An experimental technique of split Hopkinson pressure bar using fiber microdisplacement interferometer system for any reflector H. Fu, X. R. Tang, J. L. Li, and D. W. Tan Citation: Review of Scientific Instruments 85, 045120 (2014); doi: 10.1063/1.4871955 View online: http://dx.doi.org/10.1063/1.4871955 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Optical-fiber interferometer for velocity measurements with picosecond resolution Appl. Phys. Lett. 89, 111101 (2006); 10.1063/1.2335948 Thermal tuning of a fiber-optic interferometer for maximum sensitivity Rev. Sci. Instrum. 70, 3542 (1999); 10.1063/1.1149947 Design and operation of different optical fiber sensors for displacement measurements Rev. Sci. Instrum. 70, 2875 (1999); 10.1063/1.1149812 Optical fiber velocimetry: A technique for measuring velocity in two-dimensional flows Rev. Sci. Instrum. 69, 3215 (1998); 10.1063/1.1149086 Fiber interferometer-based variable temperature scanning force microscope Rev. Sci. Instrum. 68, 1776 (1997); 10.1063/1.1147992
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 045120 (2014)
An experimental technique of split Hopkinson pressure bar using fiber micro-displacement interferometer system for any reflector H. Fu,1 X. R. Tang,1 J. L. Li,1,2 and D. W. Tan1 1 National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, Sichuan, China 2 National University of Defense Technology, Changsha, Hunan 410071, China
(Received 6 November 2013; accepted 8 April 2014; published online 28 April 2014) A novel non-contact measurement technique had been developed for the mechanical properties of materials in Split Hopkinson Pressure Bars (SHPB). Instead of the traditional strain gages mounted on the surfaces of bars, two shutters were mounted on the end of bars to directly measure interfacial velocity using Fiber Micro-Displacement Interferometer System for Any Reflector. Using the new technique, the integrated stress-strain responses could be determined. The experimental technique was validated by SHPB test simulation. The technique had been used to investigate the dynamic response of a brittle explosive material. The results showed that the new experimental technique could be applied to the dynamic behavior in SHPB test. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4871955] I. INTRODUCTION
Since Hopkinson contrived original impacting bars system in 1914, the Split Hopkinson Pressure Bars (SHPB) had been developed by Kolsky1 and Davies2 to investigate the dynamic compressive behavior of engineering materials in the strain rate range of 102 –104 s−1 . Nowadays, SHPB had been widely used due to its ability to resolve the time evolution of material response and the simplicity of its operation. Over these decades, the system had also been extended for tensile,3, 4 torsion,5, 6 and shear7 responses of materials. An excellent review of the experimental technique was provided. It had been widely accepted that SHPB was a standard tool for dynamic response testing. In conventional SHPB experiment, the strain gauge and quartz-crystal transducer had been widely used.8 The strain gauges which were mounted on the surfaces of bars utilized the elasticity of the bars to deduce the properties of the material. The coefficients of strain gauges were very important for data analysis. However, the coefficients were easily influenced by ambient temperature and humidity. The situations may get more serious when semiconductor strain gauges were applied to the low-impedance, low-strength, and small strain failure brittle materials, such as rock, concrete, and explosive.9 The quartz-crystal transducers could be employed to determine the weak stress signals and examine the process of dynamic stress equilibrium for low-impedance materials during testing, but the strain of samples could not be measured. New experimental techniques for SHPB have never stopped being explored. With the development of optical technique, researchers had dedicated to the application of non-contact optical measurement techniques in SHPB. Griffith and Martin10 adopted the white light to measure the displacement of specimen end surfaces. Ramesh and Narasimhan11 investigated the radial dilatation of specimen using linear laser. Chen et al.12 used a laser gap gauge to measure the deformation of ultra soft sample directly. Those optical techniques were usually employed to determine the strain or deformations of samples, but the stress response in the 0034-6748/2014/85(4)/045120/5/$30.00
sample could not be obtained due to measuring displacement of the two ends. In this paper, we presented an optical experimental technique of SHPB using Fiber Micro-Displacement Interferometer System for Any Reflector (FMDISAR). Applying the new technique, the integrated stress-strain responses of brittle materials could be determined. In Sec. II, the conventional experimental technique of SHPB was briefly described. In Sec. III, the new experimental technique that we had developed was described. Finally, the results of simulation validation and SHPB test were presented.
II. CONVENTIONAL EXPERIMENTAL TECHNIQUE OF SHPB
As shown in Fig. 1, a conventional SHPB consisted of a striker bar, an incident bar, a transmission bar, and a sample placed between the incident and transmission bars. When the striker bar impacted the incident bar, an elastic compressive stress pulse, referred to as the incident pulse, was generated and propagates along the incident bar toward the specimen. When the incident pulse reached the specimen, part of the pulse was reflected backward into the incident bar due to the impedance mismatch at the bar-specimen interface. The remaining part of the pulse was transmitted into the specimen and, eventually, into the transmission bar. Axial strain gages mounted on the surfaces of the incident and transmission bars provided time-resolved measures of the elastic strain pulses in the bars. If the sample was in dynamic stress equilibrium, the stress, strain, and strain rate in sample were given by
85, 045120-1
σs =
ε=
EA εt (t), As
−2c u1 − u2 = l0 l0
(1) t
εr (t)dt,
(2)
0
© 2014 AIP Publishing LLC
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045120-2
Fu et al.
