Phase Field Modeling of the Evolution of Helium Bubbles in Shock Loaded Aluminum
-
摘要: 氦泡等缺陷对金属材料动态强度的影响一直是动态强度研究关注的重点。将相场方法引入冲击加载下氦泡演化行为研究中，通过与晶体塑性理论耦合，建立了可描述冲击下氦泡早期演化行为的介观模拟技术。应用该方法，针对含氦泡的金属铝材料，从介观尺度对氦泡的演化行为及其对位错集体演化行为的影响进行了研究。结果表明：氦泡结构的非均匀性导致局域应力集中和塑性变形集中，局域塑性变形集中会导致沿冲击波传播方向发射稀疏波；从能量守恒角度上看，在材料变形过程中氦泡生长与塑性变形呈竞争关系，塑性耗散的快慢直接影响氦泡的生长速率，使其发生改变。研究结果可为解读含氦泡材料的宏观屈服强度和层裂行为提供理论支撑。Abstract: Investigation of the influence of helium bubbles on the dynamic strength has drawn continuous attention. In this article, the phase field method (PFM) is applied to investigate the evolution of helium bubbles at an early stage in shock-loaded aluminum based on its advantage to describe the interface evolution. PFM is coupled with the crystal plasticity finite element method (CPFEM), which makes it possible to investigate the interaction between the helium bubbles and the collective behaviors of dislocation assembles. It is found that the heterogeneity of helium bubbles induces a local concentration of plastic deformation, which leads to a rarefaction wave along the propagation direction of the shock wave. From an energy perspective, it is inferred that both the growth of helium bubbles and the plastic deformation are driven by the strain energy, which indicates that these two processes may compete with each other.
-
Key words:
- shock loading /
- helium bubble /
- phase field method /
- crystal plasticity
-
图 3 冲击波到达后（0.1 ns时刻）氦泡附近的局域化效应
Figure 3. Localization effect near the helium bubble at the arrival of the shock wave (0.1 ns)
图 4 冲击压缩过程中可动位错密度的演化
Figure 4. Evolution of mobile dislocation density during shock compression
图 5 不同时刻氦泡周围的可动位错密度分布
Figure 5. Distribution of the mobile dislocation density around helium bubbles at different time
图 6 不同时刻氦泡序参量的空间分布
Figure 6. Spatial distribution of order parameter at different times
图 7 第1次与第2次卸载波到达后氦泡的演化行为
Figure 7. Evolution of helium bubbles when the first and second unloading waves arrive
图 9 氦泡附近纵向应力演化历史
Figure 9. Time history of longitudinal shear stress near the helium bubbles
图 10 在300 K环境温度、100 m/s的加载速度下不同模型模拟的氦泡长大速率
Figure 10. Growth rates of helium bubbles simulated by different constitutive models at 300 K and impact velocity of 100 m/s
图 11 不同环境温度下氦泡生长速率对比
Figure 11. Comparison of growth rates of helium bubble at different ambient temperatures
图 12 不同初始位错密度下氦泡生长速率的对比
Figure 12. Comparison of growth rates of helium bubble under different initial dislocation densities
图 14 1.0 ns时刻氦泡附近的可动位错密度与临界分切应力分布
Figure 14. Contours of mobile dislocation density and critical shear stress near helium bubble at 1.0 ns
图 15 两个氦泡距离较远时1.0 ns时刻的序参量分布
Figure 15. Distribution of order parameters at 1.0 ns when two helium bubbles are far apart
图 16 较多初始氦泡时的冲击演化行为
Figure 16. Impact evolution behavior of more initial helium bubbles
表 1 状态方程参数与声子拖曳系数
Table 1. Parameters of equation of states and phonon drag coefficients
Material ${\,\rho }{_{0} }/$(g·cm−3) ${c}{_{0}}/$(m·s−1) $ \lambda $ $\varGamma$ ${B}{_{0}}/$(10−5 Pa·s) ${B{'} }{_{T} }$/(10−7 Pa·s·K−1) Al 2.77 5320 1.38 2.10 1.34 1.00 
下载: 导出CSV
表 2 弹性常数及其关于温度的导数
Table 2. Elastic constants and temperature derivatives of the elastic constants
