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Article(id=1325133176812741392, tenantId=1146029695717560320, journalId=1255847867265597444, issueId=1325132844594503961, articleNumber=null, orderNo=null, doi=10.11858/gywlxb.20230817, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1702828800000, receivedDateStr=2023-12-18, revisedDate=1704124800000, revisedDateStr=2024-01-02, acceptedDate=null, acceptedDateStr=null, onlineDate=1793865969135, onlineDateStr=2026-11-05, pubDate=1707062400000, pubDateStr=2024-02-05, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793865969135, onlineIssueDateStr=2026-11-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793865969135, creator=13701087609, updateTime=1793865969135, updator=13701087609, issue=Issue{id=1325132844594503961, tenantId=1146029695717560320, journalId=1255847867265597444, year='2024', volume='38', issue='1', pageStart='1', pageEnd='015202-10', issueExtLink='null', onlineDate='null', pubDate='1707062400000', pubDateStr='2024-02-05', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793865889929, creator='13701087609', updateTime=1793865889929, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=014103-1, endPage=014103-14, ext={EN=ArticleExt(id=1325133179362878225, articleId=1325133176812741392, tenantId=1146029695717560320, journalId=1255847867265597444, language=EN, title=Quantitative Determination of Impact Reaction Energy Release for HfZrTiTaNb Based High-Entropy Alloys, columnId=1256186032609965039, journalTitle=Chinese Journal of High Pressure Physics, columnName=Dynamic Response of Matter, runingTitle=null, highlight=null, articleAbstract=

As a new type of energetic material, high-entropy alloys will release a large amount of energy during high-speed impact, which has important application value. A two-stage light gas gun system was used to load the HfZrTiTaNb high-entropy alloys projectile under vacuum environment, and the impact experiment of bearing steel was carried out. The evolution process of response parameters such as flash radiation temperature, gas overpressure, flame propagation velocity and temperature rise of container wall was measured. The energy flow direction during the impact reaction of the high-entropy alloys projectile impacting the target plate was analyzed. The enthalpy of the mixed gas, the flash radiation energy, the absorption energy of the container wall, the enthalpy of the ejected gas and the deformation energy generated by the impact on the target during the impact reaction of the high-entropy alloys in a closed container were quantitatively calculated. The effects of different elements and their contents on the energy release of high-entropy alloys were obtained. The results showed that the energy released by the impact reaction of high-entropy alloys projectiles was mainly absorbed by the quasi-closed container wall. With the increase of Cu or Al content, the unit mass release energy of HfZrTiTaNb based high-entropy alloys increased. At similar impact velocities, the high-entropy alloys containing Cu released more energy per unit mass than the high-entropy alloys containing Al.

, authors=Zihan GUO, Chuang CHEN*, Yiliang TU, Enling TANG, authorsList=Zihan GUO, Chuang CHEN, Yiliang TU, Enling TANG, authorCompany=null, correspAuthors=Chuang CHEN, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright © 2024 Chinese Journal of High Pressure Physics. All rights reserved., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1325133204411261758, articleId=1325133176812741392, tenantId=1146029695717560320, journalId=1255847867265597444, language=CN, title=HfZrTiTaNb系高熵合金的冲击反应释能定量确定, columnId=1256186033331385334, journalTitle=高压物理学报, columnName=高压下物质的动态响应, runingTitle=null, highlight=null, articleAbstract=

作为一种新型含能材料，高熵合金在高速冲击过程中会释放大量能量，具有重要的应用价值。采用二级轻气炮系统加载真空环境下的HfZrTiTaNb系高熵合金弹丸，对轴承钢进行了冲击实验，测量了闪光辐射温度、气体超压、火焰传播速度和容器壁温升等响应参数的演化过程，分析了高熵合金弹丸撞击靶板过程中的能量流向，定量计算了高熵合金在密闭容器内冲击反应的混合气体焓、闪光辐射能、容器壁的吸收能、喷出气体焓以及撞击靶板产生的变形能，得到了不同元素及其含量对高熵合金释能量的影响。结果表明，高熵合金弹丸冲击反应释放的能量主要被准密闭容器壁吸收。随着Cu或Al含量的增加，HfZrTiTaNb系高熵合金的单位质量释能量增加。在相近的撞击速度下，含Cu高熵合金的单位质量释能量比含Al高熵合金大。

, authors=郭孜涵, 陈闯*, 涂益良, 唐恩凌, authorsList=郭孜涵, 陈闯, 涂益良, 唐恩凌, authorCompany=null, correspAuthors=陈闯, authorNote=

