﻿ 镍基单晶高温合金滑移系剪应力集中分析 Analysis of Shear Stress Concentration of Slip System for Nickel-Based Single Crystal Superalloys

Open Journal of Nature Science
Vol.05 No.02(2017), Article ID:20733,13 pages
10.12677/OJNS.2017.52026

Analysis of Shear Stress Concentration of Slip System for Nickel-Based Single Crystal Superalloys

Wanchao Sun

Aircraft Strength Research Institute, Aero-Engine Strength Research Department, Xi’an Shaanxi

Received: May 6th, 2017; accepted: May 20th, 2017; published: May 27th, 2017

ABSTRACT

In order to perfect the crystal slip theory and its engineering application and evaluation of the low cycle fatigue and creep life model that developed on the crystal slip theory, the related definition of slip system shear stress concentration factor for nickel-based single crystal alloy was proposed .Through theoretical derivation and finite element method, the slip system stress concentration factor of nickel base single crystal superalloy was analyzed, it can be deduced that: 1) There exists obvious difference in stress concentration effect between isotropic alloy and nickel-based single crystal alloy. So it would be inappropriate to use the stress concentration coefficient of isotropic alloy to handle nickel-based single crystal alloy; 2) For plane problem, the shear stress concentration coefficient in slip system only determined by component’s shape and crystal orientation, and has nothing to do with the material elastic constants; 3) For nickel-based single crystal alloy, stress concentration coefficient is anisotropic with crystal orientation. Under the same shape and load conditions, stress concentration coefficient in [111] orientation takes its maximum, in [011] orientation second, and in [001] orientation the minimal.

Keywords:Stress Concentration, Slip System, Crystal Orientation, Nickel-Based Single Crystal, Shear Stress Concentration

1. 引言

2. 滑移系剪应力集中系数定义

1) 应力集中处，A滑移系簇第α滑移系剪应力绝对值与适当选取的A滑移系簇第α滑移系基准剪应力绝对值之比，定义为：A滑移系簇第α滑移系绝对理论剪应力集中系数，用符号表示

(1)

2) 应力集中处A滑移系簇的第α滑移系剪应力绝对值与适当选取的A滑移系簇中所有滑移系最大基准剪应力绝对值之比，定义为：A滑移系簇第α滑移系相对理论剪应力集中系数，即

(2)

3) 将A滑移系簇第α滑移系绝对(相对)理论剪应力集中系数与滑移系剪应力集中因素几何尺寸绘制的曲线，称为：A滑移系簇第α滑移系绝对(相对)理论剪应力集中系数曲线。

4) A滑移系簇的所有滑移系绝对(相对)理论剪应力集中系数曲线统称为：A滑移系簇绝对(相对)理论剪应力集中系数曲线。

5) A滑移系簇中最大滑移系剪应力对应的绝对(相对)理论剪应力集中系数曲线定义为：优先开启的A滑移系簇绝对(相对)理论剪应力集中系数曲线。

6) 比A滑移系簇最大剪应力绝对值小20%以内的滑移系对应的绝对(相对)理论剪应力集中系数曲线定义为：具有激活潜力的A滑移系簇绝对(相对)理论剪应力集中系数曲线。

3. 含中心圆孔的平板拉/压应力集中分析

Figure 1. {111}<110> and {111}<112> families of slip directions

Table 1. {111}<110> and {111}<112> slip systems

(A) (B)

Figure 2. A plate with round hole and slip system for the plane problem

1) 按“小孔口问题”求解，利用弹性力学的方法可得到该无限大平板应力状态的基尔斯解答如下 [26] ：

(3)

(4)

(5)

(6)

2) 孔边(x2 + y2 = r2)处的应力状态为：

(7)

(8)

3) 对含一个中心圆孔的有限大平板单向和双向拉伸(压缩)进行应力集中分析时，与含一个中心圆孔的无限大平板的分析是一样的，上述所有的公式(除了基准剪应力的选取外)都适用。

4. 含V型半圆沟槽的圆杆应力集中分析

4.1. 基准剪应力的选取

Figure 3. A V shape niked test bar

A滑移系簇第α滑移系相对理论剪应力集中系数与基准剪应力分别为：

(9)

(10)

(11)

