延性金属层裂自由面速度曲线特征多尺度模拟研究

王云天; 曾祥国; 陈华燕; 杨鑫; 王放; 祁忠鹏

doi:10.11883/bzycj-2020-0467

延性金属层裂自由面速度曲线特征多尺度模拟研究

doi: 10.11883/bzycj-2020-0467

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（Hxo2020-74）

详细信息

作者简介:
王云天（1989－　），男，博士研究生，iswangyt@163.com

通讯作者:
曾祥国（1960－　），男，博士，教授，博士生导师，xiangguozeng@scu.edu.cn

中图分类号: O382.3
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- 被引次数: 0
出版历程
- 收稿日期: 2020-12-23
- 修回日期: 2021-02-07
- 网络出版日期: 2021-07-28
- 刊出日期: 2021-08-05

Multi-scale simulation study on characteristics of free surface velocity curve in ductile metal spallation

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: 以延性金属钽为研究对象，对钽在平板撞击下的层裂行为进行了多尺度下的数值模拟研究，从微观视角对自由面速度曲线上的典型特征进行了新的解读。在宏观尺度，对比分析了光滑粒子流体动力学法（smootfied particle hydrodynamics, SPH）与Lagrange网格法以及几种本构模型的模拟结果及其适用性。通过与实验数据的对比表明，Steinberg-Cochran-Guinan本构模型在层裂模拟中与实验数据吻合较好，通过改变加载条件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自由面速度曲线中的典型特征。在微观尺度，采用分子动力学方法获得层裂区域内损伤演化情况，揭示了宏观尺度自由面速度曲线典型特征所蕴含的物理内涵。分析表明，层裂表现为材料内部微孔洞形核、长大和聚集的损伤演化过程，自由面速度曲线上的典型特征与层裂区域的损伤演化过程存在密切关联。Pullback信号是层裂区域内微孔洞形核的宏观表征；自由面速度曲线的下降幅值在一定程度上反映了微孔洞的形核条件，由此计算得到的层裂强度实际上是微孔洞的形核强度。此外，Pullback信号后的速度回跳速率反映了微损伤演化的速率。
- 平板撞击 /
- 延性金属 /
- 多尺度模拟 /
- 自由面速度曲线
Abstract: The spallation characteristics of ductile tantalum metal under planar plate impact was analyzed through a multi-scale perspective. And the typical characteristics of the free-surface velocity curve on the macro-scale were interpreted from the micro-scale to reveal the physical meanings corresponding to these typical characteristics. On the macro-scale, the spallation behaviors of the ductile tantalum metal under planar-plate impact were numerically simulated through the smooth particle hydrodynamics (SPH) and Lagrange methods, and the free-surface velocity curves of the tantalum during spallation were obtained. In addition, the free-surface velocity curves obtained by the Johnson-Cook model, Steinberg-Cochran-Guinan model and Zerilli-Armstrong model were compared in the numerical simulations. Comparison with the experimental data shows that the Steinberg-Cochran-Guinan constitutive model has a better performance in the macro-level simulation. The free-surface velocity curves at different strain rates were obtained by changing the loading conditions, and the typical characteristics of the free-surface velocity curves at different strain rates were discussed. Results show that there is an exponential relationship between spall strength and strain rate, and the spall strength obtained from the simulation has a good agreement with the experimental data. On the micro-scale, the damage evolution in the spallation region was obtained by molecular dynamics simulation conducted in the LAMMPS software, and the loading strain rate was consistent with that on the macro-scale. The micro-scale simulation reveals the physical connotation of the typical characteristics of the macro-scale free-surface velocity curve. Micro-scale analysis shows that spallation is the response of damage evolution of nucleation, growth, and aggregation of voids. From the multi-scale perspective analysis, the typical characteristics on the free-surface velocity curve are closely related to the damage evolution in the spallation area: the pullback signal is a macroscopic response of the void nucleation in the spall area; the decline amplitude of the free-surface velocity curve reflects the void nucleation condition, and the spall strength reflects the nucleation strength of the voids. What’s more, the velocity rises to the first peak beyond the minima after the pullback signal reflects the rate of damage evolution. The multi-scale perspective analysis is helpful to fully understand the physical mechanism of the spallation under planar-plate impact.
- planar plate impact /
- ductile metal /
- multi-scale simulation /
- free surface velocity curve

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图 1 平板撞击实验原理及自由面速度曲线示意图

Figure 1. The principle of the flat plate impact experiment and a schematic diagram of a typical free-surface velocity curve

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图 2 多尺度模拟模型示意图

Figure 2. Configurations of the multi-scale simulation models

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图 3 不同模型的自由面速度曲线与实验数据^[25]对比

Figure 3. Comparison of free-surface velocity profiles by different models with experiment data^[25]

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图 4 宏观尺度下不同拉伸应变率自由面速度曲线

Figure 4. Free surface velocity under various tensile strain rates at macro-scale