郭孜涵（2001－），女，硕士研究生，主要从事冲击动力学研究. E-mail：

, correspAuthorsNote=
陈　闯（1987－），男，博士，教授，主要从事爆炸与冲击动力学研究. E-mail：
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郭孜涵（2001－），女，硕士研究生，主要从事冲击动力学研究. E-mail：

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caption=Basic parameters of the experiment, figureFileSmall=null, figureFileBig=null, tableContent=
No.SpecimenSize/(mm×mm)Mass/gImpact velocity/(km·s−1)Density/(g·cm−3)
1HfZrTiTaNbCu0.2 $\varnothing $4.63×4.680.7861.359.98
2HfZrTiTaNbCu0.8 $\varnothing $4.96×4.690.9181.3010.13
3HfZrTiTaNbAl0.2 $\varnothing $4.95×4.830.8991.319.68
4HfZrTiTaNbAl0.8 $\varnothing $4.81×5.150.8531.579.12
5HfZrTiTaNbAl0.8 $\varnothing $4.76×5.110.8321.599.15
), ArticleFig(id=1325133249697162138, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=CN, label=表1, caption=

实验基本参数

, figureFileSmall=null, figureFileBig=null, tableContent=
No.SpecimenSize/(mm×mm)Mass/gImpact velocity/(km·s−1)Density/(g·cm−3)
1HfZrTiTaNbCu0.2 $\varnothing $4.63×4.680.7861.359.98
2HfZrTiTaNbCu0.8 $\varnothing $4.96×4.690.9181.3010.13
3HfZrTiTaNbAl0.2 $\varnothing $4.95×4.830.8991.319.68
4HfZrTiTaNbAl0.8 $\varnothing $4.81×5.150.8531.579.12
5HfZrTiTaNbAl0.8 $\varnothing $4.76×5.110.8321.599.15
), ArticleFig(id=1325133251655902107, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=EN, label=Table 2, caption=Calibration data for each channel of the transient fiber pyrometer, figureFileSmall=null, figureFileBig=null, tableContent=
ChannelWave length/nmImpedance/kΩVoltage/VNr/(μW·cm−2·nm−1)
1400102.934281.7
2500104.400235.5
360010.880347.1
470016.046280.7
), ArticleFig(id=1325133252138247068, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=CN, label=表2, caption=

瞬态光纤高温计各通道的标定数据

, figureFileSmall=null, figureFileBig=null, tableContent=
ChannelWave length/nmImpedance/kΩVoltage/VNr/(μW·cm−2·nm−1)
1400102.934281.7
2500104.400235.5
360010.880347.1
470016.046280.7
), ArticleFig(id=1325133252519928733, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=EN, label=Table 3, caption=Peak of overpressure and flash radiation temperature in the experiment, figureFileSmall=null, figureFileBig=null, tableContent=
No.SpecimenOverpressure/MPaTemperature/K
1HfZrTiTaNbCu0.20.221260
2HfZrTiTaNbCu0.80.241370
3HfZrTiTaNbAl0.20.211120
4HfZrTiTaNbAl0.80.201228
5HfZrTiTaNbAl0.80.201281
), ArticleFig(id=1325133252859667358, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=CN, label=表3, caption=

实验中的超压和闪光辐射温度峰值

, figureFileSmall=null, figureFileBig=null, tableContent=
No.SpecimenOverpressure/MPaTemperature/K
1HfZrTiTaNbCu0.20.221260
2HfZrTiTaNbCu0.80.241370
3HfZrTiTaNbAl0.20.211120
4HfZrTiTaNbAl0.80.201228
5HfZrTiTaNbAl0.80.201281
), ArticleFig(id=1325133253480424351, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=EN, label=Table 4, caption=Impact reaction energy release results, figureFileSmall=null, figureFileBig=null, tableContent=
No.SpecimenImpact velocity/(km·s−1)Mass/gEnergy release/kJEnergy release per unit mass/(kJ·g−1)
1HfZrTiTaNbCu0.21.350.7861.321.68
2HfZrTiTaNbCu0.81.300.9181.761.92
3HfZrTiTaNbAl0.21.310.8990.880.98
4HfZrTiTaNbAl0.81.570.8531.191.40
5HfZrTiTaNbAl0.81.590.8321.211.45
), ArticleFig(id=1325133254076015520, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=CN, label=表4, caption=

