动态载荷下铁相变的原子模拟研究进展

王昆; 肖时芳; 祝文军; 陈军; 胡望宇

doi:10.11858/gywlxb.20210729

动态载荷下铁相变的原子模拟研究进展

doi: 10.11858/gywlxb.20210729

王昆^1,,
肖时芳^2,*, ,,
祝文军³,
陈军⁴,
胡望宇^1,*, ,

1.
湖南大学材料科学与工程学院，湖南长沙　410082
2.
湖南大学物理与微电子科学学院，湖南长沙　410082
3.
中国工程物理研究院流体物理研究所冲击波物理与爆轰物理重点实验室，四川绵阳　621999
4.
北京应用物理与计算数学研究所，北京　100088

基金项目: 国家自然科学基金（51871094，51871095，51571088）；国家自然科学基金委员会-中国工程物理研究院NSAF联合基金（U1830138）；中央高校基本科研业务费

详细信息

作者简介:
王　昆（1987－），男，博士，副教授，主要从事金属高压力学行为的微介观机理分析与物理建模研究. E-mail：wangk@hnu.edu.cn

通讯作者:
肖时芳（1978－），男，博士，副教授，主要从事计算材料学研究. E-mail：shifangxiao@hnu.edu.cn

胡望宇（1965－），男，博士，教授，主要从事计算材料学研究. E-mail：wyuhu@hnu.edu.cn

中图分类号: O521.2
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出版历程
- 收稿日期: 2021-03-03
- 修回日期: 2021-04-16

Progress on Atomic Simulations of Phase Transition of Iron under Dynamic Loading

WANG Kun^1
,,
XIAO Shifang^{2,*
, ,},
ZHU Wenjun³,
CHEN Jun⁴,
HU Wangyu^{1,*
, ,}

1.
College of Materials Science and Engineering, Hunan University, Changsha 410082, Hunan, China
2.
School of Physics and Electronics, Hunan University, Changsha 410082, Hunan, China
3.
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621999, Sichuan, China
4.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

摘要

摘要: 铁的 $\alpha$ ↔ $\varepsilon$ 相变是金属高压相变研究领域的经典范例，随着测试技术的进步，其相变机制与动力学研究不断深入，基于激光加载的原位X射线观察结合非平衡分子动力学模拟研究是解决该问题最有效的手段之一。为此，综述了铁在动态载荷下塑性与相变的原子模拟研究进展，综合分析了铁的高压势函数，平面应变加载下晶体的各向异性、冲击强度、应变率、应变梯度、各种初始晶体缺陷等对铁相变机制的影响，以及铁的相变与层裂，同时报道了铁在非平面加载下响应规律研究的最新进展，最后进行了归纳总结和展望。
- 高压结构相变 /
- 塑性 /
- 层裂 /
- 分子动力学 /
- 原子间相互作用势 /
- 铁
Abstract: $\alpha$ ↔ $\varepsilon$ transformation of iron is a prototype of high-pressure phase transition in metals. With the progress of detecting technology, mechanism and dynamics of the phase transition have being investigated in depth. Laser-driven in situ X-ray observation combined with non-equilibrium molecular dynamics simulation is one of the most effective approach to the issue. In present paper, the progress of atomic investigations on plasticity and phase transformation of iron under dynamic loading is reviewed. The effects of high-pressure interatomic potential of iron, crystal anisotropy, impact strength, strain rate, strain gradient and various initial crystal defects on phase transformation mechanism, phase transformation and spalling of iron are analyzed. Meanwhile, the latest progress of our researches on nonplanar-loading responses of iron is reported. Finally, the conclusion and prospect are given.
- high-pressure structural transition /
- plasticity /
- spall /
- molecular dynamics /
- interatomic potential /
- iron

HTML全文

随着水下爆炸在国防工业领域中的应用日益广泛，研究范围也从自由场中单气泡运动延伸到复杂边界条件下的气泡运动。根据文献[1]中的实验结果，当边界大于气泡最大半径(R_max)的3倍以上时，边界影响将不明显。因此，本研究定义浅水中气泡运动的边界距离应当小于3倍气泡最大半径。当爆炸气泡在浅水中运动时，会同时受到自由面和水底壁面的作用而引起极其复杂的水面现象，气泡的运动特性与在自由场中或单一边界附近处爆炸相比会发生很大变化。在宏观尺度问题中，浅海海滩中爆炸可以产生向上高速喷射的水柱，军事上可以用来抵御贴水面飞行的物体的袭击，气泡坍塌形成的高速射流能够引起舰船结构的局部毁伤。在小尺度范围下，生物领域的激光诱导向前转移(LIFT)技术利用气泡射流将生物材料传递到接收板上。浅层水中爆炸由于受到自由液面和水底壁面的同时影响，产生了不同于无限水介质中爆炸的水面现象，可以说多界面大大增加了水下爆炸研究的困难程度。

