钽靶板在冲击下层裂过程的数值模拟

王云天; 曾祥国; 陈华燕; 杨鑫; 王放; 祁忠鹏

doi:10.11858/gywlxb.20200634

钽靶板在冲击下层裂过程的数值模拟

doi: 10.11858/gywlxb.20200634

王云天^1,,
曾祥国^1,*, ,,
陈华燕¹,
杨鑫²,
王放³,
祁忠鹏³

1.
四川大学建筑与环境学院深地科学与工程教育部重点实验室，四川成都　610065
2.
成都理工大学环境与土木工程学院地质灾害防治与地质环境保护国家重点实验室，四川成都　610059
3.
西南大学材料与能源学院，重庆　400715

基金项目: 北京应用物理与计算数学研究所计算物理重点实验室基金重点项目（Hxo2020-74）

详细信息

作者简介:
王云天（1989－），男，博士研究生，主要从事冲击动力学研究. E-mail：iswangyt@163.com

通讯作者:
曾祥国（1960－），男，博士，教授，主要从事冲击动力学研究. E-mail：xiangguozeng@scu.edu.cn

中图分类号: O382.3
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出版历程
- 收稿日期: 2020-11-06
- 修回日期: 2020-12-02

Numerical Simulation of Spalling Process of Tantalum Target under Impacts

1.
MOE Key Laboratory of Deep Earth Science and Engineering, College of Architecture and Environment, Sichuan University, Chengdu 610065, Sichuan, China
2.
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, Sichuan, China
3.
School of Materials and Energy, Southwest University, Chongqing 400715, China

摘要

摘要: 对平面冲击加载下延性金属钽的层裂行为开展了数值模拟研究。利用AUTODYN软件中的Lagrange与SPH求解模块，考察了3种本构模型Johnson-Cook、Steinberg-Cochran-Guinan与Zerilli-Armstrong的模拟结果，结合实验数据对模拟结果进行了验证；在此基础上，通过改变撞击速度与飞片厚度，获得了不同应变率下的自由面速度曲线，分析了不同应变率下的层裂特性。结果表明：在2.31×10⁴～5.40×10⁴ s⁻¹应变率范围内，SPH求解器结合Steinberg-Cochran-Guinan本构模型的结果与实验数据具有较好的一致性；金属钽的层裂强度随拉伸应变率的增加而增大，在对数坐标系下近似呈线性关系；不同层裂强度计算方法得到的结果差异可达8%；随着拉伸应变率的增加，自由面速度回跳速率随之增长。最后，对自由面速度曲线中的特征参量的物理意义进行了解读。
- 层裂 /
- 延性金属 /
- 平面碰撞 /
- 钽 /
- 自由面速度
Abstract: In this paper, the spallation characteristics of tantalum (Ta) under plate-impact loading are studied through numerical simulation. The feasibility and reliability of the Lagrange and smooth particle hydrodynamics (SPH) methods and several constitutive models (the Johnson-Cook, Steinberg-Cochran-Guinan and Zerilli-Armstrong model) are discussed. Comparison between the simulation results with experimental data, it is found that using the SPH method combined with the Steinberg-Cochran-Guinan constitutive model could produce the best consistency in the strain rate range from 2.31 × 10⁴s⁻¹ to 5.40 × 10⁴ s⁻¹ for Ta. In addition, by changing the impact velocity and the thickness of the flyer, the free surface velocity curves under different strain rates are obtained, and the spalling characteristics under different strain rates are calculated and discussed. Characteristic parameters of spallation are calculated by using the free surface velocity data. The results have shown that the spalling strength of Ta increases with the strain rate, and is approximately linear in the logarithmic coordinate. Several computation methods of spall strength are considered in this work, and the difference between the results obtained by different methods are within the range of 8%. On the other side of the spectrum, the bounce rate of the free surface velocity increases with increasing strain rate. Finally, the physical meaning of the characteristic parameters in the free surface velocity curve is also discussed.
- spallation /
- ductile metal /
- plate impact /
- tantalum /
- free surface velocity

HTML全文

图 1 平板撞击实验原理及自由面速度曲线示意图

Figure 1. Theoretical illustration of the flat plate impact test and the schematic diagram of the free surface velocity curves

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图 2 306 m/s撞击速度下平板撞击模型与模拟结果

Figure 2. Configuration of the plate impact simulations and simulation results at 306 m/s

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图 3 不同模型的自由面速度曲线与实验数据^[43]的对比（撞击速度306 m/s）

Figure 3. Comparison of free surface velocity profiles between different simulations andexperiment data^[43] (impact velocity 306 m/s)

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图 4 不同速度下SCG-SPH模型模拟结果与实验数据对比

Figure 4. Comparison of SCG-SPH model simulation results and experimental data with different velocities

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图 5 数值模拟得到的不同加载情况下的自由面速度曲线

Figure 5. Numerical simulation of free surface velocity profiles with different loading conditions

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图 6 层裂强度与拉伸应变率的关系

Figure 6. Relationship between spall strength and tensile strain rate

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图 7 对数坐标下层裂强度与拉伸应变率的关系

Figure 7. Relationship between spall strength andtensile strain rate in logarithmic coordinates