冲击反应释能结果

, figureFileSmall=null, figureFileBig=null, tableContent=
No.SpecimenImpact velocity/(km·s−1)Mass/gEnergy release/kJEnergy release per unit mass/(kJ·g−1)
1HfZrTiTaNbCu0.21.350.7861.321.68
2HfZrTiTaNbCu0.81.300.9181.761.92
3HfZrTiTaNbAl0.21.310.8990.880.98
4HfZrTiTaNbAl0.81.570.8531.191.40
5HfZrTiTaNbAl0.81.590.8321.211.45
), ArticleFig(id=1325133256110252962, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=EN, label=Table 5, caption=Atomic size difference of HfZrTiTaNb based high-entropy alloys, figureFileSmall=null, figureFileBig=null, tableContent=
xδ/%
HfZrTiTaNbCuxHfZrTiTaNbAlx
0.24.924.84
0.86.736.37
), ArticleFig(id=1325133256575820707, tenantId=1146029695717560320, journalId=1255847867265597444, articleId=1325133176812741392, language=CN, label=表5, caption=

HfZrTiTaNb系高熵合金的原子尺寸差

, figureFileSmall=null, figureFileBig=null, tableContent=
xδ/%
HfZrTiTaNbCuxHfZrTiTaNbAlx
0.24.924.84
0.86.736.37
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HfZrTiTaNb系高熵合金的冲击反应释能定量确定
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郭孜涵 , 陈闯 * , 涂益良 , 唐恩凌
高压物理学报 | 高压下物质的动态响应 2024,38(1): 014103-1-014103-14
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高压物理学报 |高压下物质的动态响应 2024 , 38 (1) : 014103-1 -014103-14
HfZrTiTaNb系高熵合金的冲击反应释能定量确定
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郭孜涵 , 陈闯* , 涂益良, 唐恩凌
作者信息
  • 沈阳理工大学辽宁省瞬态物理力学与能量转换材料重点实验室, 辽宁 沈阳　110159
通讯作者:
陈　闯（1987－），男，博士，教授，主要从事爆炸与冲击动力学研究. E-mail：
作者简介:

郭孜涵（2001－），女，硕士研究生，主要从事冲击动力学研究. E-mail：

Quantitative Determination of Impact Reaction Energy Release for HfZrTiTaNb Based High-Entropy Alloys
Zihan GUO , Chuang CHEN* , Yiliang TU, Enling TANG
Affiliations
  • Key Laboratory of Transient Physical Mechanics and Energy Conversion Materials of Liaoning Province, Shenyang Ligong University, Shenyang 110159, Liaoning, China
出版时间: 2024-02-05 doi: 10.11858/gywlxb.20230817
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摘要
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作为一种新型含能材料，高熵合金在高速冲击过程中会释放大量能量，具有重要的应用价值。采用二级轻气炮系统加载真空环境下的HfZrTiTaNb系高熵合金弹丸，对轴承钢进行了冲击实验，测量了闪光辐射温度、气体超压、火焰传播速度和容器壁温升等响应参数的演化过程，分析了高熵合金弹丸撞击靶板过程中的能量流向，定量计算了高熵合金在密闭容器内冲击反应的混合气体焓、闪光辐射能、容器壁的吸收能、喷出气体焓以及撞击靶板产生的变形能，得到了不同元素及其含量对高熵合金释能量的影响。结果表明，高熵合金弹丸冲击反应释放的能量主要被准密闭容器壁吸收。随着Cu或Al含量的增加，HfZrTiTaNb系高熵合金的单位质量释能量增加。在相近的撞击速度下，含Cu高熵合金的单位质量释能量比含Al高熵合金大。

高熵合金  /  冲击反应释能  /  能量分配  /  单位质量释能量

As a new type of energetic material, high-entropy alloys will release a large amount of energy during high-speed impact, which has important application value. A two-stage light gas gun system was used to load the HfZrTiTaNb high-entropy alloys projectile under vacuum environment, and the impact experiment of bearing steel was carried out. The evolution process of response parameters such as flash radiation temperature, gas overpressure, flame propagation velocity and temperature rise of container wall was measured. The energy flow direction during the impact reaction of the high-entropy alloys projectile impacting the target plate was analyzed. The enthalpy of the mixed gas, the flash radiation energy, the absorption energy of the container wall, the enthalpy of the ejected gas and the deformation energy generated by the impact on the target during the impact reaction of the high-entropy alloys in a closed container were quantitatively calculated. The effects of different elements and their contents on the energy release of high-entropy alloys were obtained. The results showed that the energy released by the impact reaction of high-entropy alloys projectiles was mainly absorbed by the quasi-closed container wall. With the increase of Cu or Al content, the unit mass release energy of HfZrTiTaNb based high-entropy alloys increased. At similar impact velocities, the high-entropy alloys containing Cu released more energy per unit mass than the high-entropy alloys containing Al.