对于气泡引起的流场脉动载荷以及射流载荷特性的相关研究较多。Plesset等^[2]早在1949年已对水中气泡运动进行了理论研究，提出的运动方程为众多气泡运动理论研究提供了参考。Klaseboer等^[3]研究了炸药爆炸气泡与垂直放置钢板的相互作用，其实验结果已经成为水中爆炸气泡动力学数值模拟的主要参考数据。Koukouvinis等^[4]用流体体积法模拟了加速度场中激光泡的膨胀和非球形坍塌，发现在坍塌过程中气泡底部某点较大的坍塌速度会导致动量的集中，进而引起局部坍塌。Liu等^[5]采用Front-Tracking法，模拟了固壁附近不同比例距离处的气泡运动，发现比例距离γ≤0.6时气泡完全贴附于壁面，气泡和壁面之间的水层消失，射流会引起壁面上压力的最高峰值，而气泡内部压强会引起第2个峰值。李帅等^[6]提出“气泡载荷分解法”，将气泡总载荷分解成脉动载荷和射流载荷两部分，并给出了相应的数值计算方法，计算结果与解析解高度吻合。郑监等^[7]提出气泡两次脉动引起的水面现象叠加是产生不同水冢的实质性机理，而气泡到自由液面的无量纲距离对水冢类型起着决定性作用。梁浩哲等^[8]用AUTODYN软件进行了计算，发现深水形成的射流速度约350 m/s，远大于浅水下的150 m/s，与刚性壁接触后射流头部的压力也大于浅水中的压力，说明深水环境下的射流更易对结构造成严重破坏。董琪等^[9]运用LS-DYNA对不同爆炸深度下的浅水爆炸进行数值模拟，分析了爆炸深度对浅水爆炸气泡半径和射流方向的影响。目前，关于无限水域水下爆炸气泡的研究成果非常丰富，而对多界面影响下的水下爆炸气泡的相关研究略显匮乏，浅水中气泡射流载荷造成结构破坏方面的研究也开展得比较少，有关射流冲击结构过程中的一些现象和破坏机理还没有比较深入的研究。

因为气泡在浅水中的运动主要受距离参数的影响，所以本研究改变气泡初始深度，利用电火花诱导气泡技术进行了一系列实验，并借助高速摄影设备对水下微爆炸过程进行了观察，收集了大量实验图片和数据。对气泡运动水面现象和射流载荷进行了研究，分析了自由面距离和壁面距离对浅水中气泡运动的影响。

1. 实验设计

1.1 实验平台

电火花诱导气泡原理^[1]是利用电流热效应，即通过电极燃烧产热、使水介质汽化生成气泡。电火花诱导气泡实验布置如图 1所示，本研究利用该平台进行了气泡与自由液面、水底壁面组合边界相互作用的实验。该平台包括MCH-K1205D型直流稳压电源、FASTCAM-SA1.1型高速摄像机、120 W的LED灯、电极(直径0.1 mm的细铜丝)和25 mm×25 mm×25 mm的正方形水箱。实验过程中高速摄像机设置为6000帧每秒、1024×1024像素，用于观测气泡运动以及水面现象。控制装置用于控制电火花的起爆和高速摄影的同步触发。

图 1 实验装置布置图

Figure 1. Layout of experimental equipment

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1.2 实验工况设计

气泡在自由液面或水底壁面附近运动时，会受到边界的影响而呈现非球状，在坍塌过程中气泡内部会产生射流，气泡运动过程相对于自由场也有所改变。因此，通过调整气泡与界面的距离来研究浅水中气泡运动的规律，第Ⅰ组实验令壁面距离γ_w不变，改变自由面距离γ_f来考察其影响；第Ⅱ组实验保持自由面距离γ_f不变，改变壁面距离γ_w来考察γ_w的影响。实验工况设计见表 1。

表 1 实验工况设计

Table 1. Experimental conditions

Group	Number	γ_f	γ_w
	1	0.63
Ⅰ	2	1.54	0.31
	3	2.26
	1		0.75

Ⅱ	2	0.38	1.88
	3		3.01

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| 显示表格

将特征压力选择为距离爆炸中心水平无穷远处静水压力p_∞，特征长度选择为在压力为p_∞的无黏、无旋、不可压缩自由场中球状膨胀气泡的最大半径R_max^[10]。由此引入距离参数 ${\gamma _{\rm{f}}} = d/{R_{{\rm{max}}}}$ 和 ${\gamma _{\rm{w}}} = (h - d)/{R_{{\rm{max}}}}$ ，分别为气泡到自由液面的无量纲距离γ_f和气泡到壁面的无量纲距离γ_w，其中h表示自由液面和水底固壁之间的距离，d表示气泡初始中心到自由液面的距离。本研究选取不同的无量纲距离参数，在电压为100 V时(在自由场中产生气泡最大半径为6 mm^[6])进行了实验研究，分析了不同无量纲距离下气泡运动形态和水射流发展过程。

2. 数值模型及有效性验证

本研究基于OpenFOAM软件包中的可压缩两相界面捕获求解器CompressibleInterFoam，利用流体体积方法(Volume of Fluid, VOF)求解，考虑了液体黏性、表面张力和流场中重力的存在，建立如图 2所示的轴对称模型，进行浅水中气泡运动的数值模拟，边界条件在表 2中列出，α、p、U和T分别为相分数、压强、速度和温度。

