冲击加载下多晶铝的晶体塑性有限元模拟

叶常青; 陈然; 刘桂森; 刘静楠; 胡建波; 俞宇颖; 王栋; 陈开果; 沈耀

doi:10.11858/gywlxb.20220605

冲击加载下多晶铝的晶体塑性有限元模拟

doi: 10.11858/gywlxb.20220605

叶常青^1,,
陈然¹,
刘桂森¹,
刘静楠¹,
胡建波^2,*, ,,
俞宇颖²,
王栋³,
陈开果⁴,
沈耀¹

1.
上海交通大学材料科学与工程学院, 上海　200240
2.
中国工程物理研究院流体物理研究所冲击波物理与爆轰物理重点实验室, 四川绵阳　621999
3.
西北核技术研究院, 陕西西安　710024
4.
国防科技大学物理系, 湖南长沙　410073

基金项目: 科学挑战专题（TZ2018001）

详细信息

作者简介:
叶常青（1994－），男，博士研究生，主要从事动态晶体塑性有限元研究. E-mail：yechangqing@sjtu.edu.cn

通讯作者:
沈　耀（1972－），男，博士，教授，主要从事晶体缺陷（位错、界面）行为、力学性能及塑性变形的微观机制研究. E-mail：yaoshen@sjtu.edu.cn

中图分类号: O347.3; O521.2
计量
- 文章访问数: 362
- HTML全文浏览量: 191
- PDF下载量: 84
出版历程
- 收稿日期: 2022-06-09
- 修回日期: 2022-06-26
- 网络出版日期: 2022-11-29
- 刊出日期: 2022-12-05

Crystal Plasticity Finite Element Simulation of Polycrystal Aluminum under Shock Loading

1.
School of Material Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2.
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China
3.
Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China
4.
Department of Physics, National University of Defense Technology, Changsha 410073, Hunan, China

摘要

摘要: 在多晶材料中，不同取向晶粒间的晶界往往对材料在冲击加载下的动力学响应有极大的影响。在单晶晶体塑性模型的基础上，通过考虑晶界与位错相互作用的微观机理，建立了一个包含晶界阻力、几何必需位错以及背应力的多晶晶体塑性模型，并模拟研究了基于Voronoi几何模型的多晶铝在冲击加载下的力学响应。结果表明：冲击波后的晶界单元存在极高的残余剪应力，而晶粒内部单元的剪应力趋近于零；晶界附近存在较大的塑性变形梯度，产生大量沿晶界分布的几何必需位错和背应力；由滑移不连续性引起的晶界阻力是造成冲击波后大量残余剪应力的主要因素，而几何必需位错和背应力对剪应力松弛程度的影响较小。
- 晶体塑性 /
- 冲击加载 /
- 晶界效应 /
- 晶界阻力 /
- 几何必需位错 /
- 背应力
Abstract: In polycrystalline materials, the grain boundaries between grains with different orientations have a great influence on the dynamic response of material under shock loading. On the basis of the single crystal plasticity model, a polycrystal plasticity model containing grain boundary obstacle, geometrically necessary dislocations (GND) and back-stress is established by considering the microscopic mechanism of the interaction between grain boundaries and dislocations. Based on this model, the mechanical response of polycrystalline aluminum with Voronoi geometry under shock loading was studied through simulations. The results show that: (1) the grain boundary elements after the shock loading have a very high residual shear stress, while the shear stress of the element within the grain tends to be zero; (2) a large plastic deformation gradient is found near the grain boundary, resulting in a large number of GND and back stress distributed along the grain boundary; (3) the grain boundary obstacle caused by the slip discontinuity is the main factor causing the large amount of residual shear stress, while the GND and back stress have little influence on the extent of shear stress relaxation.
- crystal plasticity /
- shock loading /
- grain boundary effect /
- grain boundary obstacle /
- geometrically necessary dislocations /
- back-stress

HTML全文

图 1 平板撞击实验示意图

Figure 1. Illustration of the plate impact experiments

下载: 全尺寸图片幻灯片

图 2 单晶铝平板撞击模拟与实验结果对比

Figure 2. Comparison of plate impact simulations and experiments for single-crystal Al

下载: 全尺寸图片幻灯片

图 3 塑性变形梯度与GND

Figure 3. Plastic strain gradient and GND

下载: 全尺寸图片幻灯片

图 4 数值实现与有限元模型

Figure 4. Numerical implementation and finite element model

下载: 全尺寸图片幻灯片

图 5 冲击加载下多晶铝的Mises剪应力分布

Figure 5. Distribution of Mises stress of polycrystalline aluminum under shock loading

