岩石SHPB测试中试样恒应变率变形的加载条件
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摘要
从分析霍布金逊压杆测试中试样变形应力、入射应力、反射应力和透射应力的相互关系入手,获得满足试样恒应变率变形所需的加载条件,即只有当加载应力和试样的变形应力具有相同的变化规律时,试样变形才处于恒应变率状态。试验结果表明,整形器法和异形冲头法都能在一定程度上实现试样的恒应变率测试,双试样法实际是整形器法的一个特例。整形器法更适合于理想弹脆性岩类的测试,异形冲头法对具有幂函数型本构曲线岩类和未知本构特征材料的测试有利,并且可重复性好。能产生半正弦波的异形冲头法可减小波形弥散对测试结果的影响。
The relationships among specimen stress,incident stress,reflected stress and transmitted stress were analyzed;and the loading condition for specimen deformation at constant strain rate was found out,i. e.,only when the loading stress and deformation stress in specimen have the same changing pattern,the specimen deforms at a constant strain rate. The tests show that constant strain rate of specimen can be achieved by pulse shaper method and special shape striker method. Double specimen method is actually a special case of pulse shaper method. Pulse shaper method is favorable for tests of perfect elastic brittle material. And special shape striker method is useful for the split Hopkinson pressure bar(SHPB) tests of materials with power function constitutive relation or materials with no foregone constitutive information. Special shape striker method has more repeatability than pulse shaper method. Special shape striker method with half-sine incident wave can reduce the influences caused by wave dispersion.
The relationships among specimen stress,incident stress,reflected stress and transmitted stress were analyzed;and the loading condition for specimen deformation at constant strain rate was found out,i. e.,only when the loading stress and deformation stress in specimen have the same changing pattern,the specimen deforms at a constant strain rate. The tests show that constant strain rate of specimen can be achieved by pulse shaper method and special shape striker method. Double specimen method is actually a special case of pulse shaper method. Pulse shaper method is favorable for tests of perfect elastic brittle material. And special shape striker method is useful for the split Hopkinson pressure bar(SHPB) tests of materials with power function constitutive relation or materials with no foregone constitutive information. Special shape striker method has more repeatability than pulse shaper method. Special shape striker method with half-sine incident wave can reduce the influences caused by wave dispersion.
引文
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[2]OKUBO S,NISHIMATSU Y,HE C.Loading rate dependence of class II rock behavior in uniaxial and triaxial compression tests—an application of a proposed new control method[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1990,27(6):559–562.
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[6]ZHU W C.Numerical modeling of the effect of rock heterogeneity on dynamic tensile strength[J].Rock Mechanics and Rock Engineering,2008,41(5):771–779.
[7]CHO S H,OGATA Y,KANEKO K.Strain-rate dependency of the dynamic tensile strength of rock[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(5):763–777.
[8]ZHOU Z L,MA G W,LI X B.Dynamic Brazilian splitting and spalling tests for granite[C]//Proceedings of the11th Congress of the ISRM2007.Lisbon,Portugal:Taylor and Francis Group,2007:1127–1130.
[9]RAVICHANDRAN G,SUBHASH G.Critical appraisal of limiting strain rates for compression testing of ceramics in a split Hopkinson pressure bar[J].J.America Ceram Soc.,1994,77(1):263–267.
[10]TEDESCO J W,ROSS C A.Strain-rate dependent constitutive equations for concrete[J].Journal of Pressure Vessel Technology,Transactions of the ASME,1998,120(4):398–405.
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[13]JEROME E L.Feasibility of a6-inch split Hopkinson pressure bar[R].AD–A243473,1991.
[14]刘孝敏,胡时胜.应力脉冲在变截面SHPB锥杆中的传播特性[J].爆炸与冲击,2000,20(2):110–114.(LIU Xiaomin,HU Shisheng.Wave propagation characteristics in cone bars used for variable cross-section SHPB[J].Explosion and Shock Waves,2000,20(2):110–114.(in Chinese))
[15]李夕兵,古德生.冲击载荷下岩石动态应力应变全图测试中的合理加载波形[J].爆炸与冲击,1993,13(2):125–131.(LI Xibing,GU Desheng.Reasonable loading wave for obtaining stress-strain curves of rock under dynamic impact[J].Explosion and Shock Waves,1993,13(2):125–131.(in Chinese))
[16]刘德顺,彭佑多,李夕兵,等.冲击活塞的动态反演设计与试验研究[J].机械工程学报,1998,34(4):78–95.(LIU Deshun,PENG Youduo,LI Xibing,et al.Inverse design and experimental study of impact piston[J].Chinese Journal of Mechanical Engineering,1998,34(4):78–84.(in Chinese))
[17]LOK T S,LI X B.Testing and response of large diameter brittle materials subjected to high strain rate[J].Journal of Materials in Civil Engineering,ASCE,2001,14(3):262–269.