图 2 自由场中气泡脉动模型的边界条件^[11]

Figure 2. Boundary patches for CFD of single bubble pulsation in a free field^[11]

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表 2 自由场中气泡脉动模型的CFD边界条件

Table 2. Boundary conditions for CFD of single bubble pulsation in a free field

Boundary	α	p	U	T
Empty (left)	Empty	Empty	Empty	Empty
Advective (right & top)	Advective	Advective	Advective	Advective
Wedge (front & back)	Wedge	Wedge	Wedge	Wedge
Wall (bottom)	zeroGradient	fixedValue(0, 0, 0)	zeroGradient	zeroGradient

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| 显示表格

为了验证OpenFOAM计算水下爆炸气泡运动过程的有效性，把仿真结果与用经验公式计算的结果进行对比，分别对半径为0.2、0.3和0.4 cm的球形TNT炸药在水面下20 cm处起爆的过程进行模拟。模拟值与经验公式计算值的对比见表 3，由表 3可以看出，虽然仿真结果与经验值存在一定偏差，但是偏差在可接受范围内，可以用该模型模拟水下爆炸气泡运动过程。其中Ⅰ(1)工况和Ⅱ(1)工况特征时刻仿真结果如图 3和图 4所示。

表 3 气泡半径和周期的对比^[11]

Table 3. Comparation of the bubble radius and the period^[11]

Charge radius r/cm	Charge amount W/g	R_m/cm			T/ms
Charge radius r/cm	Charge amount W/g	Empirical	Simulation	Deviation/%	Empirical	Simulation	Deviation/%
0.2	0.055	6.0	6.3	6.18	11.5	11.2	-2.8
0.3	0.184	8.9	8.3	-6.6	17.2	14.6	-15.3
0.4	0.437	11.9	10.6	-10.1	23.0	18.5	-19.5

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| 显示表格

图 3 工况Ⅰ(1)气泡开始收缩和射流穿透气泡瞬间数值模拟结果

Figure 3. Instantaneous simulation results of bubble shrinking and penetrated by jet in condition Ⅰ(1)

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图 4 工况Ⅱ(1)气泡开始收缩和射流穿透气泡瞬间数值模拟结果

Figure 4. Instantaneous simulation results of bubble shrinking and penetrated by jet in condition Ⅱ(1)

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3. 实验结果及讨论

3.1 自由面距离γ_f对气泡运动及水面现象的影响

γ_f取值范围是0.63~2.26，选取3种典型的实验工况如图 5、图 6、图 7所示，分别对应表 1中的工况Ⅰ(1)、工况Ⅰ(2)、工况Ⅰ(3)。工况Ⅰ(1)放电产生的气泡实测最大半径约为5.3 mm。从图 5(c)t=1.0 ms时可以看出，此工况在气泡膨胀的初期，气泡上半部分保持为球形向外膨胀，气泡下半部分与壁面紧紧贴附，中间的水层变得非常薄，自由液面在气泡上部形成向上竖直喷射的细水柱。在气泡坍塌过程中(图 5(c)~图 5(f))，气泡下表面一直贴附于壁面，下表面收缩慢，上表面收缩快，气泡整体呈倒漏斗状。

图 5 自由液面与水底固壁之间气泡运动特性(γ_w=0.31，γ_f=0.63)^[12]

Figure 5. Characteristics of bubble motion between free surface and bottom wall (γ_w=0.31, γ_f=0.63)^[12]

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图 6 自由液面与水底固壁之间气泡运动特性(γ_w=0.31，γ_f=1.54)

Figure 6. Characteristics of bubble motion between free surface and bottom wall (γ_w=0.31, γ_f=1.54)

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图 7 自由液面与水底固壁之间气泡运动特性(γ_w=0.31，γ_f=2.26)

Figure 7. Characteristics of bubble motion between free surface and bottom wall (γ_w=0.31, γ_f=2.26)

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工况Ⅰ(2)放电产生的气泡实测最大半径约为6.5 mm。气泡膨胀现象与工况Ⅰ(1)类似。在t=1.0 ms时(图 6(c))，气泡膨胀到最大体积，自由面微微凸起。随后气泡保持半球状收缩至最小体积，气泡表面不再光滑，流场变得紊乱。在第2次气泡脉动过程中(图 6(d)~图 6(i))，液面上缓慢发展出水柱，由于水裙速度大于中心水柱速度，所以初始水冢呈现内凹形。后期水柱中心速度增大，中心高度追赶上水裙高度，粗壮水柱不断发展，最大高度约为69 mm(t=93.0 ms)。

工况Ⅰ(3)放电产生的气泡实测最大半径约为7.0 mm。气泡膨胀现象同工况Ⅰ(1)和Ⅰ(2)类似，但是液面在气泡膨胀过程中抬升不明显。气泡收缩过程中(图 7(b)、图 7(c))，气泡顶端液面仍然几乎保持不变。在第2次气泡脉动过程中(图 7(c)、图 7(d)、图 7(e))，气团向四周散开，自由面上缓慢发展出顶部较尖的丘形水冢，在t=41.0 ms时，水冢达到最大高度，约为16.3 mm。

