多晶体压剪试样静态加载有限元计算

赵伟业; 赵聃; 吕品; 金涛; 马胜国

doi:10.11858/gywlxb.20190836

多晶体压剪试样静态加载有限元计算

doi: 10.11858/gywlxb.20190836

赵伟业^{1, 2, 3,},
赵聃^{1, 2, 3,*, ,},
吕品^{1, 2, 3},
金涛^{1, 2, 3},
马胜国^{1, 2, 3}

1.
太原理工大学机械与运载工程学院应用力学研究所，山西太原　030024
2.
材料强度与结构冲击山西省重点实验室，山西太原　030024
3.
太原理工大学力学国家级实验教学示范中心，山西太原　030024

基金项目: 国家自然科学基金（11602158, 11802199, 11572214）；山西省自然科学青年基金（201601D021026）；山西省“1331工程”重点创新团队

详细信息

作者简介:
赵伟业（1992－），男，硕士研究生，主要从事多晶体有限变形数值计算研究.E-mail：939029385@qq.com

通讯作者:
赵　聃（1985－），男，博士，讲师，主要从事多晶体有限变形算法及多尺度本构理论研究.E-mail：zhaodan@tyut.edu.cn

中图分类号: O344.1
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出版历程
- 收稿日期: 2019-09-19
- 修回日期: 2019-10-25
- 刊出日期: 2020-02-25

Finite Element Calculation of Polycrystalline Shear-Compression Specimens with Static Loading

ZHAO Weiye^{1, 2, 3
,},
ZHAO Dan^{1, 2, 3,*
, ,},
LÜ Pin^{1, 2, 3},
JIN Tao^{1, 2, 3},
MA Shengguo^{1, 2, 3}

1.
Institute of Applied Mechanics, School of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
2.
Shanxi Key Laboratory of Material Strength & Structural Impact, Taiyuan 030024, Shanxi, China
3.
Taiyuan University of Technology Mechanics National Experimental Teaching Demonstration Center, Taiyuan 030024, Shanxi, China

摘要

摘要: 基于晶体塑性理论研究了晶体织构对数值计算结果的影响，建立了带有织构的多晶体压剪试样（SCS）模型。从材料和试样结构两方面研究了静态加载条件下微观晶粒在有限变形过程中对试样宏观力学性能的影响。由于模型几何结构的特殊性，重点对模型斜槽部分的应力、应变及变形特点进行了分析。考虑到试样在压缩过程中受摩擦的影响，数值分析了不同摩擦系数对变形过程的影响，在此基础上计算了相同摩擦系数下不同晶粒数目、不同单元数目以及单元类型对多晶体压剪模型力学性能的影响，并对试件关键部位不同取向晶粒的应力状态进行了分析。
- 多晶体 /
- 晶体织构 /
- 晶体塑性 /
- 压剪 /
- 摩擦系数
Abstract: The effect of crystal texture on the numerical results was studied based on the theory of crystal plasticity, and the polycrystalline compression shear sample (SCS) model with texture was established. The influence of micro-grain on the macroscopic mechanical properties in the process of finite deformation under static loading condition was studied in terms of material and sample structure. Because of the particularity of model geometry, the stress, strain and deformation characteristics of skewed slot were computed. Considering the effect of friction on the specimen during compression, the influence of friction coefficients on the deformation process was analyzed numerically. The influences of grain number, element number and element type on the mechanical properties of polycrystalline compression shear model under the same friction coefficient were calculated. The stress states of grain with different orientations in key parts of the specimen were also studied.
- polycrystalline /
- crystal texture /
- crystal plasticity /
- shear-compression /
- friction coefficient

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图 1 多晶体随机织构和丝织构的极图

Figure 1. Polar graphs of polycrystalline with random texture and fiber texture

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图 2 具有不同初始织构的单向压缩应力-应变曲线

Figure 2. Unidirectional compression stress-strain curves with different initial textures

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图 3 多晶体压剪试样几何尺寸

Figure 3. Geometrical dimension of polycrystal shear-compression specimen

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图 4 多晶体压剪模型

Figure 4. Polycrystal shear-compression model

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图 5 不同摩擦系数情况下的应力云图

Figure 5. Stress nephogram with different friction coefficients

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图 6 不同摩擦系数情况下模型斜槽单元的平均切应力-平均切应变曲线

Figure 6. Average shear stress-average shear strain curve of the model’s chute element corresponding to different friction coefficients