[18]李夕兵,周子龙,王卫华.运用有限元和神经网络为SHPB装置构造理想冲头[J].岩石力学与工程学报,2005,24(23):4215–4219.(LI Xibing,ZHOU Zilong,WANG Weihua.Construction of ideal striker for SHPB device based on FEM and neural network[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(23):4215–4219.(in Chinese))
[19]NEMAT-NASSER S.ISAACS J B,STARRETT J E.Hopkinson techniques for dynamic recovery experiments[C]//Proceedings of the Royal Society of London.[S.l.]:[s.n.],1991:371–391.
[20]FREW D J,FORRESTAL M J,CHEN W.Pulse shaping techniquesfor testing brittle materials with a split Hopkinson pressure bar[J].Experimental Mechanics,2002,42(1):93–106.
[21]赵习金,卢芳云,王悟,等.入射波整形技术的试验和理论研究[J].高压物理学报,2004,18(3):231–236.(ZHAO Xijin,LU Fangyun,WANG Wu,et al.The experimental and theoretical study on the incident pulse shaping technique[J].Chinese Journal of High Pressure Physics,2004,18(3):231–236.(in Chinese))
[22]胡金生,唐德高,陈向欣,等.提高大直径SHPB装置试验精度的方法[J].解放军理工大学学报,2003,4(1):71–74.(HU Jinsheng,TANG Degao,CHEN Xiangxin,et al.Method of enhancing experimental precision for big radial size SHPB equipment[J].Journal of PLA University of Science and Technology,2003,4(1):71–74.(in Chinese))
[23]CHENG Z Q,CRANDALL J R,PILKEY W D.Wave dispersion and attenuation in viscoelastic split Hopkinson pressure bar[J].Shock and Vibration,1998,5(5/6):307–315.
[24]ZHAO H,GARY G.A three-dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar:application to experimental techniques[J].Journal of the Mechanics and Physics of Solids,1995,43(8):1335–1348.
[25]BACON C.An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar[J].Experimental Mechanics,1998,38(4):242–249.
[26]LI X B,LOK T S,ZHAO J,et al.Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic stress-strain curves for rocks[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(7):1055–1060.
[27]LI X B,ZHOU Z L,ZHAO Y S.Approach to minish scattering of results for split Hopkinson pressure bar test[J].Journal of Central South University of Technology,2007,14(3):404–407.
[28]MENG H,LI Q M.Correlation between the accuracy of a SHPB test and the stress uniformity based on numerical experiments[J].International Journal of Impact Engineering,2003,28(5):537–555.
[29]WU X J,GORHAM D A.Stress equilibrium in the split Hopkinson pressure bar test[J].Journal de Physique,1997,7(3):91–96.
[30]ELLWOOD S,GRIFFITHS L J,PARRY D J.Materials testing at high constant strain rates[J].Journal of Physics E:Scientific Instruments,1982,15(3):280–282.
[31]陶俊林,田常津,陈裕泽,等.SHPB系统试件恒应变率加载试验方法研究[J].爆炸与冲击,2004,24(5):413–418.(TAO Junlin,TIAN Changjin,CHEN Yuze,et al.Investigation of experimental method to obtain constant strain rate of specimen in SHPB[J].Explosive and Shock Waves,2004,24(5):413–418.(in Chinese))
[2]OKUBO S,NISHIMATSU Y,HE C.Loading rate dependence of class II rock behavior in uniaxial and triaxial compression tests—an application of a proposed new control method[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1990,27(6):559–562.
[3]李夕兵,古德生.岩石冲击动力学[M].长沙:中南工业大学出版社,1994:1–20.(LI Xibing,GU Desheng.Rock impact dynamics[M].Changsha:Central South University of Technology Press,1994:1–20.(Chinese))
[4]戚承志,苗启松,钱七虎.考虑强度–应变率依赖性的岩石弹塑性动力模型[J].世界地震工程,2002,18(3):52–56.(QI Chengzhi,MIAO Qisong,QIAN Qihu.Dynamical model of rocks with consideration of strength-strain rate dependence[J].World Earthquake Engineering,2002,18(3):52–56.(in Chinese))
[5]ZHAO J,LI H B.Experimental determination of dynamic tensile properties of a granite[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(5):861–866.
[6]ZHU W C.Numerical modeling of the effect of rock heterogeneity on dynamic tensile strength[J].Rock Mechanics and Rock Engineering,2008,41(5):771–779.
[7]CHO S H,OGATA Y,KANEKO K.Strain-rate dependency of the dynamic tensile strength of rock[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(5):763–777.
[8]ZHOU Z L,MA G W,LI X B.Dynamic Brazilian splitting and spalling tests for granite[C]//Proceedings of the11th Congress of the ISRM2007.Lisbon,Portugal:Taylor and Francis Group,2007:1127–1130.
[9]RAVICHANDRAN G,SUBHASH G.Critical appraisal of limiting strain rates for compression testing of ceramics in a split Hopkinson pressure bar[J].J.America Ceram Soc.,1994,77(1):263–267.
[10]TEDESCO J W,ROSS C A.Strain-rate dependent constitutive equations for concrete[J].Journal of Pressure Vessel Technology,Transactions of the ASME,1998,120(4):398–405.