Material ${c}{_{11}}$/GPa ${c}{_{12}}$/GPa ${c}{_{44}}$/GPa $\dfrac{ \mathrm{d}{c}{_{11} } }{\mathrm{d}T } \big/$(GPa·K−1) $\dfrac {\mathrm{d}{c}{_{12} } }{\mathrm{d}T} \big/$(GPa·K−1) $\dfrac {\mathrm{d}{c}{_{44} } }{\mathrm{d}T } \big/$(GPa·K−1) Al 114.22 61.94 31.60 −3.83 −0.68 −1.51
下载: 导出CSV
表 3 晶体塑性模型参数
Table 3. Parameters of the crystal plasticity model
Material ${\alpha }{_{\mathrm{H}\mathrm{N} }}$/m−2 ${\alpha }{_{\mathrm{M}\mathrm{u}\mathrm{l}\mathrm{t} } }$ ${\alpha }{_{\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{i} } }$ ${v}{_{\mathrm{I} }}$/(m·s−1) ${A}{_{\mathrm{I} } }$ ${\tau }{_{0}}$/MPa ${\,\rho }{_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} } }$/m−2 Al 1.0×1022 0.51 10 1.0 0.4 22 1×1011
下载: 导出CSV
表 4 相场模型参数
Table 4. Parameters of the phase field model
Materail $ L/ $(${\mathrm{P}\mathrm{a} }{^{-1} }{\cdot \mathrm{s} }{^{-1} }$) $\,\beta$/N $W/\left(\mathrm{J}{\cdot \mathrm{k}\mathrm{g} }{^{-1} }{\cdot \mathrm{K} }{^{-1} }\right)$ Al 500 0 0
下载: 导出CSV
-
[1] 王海燕. 氦泡对延性金属材料静态和动态力学性质影响的研究 [D]. 成都: 四川大学, 2008.WANG H Y. The influence of helium bubble to static and dynamic properties of ductile metal [D]. Chengdu: Sichuan University, 2008. [2] 万发荣. 金属材料的辐照损伤 [M]. 北京: 科学出版社, 1993.WAN F R. Irradiation damage of metal [M]. Beijing: Science Press, 1993. [3] CAWTHORNE C, FULTON E J. Voids in irradiated stainless steel [J]. Nature, 1967, 216(5115): 575–576. doi: 10.1038/216575a0 [4] WIEDERSICH H. On the theory of void formation during irradiation [J]. Radiation Effects, 1972, 12(1/2): 111–125. doi: 10.1080/00337577208231128 [5] MANSUR L K. Theory and experimental background on dimensional changes in irradiated alloys [J]. Journal of Nuclear Materials, 1994, 216: 97–123. doi: 10.1016/0022-3115(94)90009-4 [6] CALDER A F, BACON D J, BARASHEV A V, et al. On the origin of large interstitial clusters in displacement cascades [J]. Philosophical Magazine, 2010, 90(7/8): 863–884. doi: 10.1080/14786430903117141 [7] TRINKAUS H, SINGH B N. Helium accumulation in metals during irradiation: where do we stand? [J]. Journal of Nuclear Materials, 2003, 323(2/3): 229–242. doi: 10.1016/j.jnucmat.2003.09.001 [8] 王海燕, 祝文军, 邓小良, 等. 冲击加载下铝中氦泡和孔洞的塑性变形特征研究 [J]. 物理学报, 2009, 58(2): 1154–1160. doi: 10.7498/aps.58.1154WANG H Y, ZHU W J, DENG X L, et al. Plastic deformation of helium bubble and void in aluminum under shock loading [J]. Acta Physica Sinica, 2009, 58(2): 1154–1160. doi: 10.7498/aps.58.1154 [9] 张凤国, 胡晓棉, 王裴, 等. 含氦泡金属铝层裂响应的数值分析 [J]. 爆炸与冲击, 2017, 37(4): 699–704. doi: 10.11883/1001-1455(2017)04-0699-06ZHANG F G, HU X M, WANG P, et al. Numerical analysis of spall response in aluminum with helium bubbles [J]. Explosion and Shock Waves, 2017, 37(4): 699–704. doi: 10.11883/1001-1455(2017)04-0699-06 [10] REISMAN D B, WOLFER W G, ELSHOLZ A, et al. Isentropic compression of irradiated stainless steel on the Z accelerator [J]. Journal of Applied Physics, 2003, 93(11): 8952–8957. doi: 10.1063/1.1571969 [11] DÁVILA L P, ERHART P, BRINGA E M, et al. Atomistic modeling of shock-induced void collapse in copper [J]. Applied Physics Letters, 2005, 86(16): 161902. doi: 10.1063/1.1906307 [12] KUBOTA A, REISMAN D B, WOLFER W G. Dynamic strength of metals in shock deformation [J]. Applied Physics Letters, 2006, 88(24): 241924. doi: 10.1063/1.2210799 [13] RAICHER E, GLAM B, HENIS Z, et al. Equation of state for aluminum containing helium bubbles [J]. Journal of Applied Physics, 2009, 