high-entropy alloys  /  impact reaction energy release  /  energy distribution  /  unit mass release energy
郭孜涵, 陈闯, 涂益良, 唐恩凌. HfZrTiTaNb系高熵合金的冲击反应释能定量确定. 高压物理学报, 2024 , 38 (1) : 014103-1 -014103-14 . DOI: 10.11858/gywlxb.20230817
Zihan GUO, Chuang CHEN, Yiliang TU, Enling TANG. Quantitative Determination of Impact Reaction Energy Release for HfZrTiTaNb Based High-Entropy Alloys[J]. Chinese Journal of High Pressure Physics, 2024 , 38 (1) : 014103-1 -014103-14 . DOI: 10.11858/gywlxb.20230817
正文
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高熵合金（high-entropy alloys，HEAs）具有优异的力学性能（高强度、高应变率强化效应以及强剪切自锐特性）和反应释能特性，被广泛应用于反应材料领域[1–2]。高熵合金在高速撞击下破碎，诱发侵彻穿孔、高温气体、碎片云、火焰的传播与热传导等多种力学、热学、光学和化学现象并释放能量，该过程涉及复杂的物理化学变化，具有多阶段、多场耦合、多影响因素和高瞬态响应等特征。Zhang等[3]采用电弧真空熔炼法制备了一种新型HfZrTiTa0.53高熵合金，在高速撞击下，HfZrTiTa0.53高能弹丸与空气发生反应释放出大量的能量。Geantă等[4]采用口径为7.62 mm的燃烧穿甲子弹对4种不同化学成分的AlFeCrCoNi军用高熵合金试样进行了穿甲试验，样品表现出良好的韧性和力学性能，在高速撞击过程中产生了显著的侵爆破坏效应。王睿鑫[5]通过弹道试验对NbZrTiTa高熵合金进行了反应释能特性评估，结果表明，在冲击过程中，靶室内的温度和压力急剧升高产生超压，随着侵彻速度的增加，弹丸在靶室内产生的超压增大，最高达0.18 MPa。Ren等[6]研究了TiZrNbV高熵合金的压缩行为和冲击能释放特性，弹道试验后反应产物的化学反应程度和反应速率表明，高温剖面引起了严重的氧化反应，导致了冲击载荷下的化学能释放。Ma等[7]研究了Ce含量对Al0.5NbZrTi1.5Ta0.8动态压缩力学特性的影响，结果表明，含Ce的Al0.5NbZrTi1.5Ta0.8高熵合金在弹道试验中可以穿透6 mm厚的钢板，并以719 m/s的速度点燃靶后方的棉花，其释能效果随着Ce含量的增加而增强。
高熵合金作为一种新型含能材料，相较于传统含能材料具有更好的释能效果。例如，在真空环境下，TiZrHfCu0.3高熵合金弹丸冲击轴承钢靶板的释能能力为6.68 kJ/g[8]，而Al/Teflon弹丸撞击钢板的释能能力为4.663 kJ/g[9]。分析弹丸在冲击过程中的能量流向，定量评价其释能量对于高熵合金的工程应用具有重要意义。本研究按照固定的摩尔比制备HfZrTiTaNb系高熵合金，采用二级轻气炮系统加载真空环境中的HfZrTiTaNb系高熵合金弹丸，对GCr15轴承钢靶板进行冲击实验，利用红外热像仪、超压传感器以及瞬态光纤高温计测量闪光辐射温度、气体超压、火焰传播速度和容器壁温升等响应参数的演化过程，分析高熵合金弹丸撞击靶板过程中的能量流向，定量计算容器内混合气体的焓、闪光辐射能、准密闭容器壁吸收的能量、从入弹孔喷出气体的焓以及靶板的变形能，揭示不同元素及其含量对高熵合金释能量的影响。
1 能量分布
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高熵合金在高速冲击作用下会释放大量能量，其包含复杂的能量传递和转换过程。基于能量守恒定律，系统总能量由试件的动能Ev和试件与靶板撞击产生的化学能Er构成。在高熵合金释能结束后，系统总能量主要转化为5种形式，分别为容器内混合气体的焓Ee（容器内气体的内能与压力功之和）、闪光辐射能Ef（物体在冲击条件下释放的可见光能量）、准密闭容器壁吸收的能量Et、从入弹孔喷出气体的焓El（反应过程中从弹孔中喷出气体所携带的能量）以及靶板的变形能Ed（靶板受弹丸撞击后通过变形吸收的能量）。图1为准密闭容器实验系统中的能量分布。
弹丸的动能为
$ E_{\text{v}}=\frac{1}{2}mv_{\mathrm{s}}^2 $
式中：m为弹丸的质量，vs为弹丸的撞击速度。
真空条件下HfZrTiTaNb系高熵合金冲击释能系统的能量分配如图2所示，其关系式可表示为
$ {E_{\text{r}}}+{E_{\text{v}}} = {E_{\text{e}}}+{E_{\text{f}}}+{E_{\text{t}}}+{E_{\text{l}}}+{E_{\text{d}}} $
