Mechanism and Damage Model for the Dynamic Tensile Fracture of Liquid Aluminum Containing He Bubbles

doi:10.11900/0412.1961.2023.00175

Acta Metall Sin

2025, Vol. 61

Issue (4): 643-652 DOI: 10.11900/0412.1961.2023.00175

Research paper

Current Issue | Archive | Adv Search

Mechanism and Damage Model for the Dynamic Tensile Fracture of Liquid Aluminum Containing He Bubbles

ZHOU Tingting(

), ZHAO Fuqi, ZHOU Hongqiang, ZHANG Fengguo, YIN Jianwei

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Cite this article:

ZHOU Tingting, ZHAO Fuqi, ZHOU Hongqiang, ZHANG Fengguo, YIN Jianwei. Mechanism and Damage Model for the Dynamic Tensile Fracture of Liquid Aluminum Containing He Bubbles. Acta Metall Sin, 2025, 61(4): 643-652.

Download:

HTML

PDF(1861KB)
Export: BibTeX | EndNote (RIS)

Abstract

The dynamic fracture of metals in liquid state has become a subject of considerable interest in current times because of its observation in various physical and technological processes such as inertial confinement fusion and high-power laser-driven surface micromachining. In addition, it has been found that the fractures at elevated temperature are highly correlated with the microstructure of materials. He bubbles are frequently observed in many metals exposed to irradiation environments as a result of radioactive or self-irradiation. Both experimental and theoretical studies have indicated that He bubbles can substantially affect the mechanical properties of irradiated metals, resulting in hardening, swelling, and embrittlement. In recent years, attention has been drawn to understand the effects of He bubbles on the dynamic properties of materials, including shock compression, dynamic fracture, and surface ejection. This study examines the dynamic tensile fracture behavior of liquid aluminum containing He bubbles across a wide range of strain rates by utilizing molecular dynamics (MD) simulations and continuum modeling. The physical mechanism leading to the dynamic fracture is revealed to be predominated by the growth of He bubble. Under strain rates ranging from 3.0 × 10⁶ s^-1 to 3.0 × 10⁹ s^-1, tension primarily induces bubble growth. At higher strain rates, such as 3.0 × 10¹⁰ s^-1, both bubble growth and void nucleation-growth are observed, although bubble growth remains the dominant factor. The growth of He bubbles unfolds in two distinct phases: rapid growth followed by slower growth. These staged evolutionary characteristics appear to be consistent across strain rates, but the growth rate of helium bubbles markedly increases with increasing strain rates. Furthermore, the dynamic tensile strength at varying strain rates indicates a significant reduction for the metal containing He bubbles compared to the pure metal. However, this discrepancy decreases at extremely high strain rates, such as 3.0 × 10¹⁰ s^-1. In addition, a continuum damage model is constructed based on the insights obtained from MD simulations to describe the dynamic tensile fracture of liquid metal containing He bubbles. This model accounts for external tensile stress, internal pressure of He bubbles, inertia, viscosity, and surface tension. Theoretical calculations using the damage model and the binomial equation of state, which depict the pressure-volume relationship of the metal substrate, exhibit excellent agreement with MD data over a wide range of strain rates. This includes the evolution of the tensile stress and He bubble radius. The self-consistent MD-continuum model proposed in this study has the potential to be applied in macroscopic hydrodynamic simulations, to depict the dynamic tensile fracture behavior of liquid metal with He bubbles.

Key words: dynamic fracture He bubble liquid metal molecular dynamics damage model

Received: 20 April 2023

ZTFLH:

TG113.25

Fund: National Natural Science Foundation of China(12172063)

Corresponding Authors: ZHOU Tingting, associate professor, Tel: (010)59872646, E-mail: zhou_tingting@iapcm.ac.cn

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	ZHOU Tingting
	ZHAO Fuqi
	ZHOU Hongqiang
	ZHANG Fengguo
	YIN Jianwei

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00175 OR https://www.ams.org.cn/EN/Y2025/V61/I4/643

Fig.1 Initial configuration of the liquid Al sample with He Bubbles (Al-He sample) (a) and the optimized configuration (by molecular dynamics (MD) simulation) at 1100 K (b) (The sample is cut through the center to show the central He bubble)

Fig.2 Evolutions of He bubble/voids during the dynamic tension process at the strain rate ( $ε ˙$ ) of 3.0 × 10⁸ s^-1
(a) Al-He sample (b) pure Al