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图 8 层裂强度与回跳速率的关系

Figure 8. Relationship between spall strength and bounce rate

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图 9 不同冲击压力下Hugoniot弹性极限

Figure 9. Hugoniot elastic limit under different impact pressures

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图 10 自由面速度曲线第一个极小值之后的速度曲线

Figure 10. Free surface velocity profiles afterthe first minimal speed

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图 11 应变率对钽样品回跳速率的影响

Figure 11. Influence of strain rate on bounce rate of tantalum samples

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表 1 JC模型参数^[27]

Table 1. Parameters of Johnson-Cook model^[27]

Material	A/MPa	B/MPa	n	C	m
Tantalum	142	164	0.31	0.057	0.88

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表 2 ZA模型参数^[22]

Table 2. Parameters of Zerilli-Armstrong model^[22]

Material	C₁/MPa	k₁/(MPa·mm^1/2)	C₂/MPa	C₃/(10⁻³ K⁻¹)	C₄/(10⁻³ K⁻¹)	C₅/MPa	n
Tantalum	1 125	10	178	5.35	0.327	310	0.44

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表 3 SCG模型参数^[21]

Table 3. Parameters of Steinberg-Cochran-Guinan model^[21]

Material	G₀/MPa	Y₀/GPa	Y_max/GPa	β	n	$G{_p}^{'}$	$G{_T}^{'}/(\rm{MPa\text{·}K}{^{-1} } )$	$T {\rm{_m}}/\rm{K} $
Tantalum	69	0.77	1.10	10	0.1	1.005	−8.97	4 340

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表 4 Mie-Grüneisen状态方程参数^[31]

Table 4. Parameters of Mie-Grüneisen equation of state^[31]

Material	$\;\rho $₀/(kg·m⁻³)	C₀/(m·s⁻¹)	S₁	$\gamma $
Tantalum	16 690	3 340	1.20	1.67

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表 5 验证模型参数设置

Table 5. Parameter settings of simulation validation cases

No.	d_f/mm	d_s/mm	D_s/mm	v/(m·s⁻¹)	Model	Module
V-01	3.00	4.95	50.00	306	JC	Lagrange
V-02	3.00	4.95	50.00	306	JC	SPH
V-03	3.00	4.95	50.00	306	ZA	Lagrange
V-04	3.00	4.95	50.00	306	ZA	SPH
V-05	3.00	4.95	50.00	306	SCG	Lagrange
V-06	3.00	4.95	50.00	306	SCG	SPH

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表 6 层裂模型参数与结果

Table 6. Parameters of plate impact simulations and results

No.	d_f/mm	v/(m·s⁻¹)	p_s/GPa	$\dot{\varepsilon } $/(10⁴s⁻¹)	${\sigma}{_{\rm{ {spall} } } } $/GPa	u_max/(m·s⁻¹)	${\dot{\varepsilon } }{_{\rm{ {r} } }}$/(10⁴s⁻¹)
S-01	2.00	306	8.84	5.40	4.92	304.12	3.57
S-02	2.00	250	7.05	4.69	4.70	242.03	3.25
S-03	3.00	410	12.25	3.92	4.14	405.61	2.32
S-04	3.00	306	8.84	3.28	3.97	305.62	1.74
S-05	3.00	210	6.19	2.68	3.71	208.75	1.69
S-06	4.00	306	8.84	2.31	3.34	298.19	1.34

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表 7 不同计算层裂强度的公式得到的数据对比

Table 7. Comparison of data obtained by different formulas for calculating the fracture strength

No.	d_f/mm	d_s/mm	D_s/mm	v/(m·s⁻¹)	${\sigma }{_{\rm{ {spall} }}}$/GPa	${\sigma }{_{\rm{ {m1} } }}$/GPa	${\sigma }{_{\rm{ {m2} } }}$/GPa
S-01	2.00	4.95	50.00	306	4.92	5.25	5.36
S-02	2.00	4.95	50.00	250	4.71	5.02	5.32
S-03	3.00	4.95	50.00	410	4.13	4.40	4.48
S-04	3.00	4.95	50.00	306	3.97	4.23	4.32
S-05	3.00	4.95	50.00	210	3.72	3.96	4.07
S-06	4.00	4.95	50.00	306	3.35	3.57	3.58

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表 8 不同撞击速度下层裂片厚度

Table 8. Spall scab thickness at different impact velocities

No.	d_f/mm	d_s/mm	v/(m·s⁻¹)	d_sp/mm	$\delta $/%
S-01	2.00	4.95	306	1.96	2.0
S-02	2.00	4.95	250	1.92	4.0
S-03	3.00	4.95	410	3.05	2.7
S-04	3.00	4.95	306	2.89	3.4
S-05	3.00	4.95	210	2.92	2.7
S-06	4.00	4.95	306	3.91	2.3

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表 9 不同撞击速度下的Hugoniot弹性极限

Table 9. Hugoniot elastic limit at different impact velocities

No.	v/(m·s⁻¹)	p_s/GPa	$\sigma{_{\rm{HEL} }}$/GPa
S-01	306	8.84	1.96
S-02	250	7.05	1.89
S-03	410	12.25	2.09
S-04	306	8.84	1.95
S-05	210	6.19	1.77
S-06	306	8.84	1.95

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