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图 7 不同摩擦系数情况下模型斜槽单元的平均正应力-平均正应变曲线

Figure 7. Average normal stress-average normal strain curve of the model’s chute element corresponding to different friction coefficients

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图 8 摩擦系数不同时模型斜槽单元的平均Mises应力-平均等效应变曲线

Figure 8. Average Mises stress-average equivalent strain curve of the model’s chute element corresponding to different friction coefficients

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图 9 摩擦系数不同时模型顶面的力-位移曲线

Figure 9. Force-displacement curve of the top surface of the model corresponding to different friction coefficients

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图 10 模型斜槽部分一条棱上所选取的16个单元

Figure 10. 16 selected elements on an edge of the chute part of the model

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图 11 不同摩擦系数下特征晶粒在压缩方向的应变

Figure 11. Strain of characteristic grain in compression direction under different friction coefficients

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图 12 包含不同晶粒数目的压剪有限元模型

Figure 12. Finite element models of compression shear with different grain numbers

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图 13 不同晶粒数目对应模型的载荷-位移曲线

Figure 13. Force-displacement curves of models corresponding to different numbers of grains

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图 14 单元数目不同的模型

Figure 14. Models with different number of elements

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图 15 单元数目不同时模型的Mises变形云图

Figure 15. Mises deformation nephograms of models with different numbers of elements

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图 16 单元数目不同时模型的载荷-位移曲线

Figure 16. Force-displacement curves of models with different numbers of elements

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图 17 斜槽相同位置处晶粒的Mises应力-等效应变曲线

Figure 17. Mises stress-equivalent strain curve of grains at the same position in the chute

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图 18 两种单元类型对应的模型斜槽部分Mises变形云图

Figure 18. Mises deformation nephogram of the model with two element types

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图 19 两种单元类型对应的模型顶面力-位移曲线

Figure 19. Top surface force-displacement curve of model with two element types

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图 20 两种单元类型对应的模型斜槽部分单元的平均Mises应力-平均等效应变曲线

Figure 20. Average Mises stress-strain curves of the sloped part of the model with two element types

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表 1 6061铝合金材料参数^[23]

Table 1. Material parameters of 6061 aluminum alloy^[23]

C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	m	q	${ { {\dot {\gamma } } }_{{0}}}$/s^–1	h₀/MPa	τ₀/MPa	τ_s/MPa
108.200	61.300	28.500	20	1.1	1	96	23.5	54

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表 2 不同摩擦系数对应模型的数值结果比较

Table 2. Numerical results of models corresponding to different friction coefficients

Friction coefficient	Maximum shear strain	Maximum normal strain	Maximum equivalent strain	Maximum force/N
0.025	0.740	−0.331	0.741	8 899.73
0.050	0.697	−0.263	0.625	9 566.97
0.100	0.651	−0.212	0.553	10 001.50
Relative maximum difference	13.7%	56.1%	34.0%	12.4%

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表 3 特征晶粒欧拉角

Table 3. Euler angle of characteristic grains

Grain number	φ₁/(°)	$\psi$/(°)	φ₂/(°)	Grain number	φ₁/(°)	$\psi$/(°)	φ₂/(°)
1	69.24	167.34	8.61	9	334.93	38.19	29.33
2	44.05	92.39	45.56	10	30.45	127.11	356.19
3	356.63	154.92	76.61	11	59.93	105.73	313.11
4	305.74	23.07	333.37	12	88.45	166.05	33.32
5	45.14	101.42	64.90	13	74.86	154.71	302.25
6	282.88	86.40	282.11	14	76.35	51.48	307.37
7	350.37	146.78	286.51	15	79.65	77.10	351.57
8	49.77	3.76	329.80	16	357.28	56.00	72.22

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表 4 单元数目不同时模型在不同压缩距离下的载荷及其最大相对偏差

Table 4. Loads of the model with different numbers of elements at different compression distance and their maximum relative differences

Number of elements	Load/N
Number of elements	1.0 mm	1.4 mm	1.8 mm	2.5 mm
8 026	−7 790.82	−8 180.42	−8 469.96	−8 726.07
14 604	−7 487.38	−7 824.37	−8 008.19	−8 157.61
23 835	−7 669.64	−8 038.55	−8 270.62	−8 436.06
Maximum relative difference	4.05%	4.55%	5.77%	6.97%

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