2 冲击反应释能实验
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利用二级轻气炮加载HfZrTiTaNb系高熵合金弹丸，实验前通过真空泵将靶室空气抽出，使靶室环境接近真空状态。将准密闭容器置于靶室内部，容器进弹孔对准靶室入弹口，使得弹丸能够进入并撞击容器底部的GCr15轴承钢靶板。图3为高熵合金弹丸冲击反应释能实验加载与测试系统。
准密闭容器的内径为100 mm，长度为500 mm，壁厚为4 mm，容器两端用法兰盘密封，容器侧面加工一长方形视窗，尺寸为400 mm×150 mm，用于观测反应释能过程中的火焰传播。冲击反应释能实验系统由加载部分和测试设备组成，加载部分包括一级气室、二级气室、高压锥段、发射管和膨胀室等，测试设备包括瞬态光纤高温计、超压传感器、红外热像仪、高速摄像机和电磁测速系统等，通过脉冲触发器连接测试设备以实现同步触发。在冲击反应释能实验中，瞬态光纤高温计采集容器内的闪光信号，超压传感器记录容器内的气体超压信号，红外热像仪记录容器外壁温度的演化过程，高速摄像机记录火焰的流向，电磁测速系统测量高熵合金弹丸的撞击速度，示波器采集记录数据。图4为主要实验设备。
为了比较不同元素及其含量对高熵合金弹丸冲击反应释能的影响，开展了5组实验，实验基本参数列于表1。
3 能量计算
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3.1 容器内的混合气体焓
在测试闪光辐射温度之前，必须对瞬态光纤高温计进行标定。将光纤探头放置于太阳光模拟器的标准光源下，记录各通道的标定电压和其他标定结果。本研究中，使用400、500、600和700 nm的波长测量高熵合金弹丸释能过程中的闪光信号。瞬态光纤高温计各通道的标定数据如表2所示，其中Nr为光谱辐照度。
准密闭容器内气体热焓[10]可以表示为
$ {E_{\text{e}}} = pV+{n_2}{c_V}\Delta {T_{\text{e}}} $
式中：p为容器内气体的超压，Pa；V为准密闭容器的体积，V=3.274×10−3 m3；cV为气体平均比定容热容，其中cV=3R，R=8.314 J/(mol·K)为理想气体常数；n2为气体的物质的量，mol；ΔTe为准密闭容器内气体的温度变化，K。
沿靶板法线方向距容器底部10 mm处放置瞬态高温计光纤探头，确保光纤探头能完整记录准密闭容器内的闪光辐射变化过程，采集到的光信号经过传感器转化为电信号，存储在示波器中。闪光辐射强度Iexp可表示为
$ {I_{\exp }} = \frac{{{h_{\exp }}}}{{{h_{\text{c}}}}} \frac{{l_0^2}}{{{l^2}}} \frac{{{N_{\text{r}}}(\lambda )}}{{2\text{π} (1 - \cos \theta )}} $
式中：Iexp为实验测量的闪光辐射强度，μW/(nm·cm2)；hexp为示波器测量的电压幅值，V；hc为实验前标定的电压值，V；l0为标定距离，即实验前标定时光纤头部距离太阳光模拟器的距离，l0=10 mm；l为光纤探头与靶板之间的距离，l=10 mm；Nr(λ)为标准光源给定的光谱辐照度，μW/(nm·cm2)；θ为光纤探头的孔径角，θ=37°。
根据普朗克热平衡辐射理论[11]，实测闪光辐射强度与闪光辐射温度之间满足
$ I\left( {\lambda ,T} \right) = \frac{1}{2}\varepsilon \tan^2{\left( {\frac{\theta }{2}} \right)}\frac{{{C_1}}}{{{\lambda ^5}}}\exp \left( { - \frac{{{C_2}}}{{\lambda T}}} \right) $
式中：I为理论计算的闪光辐射强度，μW/(nm·cm2)；T为闪光辐射温度，K；λ为波长，nm；C1为第一辐射常数，C1=3.7418×10−16 W·m2；C2为第二辐射常数，C2=1.4388×10−2 m·K；ε为灰体表面发射率。
根据普朗克黑体辐射定律，采集4种不同波长（400、500、600和700 nm）的实验数据，计算瞬态闪光温度
$ K(T) = \frac{{{I_1}{I_2}}}{{{I_3}{I_4}}} - {\left( {\frac{{{\lambda _2}{\lambda _4}}}{{{\lambda _1}{\lambda _3}}}} \right)^5} \exp \left[ {\frac{T}{{{C_2}}}\left( {{\lambda _2}+{\lambda _4} - {\lambda _1} - {\lambda _3}} \right)} \right] $
式中：I1、I2、I3和I4为不同波长对应的闪光辐射强度，μW/(nm·cm2)；λ1、λ2、λ3和λ4为每个通道对应的波长，nm。
图5显示了实验1～实验5的原始闪光数据。根据式(4)计算闪光辐射强度，辐射强度时程曲线如图6所示。