[11]ZHAO H.A study on testing techniques for concrete-like materials under compressive impact loading[J].Cement and Concrete Composites,1998,20(4):293–299.
[12]ROSS C A,THOMPSON P Y,TEDESCO J W.Split Hopkinson pressure bar tests on concrete and mortar in tension and compression[J].ACI Materials Journal,1989,86(5):475–481.
[13]JEROME E L.Feasibility of a6-inch split Hopkinson pressure bar[R].AD–A243473,1991.
[14]刘孝敏,胡时胜.应力脉冲在变截面SHPB锥杆中的传播特性[J].爆炸与冲击,2000,20(2):110–114.(LIU Xiaomin,HU Shisheng.Wave propagation characteristics in cone bars used for variable cross-section SHPB[J].Explosion and Shock Waves,2000,20(2):110–114.(in Chinese))
[15]李夕兵,古德生.冲击载荷下岩石动态应力应变全图测试中的合理加载波形[J].爆炸与冲击,1993,13(2):125–131.(LI Xibing,GU Desheng.Reasonable loading wave for obtaining stress-strain curves of rock under dynamic impact[J].Explosion and Shock Waves,1993,13(2):125–131.(in Chinese))
[16]刘德顺,彭佑多,李夕兵,等.冲击活塞的动态反演设计与试验研究[J].机械工程学报,1998,34(4):78–95.(LIU Deshun,PENG Youduo,LI Xibing,et al.Inverse design and experimental study of impact piston[J].Chinese Journal of Mechanical Engineering,1998,34(4):78–84.(in Chinese))
[17]LOK T S,LI X B.Testing and response of large diameter brittle materials subjected to high strain rate[J].Journal of Materials in Civil Engineering,ASCE,2001,14(3):262–269.
[18]李夕兵,周子龙,王卫华.运用有限元和神经网络为SHPB装置构造理想冲头[J].岩石力学与工程学报,2005,24(23):4215–4219.(LI Xibing,ZHOU Zilong,WANG Weihua.Construction of ideal striker for SHPB device based on FEM and neural network[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(23):4215–4219.(in Chinese))
[19]NEMAT-NASSER S.ISAACS J B,STARRETT J E.Hopkinson techniques for dynamic recovery experiments[C]//Proceedings of the Royal Society of London.[S.l.]:[s.n.],1991:371–391.
[20]FREW D J,FORRESTAL M J,CHEN W.Pulse shaping techniquesfor testing brittle materials with a split Hopkinson pressure bar[J].Experimental Mechanics,2002,42(1):93–106.
[21]赵习金,卢芳云,王悟,等.入射波整形技术的试验和理论研究[J].高压物理学报,2004,18(3):231–236.(ZHAO Xijin,LU Fangyun,WANG Wu,et al.The experimental and theoretical study on the incident pulse shaping technique[J].Chinese Journal of High Pressure Physics,2004,18(3):231–236.(in Chinese))
[22]胡金生,唐德高,陈向欣,等.提高大直径SHPB装置试验精度的方法[J].解放军理工大学学报,2003,4(1):71–74.(HU Jinsheng,TANG Degao,CHEN Xiangxin,et al.Method of enhancing experimental precision for big radial size SHPB equipment[J].Journal of PLA University of Science and Technology,2003,4(1):71–74.(in Chinese))
[23]CHENG Z Q,CRANDALL J R,PILKEY W D.Wave dispersion and attenuation in viscoelastic split Hopkinson pressure bar[J].Shock and Vibration,1998,5(5/6):307–315.
[24]ZHAO H,GARY G.A three-dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar:application to experimental techniques[J].Journal of the Mechanics and Physics of Solids,1995,43(8):1335–1348.
[25]BACON C.An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar[J].Experimental Mechanics,1998,38(4):242–249.
[26]LI X B,LOK T S,ZHAO J,et al.Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic stress-strain curves for rocks[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(7):1055–1060.
[27]LI X B,ZHOU Z L,ZHAO Y S.Approach to minish scattering of results for split Hopkinson pressure bar test[J].Journal of Central South University of Technology,2007,14(3):404–407.
[28]MENG H,LI Q M.Correlation between the accuracy of a SHPB test and the stress uniformity based on numerical experiments[J].International Journal of Impact Engineering,2003,28(5):537–555.
[29]WU X J,GORHAM D A.Stress equilibrium in the split Hopkinson pressure bar test[J].Journal de Physique,1997,7(3):91–96.
[30]ELLWOOD S,GRIFFITHS L J,PARRY D J.Materials testing at high constant strain rates[J].Journal of Physics E:Scientific Instruments,1982,15(3):280–282.
[31]陶俊林,田常津,陈裕泽,等.SHPB系统试件恒应变率加载试验方法研究[J].爆炸与冲击,2004,24(5):413–418.(TAO Junlin,TIAN Changjin,CHEN Yuze,et al.Investigation of experimental method to obtain constant strain rate of specimen in SHPB[J].Explosive and Shock Waves,2004,24(5):413–418.(in Chinese))
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