4.2. 轴向/等效应力集中系数

a) θ = 60˚：(1.649 − 3.299)/(1.528 − 2.818)、(1.786 − 3.636)/(1.987 − 3.835)和(2.289 − 4.268)/(2.250 − 4.268)；

b) θ = 90˚：(1.430 − 3.264)/(1.331 − 2.785)、(1.574 − 3.611)/(1.753 − 3.785)和(1.961 − 4.355)/(1.928 − 4.294)；

c) θ = 120˚：(1.433 − 2.887)/(1.320 − 2.323)、(1.579 − 3.236)/(1.758 − 3.421)和(1.953 − 3.916)/(1.916 − 3.884)。

a) θ = 60˚：(1.444 − 3.739)/(1.355 − 3.248)、(1.608 − 4.111)/(1.765 − 4.181)和(2.103 − 4.858)/(2.057 − 4.784)；

b) θ = 90˚：(1.445 − 3.572)/(1.354 − 3.021)、(1.606 − 4.024)/(1.765 − 4.109)和(2.097 − 4.737)/(2.053 − 4.653)；

c) θ = 120˚：(1.430 − 2.975)/(1.314 − 2.443)、(1.601 − 3.498)/(1.761 − 3.661)和(2.076 − 4.267)/(2.028 − 4.204)。

Figure 4. The axial/equivalent stress concentration factor in different orientation of a V shape niked test bar

4.3. 八面体滑移系簇相对理论剪应力集中系数

a) θ = 60˚：(1.685 − 3.182)、(1.936 − 3.372)和(2.704 − 4.713)；

b) θ = 90˚：(1.479 − 3.113)、(1.700 − 3.451)和(2.367 − 4.985)；

c) θ = 120˚：(1.508 − 2.667)、(1.706 − 3.073)和(2.402 − 4.336)；

a) θ = 60˚：(1.548 − 3.581)、(1.740 − 3.843)和(2.646 − 5.836)；

b) θ = 90˚：(1.550 − 3.453)、(1.740 − 3.817)和(2.645 − 5.534)；

c) θ = 120˚：(1.517 − 2.879)、(1.725 − 3.364)和(2.615 − 4.959)；

4.4. 十二面体滑移系簇相对理论剪应力集中系数

a) θ = 60˚：(1.586 − 2.772)、(1.874 − 3.352)、(2.574 − 4.627)；

b) θ = 90˚：(1.394 − 2.840)、(1.626 − 3.387)、(2.255 − 4.748)；

c) θ = 120˚：(1.402 − 2.534)、(1.619 − 3.007)、(2.260 − 4.122)；

a) θ = 60˚：(1.420 − 3.467)、(1.677 − 3.765)、(2.477 − 5.429)；

b) θ = 90˚：(1.419 − 3.294)、(1.678 − 3.711)、(2.472 − 5.217)；

c) θ = 120˚：(1.399 − 2.704)、(1.652 − 3.238)、(2.448 − 4.625)；

Figure 5. The relative theoretic stress concentrated coefficient in different orientation of {111}<110> slip systems

Figure 6. The relative theoretic stress concentrated coefficient in different orientation of {111}<112> slip systems

5. 结论

1) 各向同性材料与镍基单晶合金的应力集中效应有着明显的差异，采用各向同性高温合金应力集中系数处理镍基单晶合金是不合适的。

2) 对于平面问题，滑移系剪应力分布只决定于构件的形状和晶体方向，而与材料的弹性常数无关。于是在试验应力分析中，对于可以简化为平面问题的构件，利用力学性质不同的镍基单晶材料制作模型，以代替真实镍基单晶材料制作的构件进行滑移系剪应力集中分析，对平面问题是精确的。

3) 对于镍基单晶合金材料，形状与载荷条件相同下，[111]取向具有最大的优先开启潜力的理论滑移系剪应力集中系数、轴向应力集中系数和等效应力集中系数，[011]取向次之，[001]取向最小。即[111]取向具有最高的缺口敏感性，[011]取向次之，[001]取向最小。

4) 各取向的优先开启潜力的理论滑移系剪应力集中系数、轴向应力集中系数和等效应力集中系数有着较大的差异。轴向应力集中系数不能反映缺口试棒的多轴应力状态，而滑移系剪应力集中系数和等效应力集中系数可以反映出多轴应力状态。

5) 利用不同的方法评估镍基单晶合金部件的疲劳、蠕变寿命和裂纹扩展，应采用相应的应力集中系数作为准则设计模拟试件。

Analysis of Shear Stress Concentration of Slip System for Nickel-Based Single Crystal Superalloys[J]. 自然科学, 2017, 05(02): 190-202. http://dx.doi.org/10.12677/OJNS.2017.52026

1. 1. Arakere, N.K. (2004) High-Temperature Fatigue Properties of Single Crystal Superalloys in Air and Hydrogen. ASME Journal of Engineering for Gas Turbines and Power, 126, 590-603. https://doi.org/10.1115/1.1501075

2. 2. Wahi, R.P., Auerswald, J., Mukherji, D., Dudka, A., Fecht, H.J. and Chen, W. (1997) Damage Mechanisms of Single Andpolycrystalline Nickel Base Superalloys SC16 and IN738LC under High Temperature LCF Loading. International Journal of Fatigue, 19, S89-S94. https://doi.org/10.1016/S0142-1123(97)00038-8

3. 3. Dalal, R.P., Thomas, C.R. and Dardi, L.E. (1984) The Effect of Crystallographic Orientation on the Physical and Mechanical Properties of an Investment Cast Single Crystal Nickel-Base Superalloy. TMS-AIME, Warrendale, 185-197.