根据式(6)计算闪光辐射温度，图7显示了实验1～实验5准密闭容器内的气体超压和闪光辐射温度时程曲线。表3列出了实验中超压和闪光辐射温度的峰值。
将测得的超压p、容器内的气体温度变化ΔTe、准密闭容器体积V、平均比定容热容cV代入式(3)，计算实验1～实验5中准密闭容器内的混合气体焓Ee，分别为761、834、729、698和701 J。受准密闭容器约束，向预留孔运动的反应产物在容器内壁发生反射并相互作用，因此，实验1～实验5的超压在达到峰值后振荡下降。在实验1、实验3和实验4中，弹丸的碎片部分在撞击靶板时发生反应，其闪光辐射温度达到最大峰值后还出现了多次较小峰值。
3.2 闪光辐射能
闪光辐射能量Ef[12]可表示为
$ E_{\text{f}}=\int_{t_1}^{t_2}\mathrm{d}t\int_{\lambda_1}^{\lambda_2}\frac{2hc^2}{\lambda^5}\frac{1}{\exp[hc/(\lambda k_{\mathrm{B}}T)]-1}\mathrm{d}\lambda $
式中：t为时间，s；c为光速，c=3×108 m/s；h为普朗克常数，h=6.62×10−34 J·s；kB为玻尔兹曼常数，kB=1.38×10−23 J/K。
将式(7)的闪光辐射强度先对波长积分，再对闪光持续时间积分，得到闪光辐射能量。图8显示了实验1和实验5的闪光辐射能量曲线，可以看出，实验1和实验5的闪光辐射能量分别从1.08和1.10 ms开始上升，并在1.19和1.14 ms达到最大值，与瞬态光纤高温计的监测结果一致。实验1～实验5的闪光辐射能分别为0.52、0.57、0.46、0.51和0.50 J。
3.3 准密闭容器壁吸收的能量
反应产物在热辐射、热对流和热传导的协同作用下加热容器壁，准密闭容器的内能增加，可以表示为[12]
$ {E_{\text{t}}} = {c_3}{m_3}\Delta {T_{\text{t}}} $
式中：c3为准密闭容器材料的比定压热容，c3=0.46 kJ/(kg·K)；m3为准密闭容器的质量，m3=6.618 kg；$\Delta {T_{\text{t}}}$为准密闭容器的温升，K。
实验中，由红外摄像机记录准密闭容器的外壁温度变化情况，通过配套软件分析得到实际观测区域的温度变化。图9显示了准密闭容器的实际观测区域和红外视图。
图10(a)显示了准密闭容器的外壁温度时程曲线。弹丸冲击靶板后，观测区域吸收冲击反应产生的热量，导致准密闭容器的外壁温度急剧上升。实验1～实验5中，实际观测区域的温度分别上升0.35369、0.50296、0.25286、0.45865和0.46616 K。根据式(8)计算实验1～实验5中准密闭容器壁吸收的能量Et，分别为1077、1531、769、1396和1419 J。图10(b)显示了t=2 s时实验1～实验5中准密闭容器壁的红外视图。
3.4 反应产物经进弹孔消耗的能量
图11～图15显示了准密闭容器内HfZrTiTaNb系高熵合金弹丸高速冲击轴承钢靶板的反应过程。
在撞击靶板过程中弹丸反应形成的高温气体产物从形成弹坑位置以不同的速度向准密闭容器的预留孔流动，并从预留孔中逸出。忽略摩擦和热交换，流动参数在垂直截面上均匀分布，该流动可简化为一维定常等熵流动。
在一维定常等熵流动中，流场的控制方程组为[13]
$ \left\{\begin{gathered}\mathrm{d}m=A\mathrm{d}\rho\mathrm{d}u=\mathrm{const} \\ \mathrm{d}p=\rho u\mathrm{d}u \\ \mathrm{d}(h_{\text{j}}+0.5u^2)=0 \\ \end{gathered}\right. $
式中：A为弹孔的横截面积，m2；ρ为通过的气体密度，g/cm3；u为通过的气体流速，m/s；hj为气体产物的焓，J。
反应产物经进弹孔实时喷射到准密闭容器外的质量流出速率为[14]
$ \frac{\mathrm{d}m_1}{\mathrm{d}t}=A\sqrt{\frac{\gamma m_1p_{\text{j}}}{V}}\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}} $
式中：γ为绝热指数，γ=1.4；m1为预留孔喷射气体的质量，g；pj为压力，MPa；t为时间，s。
反应气体产物经进弹孔丢失的能量可表示为
$ {E_{\text{l}}} = n{c_p}\Delta T $
式中：n为喷出气体的物质的量，mol；cp=4R为比定压热容。
根据式(11)计算实验1～实验5中反应气体产物经进弹孔丢失的能量El，分别为58.67、63.79、55.87、57.18和59.64 J。
采用Fluent软件模拟准密闭容器内实验1的反应气体流动过程[8]，为提高计算效率，选择二维轴对称模型，加密入口和通道处的网格，网格模型如图16所示。将实验的气体运动速度和温度作为数值模拟的边界条件，求解弹孔溢出气体的质量时程曲线和准密闭容器内气体的温度时程曲线。图17显示了不同时刻准密闭容器内的数值模拟温度云图。
图18(a)显示了实验中距容器底部10 mm处的数值模拟温度时程曲线，模拟的气体温度峰值（1252 K）比实验结果小8 K。模拟的从准密闭容器弹孔喷出的气体产物能量为50.88 J（见图18(b)），比实验结果低13.2%。
3.5 靶板变形能
冲击作用下，准密闭容器底部的靶板形成外围呈“翻唇”形的半球形弹坑，弹坑周围的靶板受应力波作用形成应变区。弹丸撞击靶板形成的弹坑及其剖面如图19所示。
靶板材料的变形能包含体积应变能EV和剪切应变能Eτ[15]
$ {E}_{\text{d}}={E}_{\text{V}}+{E}_{\tau }=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{+\infty }\sigma {\varepsilon }_{\text{V}}{r}^{2}\text{d}r+2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{+\infty }\tau \gamma {r}^{2}\text{d}r $
式中：σ为压缩应力，τ为剪切应力，εV为体积应变，γ为剪切应变。Ed由弹坑内部的能量E1和孔洞外部的能量E2组成
$ {E}_{1}=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{{r}_{0}}\sigma {\varepsilon }_{\text{V}}{r}^{2}\text{d}r+2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{{r}_{0}}\tau \gamma {r}^{2}\text{d}r $
$ {E}_{2}=2\text{π} {\displaystyle {\int }_{ {r}_{0}}^{+\infty }\sigma {\varepsilon }_{\text{V}}{r}^{2}\text{d}r}+2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ {r}_{0}}^{+\infty }\tau \gamma {r}^{2}\text{d}r $
弹丸侵彻靶板时，撞击点处的部分靶板熔化或者汽化，该过程产生的能量主要以闪光辐射的形式发散出去。弹坑内部吸收的能量由相应冲击条件下的破坏应力和温度决定，因此，弹坑内部能量E1为
$ {E}_{1}=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{{r}_{0}}{\sigma }_{\text{m}}{\varepsilon }_{\text{m}}{r}^{2}\text{d}r+2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{{r}_{0}}{\tau }_{\text{m}}{\gamma }_{\text{m}}{r}^{2}\text{d}r=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{{r}_{0}}\left({\sigma }_{\text{m}}{\varepsilon }_{\text{m}}+{\tau }_{\text{m}}{\gamma }_{\text{m}}\right){r}^{2}\text{d}r $
式中：σm为破坏压缩应力，τm为剪切破坏应力，εm为破坏压缩体积应变，γm为剪切破坏应变。
将$ {\sigma _{\text{m}}}{\varepsilon _{\text{m}}}+{\tau _{\text{m}}}{\gamma _{\text{m}}} = {\sigma _{\text{u}}}{\varepsilon _{\text{u}}} $代入式(15)，可得
$ {E}_{1}=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{{r}_{0}}{\sigma }_{\text{u}}{\varepsilon }_{\text{u}}{r}^{2}\text{d}r=\frac{2}{3}\text{π} {r}_{0}^{3}{\sigma }_{\text{u}}{\varepsilon }_{\text{u}} $
式中：σu为破坏压缩应力，εu为破坏应变。
弹坑外部能量E2为
$ {E_2} = 2\text{π} \int_{{r_0}}^{+\infty} {\left( {\sigma {\varepsilon _{\text{V}}}+\tau \gamma } \right){r^2}{\text{d}}r} = 2\text{π} \int_{{r_0}}^{+\infty} {\sigma \varepsilon {r^2}{\text{d}}r} $
根据靶材硬度与应变之间的关系，可得应变区到孔洞中心的距离（r）与形变（ε）之间的关系
$ \varepsilon {\text{ = }}{{\text{e}}^{ - {{B}}\left( {r - {{C}}} \right)}} $
式中：B和C为常数。当r=r0（r0为弹坑内部半径）时，ε=εu。所以
$ \varepsilon_{\text{u}}\text{ = }\text{e}^{\mathit{\mathrm{-}{B}}\left(r_0-\sigma\right)} $
将$ \sigma {\text{ = }}{\sigma _{\text{u}}}r_0^2/{r^2} $和式(19)代入式(17)，得到弹坑外部的能量E2
$ {E}_{2}=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{+\infty }\sigma \varepsilon {r}^{2}\text{d}r=2\text{π} {{{\displaystyle \int }}^{\text{}}}_{ 0}^{+\infty }{\sigma }_{\text{u}}\frac{{r}_{0}^{2}}{{r}^{2}}{\text{e}}^{-{B}(r-{C})}{r}^{2}\text{d}r=2\text{π} {\sigma }_{\text{u}}{\varepsilon }_{\text{u}}\frac{{r}_{0}^{2}}{{\rho }_{\text{t}}} $
式中：ρt为靶板材料的密度，ρt=7.8×103 kg/m3；σu为轴承钢靶板的破坏应力，σu=2.2 GPa；εu=0.1[16]。实验1～实验5中，弹丸侵彻靶板形成的弹坑直径分别为13.16、12.05、11.80、11.24和10.92 mm。根据式(20)计算实验1～实验5中的靶板变形能，分别为138、107、101、86和80 J。
3.6 冲击反应释能总量
将Ev、Ee、Ef、Et、El、Ed代入式(2)计算高熵合金的冲击反应释能Er，再将Er除以试件质量得到单位质量HfZrTiTaNb系高熵合金的反应释能量。从表4可以看出，随着Cu或Al含量的增加，HfZrTiTaNb系高熵合金的单位质量释能量增大。对比实验2、实验4和实验5，在相近的撞击速度下，含Cu高熵合金的单位质量释能量比含Al高熵合金大。
3.7 释能分析
Cu和Al的原子尺寸不同，如图20所示，原子尺寸会影响合金晶格畸变的程度。
由于Cu的原子半径小于Al，当Cu被引入合金中时，会引起更大的合金族原子尺寸差异。原子尺寸差（δ）可表示为[17]
$ \delta = \sqrt {\sum\limits_{i = 1}^n {{c_i}\left(1 - {r_i}\Big/\sum\limits_{i = 1}^n {c_i}{r_i}\right)^2} } $
式中：ci为第i类原子在合金内的原子比，ri为第i类原子的原子半径。
HfZrTiTaNb系高熵合金的原子尺寸差列于表5。在合金元素摩尔比（x）相同的情况下，含Cu高熵合金的原子尺寸差比含Al的大。Cu元素的添加使合金更易产生晶格畸变和相变，在冲击载荷下合金更易破裂，从而释放更多的能量。
4 结　论
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基于二级轻气炮实验加载系统，通过超压传感器、瞬态光纤高温计、红外热像仪以及高速摄像机等实验设备，研究了真空环境下HfZrTiTaNb系高熵合金弹丸在撞击靶板过程中引发的力学、热学、光学和化学效应，计算了单位质量高熵合金冲击反应的释能量，得到以下主要结论。
(1) 在高熵合金弹丸撞击靶板过程中，系统释放的能量表现为靶板变形能、闪光辐射能、容器内的混合气体焓、准密闭容器壁吸收的能量和反应产物经进弹孔丢失的能量，其中准密闭容器壁吸收的能量占比最高。
(2) 随着Cu或Al含量的增加，HfZrTiTaNb系高熵合金的单位质量释能量增加。在相近的撞击速度下，含Cu高熵合金的单位质量释能量比含Al高熵合金高。

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doi: 10.11858/gywlxb.20230817
  • 接收时间：2023-12-18
  • 首发时间：2026-11-05
  • 出版时间：2024-02-05
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  • 收稿日期：2023-12-18
  • 修回日期：2024-01-02
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    沈阳理工大学辽宁省瞬态物理力学与能量转换材料重点实验室, 辽宁 沈阳　110159

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陈　闯（1987－），男，博士，教授，主要从事爆炸与冲击动力学研究. E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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