错的密度越高，对位错移动的阻碍越大^[14]。因而如图5a所示，随着晶界取向差的增大，DD6双晶样品的常温和760 ℃的抗拉强度都有所降低。

随着温度的提高，高温合金晶界的变形量明显增大^[17]。在常温下双晶样品的拉伸总变形量中晶界变形的占比较小，因此如图5b所示，晶界取向差的变化几乎不影响常温拉伸断后伸长率。随着拉伸温度的提高，双晶拉伸的总变形量以晶界变形为主。因此，如图5b所示，随着晶界取向差的增大，较差的晶界变形能力使DD6双晶样品在760 ℃拉伸断后的伸长率随着晶界取向差的增大而降低。

如图5a所示，晶界取向差小于8°时，单晶高温合金的强度受晶界的影响较小，更多地取决于单晶基体的强度。高温合金的屈服效应反常，在一定温度范围内其屈服强度随着温度的升高而提高^[17]。因此，晶界取向差小于8°的样品，其760 ℃抗拉强度高于常温抗拉强度，且随着取向差的变化趋势较为平缓。随着晶界取向差的增大，晶界取向差大于8°的DD6双晶样品，其760 ℃拉伸断裂为沿晶断裂，即拉伸断裂过程转变为晶界主导，使抗拉强度大幅度降低。DD6双晶抗拉强度的大幅度降低，与其晶界结构有关。DD6高温合金晶界取向差从8°增大到12°，在晶界处析出大量 $μ$ 相。 $μ$ 相属于TCP相，在阻碍位错运动的同时还是裂纹萌生的起点，能大幅度弱化高温合金的性能^[17]。DD6高温双晶合金晶界处 $μ$ 相的析出阻碍位错运动和弱化晶界结合力，使其拉伸性能大幅度降低。

高温合金晶界取向差的增大使晶界析出相出现，劣化了单晶高温合金的性能。如图10所示，Zhu等^[10]研究SRR99高温合金双晶的拉伸行为时发现，晶界取向差达到16°时裂纹从SRR99双晶碳化物处萌生，使其常温拉伸性能加速降低。同时，DD10第三代单晶高温合金的晶界取向差达到15°时，在晶界处析出的层状TCP相使其性能劣化^[25]。Hu等^[26]研究Ni-Cr-W高温合金时发现，随着晶界取向差的增大晶界有大量的层片状M₂₃C₆析出，降低了晶界结合力使其性能弱化。这表明，晶界取向差的增大使有害相在晶界析出，进而使高温合金的性能弱化。

图10

图10 SRR99常温抗拉强度与晶界取向差的关系^[10]

Fig.10 Tensile strength vs. the GB misorientation for SRR99 at ambient temperature^[10]

同时，晶界 $γ'$ 相的比例也影响晶界对位错移动的阻碍。当晶界取向差较小时，晶界几乎完全由 $γ$ 相构成。 $γ$ 相有连接晶粒的作用，从而协调晶粒的变形。但是，随着晶界取向差的增大晶界 $γ'$ 沉淀强化相的比例增大，使长条状 $γ'$ 相阻碍位错穿过晶界。因此，晶界取向差的增大使晶界处 $γ'$ 相的比例增大，增强了晶界阻碍位错移动的能力，使位错容易塞积在晶界产生应力集中而使高温合金开裂。这也是高温合金的性能随着晶界取向差的增大而降低的原因^[11,27,28]。

因此，可根据晶界的结构解释取向差对拉伸性能的影响。如图11a所示，晶界取向差较小时DD6双晶晶界对位错运动的阻力较小，位错能从晶界通过，双晶的性质更接近于单晶；这表明，较小的晶界取向差对拉伸性能的影响不大。随着晶界取向差的增大，如图11b所示，在DD6双晶的晶界出现TCP相等缺陷；同时， $γ'$ 相含量的提高使晶界对位错运动的阻碍增强，位错塞积在晶界产生应力集中；晶界处析出的有害析出相弱化了晶界结合力，当晶界结合强度不足以抵抗外加应力时出现沿晶断裂，使拉伸性能大幅度降低。

图11

图11 晶界取向差对DD6双晶样品拉伸断裂机制的影响

Fig.11 Effect of GB misorientation on tensile fracture mechanism of DD6 bicrystal samples