下载: 全尺寸图片幻灯片

图 6 冲击加载下多晶铝的累积塑性滑移量分布

Figure 6. Distribution of accumulated slip of polycrystalline aluminum under shock loading

下载: 全尺寸图片幻灯片

图 7 冲击加载下多晶铝的GND和背应力分布

Figure 7. Distribution of GND and back-stress of polycrystalline aluminum under shock loading

下载: 全尺寸图片幻灯片

图 8 冲击加载下不同模型的平均残余剪应力

Figure 8. Average residual shear stress for different models under shock loading

下载: 全尺寸图片幻灯片

表 1 单晶铝的晶体塑性本构参数

Table 1. Parameters of crystal plasticity model for single-crystal Al

g₀	h_αβ	q₁	q₂	ν_d/μs⁻¹	$B' $/(Pa∙s∙K⁻¹)
0.6	0.25^[11]	0.336	1.155	6×10^6[11]	1.2×10⁻⁸

$\,{\rho }{_{0} ^{\alpha } }$/μm⁻²	C_m	A/(m⁻²∙Pa⁻²)	τ_min/MPa	C_a
0.064	0.08	1×10^−6[12]	100^[10]	24

下载: 导出CSV

表 2 单晶铝的超弹性本构参数

Table 2. Parameters of hyper-elastic model for single-crystal Al

Subscript	C_ij/MPa	$\dfrac{\partial {C}{_{ij} } }{\partial T}\bigg/$(MPa∙K⁻¹)	$\dfrac{\partial {C}{_{ij}} }{\partial p}$	$\, \widetilde{\rho }$/(g∙cm⁻³)	K₀/GPa	$K{'}$	c_V / (J∙kg⁻¹∙K⁻¹)	β/ (10⁻⁵ K⁻¹)
11	106.75^[33]	−35.10^[33]	6.35^[34]	2.7^[33]	73^[34]	4.6^[34]	890^[11]	2.3^[35]
12	60.41^[33]	−6.70^[33]	3.45^[34]
44	28.34^[33]	−14.50^[33]	2.10^[34]

下载: 导出CSV

参考文献(41)