Fig.3 Time (t) evolutions of tensile stress (P) (a), He bubble radius (R) (b), and the internal pressure of He bubble (P_g) (c) of Al-He sample during the dynamic tension process at $ε ˙$ = 3.0 × 10⁸ s^-1 (In Fig.3b, the black curve represents the fast growth of He bubble and the blue curve shows the slower growth of He bubble; the same in Fig.6)

Fig.4 Time evolutions of P (a) and volume of voids/He bubble (b) during the dynamic tension process at $ε ˙$ = 3.0 × 10⁸ s^-1 for pure Al sample and Al-He sample

Fig.5 Evolutions of He bubble during the dynamic tension process at $ε ˙$ = 3.0 × 10⁹ s^-1 (a) and $ε ˙$ = 3.0 × 10⁷ s^-1 (b) for Al-He sample

Fig.7 Variations of dynamic tensile strength with $ε ˙$ for pure Al sample and Al-He sample

Fig.8 Microstructure evolutions for the sample with He bubble during the dynamic tension process at $ε ˙$ = 3.0 × 10¹⁰ s^-1 (The central large pore is He bubble, and the other small pores are new nucleated voids)

$ε ˙$ / s^-1	R₀ / nm	$p g 0$ / GPa	γ / (J·m^-2)	n	K₁ / GPa	K₂ / GPa	η / (Pa·s)
3.0 × 10⁶	1.868	0.632	0.59	4.6	51	130	0.03
3.0 × 10⁷	1.868	0.632	0.59	4.6	51	130	0.006
3.0 × 10⁸	1.868	0.632	0.59	4.6	51	130	0.0025
3.0 × 10⁹	1.868	0.632	0.59	4.6	51	130	0.0012

Table 1 Parameters in the present damage model

Fig.9 Time evolutions of P (a) and R (b), and dynamic tensile strength (c) at various strain rates obtained from MD simulations and the present continuum model

Fig.10 Viscosity coefficients at different $ε ˙$ used in the present continuum model (dots) and the fitting curve using Eq.(7)

