斜波压缩下锡的相变动力学特性

种涛; 赵剑衡; 谭福利; 王桂吉

doi:10.11858/gywlxb.20190828

斜波压缩下锡的相变动力学特性

doi: 10.11858/gywlxb.20190828

中国工程物理研究院流体物理研究所，四川绵阳　621999

基金项目: 国家自然科学基金青年基金（11702276）；四川省青年科技创新研究团队专项计划项目（2016TD0022）

详细信息

作者简介:
种　涛（1986－），男，博士，主要从事动高压实验加载技术和材料动力学行为研究.E-mail: maoda318@163.com

通讯作者:
赵剑衡（1969－），男，博士，研究员，博士生导师，主要从事强激光破坏机理、爆轰物理、冲击动力学、超高速发射和超高压力加载技术研究. E-mail: jianh_zhao@sina.com

中图分类号: O521.2
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出版历程
- 收稿日期: 2019-08-28
- 修回日期: 2019-09-26

Dynamic Characteristics of Phase Transition of Tin under Ramp Wave Loading

Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, Sichuan, China

摘要

摘要: 利用磁驱动加载装置（CQ-4）和高精度速度测试装置（DPV），开展了斜波加载下锡的动态压缩实验。实验结果表明：锡在加载阶段经历了弹塑性转变和相变等物理过程，相变压力约为7.5 GPa。β–γ相变对应的特征速度随着锡厚度的增加，从676.3 m/s减小到636.8 m/s，对应的压力从7.62 GPa降低到7.11 GPa。结合Hayes多相状态方程和非平衡相变动力学模型，对锡的斜波压缩实验过程进行了模拟，数值计算结果可以较好地描述锡在加载阶段的弹塑性转变和相变等物理过程。讨论了体模量在不同热力学过程中的物理形式，计算结果显示，斜波压缩过程需考虑压力对体模量的修正。分析了相变弛豫时间、体模量等典型物理参数对速度波形的影响，结果表明，相变弛豫时间和各相初始自由能主要影响混合区部分速度波形，γ相的体模量参数只影响相变后的速度波形，β相的体模量参数会影响整体速度波形。
- 相变 /
- 多相状态方程 /
- 斜波加载 /
- 锡
Abstract: The dynamics of phase transition of tin under ramp wave loading was studied with experiment and simulation. The ramp wave compression experiment of tin was carried out with photonic Doppler velocimetry (PDV) and compact pulsed power generator CQ-4. The velocity wave profiles obtained experimentally show that tin undergoes physical processes such as elastoplastic transition and phase transition in the loading section, and the phase transition pressure is about 7.5 GPa. As the increase of thickness of tin, the characteristic velocity corresponding to the onset of phase transition decreased slightly from 676.3 m/s to 636.8 m/s, and the corresponding pressure was from 7.62 GPa to 7.11 GPa. The Hayes multi-phase equation of state and non-equilibrium phase transition kinetic model were employed to simulate the experimental process, and the numerical results can well describe the physical processes such as elastoplastic transformation and phase transformation in the loading section. The calculated results revealed that the correction of the bulk modulus with pressure needed to be considered under ramp wave compression. The influence of typical physical parameters, such as phase transition relaxation time and bulk modulus, on the velocity waveform was discussed. The results show that phase transition relaxation time and initial free energy mainly affect the velocity waveform in the mixing zone, the bulk modulus of the two phases affect the velocity waveform after phase transition and overall velocity waveform respectively.
- phase transition /
- multi-phase equation of state /
- ramp wave loading /
- tin

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图 1 磁驱动斜波实验负载区样品布局图

Figure 1. Schematic diagram of magnetically driven ramp wave loading and the samples

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图 2 Shot 714实验测量的自由面速度剖面

Figure 2. Experimental free surface velocities of shot 714

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图 3 实验加载压力（a）以及计算与实验速度波形（b）

Figure 3. The loading pressure(a) and the calculated and experimental velocities (b)

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图 4 计算和实验自由面速度对比

Figure 4. Comparison of measured free surface velocitywith calculated values

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图 5 0.7 μs时压力和γ相质量分数沿样品厚度方向分布

Figure 5. Pressure and mass fraction of γ phase along the thickness of the sample at 0.7 μs

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图 6 $\tau $对相变速度波形的影响

Figure 6. Influence of $\tau $ on velocity waveform

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图 7 Φ₀对相变速度波形的影响

Figure 7. Influence of Φ₀ on velocity waveform

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图 8 B_R_β对相变速度波形的影响

Figure 8. Influence of B_R_β on velocity waveform

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图 9 $B_{\scriptstyle{\rm{R}}\beta }'$对相变速度波形的影响

Figure 9. Influence of $B_{{\rm{R}}\beta }'$ on velocity waveform

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图 10 B_R_γ对相变速度波形的影响

Figure 10. Influence of B_R_γ on velocity waveform

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图 11 $B_{\scriptstyle{\rm{R}}\gamma }'$对相变速度波形的影响

Figure 11. Influence of $B_{{\rm{R}}\gamma }'$on velocity waveform

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表 1 实验条件

Table 1. Experimental condition

Exp. No.	Position	Material	Size/(mm × mm)
	Plate_top left	1100Al	8.0 × 1.006
	Sample_top left	Sn	$\varnothing $8.0 × 1.278
	Plate_top right	1100Al	8.0 × 1.006
Shot 696	Sample_top right	Sn	$\varnothing $8.0 × 1.568
	Plate_bottom left	1100Al	8.0 × 0.998
	Sample_bottom left	Sn	$\varnothing $8.0 × 1.871
	Plate_bottom right	1100Al	8.0 × 0.996

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表 2 速度波剖面上的特征值

Table 2. Characteristic values of the velocity profiles

Thickness of Sn/mm	u_EP/(m·s^–1)	u_PT/(m·s^–1)	p_PT/GPa
1.278	40.0	676.3	7.62
1.568	39.6	660.0	7.41
1.871	40.2	636.8	7.11

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表 3 锡的Helmholtz自由能计算参数^[34]

Table 3. Parameters for the Helmholtz free energy of tin^[34]

Phase	v_R/(cm³·g^–1)	T_R/K	p_R/GPa	$\varTheta ({v_{{\rm R}}})$/K	q₁	B_R/GPa	$B_{{\rm R}}'$	Φ₀/(J·kg^–1)	Γ/(J·kg^–1·K^–2)	α
β	0.137 2	298.15	0	180.91	1.60	58.0	2.8	0	0.015	1.0
γ	0.119 8	298.15	8.664	187.77	1.38	78.1	0.2	85.3 × 10³	0.015	1.0

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表 4 锡的Steinberg模型^[38]参数

Table 4. Parameters for the Steinberg model^[38] of tin

$\tau $/ns	$\Delta {\varepsilon ^v}$	Y₀/GPa	$\kappa $	${\varepsilon _{\rm{i}}}$	n	A/GPa^–1	C/K^–1
6.0	–0.018	0.2	2 000.0	0.0	0.06	8.66	2.12 × 10^–3

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