(a) cleavage-like fracture, (b) intergranular fracture

3.2 拉伸断裂机制的转变

晶界取向差和温度影响高温合金的晶界结构，增大晶界对位错运动的阻力，使其性能降低和拉伸断裂机制由类解理断裂转变为沿晶断裂。这种影响的过程比较复杂，但是可根据晶界能量描述拉伸断裂机制的变化。裂纹萌生是塑性应变能累积的结果^[29]，而晶界取向差影响拉伸过程中晶界处位错的塞积，即影响拉伸过程中晶界能量的积累。Zhu等^[10]研究SRR99高温合金双晶常温拉伸行为时发现，随着晶界取向差的增大SRR99高温合金双晶也出现了从类解理开裂到沿晶断裂的拉伸断裂机制转变；并且认为，两种拉伸机制的变化取决于滑移带和晶界能量累积的速度，并提出一个基于吉布斯自由能变的定性模型，可解释DD6双晶断裂机制的变化。

这个模型^[10,30]提出滑移带萌生裂纹的吉布斯自由能变ΔG为

Δ G = - W_{e} - A δ + 2 A γ_{s}

(1)

其中 $W_{e}$ 为指裂纹形成时释放的弹性能， $δ$ 为裂纹张开时储存的机械能， $A$ 为虚拟裂纹的面积， $γ_{s}$ 为裂纹的表面能。裂纹萌生的条件为

∆ G \leq 0

(2)

于是式(1)可写成

2 γ_{s} - \frac{W_{e}}{A} \leq δ

(3)

由于双晶取向差不同样品是同一种金属材料，拉伸过程中的弹性能相同。因此，在两种拉伸断裂机制竞争过程中可忽略弹性能的变化，即可忽略式(3)中的 $\frac{W_{e}}{A}$ ，于是裂纹萌生的能量条件式(3)可改写为^[10]

2 E_{S} = 2 γ_{s} = E_{0} + E_{i n}

(4)

其中 $2 E_{S}$ 为新裂纹的表面能， $E_{0}$ 为界面初始能量， $E_{i n}$ 为拉伸过程中界面增加的能量。描述滑移带(SB)开裂何沿晶界(GB)开裂所需要的能量条件分别为

2 E_{S} = E_{0}^{S B} + E_{i n}^{S B}

(5)

2 E_{S} = E_{0}^{G B} + E_{i n}^{G B}

(6)

其中 $E_{0}^{S B}$ 与 $E_{0}^{G B}$ 分别为滑移带和晶界初始能量， $E_{i n}^{S B}$ 与 $E_{i n}^{G B}$ 分别为拉伸过程中满足滑移带与晶界开裂所需要的能量积累条件。于是，可用 $E_{i n}^{S B}$ 与 $E_{i n}^{G B}$ 表述双晶样品中两种断裂机制的竞争关系：在拉伸过程中，双晶样品中的裂纹从先达到能量积累条件的界面萌生。因此，定义拉伸过程中能量积累速度 $V$ ，则双晶样品裂纹萌生所需时间为

t_{S B} = \frac{E_{i n}^{S B}}{V_{S B}} = \frac{2 E_{S} - E_{0}^{S B}}{V_{S B}}

(7)

t_{G B} = \frac{E_{i n}^{G B}}{V_{G B}} = \frac{2 E_{S} - E_{0}^{G B}}{V_{G B}}

(8)

其中 $t_{S B}$ 与 $t_{G B}$ 分别为假定裂纹从滑移带与晶界萌生所需时间， $V_{S B}$ 与 $V_{G B}$ 分别为拉伸过程中滑移带与晶界处能量积累速度。由此可得两种断裂机制的判据为： $t_{S B} < t_{G B}$ ，滑移带开裂； $t_{S B} \approx t_{G B}$ ，两种开裂混合； $t_{S B} > t_{G B}$ ，沿晶界开裂。

由于双晶样品晶界两端的单晶材料完全相同，因此在同一温度下不同晶界取向差样品中滑移带的有关参数 $E_{i n}^{S B}$ 、 $V_{S B}$ 、 $E_{0}^{S B}$ 基本相同，即在一定温度下 $t_{S B}$ 不随晶界取向差变化。但是，涉及到与晶界有关的参数，必然与双晶样品两端单晶的取向差有关。本文采用的晶界取向差小于12°，属于小角度晶界。小角晶界可看作由位错构成，其晶界能与位错密度有关。而小角晶界的位错密度与晶界取向差呈正相关^[31,32]，即小角晶界能与取向差的关系为