在壁面距离γ_w保持为0.31时，不同的自由面距离γ_f可产生不同形态的水面现象。γ_f较小时，二次脉动形成的水裙未能追赶上初次水柱，形成细长、不稳定的喷射型水冢，二次水裙若能追赶上初次水柱，则会形成内凹型水冢；γ_f较大时，二次脉动的水裙与初次水柱融合，二者形状差距不大，则形成较稳定的丘型水冢。可以看出，气泡距离自由面越近，其受自由面的影响越大，水面现象越激烈。

3.2 壁面距离γ_w对气泡运动及水面现象的影响

γ_w介于0.75和3.01之间，3种典型的工况如图 8、图 9、图 10所示，分别对应工况Ⅱ(1)、工况Ⅱ(2)、工况Ⅱ(3)。工况Ⅱ(1)放电产生的气泡实测最大半径约为5.3 mm，从图中可以看出，在气泡膨胀的初期(图 8(c)，t=0.67 ms)，气泡贴近水底壁面呈圆柱状向外扩展，自由液面在气泡上部闭合后形成竖直向上喷射的细水柱。在气泡坍塌过程中(图 8(d)、图 8(e)、图 8(f))，靠近自由液面的部分收缩速度快，靠近水底固壁的部分收缩速度慢。工况Ⅱ(2)最大半径约为5.3 mm。在气泡产生的初期(图 9(a))，自由液面破碎后迅速闭合。气泡收缩过程中，自由液面的排斥作用和刚性壁面的吸引作用都很剧烈，气泡顶部变得扁平，底部呈尖角状，气泡内部形成向下的、较强的、冲向壁面的射流，如图 9(b)。气泡底部受到壁面吸引，贴近壁面发生坍塌过程(图 9(d)、图 9(e)、图 9(f))。在第2次气泡脉动过程中，自由面不断上升，发展出粗壮的水柱，最大高度约为74 mm。工况Ⅱ(3)放电产生的气泡实测最大半径约为5.3 mm，过程与工况Ⅱ(2)类似。

图 8 自由液面与水底固壁之间气泡运动特性(γ_f=0.38，γ_w=0.75)^[12]

Figure 8. Characteristics of bubble motion between free surface and bottom wall (γ_f=0.38, γ_w=0.75)^[12]

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图 9 自由液面与水底固壁之间气泡运动特性(γ_f=0.38，γ_w=1.88)

Figure 9. Characteristics of bubble motion between free surface and bottom wall (γ_f=0.38, γ_w=1.88)

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图 10 自由液面与水底固壁之间气泡运动特性(γ_f=0.38，γ_w=3.01)

Figure 10. Characteristics of bubble motion between free surface and bottom wall (γ_f=0.38, γ_w=3.01)

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可以发现，气泡形态演化受刚性壁面约束较大，水冢形态基本不受壁面影响。气泡越靠近刚性壁面，其形状越难保持为球形。壁面距离较小时，气泡会被壁面限制发展；随着壁面距离的增大，壁面和气泡之间存在水层，气泡在收缩过程中会受到壁面的吸引作用，底部呈现尖角状；壁面距离大于3倍气泡最大半径时，壁面对气泡的形态变化无明显影响。

现将无量纲的自由面距离γ_f和壁面距离γ_w对气泡和水冢形态的影响分类归纳成图 11的分布图。图 11横坐标轴为γ_f，随着γ_f的逐渐增大，水冢形态依次经历了破碎型、喷射型、皇冠型、内凹型和丘型；纵坐标为γ_w，随着γ_w的逐渐增大，水冢形态无明显变化。

图 11 水冢形态分布

Figure 11. Distribution of water mounds shape

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4. 距离参数对气泡动力学的影响

不同的距离参数下，壁面附近气泡的形态差异很大，指向壁面射流的速度大小、冲击压力等变化也很明显。为了研究自由面无量纲距离γ_f和壁面无量纲距离γ_w的影响，分别改变γ_f和γ_w以研究不同距离参数下气泡射流冲击载荷变化规律。在气泡与双重界面相互作用的过程中，水冢速度v_w是指水冢顶端的液体前进速度，射流速度v_j是指射流顶端的液体前进速度，壁面压力p是指在气泡射流载荷作用下壁面上受到的压力大小，三者关系如图 12所示。射流穿透气泡瞬间，气泡正下方壁面压力较大，壁面上的压力沿径向迅速减小，图 13给出了压力剖面的示意图，取气泡正下方压力较大的部分，其宽度为射流载荷作用的有效宽度w。当气泡与壁面距离较近时，将产生接触射流^[13]，即射流直接作用于壁面而不是有一定缓冲作用的水层，如图 14所示，当距离参数较大时，则发生非接触射流。