1	Antoun T, Curran D R, Razorenov S V, et al. Spall Fracture [M]. New York: Springer, 2003: 1
2	Curran D R, Seaman L, Shockey D A. Dynamic failure of solids [J]. Phys. Rep., 1987, 147: 253
3	Johnson J N. Dynamic fracture and spallation in ductile solids [J]. J. Appl. Phys., 1981, 52: 2812
4	Andriot P, Chapron P, Lambert V, et al. Influence of melting on shocked free surface behavior using Doppler laser interferometry and X ray densitometry [A]. Shock Waves in Condensed Matter 1983 [M]. Amsterdam: Elsevier, 1984: 277
5	Luo S N, An Q, Germann T C, et al. Shock-induced spall in solid and liquid Cu at extreme strain rates [J]. J. Appl. Phys., 2009, 106: 013502
6	Smalyuk V A, Weber S V, Casey D T, et al. Hydrodynamic instability experiments with three-dimensional modulations at the national ignition facility [J]. High Power Laser Sci. Eng., 2015, 3: 1
7	Orth C D. Spallation as a dominant source of pusher-fuel and hot-spot mix in inertial confinement fusion capsules [J]. Phys. Plasmas, 2016, 23: 343
8	Tsakiris N, Anoop K K, Ausanio G, et al. Ultrashort laser ablation of bulk copper targets: Dynamics and size distribution of the generated nanoparticles [J]. J. Appl. Phys., 2014, 115: 243301
9	Oboňa J V, Ocelík V, Rao J C, et al. Modification of cu surface with picosecond laser pulses [J]. Appl. Surf. Sci., 2014, 303: 118
10	Shugaev M V, Shih C Y, Karim E T, et al. Generation of nanocrystalline surface layer in short pulse laser processing of metal targets under conditions of spatial confinement by solid or liquid overlayer [J]. Appl. Surf. Sci., 2017, 417: 54
11	Kanel G I, Savinykh A S, Garkushin G V, et al. Dynamic strength of tin and lead melts [J]. JETP Lett., 2015, 102: 548
12	de Rességuier T, Signor L, Dragon A, et al. Dynamic fragmentation of laser shock-melted tin: Experiment and modelling [J]. Int. J. Fract., 2010, 163: 109
13	de Rességuier T, Signor L, Dragon A, et al. Experimental investigation of liquid spall in laser shock-loaded tin [J]. J. Appl. Phys., 2007, 101: 013506
14	Signor L, de Rességuier T, Dragon A, et al. Investigation of fragments size resulting from dynamic fragmentation in melted state of laser shock-loaded tin [J]. Int. J. Impact Eng., 2010, 37: 887
15	Chen Y T, Hong R K, Chen H Y, et al. An improved Asay window technique for investigating the micro-spall of an explosively-driven tin [J]. Rev. Sci. Instrum., 2017, 88: 013904
16	Vogan W S, Anderson W W, Grover M, et al. Piezoelectric characterization of ejecta from shocked tin surfaces [J]. J. Appl. Phys., 2005, 98: 113508
17	Zaretsky E B. Experimental determination of the dynamic tensile strength of liquid Sn, Pb, and Zn [J]. J. Appl. Phys., 2016, 120: 025902
18	Zaretsky E B, Kanel G I. Response of copper to shock-wave loading at temperatures up to the melting point [J]. J. Appl. Phys., 2013, 114: 083511
19	Razorenov S V, Savinykh A S, Zaretsky E B. Elastic-plastic deformation and fracture of shock-compressed single-crystal and polycrystalline copper near melting [J]. Tech. Phys., 2013, 58: 1437
20	Kanel G I, Razorenov S V, Bogatch A, et al. Spall fracture properties of aluminum and magnesium at high temperatures [J]. J. Appl. Phys., 1996, 79: 8310
21	Garkushin G V, Kanel G I, Savinykh A S, et al. Influence of impurities on the resistance to spall fracture of aluminum near the melting temperature [J]. Int. J. Fract., 2016, 197: 185
22	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]. J. Appl. Phys., 2001, 90: 136
23	Xiang M Z, Hu H B, Chen J, et al. Molecular dynamics simulations of micro-spallation of single crystal lead [J]. Modell. Simul. Mater. Sci. Eng., 2013, 21: 055005
24	Shao J L, Wang P, He A M, et al. Spall strength of aluminium single crystals under high strain rates: molecular dynamics study [J]. J. Appl. Phys., 2013, 114: 173501
25	Mayer A E, Mayer P N. Strain rate dependence of spall strength for solid and molten lead and tin [J]. Int. J. Fract., 2020, 222: 171
26	Mayer A E, Mayer P N. Evolution of pore ensemble in solid and molten aluminum under dynamic tensile fracture: Molecular dynamics simulations and mechanical models [J]. Int. J. Mech. Sci., 2019, 157-158: 816
27	Mayer P N, Mayer A E. Evolution of foamed aluminum melt at high rate tension: A mechanical model based on atomistic simulations [J]. J. Appl. Phys., 2018, 124: 035901
28	Ullmaier H. Radiation damage in metallic materials [J]. MRS Bull., 1997, 22: 14
29	Trinkaus H, Singh B N. Helium accumulation in metals during irradiation—Where do we stand? [J]. J. Nucl. Mater., 2003, 323: 229
30	Hou P F, Wang X H, Liu Y X, et al. A neutron irradiation-induced displacement damage of indium vacancies in α-In₂Se₃ nanoflakes [J]. Phys. Chem. Chem. Phys., 2020, 22: 15799
31	Xie H X, Gao N, Xu K, et al. A new loop-punching mechanism for helium bubble growth in tungsten [J]. Acta Mater., 2017, 141: 10
32	Schwartz A J, Wall M A, Zocco T G, et al. Characterization and modelling of helium bubbles in self-irradiated plutonium alloys [J]. Philos. Mag., 2005, 85: 479