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图 5 层裂强度与拉伸应变率关系

Figure 5. Relationship between spall strength and tensile strain rate

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图 6 对数坐标下层裂强度与拉伸应变率的关系

Figure 6. Relationship between spall strength and tensile strain rate in logarithmic coordinates

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图 7 Pullback信号及其对应的MD模型应力与空洞演化情况

Figure 7. Pullback signal and the stress and void volume evolution in the MD model

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图 8 Pullback信号持续时间Δt内空洞演化情况

Figure 8. Void evolution during Pullback signal duration Δt

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图 9 空洞体积演化与应力及空洞数量的关系

Figure 9. Relationship of the evolution of void volume with stress and void numbers

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图 10 阶段1的空洞数量演化情况

Figure 10. Void number evolution during stage 1

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图 11 阶段2与3的空洞长大与聚集情况

Figure 11. Void growing and coalescence during stage 2 and stage 3

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图 12 自由面速度回跳曲线

Figure 12. Free surface velocity curve from spall signal

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图 13 层裂强度与回跳速率的关系

Figure 13. Relationship between spalling strength and rebound rate

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图 14 不同拉伸应变率下自由面速度回跳速率

Figure 14. Free surface bounce rate under various tensile strain rates

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图 15 不同应变率下应力时程曲线

Figure 15. Histories of stress under different strain rates

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图 16 不同应变率下损伤演化情况

Figure 16. Damage evolution under different strain rates

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表 1 Mie-Grüneisen状态方程参数

Table 1. Parameters for Mie-Grüneisen equation of state

材料	ρ₀ /(kg·m⁻³)	c₀/(m·s⁻¹)	S₁	γ
Ta	16690	3340	1.20	1.67

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表 2 Johnson-Cook模型参数

Table 2. Parameters for the Johnson-Cook model

材料	A/MPa	B/MPa	n	C	m
Ta	142	164	0.31	0.057	0.88

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表 3 Zerilli-Armstrong模型参数

Table 3. Parameters for the Zerilli-Armstrong model

材料	C₀/MPa	k₁/（MPa·m^−3/2）	C₂/MPa	C₃/K⁻¹	C₄/K⁻¹	C₅/MPa	n
Ta	1125	10	178	5.35×10⁻³	0.327×10⁻³	310	0.44

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表 4 Steinberg-Cochran-Guinan模型参数

Table 4. Parameters for the Steinberg-Cochran-Guinan model

材料	G₀/GPa	Y₀/GPa	Y_max/GPa	β	n	$ {G}_{\rm{p}}^{'} $	$ {G}_{\rm{T}}^{'} $/（MPa ·K⁻¹）	T_m0/K
Ta	69	0.77	1.10	10	0.1	1.005	−8.97	4340

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表 5 用于验证的模型编号及参数设置

Table 5. Model number and parameter settings for validation

模型编号	飞片厚度/mm	样片厚度/mm	强度模型	方法
V-01	3	4.95	JC	Lagrange
V-02	3	4.95	JC	SPH
V-03	3	4.95	ZA	Lagrange
V-04	3	4.95	ZA	SPH
V-05	3	4.95	SCG	Lagrange
V-06	3	4.95	SCG	SPH

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表 6 不同应变率下平面撞击层裂模型参数与结果

Table 6. Parameters of planar plate impact simulations and results under various strain rates

模型编号	飞片厚度/mm	样片厚度/mm	加载速度/(m·s⁻¹)	p/GPa	$ {\dot{\varepsilon }}_{\rm{s}} $/s⁻¹	$ {\sigma }_{\rm{spall}} $/GPa	$ {\dot{\varepsilon }}_{\rm{r}} $/s⁻¹
S-01	2	4.95	306	8.84	5.40×10⁴	4.92	3.57×10⁴
S-02	2	4.95	250	7.05	4.69×10⁴	4.70	3.25×10⁴
S-03	3	4.95	410	12.25	3.92×10⁴	4.14	2.32×10⁴
S-04	3	4.95	306	8.84	3.28×10⁴	3.97	1.74×10⁴
S-05	3	4.95	210	6.19	2.68×10⁴	3.71	1.69×10⁴
S-06	4	4.95	306	8.84	2.31×10⁴	3.34	1.34×10⁴

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表 7 不同计算公式得到的层裂强度

Table 7. Spall strengths obtained by different formulas

模型编号	$ {\sigma }_{\rm{spall}} $/GPa	$ {\sigma }_{\rm{spall}}^{\left(1\right)} $/GPa	$ {\sigma }_{\rm{spall}}^{\left(2\right)} $/GPa
S-01	4.92	5.25	5.36
S-02	4.71	5.02	5.32
S-03	4.13	4.40	4.48
S-04	3.97	4.23	4.32
S-05	3.72	3.96	4.07
S-06	3.35	3.57	3.58

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