图 12 气泡运动模型图

Figure 12. Bubble motion model diagram

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图 13 壁面压力沿气泡径向分布图

Figure 13. Distribution diagram of pressure on the wall along the bubble radius

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图 14 “接触射流”与“非接触射流”示意图

Figure 14. Schematic diagram of "contact jet" and "non-contact jet"

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4.1 水冢顶端速度v_w分析

根据实验图像，提取不同时刻水冢顶点高度，进而得到水冢顶点速度v_w随时间的变化。图 15为第I组实验v_w-t曲线。因为不同自由面距离γ_f导致了不同的水冢类型，所以v_w变化趋势相差比较大。对比3个工况可以看出，工况Ⅰ(1)(γ_w=0.31)水冢最大速度为15.9 m/s，水冢形成时间约为5.7 ms；工况Ⅰ(2)(γ_w=1.54)水冢形成时间约为20 ms，水裙吞没水冢后在顶端封闭，流体冲击使顶端产生微射流^[1]，所以图 15(b)中会有急剧凸起的尖端，最大速度约为5.7 m/s；工况Ⅰ(3)(γ_w=0.31)最大速度为0.78 m/s，在38.3 ms时水冢形态比较稳定。可见，气泡距离自由面越远，水面运动越缓和，水冢速度越小，形成水冢稳定形态的时间越长。

图 15 水冢速度v_w-时间曲线(γ_w=0.31)

Figure 15. Variation of the velocity at the top of the dome with time (γ_w=0.31)

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图 16为第Ⅱ组实验水冢顶点速度v_w随时间的变化曲线。从图 16可以看出，在气泡坍塌阶段，水冢开始减速上升。随后气泡顶端和水冢之间形成高压区^[8]，使水冢速度也重新上升，在射流穿透气泡瞬间，水冢顶端速度达到第2个极值。与γ_w=0.91工况相比，γ_w=1.82的工况中水冢上升速度更高，壁面使水冢顶端最大速度增加了约9.9%。这是因为中远壁面距离时，壁面对气泡发展过程的阻碍作用变小，使水冢运动速度和剧烈程显著增加。

图 16 水冢速度v_w-时间曲线(γ_f=0.91，γ_w=0、0.91和1.82)

Figure 16. Variation of the velocity at the top of the dome with time (γ_f=0.91;γ_w=0, 0.91 and 1.82)

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4.2 距离参数对射流速度v_j的影响

用OpenFOAM软件进行仿真，选取γ_w=0.31、0.63和0.91时的3组实验，提取每个工况中射流速度v_j的最大值，图 17为射流速度v_j随距离参数的变化曲线，其中符号为仿真值，实线为拟合曲线。从图 17可以看出，在γ_w=0.31、0.63和0.91时的3组数据中，v_j随着γ_f的增加而减少。倪宝玉^[13]指出，当γ_w < 0.6时，v_j随γ_w减小而增大；当γ_w>0.6时，v_j随γ_w增大而增大。在图 17中，γ_w=0.63时的速度曲线位于γ_w=0.31和γ_w=0.91的下方，说明γ_w=0.63的工况v_j更小，这与文献[13]所得结论一致。对于壁面冲击压力而言，接触射流的毁伤性更大，此外，非接触射流速度不可能随着距离参数的增加而无限增大。当距离参数更大后(大约γ_w>3^[13])，气泡将不会形成指向壁面的射流，气泡的运动与自由场中气泡运动类似。

图 17 气泡射流速度v_j随距离参数的变化

Figure 17. The curve of bubble jet velocity with distance parameter

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4.3 距离参数对壁面压力的影响

用OpenFOAM进行仿真，当γ_w=0.31时，γ_f从0.62变化到1.69，提取各工况射流穿透气泡瞬间壁面压力分布进行对比，如图 18所示。可以看出，随着γ_f的增加，射流穿透瞬间壁面中心(x=0 mm)处的压力逐渐减小。其主要原因是：γ_f越小，自由液面对气泡的击退效应越显著，射流穿透气泡瞬间，气泡内部形成的射流越完整，使壁面中心压力越大；γ_f >1.2，γ_f过大时，气泡内部射流微弱，以致壁面中心压力变化不明显。当γ_f=0.91时，γ_w从0.15变化到1.82，提取各工况射流穿透瞬间壁面压力分布进行对比，如图 19所示。

图 18 壁面压力p随自由面距离γ_f的变化

Figure 18. Variation of wall pressure with free surface distance parameter

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图 19 壁面压力p随壁面距离γ_w的变化

Figure 19. Variation of wall pressure with wall distance parameter

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随着γ_w的增大，壁面中心(x=0 mm)处的压力逐渐降低。这是因为γ_w较小时，气泡产生了“接触射流”，如图 12所示，射流穿透气泡瞬间直接作用于壁面，而不是作用在有一定缓冲作用的水层上，导致气泡距离壁面越近，射流压力越大。根据图 20和图 21，压力有效宽度w随着γ_f和γ_w的增加而增加。虽然γ_f和γ_w较大时，射流冲击壁面的有效宽度有所增加，但是射流作用在壁面上的压力幅值下降明显，射流对壁面的作用由局部小区域的较强作用转变为较大区域的较弱作用。