33	Li Q, Parish C M, Powers K A, et al. Helium solubility and bubble formation in a nanostructured ferritic alloy [J]. J. Nucl. Mater., 2014, 445: 165
34	Chung B W, Thompson S R, Lema K E, et al. Evolving density and static mechanical properties in plutonium from self-irradiation [J]. J. Nucl. Mater., 2009, 385: 91
35	Schäublin R, Chiu Y L. Effect of helium on irradiation-induced hardening of iron: A simulation point of view [J]. J. Nucl. Mater., 2007, 362: 152
36	Osetsky Y N, Stoller R E. Atomic-scale mechanisms of helium bubble hardening in iron [J]. J. Nucl. Mater., 2015, 465: 448
37	Ding M S, Tian L, Han W Z, et al. Nanobubble fragmentation and bubble-free-channel shear localization in helium-irradiated submicron-sized copper [J]. Phys. Rev. Lett., 2016, 117: 215501
38	Ding M S, Du J P, Wan L, et al. Radiation-induced helium nanobubbles enhance ductility in submicron-sized single-crystalline copper [J]. Nano Lett., 2016, 16: 4118
39	Li S H, Zhang J, Han W Z. Helium bubbles enhance strength and ductility in small-volume Al-4Cu alloys [J]. Scr. Mater., 2019, 165: 112
40	Glam B, Eliezer S, Moreno D, et al. Dynamic fracture and spall in aluminum with helium bubbles [J]. Int. J. Fract., 2010, 163: 217
41	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]. Int. J. Impact Eng., 2014, 65: 1
42	Li Y H, Chang J Z, Zhang L, et al. Experimental investigation of spall damage in pure aluminum with helium bubbles [J]. Chin. J. High Press. Phys., 2021, 35: 054101
	李英华, 常敬臻, 张林等. 氦泡铝的层裂特性实验研究 [J]. 高压物理学报, 2021, 35: 054101
43	Xiao D W, He L F, Zhou P, et al. Spall in aluminium with helium bubbles under laser shock loading [J]. Chin. Phys. Lett., 2017, 34: 056201
44	Qi M L, He H L, Wang Y G, et al. Dynamic analysis of helium bubble growth in the pure al under high strain-rate loading [J]. Chin. J. High Press. Phys., 2007, 21: 145
	祁美兰, 贺红亮, 王永刚等. 高应变率拉伸下纯铝中氦泡长大的动力学研究 [J]. 高压物理学报, 2007, 21: 145
45	Zhang F G, Hu X M, Wang P, et al. Numerical analysis of spall response in aluminum with helium bubbles [J]. Expl. Shock Waves, 2017, 37: 699
	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: 699
46	Kubota A, Reisman D B, Wolfer W G. Dynamic strength of metals in shock deformation [J]. Appl. Phys. Lett., 2006, 88: 241924
47	Wang H Y, Li X S, Zhu W J, et al. Atomistic modelling of the plastic deformation of helium bubbles and voids in aluminium under shock compression [J]. Radiat. Eff. Defects Solids, 2014, 169: 109
48	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]. Modell. Simul. Mater. Sci. Eng., 2014, 22: 025012
49	Zhou T T, He A M, Wang P, et al. Spall damage in single crystal Al with helium bubbles under decaying shock loading via molecular dynamics study [J]. Comput. Mater. Sci., 2019, 162: 255
50	Zhou T T, He A M, Wang P. Dynamic evolution of He bubble and its effects on void nucleation-growth and thermomechanical properties in the spallation of aluminum [J]. J. Nucl. Mater., 2020, 542: 152496
51	Zhou T T, Zhao F Q, Zhou H Q, et al. Atomistic simulation and continuum modeling of the dynamic tensile fracture and damage evolution of solid single crystalline al with He bubble [J]. Int. J. Mech. Sci., 2022, 234: 107681
52	Zope R R, Mishin Y. Interatomic potentials for atomistic simulations of the Ti-Al system [J]. Phys. Rev., 2003, 68B: 024102
53	Young D A, McMahan A K, Ross M. Equation of state and melting curve of helium to very high pressure [J]. Phys. Rev., 1981, 24B: 5119
54	Plimpton S. Fast parallel algorithms for short-range molecular dynamics [J]. J. Comput. Phys., 1995, 117: 1
55	Stukowski A. Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool [J]. Modell. Simul. Mater. Sci. Eng., 2010, 18: 015012
56	Reif F. Fundamentals of Statistical and Thermal Physics [M]. New York: McGraw-Hill, 1965: 1
57	Ibach H. Physics of Surfaces and Interfaces [M]. Berlin: Springer, 2006: 1
58	Agranat M B, Anisimov S I, Ashitkov S I, et al. Strength properties of an aluminum melt at extremely high tension rates under the action of femtosecond laser pulses [J]. JETP Lett., 2010, 91: 471
59	Kuksin A, Norman G, Stegailov V, et al. Dynamic fracture kinetics, influence of temperature and microstructure in the atomistic model of aluminum [J]. Int. J. Fract., 2010, 162: 127
60	Ashitkov S I, Agranat M B, Kanel G I, et al. Behavior of aluminum near an ultimate theoretical strength in experiments with femtosecond laser pulses [J]. JETP Lett., 2010, 92: 516
61	Ashitkov S I, Komarov P S, Ovchinnikov A V, et al. Strength of liquid tin at extremely high strain rates under a femtosecond laser action [J]. JETP Lett., 2016, 103: 544
62	Kanel G I. Spall fracture: Methodological aspects, mechanisms and governing factors [J]. Int. J. Fract., 2010, 163: 173
63	Grady D E. Strain-rate dependence of the effective viscosity under steady-wave shock compression [J]. Appl. Phys. Lett., 1981, 38: 825
64	Chivapornthip P, Bohez E L J. Dependence of bulk viscosity of polypropylene on strain, strain rate, and melt temperature [J]. Polym. Eng. Sci., 2017, 57: 830