[1]	ZHAKHOVSKY V V, BUDZEVICH M M, INOGAMOV N A, et al. Two-zone elastic-plastic single shock waves in solids [J]. Physical Review Letters, 2011, 107(13): 135502. doi: 10.1103/PhysRevLett.107.135502
[2]	ZARETSKY E B, KANEL G I. Tantalum and vanadium response to shock-wave loading at normal and elevated temperatures. non-monotonous decay of the elastic wave in vanadium [J]. Journal of Applied Physics, 2014, 115(24): 243502. doi: 10.1063/1.4885047
[3]	KOSITSKI R, STEINBERGER D, SANDFELD S, et al. Shear relaxation behind the shock front in <110> molybdenum: from the atomic scale to continuous dislocation fields [J]. Computational Materials Science, 2018, 149: 125–133. doi: 10.1016/j.commatsci.2018.02.058
[4]	AUSTIN R A. Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature [J]. Journal of Applied Physics, 2018, 123(3): 035103. doi: 10.1063/1.5008280
[5]	刘静楠, 叶常青, 陈开果, 等. <100>LiF高速冲击变形过程的晶体塑性有限元模拟 [J]. 高压物理学报, 2019, 33(1): 014101. doi: 10.11858/gywlxb.20180551 LIU J N, YE C Q, CHEN K G, et al. Crystal plasticity finite element simulation of high-rate shock deformation process of <100> LiF [J]. Chinese Journal of High Pressure Physics, 2019, 33(1): 014101. doi: 10.11858/gywlxb.20180551
[6]	GURRUTXAGA-LERMA B, BALINT D S, DINI D, et al. Attenuation of the dynamic yield point of shocked aluminum using elastodynamic simulations of dislocation dynamics [J]. Physical Review Letters, 2015, 114(17): 174301. doi: 10.1103/PhysRevLett.114.174301
[7]	刘静楠, 叶常青, 刘桂森, 等. 高温、高压、高应变速率动态过程晶体塑性有限元理论模型及其应用 [J]. 高压物理学报, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874 LIU J N, YE C Q, LIU G S, et al. Crystal plasticity finite element theoretical models and applications for high temperature, high pressure and high strain-rate dynamic process [J]. Chinese Journal of High Pressure Physics, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874
[8]	郑松林. 晶体塑性有限元在材料动态响应研究中的应用进展 [J]. 高压物理学报, 2019, 33(3): 030108. doi: 10.11858/gywlxb.20190725 ZHENG S L. Advances in the study of dynamic response of crystalline materials by crystal plasticity finite element modeling [J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030108. doi: 10.11858/gywlxb.20190725
[9]	LUSCHER D J, ADDESSIO F L, CAWKWELL M J, et al. A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine [J]. Journal of the Mechanics and Physics of Solids, 2017, 98: 63–86. doi: 10.1016/j.jmps.2016.09.005
[10]	LLOYD J T, CLAYTON J D, BECKER R, et al. Simulation of shock wave propagation in single crystal and polycrystalline aluminum [J]. International Journal of Plasticity, 2014, 60: 118–144. doi: 10.1016/j.ijplas.2014.04.012
[11]	AUSTIN R A, MCDOWELL D L. A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates [J]. International Journal of Plasticity, 2011, 27(1): 1–24. doi: 10.1016/j.ijplas.2010.03.002
[12]	MANDAL A, GUPTA Y M. Elastic-plastic deformation of molybdenum single crystals shocked along [100] [J]. Journal of Applied Physics, 2017, 121(4): 045903. doi: 10.1063/1.4974475
[13]	BECKER R. Effects of crystal plasticity on materials loaded at high pressures and strain rates [J]. International Journal of Plasticity, 2004, 20(11): 1983–2006. doi: 10.1016/j.ijplas.2003.09.002
[14]	VOGLER T J, CLAYTON J D. Heterogeneous deformation and spall of an extruded tungsten alloy: plate impact experiments and crystal plasticity modeling [J]. Journal of the Mechanics and Physics of Solids, 2008, 56(2): 297–335. doi: 10.1016/j.jmps.2007.06.013
[15]	HILL R, RICE J R. Constitutive analysis of elastic-plastic crystals at arbitrary strain [J]. Journal of the Mechanics and Physics of Solids, 1972, 20(6): 401–413. doi: 10.1016/0022-5096(72)90017-8
[16]	ASARO R J, NEEDLEMAN A. Overview No. 42 texture development and strain hardening in rate dependent polycrystals [J]. Acta Metallurgica, 1985, 33(6): 923–953. doi: 10.1016/0001-6160(85)90188-9
[17]	PEIRCE D, ASARO R J, NEEDLEMAN A. An analysis of nonuniform and localized deformation in ductile single crystals [J]. Acta Metallurgica, 1982, 30(6): 1087–1119. doi: 10.1016/0001-6160(82)90005-0
[18]	HUANG Y. A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program [M]. Cambridge: Harvard University, 1991.
[19]	LUSCHER D J, BRONKHORST C A, ALLEMAN C N, et al. A model for finite-deformation nonlinear thermomechanical response of single crystal copper under shock conditions [J]. Journal of the Mechanics and Physics of Solids, 2013, 61(9): 1877–1894. doi: 10.1016/j.jmps.2013.05.002