106(8): 083519. doi: 10.1063/1.3247960 [14] GLAM B, ELIEZER S, MORENO D, et al. Helium bubbles formation in aluminum: bulk diffusion and near-surface diffusion using TEM observations [J]. Journal of Nuclear Materials, 2009, 392(3): 413–419. doi: 10.1016/j.jnucmat.2009.03.057 [15] GLAM B, ELIEZER S, MORENO D, et al. Dynamic fracture and spall in aluminum with helium bubbles [J]. International Journal of Fracture, 2010, 163(1/2): 217–224. doi: 10.1007/s10704-009-9437-1 [16] GLAM B, STRAUSS M, ELIEZER S, et al. The preheating effect on the dynamic strength of aluminium containing helium bubbles [J]. Journal of Physics: Conference Series, 2014, 500(18): 182012. doi: 10.1088/1742-6596/500/18/182012 [17] GLAM B, STRAUSS M, ELIEZER S, et al. Shock compression and spall formation in aluminum containing helium bubbles at room temperature and near the melting temperature: experiments and simulations [J]. International Journal of Impact Engineering, 2014, 65: 1–12. doi: 10.1016/j.ijimpeng.2013.10.010 [18] SHAO J L, WANG P, HE A M, et al. Influence of voids or He bubbles on the spall damage in single crystal Al [J]. Modelling and Simulation in Materials Science and Engineering, 2014, 22(2): 025012. doi: 10.1088/0965-0393/22/2/025012 [19] SHAO J L, PEI W, HE A M. Compression-induced stacking fault tetrahedra around He bubbles in Al [J]. Journal of Applied Physics, 2014, 116(16): 163516. doi: 10.1063/1.4900784 [20] HE A M, PEI W, SHAO J L. Effects of defects and microstructure on release melting of shock-loaded copper: atomistic simulations [J]. Journal of Applied Physics, 2018, 123(1): 015901. doi: 10.1063/1.5005000 [21] LI B, WANG L, E J C, et al. Shock response of He bubbles in single crystal Cu [J]. Journal of Applied Physics, 2014, 116(21): 213506. doi: 10.1063/1.4903732 [22] LI B, WANG L, JIAN W R, et al. Irradiation-initiated plastic deformation in prestrained single-crystal copper [J]. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2016, 368: 60–65. doi: 10.1016/j.nimb.2015.12.011 [23] BRINGA E M, CARO A, WANG Y M, et al. Ultrahigh strength in nanocrystalline materials under shock loading [J]. Science, 2005, 309(5742): 1838–1841. doi: 10.1126/science.1116723 [24] SLIWA M, MCGONEGLE D, WEHRENBERG C, et al. Femtosecond X-ray diffraction studies of the reversal of the microstructural effects of plastic deformation during shock release of tantalum [J]. Physical Review Letters, 2018, 120(26): 265502. doi: 10.1103/PhysRevLett.120.265502 [25] MILATHIANAKI D, BOUTET S, WILLIAMS G J, et al. Femtosecond visualization of lattice dynamics in shock-compressed matter [J]. Science, 2013, 342(6155): 220–223. doi: 10.1126/science.1239566 [26] KANEL G I. Unusual behaviour of usual materials in shock waves [J]. Journal of Physics: Conference Series, 2014, 500(1): 012001. doi: 10.1088/1742-6596/500/1/012001 [27] KRASNIKOV V S, MAYER A E, YALOVETS A P. Dislocation based high-rate plasticity model and its application to plate-impact and ultra short electron irradiation simulations [J]. International Journal of Plasticity, 2011, 27(8): 1294–1308. doi: 10.1016/j.ijplas.2011.02.008 [28] YAO S L, PEI X Y, LIU Z L, et al. Numerical investigation of the temperature dependence of dynamic yield stress of typical BCC metals under shock loading with a dislocation-based constitutive model [J]. Mechanics of Materials, 2020, 140: 103211. doi: 10.1016/j.mechmat.2019.103211 [29] YAO S L, YU J D, CUI Y N, et al. Revisiting the power law characteristics of the plastic shock front under shock loading [J]. Physical Review Letters, 2021, 126(8): 085503. doi: 10.1103/PHYSREVLETT.126.085503 [30] 唐志平. 