E = E_{0} θ (A_{0} - l n θ)

(9)

其中 $E$ 为晶界能， $A_{0}$ 为积分常数。这表明，随着晶界取向差的增大DD6双晶晶界的初始能量 $E_{0}^{G B}$ 逐渐增大。如上所述，随着晶界取向差的增大晶界处逐渐出现析出相，晶界结构更加复杂，使晶界的初始能量 $E_{0}^{G B}$ 有所增大，降低了沿晶开裂的能量条件，使 $E_{i n}^{G B}$ 降低。晶界取向差为0即没有晶界，则 $E_{0}^{G B}$ 与 $E_{0}^{S B}$ 相同。因此，随着晶界取向差的增大， $E_{0}^{G B}$ 与 $E_{0}^{S B}$ 的变化定性地随着晶界取向差增大。 $E_{0}^{G B}$ 逐渐增大使 $E_{i n}^{G B}$ 逐渐减小并小于 $E_{i n}^{S B}$ ，即沿晶开裂的能量 $E_{i n}^{G B}$ 更小。

随着取向差的增大 $V_{S B}$ 保持不变，但是 $V_{G B}$ 有所增大。在拉伸过程中晶界应变能的积累取决于其对位错的阻挡，或取决于晶界的位错塞积速度。随着晶界取向差的增大DD6双晶晶界处 $γ'$ 相和TCP相的含量提高，使晶界对位错移动的阻碍增强，即晶界能量积累的速度提高。于是可以定性认为，随着晶界取向差的增大DD6双晶晶界能量的积累速度 $V_{G B}$ 随之提高。晶界取向差达到一定程度时，晶界能量积累的速度 $V_{G B}$ 大于 $V_{S B}$ 。

因此，这个模型可解释在760 ℃拉伸DD6双晶的拉伸断裂机制的变化。在760 ℃拉伸，随着晶界取向差的增大沿晶开裂的能量 $E_{i n}^{G B}$ 逐渐减小，且小于滑移带开裂能量 $E_{i n}^{S B}$ ；晶界能量积累的速度 $V_{G B}$ 有所提高使晶界裂纹萌生所需时间 $t_{G B}$ 逐渐缩短，但是 $t_{S B}$ 不变。图12定性地描述了在拉伸断裂机制变化的过程中 $t_{G B}$ 与 $t_{S B}$ 随晶界取向差的变化。如图12所示，对于存在拉伸断裂机制变化的双晶拉伸实验，有 $θ \approx θ_{0}$ 时 $t_{S B} \approx t_{G B}$ 。这表明，晶界取向差 $θ < θ_{0}$ 时 $t_{S B} < t_{G B}$ ，样品沿滑移带开裂；取向差 $θ \approx θ_{0}$ 时 $t_{S B} \approx t_{G B}$ ，样品断口具有两种断裂机制混合特征；晶界取向差 $θ > θ_{0}$ 时则 $t_{S B} > t_{G B}$ ，样品发生完全沿晶断裂。对于在760 ℃的DD6双晶拉伸实验， $θ_{0}$ 可近似为8°。

图12

图12 $t$ 随晶界取向差变化的定性描述

Fig.12 A qualitatively description for variations $t$ with the GB misorientation

这个模型采用了滑移带与晶界处的能量竞争关系，定性地解释了随着取向差的增大高温合金双晶拉伸断裂机制的转变。SRR99双晶常温拉伸^[10]和DD6双晶在760 ℃的拉伸都存在拉伸断裂机制由类解理断裂到沿晶断裂的转变，因此都可用该模型解释。该模型适用于解释高温合金双晶拉伸过程中断裂机制由类解理断裂到沿晶断裂的转变，例如SRR99双晶的常温拉伸^[10]和DD6双晶在760 ℃的拉伸。

4 结论

(1) 双晶样品在760 ℃的拉伸性能优于常温，但是晶界对拉伸性能的影响更加显著。高温合金的晶界取向差从0°增大到12°其断后伸长率不变，但是常温抗拉强度降低了173 MPa；而760 ℃的抗拉强度降低了270 MPa，断后伸长率降低了9%。随着晶界取向差的增大，双晶样品的常温拉伸性能变化更为均匀，而760 ℃拉伸性能大幅度降低。