[20]	TYUTEREV V G, VAST N. Murnaghan’s equation of state for the electronic ground state energy [J]. Computational Materials Science, 2006, 38(2): 350–353. doi: 10.1016/j.commatsci.2005.08.012
[21]	SHYUE K M. A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state [J]. Journal of Computational Physics, 2001, 171(2): 678–707. doi: 10.1006/jcph.2001.6801
[22]	HANSEN B L, BEYERLEIN I J, BRONKHORST C A, et al. A dislocation-based multi-rate single crystal plasticity model [J]. International Journal of Plasticity, 2013, 44: 129–146. doi: 10.1016/j.ijplas.2012.12.006
[23]	SHAHBA A, GHOSH S. Crystal plasticity FE modeling of Ti alloys for a range of strain-rates. part Ⅰ: a unified constitutive model and flow rule [J]. International Journal of Plasticity, 2016, 87: 48–68. doi: 10.1016/j.ijplas.2016.09.002
[24]	KUKSIN A Y, YANILKIN A V. Atomistic simulation of the motion of dislocations in metals under phonon drag conditions [J]. Physics of the Solid State, 2013, 55(5): 1010–1019. doi: 10.1134/S1063783413050193
[25]	BLASCHKE D N, BURAKOVSKY L, PRESTON D L. On the temperature and density dependence of dislocation drag from phonon wind [J]. Journal of Applied Physics, 2021, 130(1): 015901. doi: 10.1063/5.0054536
[26]	KANEL G I, RAZORENOV S V, BAUMUNG K, et al. Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point [J]. Journal of Applied Physics, 2001, 90(1): 136–143. doi: 10.1063/1.1374478
[27]	CHOUDHURI D, GUPTA Y M. Shock compression of aluminum single crystals to 70 GPa: role of crystalline anisotropy [J]. Journal of Applied Physics, 2013, 114(15): 153504. doi: 10.1063/1.4824825
[28]	王礼立, 胡时胜, 杨黎明, 等. 材料动力学 [M]. 合肥: 中国科学技术大学出版社, 2017.
[29]	胡建波, 俞宇颖, 谭华, 等. 铝的动态屈服强度测量 [C]//第四届全国爆炸力学实验技术学术会议论文集. 武夷山: 安徽省力学学会, 2006.
[30]	ANDERSSON S, BACKSTROM G. Thermal conductivity and heat capacity of single-crystal LiF and CaF₂ under hydrostatic pressure [J]. Journal of Physics C: Solid State Physics, 1987, 20(35): 5951–5952. doi: 10.1088/0022-3719/20/35/011
[31]	MILLER R A, SMITH C S. Pressure derivatives of the elastic constants of LiF and NaF [J]. Journal of Physics and Chemistry of Solids, 1964, 25(12): 1279–1292. doi: 10.1016/0022-3697(64)90043-5
[32]	RODRÍGUEZ-MARTÍNEZ J A, RODRÍGUEZ-MILLÁN M, RUSINEK A, et al. A dislocation-based constitutive description for modeling the behavior of fcc metals within wide ranges of strain rate and temperature [J]. Mechanics of Materials, 2011, 43(12): 901–912. doi: 10.1016/j.mechmat.2011.09.008
[33]	TALLON J L, WOLFENDEN A. Temperature dependence of the elastic constants of aluminum [J]. Journal of Physics and Chemistry of Solids, 1979, 40(11): 831–837. doi: 10.1016/0022-3697(79)90037-4
[34]	THOMAS JR J F. Third-order elastic constants of aluminum [J]. Physical Review, 1968, 175(3): 955–962. doi: 10.1103/PhysRev.175.955
[35]	NIX F C, MACNAIR D. The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron [J]. Physical Review, 1941, 60(8): 597–605. doi: 10.1103/PhysRev.60.597
[36]	RAVAJI B, JOSHI S P. A crystal plasticity investigation of grain size-texture interaction in magnesium alloys [J]. Acta Materialia, 2021, 208: 116743. doi: 10.1016/j.actamat.2021.116743
[37]	刘晶, 刘韧, 季忠, 等. 基于晶粒晶界有限元的激光微冲击成形数值分析 [J]. 中国激光, 2010, 37(1): 291–295. doi: 10.3788/CJL20103701.0291 LIU J, LIU R, JI Z, et al. Numerical analysis of micro laser peen forming based on grain and grain boundary element [J]. Chinese Journal of Lasers, 2010, 37(1): 291–295. doi: 10.3788/CJL20103701.0291
[38]	LIM H, LEE M G, KIM J H, et al. Simulation of polycrystal deformation with grain and grain boundary effects [J]. International Journal of Plasticity, 2011, 27(9): 1328–1354. doi: 10.1016/j.ijplas.2011.03.001
[39]	SHEN Z, WAGONER R H, CLARK W A T. Dislocation pile-up and grain boundary interactions in 304 stainless steel [J]. Scripta Metallurgica, 1986, 20(6): 921–926. doi: 10.1016/0036-9748(86)90467-9
[40]	YUAN W, PANIGRAHI S K, SU J Q, et al. Influence of grain size and texture on Hall-Petch relationship for a magnesium alloy [J]. Scripta Materialia, 2011, 65(11): 994–997. doi: 10.1016/j.scriptamat.2011.08.028
[41]	ZHOU G, JEONG W, HOMER E R, et al. A predictive strain-gradient model with no undetermined constants or length scales [J]. Journal of the Mechanics and Physics of Solids, 2020, 145: 104178. doi: 10.1016/j.jmps.2020.104178