冲击相变 [M]. 北京: 科学出版社, 2008.TANG Z P. Impact phase transition [M]. Beijing: Science Press, 2008. [31] DE S, ZAMIRI A R, RAHUL N. A fully anisotropic single crystal model for high strain rate loading conditions with an application to α-RDX [J]. Journal of the Mechanics and Physics of Solids, 2014, 64: 287–301. doi: 10.1016/J.JMPS.2013.10.012 [32] LUKYANOV A A. Constitutive behaviour of anisotropic materials under shock loading [J]. International Journal of Plasticity, 2008, 24(1): 140–167. doi: 10.1016/j.ijplas.2007.02.009 [33] 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 [34] 潘金生, 仝健民, 田民波. 材料科学基础 [M]. 北京: 清华大学出版社, 2011.PAN J S, TONG J M, TIAN M B. Fundamentals of materials science [M]. Beijing: Tsinghua University Press, 2011. [35] ROOS A, DE HOSSON J T M, VAN DER GIESSEN E. A two-dimensional computational methodology for high-speed dislocations in high strain-rate deformation [J]. Computational Materials Science, 2001, 20(1): 1–18. doi: 10.1016/S0927-0256(00)00117-8 [36] HIRTH J P, ZBIB H M, LOTHE J. Forces on high velocity dislocations [J]. Modelling and Simulation in Materials Science and Engineering, 1999, 6(2): 165. [37] 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 [38] AUSTIN R A, MCDOWELL D L. Parameterization of a rate-dependent model of shock-induced plasticity for copper, nickel, and aluminum [J]. International Journal of Plasticity, 2012, 32/33: 134–154. doi: 10.1016/j.ijplas.2011.11.002 [39] 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 [40] 于继东. 冲击相变动力学过程的相场模型研究 [D]. 绵阳: 中国工程物理研究院, 2014.YU J D. Phase field study on the kinetics in shock-induced phase transitions [D]. Mianyang: China Academy of Engineering Physics, 2004. [41] CHU D Y, LI X, LIU Z L. Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling [J]. International Journal of Fracture, 2017, 208(1): 115–130. doi: 10.1007/s10704-017-0220-4 [42] WANG T, LIU Z L, CUI Y N, et al. A thermo-elastic-plastic phase-field model for simulating the evolution and transition of adiabatic shear band. Part Ⅰ. theory and model calibration [J]. Engineering Fracture Mechanics, 2020, 232: 107028. doi: 10.1016/j.engfracmech.2020.107028 [43] WANG T, LIU Z L, CUI Y N, et al. A thermo-elastic-plastic phase-field model for simulating the evolution and transition of adiabatic shear band. Part Ⅱ. dynamic collapse of thick-walled cylinder [J]. Engineering Fracture Mechanics, 2020, 231: 107027. doi: 10.1016/j.engfracmech.2020.107027 [44] YU J D, WANG W Q, WU Q. Nucleation and growth in shock-induced phase transitions and how they determine wave profile features [J]. Physical Review Letters, 2012, 109(11): 115701. doi: 10.1103/PhysRevLett.109.115701 [45] YAO S L, PEI X Y, YU J D, et al. Scale dependence of thermal hardening of fcc metals under shock loading [J]. Journal of Applied Physics, 2020, 128(21): 215903. doi: 10.1063/5.0026226 [46] 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 -
下载:
点击查看大图
计量
- 文章访问数: 1388
- HTML全文浏览量: 647
- PDF下载量: 52