[1]

Download

[1]	BAI Zhiwen, DING Zhigang, ZHOU Ailong, HOU Huaiyu, LIU Wei, LIU Feng. Molecular Dynamics Simulation of Thermo-Kinetics of Tensile Deformation of α-Fe Single Crystal[J]. 金属学报, 2024, 60(6): 848-856.
[2]	MENG Zikai, MENG Zhichao, GAO Changyuan, GUO Hui, CHEN Hansen, CHEN Liutao, XU Dongsheng, YANG Rui. Molecular Dynamics Simulation of Creep Mechanism in Nanocrystalline α-Zirconium Under Various Conditions[J]. 金属学报, 2024, 60(5): 699-712.
[3]	REN Junqiang, SHAO Shan, WANG Qi, LU Xuefeng, XUE Hongtao, TANG Fuling. Molecular Dynamics Simulation of Tensile Mechanical Properties and Deformation Mechanism of Oxygen-Containing Nano-Polycrystalline α-Ti[J]. 金属学报, 2024, 60(2): 220-230.
[4]	CHEN Mingyi, HU Junwei, YU Yaochen, NIU Haiyang. Advances in Machine Learning Molecular Dynamics to Assist Materials Nucleation and Solidification Research[J]. 金属学报, 2024, 60(10): 1329-1344.
[5]	LIU Shi, HUANG Jiawei, WU Jing. Application of Machine Learning Force Fields for Modeling Ferroelectric Materials[J]. 金属学报, 2024, 60(10): 1312-1328.
[6]	LI Zhishang, ZHAO Long, ZONG Hongxiang, DING Xiangdong. Machine-Learning Force Fields for Metallic Materials: Phase Transformations and Deformations[J]. 金属学报, 2024, 60(10): 1388-1404.
[7]	WU Xinqiang, RONG Lijian, TAN Jibo, CHEN Shenghu, HU Xiaofeng, ZHANG Yangpeng, ZHANG Ziyu. Research Advance on Liquid Lead-Bismuth Eutectic Corrosion Resistant Si Enhanced Ferritic/Martensitic and Austenitic Stainless Steels[J]. 金属学报, 2023, 59(4): 502-512.
[8]	LI Haiyong, LI Saiyi. Effect of Temperature on Migration Behavior of <111> Symmetric Tilt Grain Boundaries in Pure Aluminum Based on Molecular Dynamics Simulations[J]. 金属学报, 2022, 58(2): 250-256.
[9]	LIANG Jinjie, GAO Ning, LI Yuhong. Interaction Between Interstitial Dislocation Loop and Micro-Crack in bcc Iron Investigated by Molecular Dynamics Method[J]. 金属学报, 2020, 56(9): 1286-1294.
[10]	LI Meilin, LI Saiyi. Motion Characteristics of <c+a> Edge Dislocation on the Second-Order Pyramidal Plane in Magnesium Simulated by Molecular Dynamics[J]. 金属学报, 2020, 56(5): 795-800.
[11]	LI Yuancai, JIANG Wugui, ZHOU Yu. Effect of Nanopores on Tensile Properties of Single Crystal/Polycrystalline Nickel Composites[J]. 金属学报, 2020, 56(5): 776-784.
[12]	LI Yuancai, JIANG Wugui, ZHOU Yu. Effect of Temperature on Mechanical Propertiesof Carbon Nanotubes-Reinforced Nickel Nano-Honeycombs[J]. 金属学报, 2020, 56(5): 785-794.
[13]	ZHOU Xia,LIU Xiaoxia. Mechanical Properties and Strengthening Mechanism of Graphene Nanoplatelets Reinforced Magnesium Matrix Composites[J]. 金属学报, 2020, 56(2): 240-248.
[14]	MA Xiaoqiang,YANG Kunjie,XU Yuqiong,DU Xiaochao,ZHOU Jianjun,XIAO Renzheng. Molecular Dynamics Simulation of DisplacementCascades in Nb[J]. 金属学报, 2020, 56(2): 249-256.
[15]	Junqin SHI,Kun SUN,Liang FANG,Shaofeng XU. Stress Relaxation and Elastic Recovery of Monocrystalline Cu Under Water Environment[J]. 金属学报, 2019, 55(8): 1034-1040.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed