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Article(id=1241442314070061243, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241442313185063097, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2023.01.003, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1665676800000, receivedDateStr=2022-10-14, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773912512557, onlineDateStr=2026-03-19, pubDate=1677600000000, pubDateStr=2023-03-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773912512557, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773912512557, creator=13701087609, updateTime=1773912512557, updator=13701087609, issue=Issue{id=1241442313185063097, tenantId=1146029695717560320, journalId=1240670690148397066, year='2023', volume='40', issue='1', pageStart='1', pageEnd='220', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773912512346, creator=13701087609, updateTime=1773912765519, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241443375145079400, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241442313185063097, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241443375145079401, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241442313185063097, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=21, endPage=29, ext={EN=ArticleExt(id=1241442314351079617, articleId=1241442314070061243, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Dynamic Properties and Failure Modes Analysis of Magnetite Ore under Dynamic Loading, columnId=1240702071733801442, journalTitle=Blasting, columnName=THEORETICAL AND TECHNOLOGICAL EXPLORATION, runingTitle=null, highlight=null, articleAbstract=

In view of the problem that mining and crushing of magnetite ore require huge energy consumption, the split Hopkinson pressure bar (SHPB) is used to test and analyze the dynamic mechanical properties and energy dissipation characteristics of magnetite ore during crushing process under different strain rates. Meanwhile, the complete dynamic failure process of the sample is simulated by ANSYS/LS-DYNA software. The results show that the dynamic compressive strength of the magnetite ore samples has a significant strain rate correlation, and increases from 126.77 MPa to 220.62 MPa when the strain rate ranges from 43.94 s-1 to 147.75 s-1. Besides, The analysis of energy transfer law shows that the increase trend of reflected energy become more obvious with the increase of incident energy, and the maximum proportion accounts for about 22% of the total incident energy. However, The increase trend of transmission energy become weaker, and the proportion of transmission energy decreases from 78% at low incident energy to 38% at high incident energy. At the same time, the dissipated energy used for specimen crushing increases gradually, which has a linear relationship with the incident energy. The failure mode changes from the splitting failure at low and medium strain rates to crushing failure at a high strain rate. In terms of the crushing scale, most of the fragments at low and medium strain rates are large, while the fragments at high strain rates are small and mostly fine-grained and needle shaped. Numerical simulation results indicate that the initial failure is caused by the "cross" shaped reflected tensile waves on the incident end of the specimen. The results of this study can provide a reference for judging the difficulty of dynamic crushing of magnetite ore and improving the efficiency of rock breaking by impact.

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针对磁铁矿石在采选和破碎过程中耗能巨大的问题，借助分离式霍普金森压杆（SHPB）试验装置，对磁铁矿石进行不同应变率条件下的冲击压缩试验，分析磁铁矿石的动态力学特性及其破坏过程中的能量耗散特征，并借助ANSYS/LS-DYNA软件模拟试样完整动态破坏过程。研究结果表明：磁铁矿石试样的动态抗压强度具有显著的应变率相关性，应变率从43.94~147.75 s-1，其动态抗压强度从126.77 MPa提高到220.62 MPa。能量传递规律分析表明，随着入射能的增大，反射能增长趋势增大，最大占比约占总入射能的22%；而透射能增长趋势减小，且透射能占比从低入射能下的78%降低至高入射能下的38%，用于试件破碎的耗散能量逐步增多，与入射能呈线性关系。其破坏模式从中低应变率下的劈裂破坏转为高应变率下的压碎破坏，从破碎尺度来看，中低应变率下碎块多为大块状，而高应变率下碎块尺度较小且多呈细粒状及针状。数值仿真计算表明试件最开始发生破坏是由试件入射杆端面的“十字”反射拉伸波引起的。研究结果可为判断磁铁矿石动力破碎的难易程度以及提高冲击破岩效率提供参考。

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张智宇（1973-），男，广东韶关，教授，主要从事工程爆破及岩石破碎方面的研究，（E-mail）。
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刘浩杉（1998-），男，云南文山，在读硕士，从事工程爆破方面研究，（E-mail）。

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刘浩杉（1998-），男，云南文山，在读硕士，从事工程爆破方面研究，（E-mail）。

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刘浩杉（1998-），男，云南文山，在读硕士，从事工程爆破方面研究，（E-mail）。

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International Journal of Impact Engineering, 2016, 95: 61-71., articleTitle=Numerical predictions of cratering and scabbing in concrete slabs subjected to projectile impact using a modified version of HJC material model, refAbstract=null), Reference(id=1241442340271878258, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, doi=null, pmid=null, pmcid=null, year=2010, volume=31, issue=S1, pageStart=216, pageEnd=222, url=null, language=null, rfNumber=[18], rfOrder=29, authorNames=贾彬, 李正良, 陶俊林, journalName=固体力学学报, refType=null, unstructuredReference=贾彬, 李正良, 陶俊林, 等. 混凝土SHPB试验数值模拟研究[J]. 固体力学学报, 2010, 31(S1): 216-222., articleTitle=混凝土SHPB试验数值模拟研究, refAbstract=null), Reference(id=1241442340410290294, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, doi=null, pmid=null, pmcid=null, year=2010, volume=31, issue=S1, pageStart=216, pageEnd=222, url=null, language=null, rfNumber=[18], rfOrder=30, authorNames=LI Zheng-liang, TAO Jun-lin, YAO Hua-chuan, journalName=Acta Mechanica Solida Sinica, refType=null, unstructuredReference=LI Zheng-liang, TAO Jun-lin, YAO Hua-chuan, et al. 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(in Chinese), articleTitle=Research on numerical simulation of shpb concrete tests, refAbstract=null), Reference(id=1241442340561285243, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, doi=null, pmid=null, pmcid=null, year=2019, volume=38, issue=12, pageStart=25, pageEnd=31, url=null, language=null, rfNumber=[19], rfOrder=31, authorNames=张社荣, 宋冉, 王超, journalName=振动与冲击, refType=null, unstructuredReference=张社荣, 宋冉, 王超, 等. 碾压混凝土HJC动态本构模型修正及数值验证[J]. 振动与冲击, 2019, 38(12): 25-31., articleTitle=碾压混凝土HJC动态本构模型修正及数值验证, refAbstract=null), Reference(id=1241442340670337151, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, doi=null, pmid=null, pmcid=null, year=2019, volume=38, issue=12, pageStart=25, pageEnd=31, url=null, language=null, rfNumber=[19], rfOrder=32, authorNames=ZHANG She-rong, SONG Ran, WANG Chao, journalName=Journal of Vibration and Shock, refType=null, unstructuredReference=ZHANG She-rong, SONG Ran, WANG Chao, et al. 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tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=EN, label=Fig. 14, caption=Damage cloud diagram of magnetite ore under velocity of 16.18 m/s, figureFileSmall=ye6QxnlfEzU1xfDqto3uTQ==, figureFileBig=konDtkQvGUMivwpZZ60zkQ==, tableContent=null), ArticleFig(id=1241442332537582504, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=CN, label=图14, caption=16.18 m/s冲击速度下磁铁矿石破坏云图, figureFileSmall=ye6QxnlfEzU1xfDqto3uTQ==, figureFileBig=konDtkQvGUMivwpZZ60zkQ==, tableContent=null), ArticleFig(id=1241442332625662889, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=EN, label=Table 1, caption=

Static mechanical parameters of magnetite ore

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密度/（g·cm-3）抗压强度/MPa抗拉强度/MPa弹性模量/GPa泊松比
3.6117.76.987.510.25
), ArticleFig(id=1241442332747297710, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=CN, label=表1, caption=

磁铁矿石静态力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
密度/（g·cm-3）抗压强度/MPa抗拉强度/MPa弹性模量/GPa泊松比
3.6117.76.987.510.25
), ArticleFig(id=1241442332868932535, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=EN, label=Table 2, caption=

Test parameters of rock samples under impact loads

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试样编号冲击气压/MPa冲击速度/（m·s-1）平均应变率/（s-1）动态抗压强度/MPa动态强度因子K
试验值平均值
1#0.38.3243.94126.771.081.06
2#8.2442.56123.631.05
3#8.2942.88125.491.07
4#0.411.1956.42155.491.321.32
5#11.0553.73152.761.30
6#11.2857.94156.351.33
7#0.514.4882.59175.691.491.48
8#14.2679.98172.101.46
9#14.3281.86174.311.48
10#0.616.18116.94203.491.731.74
11#16.47117.21204.631.74
12#16.80120.23206.421.75
13#0.719.36146.53218.581.861.86
14#19.24146.22217.391.85
15#19.53147.75220.621.87
), ArticleFig(id=1241442333036704702, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=CN, label=表2, caption=

冲击荷载下岩样试验参数

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试样编号冲击气压/MPa冲击速度/（m·s-1）平均应变率/（s-1）动态抗压强度/MPa动态强度因子K
试验值平均值
1#0.38.3243.94126.771.081.06
2#8.2442.56123.631.05
3#8.2942.88125.491.07
4#0.411.1956.42155.491.321.32
5#11.0553.73152.761.30
6#11.2857.94156.351.33
7#0.514.4882.59175.691.491.48
8#14.2679.98172.101.46
9#14.3281.86174.311.48
10#0.616.18116.94203.491.731.74
11#16.47117.21204.631.74
12#16.80120.23206.421.75
13#0.719.36146.53218.581.861.86
14#19.24146.22217.391.85
15#19.53147.75220.621.87
), ArticleFig(id=1241442333141562306, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=EN, label=Table 3, caption=

Energy calculation results of typical samples under different strain rates

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试件编号冲击气压/MPa子弹速度v/（m·s-1）入射能WI/J反射能WR/J透射能WT/J吸收能WS/J能耗密度/（J·cm-3）破碎耗能占比P
1#0.38.3248.314.6837.935.680.0570.117
2#0.411.1985.1610.0856.5218.560.1890.217
3#0.514.48154.4621.7779.7752.920.5390.344
4#0.616.18210.5043.0595.2172.240.7360.343
5#0.719.36273.2460.67104.58107.991.1000.395
), ArticleFig(id=1241442333242225607, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241442314070061243, language=CN, label=表3, caption=

不同应变率下典型试样能量计算结果

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试件编号冲击气压/MPa子弹速度v/（m·s-1）入射能WI/J反射能WR/J透射能WT/J吸收能WS/J能耗密度/（J·cm-3）破碎耗能占比P
1#0.38.3248.314.6837.935.680.0570.117
2#0.411.1985.1610.0856.5218.560.1890.217
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4#0.616.18210.5043.0595.2172.240.7360.343
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HJC model parameters for magnetite ore

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参数ρ（kg·m-3）G/GPaFc/MPaABCNSmaxT/MPaPc/MPaμc
数值25866.531180.91.10.0070.6174.020.20.0017
参数P1/GPaμ1K1/GPaK2/GPaK3/GPaD1D2EPS0FSεf，min 
数值1.20.182-1712080.041.012.00.004 
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磁铁矿石HJC模型参数

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参数ρ（kg·m-3）G/GPaFc/MPaABCNSmaxT/MPaPc/MPaμc
数值25866.531180.91.10.0070.6174.020.20.0017
参数P1/GPaμ1K1/GPaK2/GPaK3/GPaD1D2EPS0FSεf，min 
数值1.20.182-1712080.041.012.00.004 
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动载下磁铁矿石的动力学特性及破坏模式分析
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刘浩杉 1 , 张智宇 1, 2 , 李祥龙 1 , 黄永辉 3 , 王建国 1
爆破 | 理论与技术探索 2023,40(1): 21-29
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爆破 | 理论与技术探索 2023, 40(1): 21-29
动载下磁铁矿石的动力学特性及破坏模式分析
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刘浩杉1 , 张智宇1, 2 , 李祥龙1, 黄永辉3, 王建国1
作者信息
  • 1.昆明理工大学　国土资源工程学院，昆明　650093
  • 2.云南省中—德蓝色矿山与特殊地下空间开发利用重点实验室，昆明　650093
  • 3.昆明理工大学　电力工程学院　，昆明　650500

    • 刘浩杉（1998-），男，云南文山，在读硕士，从事工程爆破方面研究，（E-mail）。

通讯作者:

张智宇（1973-），男，广东韶关，教授，主要从事工程爆破及岩石破碎方面的研究，（E-mail）。
Dynamic Properties and Failure Modes Analysis of Magnetite Ore under Dynamic Loading
Hao-shan LIU1 , Zhi-yu ZHANG1, 2 , Xiang-long LI1, Yong-hui HUANG3, Jian-guo WANG1
Affiliations
  • 1.Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China
  • 2.Yunnan Key Laboratory of Sino-German Bluc Mining and Utilization of Special Underground Space, Kunming 650093, China
  • 3.Faculty school of Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China
出版时间: 2023-03-01 doi: 10.3963/j.issn.1001-487X.2023.01.003
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摘要
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针对磁铁矿石在采选和破碎过程中耗能巨大的问题，借助分离式霍普金森压杆（SHPB）试验装置，对磁铁矿石进行不同应变率条件下的冲击压缩试验，分析磁铁矿石的动态力学特性及其破坏过程中的能量耗散特征，并借助ANSYS/LS-DYNA软件模拟试样完整动态破坏过程。研究结果表明：磁铁矿石试样的动态抗压强度具有显著的应变率相关性，应变率从43.94~147.75 s-1，其动态抗压强度从126.77 MPa提高到220.62 MPa。能量传递规律分析表明，随着入射能的增大，反射能增长趋势增大，最大占比约占总入射能的22%；而透射能增长趋势减小，且透射能占比从低入射能下的78%降低至高入射能下的38%，用于试件破碎的耗散能量逐步增多，与入射能呈线性关系。其破坏模式从中低应变率下的劈裂破坏转为高应变率下的压碎破坏，从破碎尺度来看，中低应变率下碎块多为大块状，而高应变率下碎块尺度较小且多呈细粒状及针状。数值仿真计算表明试件最开始发生破坏是由试件入射杆端面的“十字”反射拉伸波引起的。研究结果可为判断磁铁矿石动力破碎的难易程度以及提高冲击破岩效率提供参考。

霍普金森压杆  /  磁铁矿石  /  动力学特性  /  破坏模式  /  数值模拟

In view of the problem that mining and crushing of magnetite ore require huge energy consumption, the split Hopkinson pressure bar (SHPB) is used to test and analyze the dynamic mechanical properties and energy dissipation characteristics of magnetite ore during crushing process under different strain rates. Meanwhile, the complete dynamic failure process of the sample is simulated by ANSYS/LS-DYNA software. The results show that the dynamic compressive strength of the magnetite ore samples has a significant strain rate correlation, and increases from 126.77 MPa to 220.62 MPa when the strain rate ranges from 43.94 s-1 to 147.75 s-1. Besides, The analysis of energy transfer law shows that the increase trend of reflected energy become more obvious with the increase of incident energy, and the maximum proportion accounts for about 22% of the total incident energy. However, The increase trend of transmission energy become weaker, and the proportion of transmission energy decreases from 78% at low incident energy to 38% at high incident energy. At the same time, the dissipated energy used for specimen crushing increases gradually, which has a linear relationship with the incident energy. The failure mode changes from the splitting failure at low and medium strain rates to crushing failure at a high strain rate. In terms of the crushing scale, most of the fragments at low and medium strain rates are large, while the fragments at high strain rates are small and mostly fine-grained and needle shaped. Numerical simulation results indicate that the initial failure is caused by the "cross" shaped reflected tensile waves on the incident end of the specimen. The results of this study can provide a reference for judging the difficulty of dynamic crushing of magnetite ore and improving the efficiency of rock breaking by impact.

hopkinson pressure bar  /  magnetite ore  /  dynamic characteristics  /  failure modes  /  numerical simulation
刘浩杉, 张智宇, 李祥龙, 黄永辉, 王建国. 动载下磁铁矿石的动力学特性及破坏模式分析. 爆破, 2023 , 40 (1) : 21 -29 . DOI: 10.3963/j.issn.1001-487X.2023.01.003
Hao-shan LIU, Zhi-yu ZHANG, Xiang-long LI, Yong-hui HUANG, Jian-guo WANG. Dynamic Properties and Failure Modes Analysis of Magnetite Ore under Dynamic Loading[J]. Blasting, 2023 , 40 (1) : 21 -29 . DOI: 10.3963/j.issn.1001-487X.2023.01.003
正文
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磁铁矿石作为重要的工业原材料于国民经济发展起着重要作用。冲击破碎是矿岩破碎的基本方法，在消耗一定能量的情况下矿岩破碎成不同粒径，其在冲击过程中的能量耗散不可逆转，破碎耗能与岩块数量、破坏模式之间的关系是一个不可忽视的问题。
SHPB装置现已成为为研究高应变率（10~103 s-1）下岩石的动态力学特性的基本手段[1-4]。关于不同应变率下岩石这种非均质材料所表现出的动态力学特性，国内外学者进行了大量的研究：姜峰和Wang等对花岗岩进行了不同应变率下的动态压缩试验[5,6]，发现花岗岩在高应变率下动态强度突变的特性且岩样在高应变率下的失效和裂纹扩展会消耗更多能量，同时岩样更加破碎。平琦等对不同高温作用后的石灰岩进行动力特性试验[7]，发现其动态抗压强度与温度的关系呈二次函数形式。在岩石材料的破坏模式上，卢志堂等对中高应变率下的花岗岩的裂纹扩展进行了研究[8]，指出岩石在单轴冲击下呈劈裂破坏。王伟等利用CT扫描技术获得不同受力情况下砂岩的裂纹密度[9]，并指出在单轴，一维、三维动静组合下情况下砂岩的破坏形式。武仁杰研究了不同层理倾角岩石的能量耗散情况与破碎程度之间的关系[10]，指出岩石倾角在45°~67.5°时，能量利用率高并且岩石更加破碎。同时，试验快捷、低成本的数值模拟现已成为SHPB室内试验的良好补充。李明利用ANSYS/LS-DYNA软件对长径比为0.5，直径为74 mm的砂岩试样进行了SHPB数值模拟试验[11]，研究了砂岩在不同冲击速度下的力学性能和能耗规律。张明涛用ANSYS/LS-DYNA软件对不同冲击速度下有无轴压的两种情况的砂岩进行了数值模拟研究[12]，采用微裂纹密度法定量表征了砂岩的损伤程度并直观展示了其破坏过程。Wu等人利用Holmquist-Johnson-Cook（HJC）本构模型对混凝土进行了数值模拟[13]，并将试验应力应变曲线与模拟得到的进行比较。
上述关于岩石动态力学特性以及破坏模式的研究结论大多数都是基于工程地质岩体开展的，对于金属类型的矿山开采下的矿石研究较少。利用分离式霍普金森杆对攀枝花市白马铁矿磁铁矿石进行动态冲击实验，通过研究不同应变率下磁铁矿石的动态力学性能、冲击破坏过程中的能量转化利用以及试件破坏模式来反映该磁铁矿石破碎情况。
1　磁铁矿石冲击压缩试验
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1.1　试验装置与基本原理
本次试验采用国际岩石力学学会推荐标准岩石动力学测试工具，分离式霍普金森压杆（SHPB）。SHPB试验装置采用纺锤形子弹，长0.4 m，可产生近似恒应变率的半正弦波形，避免Pochhammer-Chree振荡问题[14]。入、透射杆件材质为40Cr高强度合金钢。直径50 mm，长度2 m，密度7784 kg/m3，弹性模量250 GPa，弹性杆纵波波速5667 m/s。装置结构如图1所示。
由应变片上信号可求得应力σ（t）、应变ε（t）和应变率。
式中：A、E、C分别为压杆的横截面积、弹性模量、纵波波速；AS、lS分别为试样的横截面积和长度，εI（t）、εR（t）、εT（t）为t时刻压杆的入射应变、反射应变、透射应变。
1.2　试件中耗能计算
入射能WI、反射能WR和透射能WT在基于一维波理论及能量守恒的情况下可由式（2）计算获得。
试件吸收的耗散能等于入射能减去反射能和透射能，即
假设试件耗散能全部用于岩石破碎，忽略试样的体积影响，采用破碎耗能密度η进行试样的破碎耗能特性分析，计算公式如下
式中，V为试样的体积。
1.3　岩石试样制备及试验方案
试验所用岩样为攀枝花白马铁矿的钒钛磁铁矿石，选择完整性较好的岩块加工成长径比接近于1圆柱体，并对试样两端进行打磨，使其不平整度和不垂直度均小于0.02 mm。试样为直径50 mm，高50 mm的圆柱体，长径比约为1.0。加工完成的岩石试样如图2。
为避免冲击气压过小试样未发生破坏或者气压过大试样发生粉碎性破坏，通过对磁铁矿石试冲后确定其冲击气压范围，试验共设计了0.3~0.7 MPa 5种不同的冲击气压，气压梯度为0.1 MPa，每个冲击气压下3个试样，共计15个试样。以研究不同冲击荷载下磁铁矿石的动力学性质及破坏模式。
2　试验结果及分析
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试件基本力学参数如表1所示。
2.1　动态应力平衡验证
SHPB试验合理性是基于一维传播理论而存在。如图3所示，入射波形与反射波形在经平移相加后，所得到的入射加反射波形与透射波几乎重合，说明磁铁矿石试样在破坏前两端应力大小接近。试样在破坏前两端的应力已达到平衡，试验结果有较高的可靠性。
2.2　SHPB试验结果
为了表征岩样在冲击荷载下的强度变化，引入动态强度因子K来定量描述不同冲击应变率下岩石动态抗压强度相对于静态抗压强度的增幅。
式中：K为动态强度因子；σD、σS为试样的动态、静态抗压强度。
通过式（1）及式（5）计算得到应力、应变、应变率及动态强度因子K等参数。冲击试验结果如表2所示。
2.3　磁铁矿石动态力学特性分析
试验可获得入射、反射、透射波三种信号，根据三波法原理绘制试样在不同应变率下的应力-应变曲线，其大致可划分为压密、弹性变形、塑性变形以及破坏四个阶段。如图4所示。
在入射杆的撞击下，试件的内部孔隙被挤压，在极短时间内孔隙闭合，之后动态应力应变曲线进入弹性变形阶段，此阶段动态应力应变曲线接近为一条直线。之后应力持续增加，在达到峰值应力的80%左右时，试件进入弹塑性阶段，应力应变曲线斜率降低，即在应力缓慢增加的同时，试样应变不断加大。中低应变率（43.94 s-1、58.42 s-1、82.59 s-1）下的试样无明显塑性变形阶段，而高应变率（147.75 s-1）下试样的曲线具有明显的塑性阶段，即应力大致保持不变的情况下应变持续增长，并且在其曲线下降阶段趋势相对缓慢。
如图5所示，随着应变率不断增加，试件的动态强度因子K也随之变大，说明磁铁矿石是率敏感性材料，与其他岩石的动态力学特性基本一致[15,16]。这是因为冲击时间很短，矿石没有足够的时间积累能量，只能暂时性提高自身强度来应对外界冲击能量。在应变率为147.75 s-1的情况下，试件的动态抗压强度为220.62 MPa，对比其单轴抗压强度117.7 MPa，增大了约1.86倍。
3　试件能量吸收及破坏形态分析
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3.1　入射能与透、反射能量的关系
为更全面分析磁铁矿石冲击破坏特性，根据式（2）、（3）、（4）对试件能量利用情况进行计算分析，得到了不同冲击气压下的试件入射能、反射能、透射能、耗散能。并将3种能量与入射能的比值称为能量反射率、能量透射率、能量耗散率。计算结果见表3。
磁铁矿石在冲击载荷作用下，吸收的能量用于其内部的裂隙的发育发展、贯通。冲击破碎过程中从入射杆传递的总入射能经岩样破碎后发生耗散，一部分转变为岩石破碎吸收能，一部分发生透射转变为透射能，其他部分主要以弹性波的形式反射回冲击机构转变为反射能。由图6可知在入射能从48 J增至273 J过程中，反射率从10%增至22%，试件耗散率从12%大幅增加至40%，而能量透射率从78%降低至38%。
各能量占入射能的百分比见图6，磁铁矿石入射能与透射能、反射能的关系见图7。
从图7中可以看出，透射能随入射能的增大逐渐变大，其增幅逐渐变小，二者呈对数关系。这是因为入射能在较低情况下，试件处于弹性变形阶段，试件内部孔隙被压密，故透射能大幅增加。而随着入射能的增加，相应的试件吸收的能量也增多，这些吸收的能量用于试件内部的孔隙发育，其内部损伤增加，故减弱了透射波的传播，透射波增幅减小。
入射能较小时，反射能随着入射能的增加而增大，且反射能增大的幅度也在逐渐增加，二者呈指数关系，不同入射能作用下磁铁矿石所表现出的变形特性是不同，当入射应力波能量较小时，岩石呈似脆性，吸能效果较差，能量主要以透射能形式耗散；当入射应力波能量较大时，岩石呈脆延性，岩石吸能效率随入射应力波能量的增大而增加。岩石吸能效率达到最高可达到约入射能量的40%；说明一半以上的能量在杆件上以弹性波的形式耗散。
3.2　破碎耗能与入射能量
磁铁矿石破碎耗能密度与应变率的关系见图8。
由图8可以看出，能耗密度与应变率之间呈线性关系。在磁铁矿石的冲击破碎行为中，破碎耗能密度越大，其吸收的能量也就越多，其内部的微裂纹数目也就越多，裂纹不断扩展贯通导致磁铁矿石的破碎程度也更加剧烈。
3.3　磁铁矿石破坏形态
从图9中破坏形态可以看出：宏观的破坏过程一般为边缘破裂、产生裂纹或裂隙、裂纹裂隙扩展、试件破碎。
应变率为43.94~82.59 s-1时，入射能较小，应力波通过岩石会导致岩石损伤，裂纹低速扩展，最终试块沿裂纹贯通分散为2~4大块；应变率为118.34 s-1时，入射能量逐渐增大，试块多破碎为大碎块，掺杂个别小块，碎块呈柱状和细粒状形态；在147.75 s-1的应变率下可见矿石被破碎为碎屑粉末，冲击杆速度较高的时候试件的应变率也相对较高，入射应力波携带的能量也相应地增多，从而试件内部获得极高的能量，激发出试样内的更多裂隙，并在此基础上形成了新的裂纹，原有的裂纹与新产生的裂纹相互交叉贯通，导致试样破碎成小块或细小碎屑，并伴随着粉末的产生。
4　有限元模型建立
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4.1　模拟方法及参数确定
建模在软件ANSYS中完成，使用LS-PREPOST软件进行后处理。其中试样采用适用于岩石材料高应变率、大变形问题的HJC本构。其中部分的参数确定可通过试验获得，其余参数参考相关成果[17-19]。见表4。
表中：强度参数：A、B、C、N分别表示标准化内聚力强度、标准化压力硬化系数、应变率系数、压力硬化系数，SFMAX为材料所能达到的最大标准化强度；压力参数：单轴压缩岩样的压碎体积压力和压碎体积应变分别对应Pc、μc，P1、μl分别为压实压力和压实体积应变，T为岩样最大拉伸应力，K1、K2、K3为常数；损伤参数：D1、D2为损伤常数，EFMIN为材料最小塑性应变。剩余两个参数为参考应变率EPS0和失效类型fs。
4.2　模型构建
依据实际装置尺寸建立有限元模型，采用映射网格划分。入射杆和透射杆沿径向划分20份，轴向划分200份，试样沿径向划分40份，轴向划分34份。总单元数为236266。有限元模型如图10所示。纺锤形子弹和入射杆采用CONTACT_AUTOMATIC_SURFACE_TO_SURFACE接触、试样与入射杆、透射杆之间采用CONTACT_EROSION_SURFACE_TO_SURFACE接触。为减少沙漏效应接触算法采用罚函数算法，罚函数因子K取2.0。
4.3　模型及参数有效性验证
利用ANSYS/LS-DYNA软件求解，将所得数值模拟结果导入后处理软件LS-PREPOST中，选取入射杆、透射杆中间位置提取入射、反射、透射应力波形。图11为典型的应力时程曲线。
从图11中可以看出，模拟入射波形近似为半正弦波，与试验得到波形接近。说明对试样加载的荷载，模拟与试验误差极小。证明了本次数值模拟的可靠性。
由于ANSYS中不可以设置应变率的大小，故由试验数据中应变率所对应的冲击速度来模拟不同冲击速度下的破坏形态。冲击速度8.32 m/s、16.18 m/s对应的应变率为43.94 s-1、118.34 s-1。
在LS-PREPOST后处理软件中选取冲击后试样前中后各3个单元点，得出试件的应力应变信息并绘制应力应变曲线。由图12可知，数值模拟的应力应变曲线与试验的曲线基本吻合。无较大量级差异，说明建模过程以及模型划分精度合格。同时也证明了HJC参数选择较合理。
4.4　模拟破坏形态分析
图13是模拟岩样在冲击速度8.32 m/s（43.94 s-1）下的破坏过程。从图13中可见，应力波在419 μs左右到达试样端面，之后在十几微秒的时间内应力波均匀作用于试件表面。在639 μs时，压应力到达试件边缘。在边缘处四个角应力明显大于入射端表面。之后随着应力波继续传播，在674 μs压应力反射成为拉伸波，在试件入射端面出现一个类似“十字”的反射拉伸波。随着时间增加，在724 μs反射拉伸波集中于试件入射杆端面一角，由于岩石类材料抗拉强度远小于抗压强度，试件边缘发生破坏。与试验在8.32 m/s冲击速度下的磁铁矿石破坏形态十分符合。
随着冲击速度的增大，入射应力在更短时间内到达了试件表面，429 μs时，入射应力均匀施加在试样入射杆端面。在529 μs时试件沿着圆周剥去一圈后同样反射拉伸波集中于试件一角，而此处就是试样最开始发生破坏的地方。559 μs时试件开始发生破坏。在749 μs从试件中心位置产生了轴向劈裂，裂纹贯穿了试件上下表面，试件形成了沿轴向的较大块体，此时的磁铁矿石试样破坏模式为轴向劈裂拉伸破坏。之后在849 μs时，试件内部应力持续升高，试件内部吸收能量增多，更多的裂隙发育扩展。部分大块岩石碎块被压碎成更小的碎块。故试样在冲击荷载下成为少量大块以及若干柱状小块。见图14。
5　结论
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基于分离式霍普金森压杆开展了不同冲击气压下对磁铁矿石的动态力学试验及破坏模式分析，试验结果如下：
（1）磁铁矿石在高应变率（147.75 s-1）下具有明显塑性变形，而在中低应变率下（43.94 s-1、58.42 s-1、82.59 s-1）下无明显塑性变形。其动态强度因子K与应变率呈良好线性拟合关系，K值增长范围在1.06至1.86之间，说明磁铁矿石是率敏感性材料。
（2）随着入射能从小到大地增加，反射能占比从10%增加至22%；透射能占比从78%降至38%，中低应变率下磁铁矿石无用功多以透射波形式耗散。而试件耗能呈线性上升趋势，在冲击气压0.7 MPa，入射能为273 J时，试件耗能占比达最大为40%。
（3）随冲击气压升高，磁铁矿石试样的破坏以劈裂破坏为主转化为以压碎破坏为主。磁铁矿石吸收能量增多，破坏程度也更加剧烈，破坏后粒度不断减小，由大块状变为针状和细粒状。
（4）利用ANSYS/LS-DYNA软件模拟了磁铁矿石在8.32 m/s（43.94 s-1）和16.18 m/s（147.75 s-1）速度下的破坏形态，很好地展现了磁铁矿石在不同冲击速度下的破坏过程。两种应变率下的试样都在入射杆端面形成一个“十字”拉伸波，且从边角处最开始发生破坏。结果和分析可以相关数值模拟试验提供选择参考。
基金
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  • 国家自然科学基金资助项目(52064025)
文献
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2023年第40卷第1期
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doi: 10.3963/j.issn.1001-487X.2023.01.003
  • 接收时间：2022-10-14
  • 首发时间：2026-03-19
  • 出版时间：2023-03-01
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  • 收稿日期：2022-10-14
基金
国家自然科学基金资助项目(52064025)
作者信息
    1.昆明理工大学　国土资源工程学院，昆明　650093
    2.云南省中—德蓝色矿山与特殊地下空间开发利用重点实验室，昆明　650093
    3.昆明理工大学　电力工程学院　，昆明　650500

通讯作者:

张智宇（1973-），男，广东韶关，教授，主要从事工程爆破及岩石破碎方面的研究，（E-mail）。
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https://castjournals.cast.org.cn/joweb/bp/CN/10.3963/j.issn.1001-487X.2023.01.003
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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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