(2) 双晶样品在常温下的断裂方式为解理断裂。晶界取向差从0°增大到8°，双晶样品的760 ℃拉伸断裂方式为类解理断裂;晶界取向差从8°增大到12°，断裂方式由类解理断裂转变为沿晶断裂。随着晶界取向差的增大DD6高温合金晶界处 $γ'$ 相的比例提高并析出TCP相，使晶界对位错移动的阻力增大和位错塞积于晶界，最终导致沿晶断裂。

(3) 随着晶界取向差的增大晶界结构逐渐复杂。晶界开裂能量门槛的降低和晶界能量积累速度的提高，使拉伸断裂机制由类解理断裂转变为沿晶断裂。

参考文献

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[J]. 材料工程, 2019, 47(8): 169

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X H

, Quan

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, et al.

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[J]. Mater. Sci. Eng., 2015, 636A: 608

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, Zhang

, Li

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, et al.

Fatigue cracking at twin boundaries: effects of crystallographic orientation and stacking fault energy

[J]. Acta Mater., 2012, 60(6-7): 3113

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, Wang

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, Zhou

Y Z

, et al.

Investigation on in situ tensile behavior of superalloy bicrystals with different GB misorientations

[J]. Metall. Mater. Trans., 2014, 45A(9): 3876

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, Ding

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, et al.

Misorientation effect of grain boundary on the formation of discontinuous precipitation in second and third generation single crystal superalloys

[J]. MATEC Web Conf., 2014, 14: 11006

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, Li

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, et al.

Precipitation behavior of grain boundary M₂₃C₆ and its effect on tensile properties of Ni-Cr-W based superalloy

[J]. Mater. Sci. Eng., 2012, 548A: 83

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, Eggeler

G F

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M J

γ′-cutting as rate-controlling recovery process during high-temperature and low-stress creep of superalloy single crystals

[J]. Acta Mater., 2000, 48: 4867

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, van der Zwaag

Microstructure and dislocation structure evolution during creep life of Ni-based single crystal superalloys

[J]. J. Mater. Sci. Technol., 2020, 45: 207

The high performance of Ni single crystal superalloys during high temperature low stress creep service, is intrinsically determined by the combined effects of microstructural evolution and the dislocation behaviour. In the field of the evolution of dislocation network, two main recovery mechanism based on dislocation migration dominate the process. One is superdislocations shearing into γ’ rafts through a two-superpartials-assisted approach. Another is the compact dislocations migrating along γ/γ′ interface. These two mechanisms are similarly climb-rate-controlled process. In this work, a model for the minimum creep rate based on thermodynamic and kinetic calculations and using an existing detailed dislocation dynamics model has been built by taking the dislocation migration behaviours as well as the rafted microstructure into consideration, which can well reproduce the ([100] tensile) creep properties of existing Ni superalloy grades, without the need to make the dislocation parameter values composition dependent.

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Y W

, Lee

W J

Cyclic plastic strain energy as a damage criterion and environmental effect in Nb-bearing high strength, low alloy steel

[J]. Mater. Sci. Eng., 1994, 186A(1-2): 121

[30]

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M E

, Bhat

S P

A model of fatigue crack nucleation in single crystal iron and copper

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[31]

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, Zhang

W G

, Xu

J Q

, et al.

The impact of misorientation on the grain boundary energy in bi-crystal copper: an atomistic simulation study

[J]. J. Mol. Model., 2022, 28(2): 47

DOI PMID [本文引用: 1]

Atomistic simulations were performed to investigate the relationships among the misorientation, dislocation density, and grain boundary energy of twist and tilt bi-crystal grain boundaries. In this work, the grain boundary energies were calculated based on the embedded-atom method interatomic potential for Cu. The results show that the dislocation density of the grain boundary changes with the rotation angle, thereby affecting the grain boundary energy. Furthermore, the grain boundary energy of a grain boundary with no dislocations is greater than that of a grain boundary with dislocations, which results from the distribution of the atomic potential energy on the grain boundaries. Additionally, the grain boundary energy increases with the dislocation density of the grain boundary in the case of dislocations on the grain boundary. On this basis, a new relationship is proposed for the misorientation angle and grain boundary energy. We assume that when the driving force of dislocation nucleation breaks through the grain boundary energy barrier, the grain boundary energy declines.© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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M D

, Sehitoglu

, Maier

H J

, et al.

Grain boundary characterization and energetics of superalloys

[J]. Mater. Sci. Eng., 2010, 527A(26): 7115