图 20 压力有效宽度随自由面距离γ_f的变化

Figure 20. Curve of pressure width with free surface distance parameter

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图 21 压力有效宽度随壁面距离γ_w的变化

Figure 21. Curve of pressure width with wall distance parameter

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5. 结论

利用电火花诱导气泡技术对浅水中不同距离参数下的气泡运动进行了实验，同时考虑了自由液面和水底壁面的影响，总结了距离参数对水面现象的影响；同时，结合OpenFOAM软件，对应实验工况建立了仿真模型，研究了距离参数对射流载荷的影响。

(1) 不同的自由面距离可产生不同形态的水面现象，水冢形态受自由面的影响比较大；壁面距离对水冢形态影响不明显，但是对气泡运动形态影响大。

(2) 自由面无量纲距离范围为0 < γ_f < 3时，气泡射流速度随着γ_f的增加而减少。壁面距离γ_w对射流速度的影响分为两段：当0 < γ_w < 0.6时，气泡射流速度随着γ_w减小而增大；当0 < γ_w < 2时，气泡射流速度随着γ_w增大而增大。这是因为0 < γ_w < 0.6时，气泡坍塌时内部产生“接触射流”，导致气泡距离壁面越近，射流的速度越大。对于中远距离壁面附近的气泡，壁面的存在会阻碍气泡的完全发展，从而也会阻碍射流的充分发展，所以射流速度随着壁面距离的增大而增大。

(3) 射流穿透瞬间，随着自由面无量纲距离的增加(0 < γ_f < 2)，自由面对气泡的排斥作用逐渐减弱，Bjerknes力也变小，导致壁面中心处的压力逐渐减小；随着壁面距离的增大(0 < γ_w < 2)，同样地，壁面Bjerknes力越来越小，使壁面中心处的压力也逐渐降低。此外，在0 < γ_f < 2和0 < γ_w < 2时，壁面压力随距离增大而减小，但有效宽度与距离呈正相关，因此需综合考虑压力大小和有效宽度两个因素来确定射流载荷对壁面的破坏效果。

图 1 铁的高压相图^[17]

Figure 1. High-pressure phase diagram of iron^[17]

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图 2 单晶铁沿[001]晶向冲击的相变机制^[27]

Figure 2. Phase transition mechanism of single crystalline iron under the shock along [001] direction^[27]

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图 3 (a) MAEAM势预测的物态方程与实验及第一原理计算结果的对比，(b) 采用MAEAM势与改进的Ackland势的计算结果对比^{[49, 52-54]}

Figure 3. (a) Comparison of equations of states predicted by MAEAM potential with experiments and the first-principle calculations, (b) Comparison of the results between MAEAM potential and modified Ackland potential^{[49, 52-54]}

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图 4 MAEAM势(a)和改进Ackland势(b)预测的简并<111>/2螺位错芯结构^[21]

Figure 4. Degenerate core structure of <111>/2 screw dislocations predicted by (a) MAEAM and (b) modified Ackland potential^[21]

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图 5 弹性压缩和相变的截面轮廓(a)，模拟的未冲击样品(b)和相变后样品(c)的实验衍射图样^[36]

Figure 5. Line profile from elastically compressed and phase changed sections of samples (a), and the simulated diffraction patterns in an experimental geometry: (b) unshocked and (c) phase-changed sample^[36]

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图 6 实现高应变率加卸载的3种方法：(a)活塞加载，(b)对称撞击，(c)均匀单轴压缩（“M”表示材料，箭头表示活塞或材料的运动方向，灰色梯度表示材料受到碰撞时形成的冲击波）

Figure 6. Three simulation approaches of de-/compression under high strain rates: (a) piston loadings, (b) symmetric impingements and (c) uniform uniaxial compressions, where “M” represents materials and the arrows show the motion directions of the piston and materials, and shock waves initiated around the impinging moment are illustrated by the grayscale

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图 7 单晶铁的冲击雨贡纽关系^[34]

Figure 7. Shock Hugoniot relation of single crystalline iron^[34]

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图 8 (a)不同冲击晶向与冲击强度下单晶铁的相变（红色、黄色、浅蓝色和深蓝色分别表示hcp原子、fcc原子、bcc原子和缺陷原子），(b)冲击晶向与惯习面的关系^[34]

Figure 8. (a) Phase transition of single crystalline iron under different shock directions and shock strength (The meaning of the colors is: red (hcp atoms), yellow (fcc atoms), light blue (bcc atoms) and dark blue (defects).); (b) relationship between the shock direction and habit plane^[34]

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图 9 铁的相变压力阈值随加载应变率的变化^[61]

Figure 9. Transition pressure of iron as a function of uniaxial strain rate^[61]

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图 10 冲击下铁相变的微结构演化：(a)～(e)显示相变机制，(f)～(g)显示新相生长^[63]

Figure 10. Microstructure evolutions during the process of shock-induced phase transition of iron: (a)–(e) phase transition mechanism, (f)–(g) growth of the new phase^[63]