4. 4. Taylor, G.I. and Elam, C.F. (1925) The Plastic Extension and Fracture of Aluminum Crystals. Proceedings of the Royal Society, 108, 25-51. https://doi.org/10.1098/rspa.1925.0057

5. 5. Schmid, E. (1935) Plasticity of Crystal. Oxford University Press, New York.

6. 6. Myoung, G.L., Wagoner, R.H. and Kim, S.J. (2008) Comparative Study of Single Crystal Constitutive Equations for Crystal Plasticity Finite Element Analysis. International Journal of Modern Physics, 22, 5388-5393. https://doi.org/10.1142/S0217979208050541

7. 7. Czech, N. and Stamm, W. (1996) Thermal Cycle Fatigue Properties of Coated and Uncoated Single Crystal Superalloy. Surface and Coatings Technology, 86, 15-21. https://doi.org/10.1016/S0257-8972(96)02947-7

8. 8. Antelo, M.A., Johnson, P.K., Ostolaza, K.M. and Bressers, J. (1998) Analysis of the Fracture Behaviour of an Aluminide Coating on a Single-Crystal Superalloy under Tensile Conditions. Materials Science and Engineering, A247, 40- 50. https://doi.org/10.1016/S0921-5093(98)00477-8

9. 9. Czech, N. and Stamm, W. (1996) Thermal Cycle Fatigue Properties of Coated and Uncoated Single Crystal Superalloy. Surface and Coatings Technology, 86, 15-21. https://doi.org/10.1016/S0257-8972(96)02947-7

10. 10. Gui, T.S., Wang, M.G., Li, T., Qian, B.J. and Xie, J. (2010) Influence of TCP Phase and Its Morphology on Creep Properties of Single Crystal Nickel-Based Superalloys. Materials Science and Engineering, A527, 5444-5451. https://doi.org/10.1016/j.msea.2010.05.027

11. 11. 孙万超, 陆山. 考虑应力集中的镍基单晶合金低周疲劳公式[J]. 应用力学学报, 2013, 33(2): 273-277.

12. 12. 张超, 秦义校, 李艳青, 等. 桥式起重机箱型主梁典型缺陷应力集中分析[J]. 机械工程与自动化, 2012(1): 122- 123.

13. 13. 王子. 典型船舶焊接接头应力集中系数有限元分析[J]. 船海工程, 2012, 43(3): 4-6.

14. 14. 何川, 封坤, 晏启祥. 高速铁路水下盾构隧道管片内力分布规律研究[J]. 铁道学报, 2012, 34(4): 101-109.

15. 15. 王志良, 申林方, 姚激. 开槽预应力闸墩应力集中特性研究[J]. 水利水电技术, 2012, 43(9): 46-49.

16. 16. 陈亮, 郑廷银. 腹板几何尺寸变化对梯形波纹腹板工字钢梁应力集中的影响[J]. 南京工业大学学报, 2012, 34(4): 138-144.

17. 17. 段钢文. 桥梁结构钢筋应力集中、疲劳研究[J]. 黑龙江交通科技, 2012(2): 96.

18. 18. 航空工业部科学技术委员会. 应力集中系数手册[M]. 北京: 高等教育出版社, 1990.

19. 19. 董志航, 廖志忠. 理论应力集中系数的有限元求法[J]. 航空兵器, 2005(3): 15

20. 20. 陆山, 王春光, 陈军. 任意最大梯度路径轮盘模拟件设计方法[J]. 航空动力学报, 2010, 25(9): 2000-2005.

21. 21. Filippini, M. (2011) Notched Fatigue Strength of Single Crystals at High Temperature. Procedia Engineering, 10, 3787-3792. https://doi.org/10.1016/j.proeng.2011.04.618

22. 22. 赵萍, 何清华, 李维, 等. 单晶切口试样低周疲劳特性研究[J]. 航空动力学报, 2010, 25(11): 2632-2636.

23. 23. Asaro, R.J. (1983) Crystal Plasticity. ASME Journal of Applied Mechanics, 50, 921-934. https://doi.org/10.1115/1.3167205

24. 24. 孙万超, 陆山. 用于单晶叶片应力分析的滑移本构模型研究[J]. 推进技术, 2012, 33(5): 754-759.

25. 25. Arakere, N.K. and Swanson, G. (2002) Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys. ASME Journal of Engineering for Gas Turbines and Power, 124, 161-176. https://doi.org/10.1115/1.1413767

26. 26. 孙万超. 镍基单晶合金力学性能及低周疲劳分析与应用[D]: [博士学位论文]. 西安: 西北工业大学, 2013.