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图 11 在应变率为1.25 × 10⁹ s^–1的单轴均匀压缩下hcp相的形核与生长^[65]

Figure 11. Nucleation and growth of hcp phase under unform uniaxial compressions with a strain rate of 1.25 × 10⁹ s^–1^[65]

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图 12 （a）斜波加载下临界失稳应变与应变梯度的依赖关系；（b） $\widetilde {{{B}}}$ 的最小本征值（C_min）随单轴应变的变化；（c）～（d）分别以 ${\widetilde {T}}_{\rm{min}}^{1}$ 和 ${\widetilde {T}}_{\rm{min}}^{3}$ 表示的应变-应变梯度空间中的等高图（ ${\widetilde {T}}_{\rm{min}}^{1}$ 和 ${\widetilde {T}}_{\rm{min}}^{3}$ 分别为 $\widetilde {{T}}$ 沿x和z方向分量的最小本征值，图中所有的A对应于相同的应变）^[62]

Figure 12. (a) Critical instability strain versus strain gradient under ramp compressions; (b) minimumeigenvalue of $\widetilde {{{B}}}$ versus uniaxial strain; (c) and (d) are the contour plot ${\widetilde {T}}_{\rm{min}}^{1}$ and ${\widetilde {T}}_{\rm{min}}^{3}$ in the strain vs. strain gradient space, where ${\widetilde {T}}_{\rm{min}}^{1}$ and ${\widetilde {T}}_{\rm{min}}^{3}$ are the minimum eigenvalue of the x- and z-component of $\widetilde {{T}}$ (In the figures, “A” corresponds to the same strain.)^[62]

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图 13 相变形核时间与过压程度（ $\Delta p$ ）的关系：(a)有纳米孔洞存在时MD模拟结果^[68]，（b）实验结果^[69]

Figure 13. Nucleation time of phase transition versus overpressurization observed in (a) MD simulations at presence of a nonvoid^[68] and (b) experiments^[69]

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图 14 相变在纳米孔洞附近的形核（红色表示hcp原子，黄色表示bcc原子，其他颜色为非晶原子）^[71]

Figure 14. Nucleation of phase transition around a nonvoid, where red denotes hcp atoms, yellow denotes bcc atoms and the other color denotes amorphous atoms^[71]

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图 15 在0.7 km/s的冲击速度下加载15 ps时多晶铁样品的局部结构（图中仅显示缺陷原子，颜色代表原子离观察者的距离）^[73]

Figure 15. Local structure of polycrystalline iron at 15 ps under the shock with a impacting velocity of 0.7 km/s, where only defect atoms are shown (The color represents the distance from the observer.)^[73]

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图 16 含有孪晶的双晶铁样品在最大粒子速度为0.4 km/s的斜波压缩下31 ps时的局部构型（红色表示hcp原子，蓝色表示bcc原子，右图hcp晶胞中黄色的原子面对应于左图中黄色方框标记的原子面）^[74]

Figure 16. Local configuration of bicrystal iron sample containing a twin at 31 ps under ramp compressions with a maximum particle velocity of 0.4 km/s (Red denotes hcp atom and blue denotes bcc atom. The right figure shows a unit cell of hcp phase, where the yellow atomic face corresponds to the atomic face marked with yellow square in the left figure.)^[74]

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图 17 在0.5 km/s的粒子速度下 $\varSigma3$ 扭转晶界(a)与 $\varSigma3$ 倾斜晶界(b)的冲击塑性与相变（冲击波沿z方向传播，在两种样品中分别对应于<110>和<111>晶向）^[75]

Figure 17. Shock-induced plasticity and phase transition of $\varSigma3$ twist grain boundary (a) and $\varSigma3$ tilt grain boundary (b) under the shock with a particle velocity of 0.5 km/s, where shock wave propagates along z direction, corresponding to <110> and <111> crystallographic direction, respectively^[75]

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图 18 受塑性控制的相变（bcc→hcp）过程示意图（红色与蓝色原子分别位于相邻的两个原子面上）^[76]

Figure 18. Schematic diagram showing the plasticity-controlled bcc→hcp phase transition, where the red and yellow atoms locate in two adjacent atom planes^[76]

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图 19 采用Machová势(a)和改进的Ackland势(b)得到的多晶铁层裂的MD模拟结果^[4]

Figure 19. Spallation of polycrystalline iron by MD simulations using (a) Machová potential and (b) modified Ackland potential^[4]

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图 20 激光冲击实验回收的铁样品：(a)样品初始温度293 K，层裂面处的最高加载状态处于 $\alpha$ → $\varepsilon$ 相变边界上；(b) 样品初始温度673 K，层裂面处的最高加载状态处于两相共存区^[81]

Figure 20. Iron samples recovered after laser shocks (a) at 293 K, where the maximum loading state of the spall plane is on the $\alpha$ → $\varepsilon$ phase transition boundary, and (b) at 673 K, where the maximum loading state of the spall plane locates at the two-phase-coexistence region^[81]

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图 21 柱面内爆(a)和外爆(b)冲击加载示意图（蓝色表示试样，紫色圆环表示柱形势能面，红色箭头表示加载方向）

Figure 21. Schematic diagram of the shock loading by cylindrical (a) implosion and (b) explosion (The blue part represents the sample, the purple ring represents the energy surface of the column, and the red arrow represents the loading direction.)

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图 22 （a）柱面轴沿单晶Fe [001]晶向在内爆冲击下垂直于柱面轴的横截面内的原子速率分布，（b）10 ps时垂直柱面轴横截面内的局域温度分布

Figure 22. (a) Atom velocity distribution in the cross section perpendicular to the cylindrical axis under implosion impact along [001] direction of Fe single crystal, and (b) the local temperature distribution in the cross section perpendicular to the cylindrical axis at 10 ps

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图 23 柱面轴沿单晶Fe [001]晶向在内爆冲击下（v_p = 0.6 km/s）局域微结构随时间的演变（红色表示hcp结构原子，绿色表示以层错形式出现的fcc结构原子，灰色表示位错线周围的其他结构类型的原子，为清晰起见，未相变的bcc结构原子已被删除）

Figure 23. Evolutions of local microstructures with time under the implosive impacting with the cylindrical axis along [001] direction of Fe single crystal (v_p = 0.6 km/s) (Red indicates hcp atoms, green indicates fcc atoms in the forms of stacking faults, and gray indicates other atoms distributed around dislocation lines. For clarity, bcc atoms without phase transition have been removed.)

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图 24 柱面外爆冲击后试样内局域微结构、速度波剖面、应力波剖面和温度分布

Figure 24. Local microstructure, velocity profile, stress profile and temperature distribution in the sample after cylindrical explosions

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图 25 柱面外爆冲击后试样内部的局域微结构(a)以及hcp相变变体c轴取向极图(b)

Figure 25. Local microstructure inside the sample (a) and polar figure of the c-axis showing different hcp variants (b)

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表 1 改进的Ackland势参数^[36]

Table 1. Parameters of modified Ackland potential^[36]

a₁	a₂	a₃	a₄	a₅	a₆	A₁	A₂
−31.807065	36.158663	12.237970	−72.863506	156.864024	200.148093	72.868383	−100.944857

r₁	r₂	r₃	r₄	r₅	r₆	R₁	R₂
1.450000	1.430000	1.080000	0.990000	0.930000	0.866025	1.300000	1.200000

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表 2 MAEAM势参数^[34]

Table 2. Parameters of MAEAM potential^[34]

m	n	F₀	g₀	$\alpha$	$\;\beta$	$\gamma$
55.847	0.289	2.1952807	1	9.17×10⁻³	4.15	5.01

$\;\rho$ _e	P_e	k₀	k₁	k₂	k₃	k_c
10.875221	10.443309	−3.6918979	−0.3369724	−0.4937837	−0.3210981	0.3

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表 3 改进的Ackland势与MAEAM势预测的铁主要物理性质与有关第一原理计算及实验结果的对比

Table 3. Comparisons of key properties of iron predicted using modified Ackland potential and MAEAM potential with the first-principle-base calculations or experimental results

Method	Basic properties
Method	a₀/Å	$E{\rm{_c}}$ /eV	$E{ \rm{^{f,1}_{1v} }}$ /eV	$E{ \rm{^{f,2}_{1v} }}$ /eV	${\gamma }{_{\rm{unf} }^{110}}$ /(J·m⁻²)	${\gamma }{_{\rm{unf} }^{112}}$ /(J·m⁻²)
Modified-Ackland	2.866	4.316	1.89	1.83	0.669	0.769
MAEAM	2.8606	4.28	2.09	1.86	0.652	0.710
Ref.	2.8606^[41] 2.88^[42] 2.86^[43]	4.28^[44]	2.07^[42] 1.95^[43]	2.0^[37]	0.47 (GGA)^[45] 0.59 (LDA)^[45]

Method	Basic properties		Elastic			Vibrational
Method	$\Delta$ E_fcc-bcc/eV	$\Delta$ E_hcp-bcc/eV	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	${\nu }{_{N}^{ {\rm{T} }1}}$ /THz
Modified-Ackland	0.135	0.191	243.7	145.3	116.3	10.83
MAEAM	0.034	0.016	243	138	127	9.39
Ref.			243.1^[46] 243.0^[47]	138.1^[46] 138.0^[47]	121.9^[46] 127.0^[47]	9.26^[48]

Method	Vibrational				Others
Method	${\nu }{_{N}^{ {\rm{T} }2} }$ /THz	${\nu }{_{N}^{\rm{L} }}$ /THz	${\nu }{_{H}}$ /THz	${\nu }{_{P}}$ /THz	$p{_T}$ /GPa	$T{\rm{_m}}$ /K
Modified-Ackland	5.99	3.85	9.77	8.61	13.75
MAEAM	5.93	2.86	9.18	7.16	11	1807
Ref.	6.46^[48]	4.47^[48]	8.49^[48]	7.19^[48]	10^[49] 10.5^[50]	1813^[51]

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