Rev. Sci. Instrum. 85, 045120 (2014)
FIG. 1. Schematic of a conventional SHPB.
v1 − v2 −2c ε˙ = = εr (t), l0 l0
(3)
where E, A, and c were the Young’s modulus, cross-sectional area, and wave speed of the bars, respectively. As and l0 were the initial cross-sectional area and initial length of specimen. εr (t) and εt (t) were reflected strain pulse and transmitted strain pulse measured by strain gages. u1 and u2 were the displacements at the sample-bar interfaces. v1 and v2 were the velocities at the sample-bar interfaces. We took subscripts 1 and 2 to represent the locations of the ends of the sample. Thus, the strain rate and strain in the specimen could be determined from the reflected pulse, and the stress in the specimen could be determined from the transmitted pulse, the above pulses were commonly obtained by strain gauges mounted on the surfaces of bars. The conventional experimental technique using strain gages had some limitations. The coefficients of strain gauge were difficult to determine accurate value. Since the resistance of strain gauges would be easily influenced by itself deformation, ambient temperature, and humidity. Furthermore, the conventional calibration work of the coefficients were carried out using laser-beam measurement velocity equipment before the formal test. However, the traditional laser-beam system was not accurate enough to measure the speed of striker. The striker would slow down and incline when getting out of the gun barrel. The measured speed was an average velocity of the striker moving through the laser-beam equipment, the velocity value would be bigger than the instantaneous velocity of striker impacting incident bar. Therefore, the obtained coefficients of strain gauges were not so accurate, these factors resulted in some uncertainty, especially for semiconductor strain gauges. III. A NEW EXPERIMENTAL TECHNIQUE OF SHPB
The main characteristic of the new technique was that the interfacial velocity profiles between the bars and specimen were determined instead of the reflected and transmitted strain pulse in the middle of bars. Schematic diagram of the new technique was shown in Fig. 2. Since the experimental operation was inconvenient to determine the interfaces velocity of original bars and specimen directly due to the limitations of space, the shutters with reflector slices were designed. Two 2.5 mm thick shutters, made of the same material with the bars, were attached at the front and back ends of the sample. The diameter of shutter was the same size with the bar (D = 20 mm), the radius of reflector slice R was the tenth of the diameter, R = 2 mm. As a part of shutter, a small step (0.2 mm thickness) was against the contact surface of sample.
The velocity of reflector slices were measured and used as the interfacial velocity between the bars and specimen. The velocity of two reflector slices were measured using a non-contact optical method, called Optical FMDISAR. The FMDISAR was based on the selected frequency character of the optical resonant cavity to measure the displacement or velocity history of the moving object. The laser beam from the light source was past-through a fiber circular and directed to the optic probe. The reflected light by the probe was as reference beam. The transmission light illuminates the moving surface by means of the optic probe. The signal beam, which carried the Doppler-shifted information of the object, would transmit again through the fiber circulator and enter the fiber magnifier. Finally, the signal beam interfered with the reference beam and outputs signals, which would be detected by photodetector and recorded by digital oscillograph. It was easy to calculate the moving displacement or velocity of the moving object from output signal by Fourier transformation. In comparison with other traditional methods, the FMDISAR was a non-contact, stable, reliable, and high accuracy velocity measurement system. It could be applied in the field of verberation, ultrasonic, micro-displacement, and so on, the displacement resolution could reach to 0.1 μm. Once the velocity of two reflector slices were determined using FMDISAR, the engineering strain rate and strain of specimen were determined directly from these signals: ε˙ (t) = ε(t) = 0
t
v1 (t) − v2 (t) , l0
(4)
v1 (t) − v2 (t) dt, l0
(5)
where v1 (t) and v2 (t) were the measurement velocity of reflector slices attached at the ends of incident and transmission bars, respectively. Since there was relationship between the
FIG. 2. Schematic of a new experimental technique.
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045120-3
Fu et al.
Rev. Sci. Instrum. 85, 045120 (2014)
velocity and strain in bars: εt (t) =
v2 (t) . c0
(6)
Specimen stress may be determined using the velocity of reflector slices mounted on the end of the transmission bar, the stress of specimen was given from Eq. (1): σ =
EAv2 (t) . A0 c0
(7)
Accordingly, the integrated stress-strain response of specimen was obtained directly by Eqs. (5) and (7). There was no need to account for dispersion or the propagation of stress wave in bars because the measurement was made exactly at the point of interest. The primary disadvantage of this technique was that there was no way to measure the stress at the incident bar-specimen interface and the dynamic stress equilibrium in sample could not be examined. However, for the reasons discussed above, this was not usually a serious drawback. In cases when this was important, a technique involving measurement of the incident stress pulse can be employed, such as quartz-crystal transducers embedded in the end of incident bars. IV. SIMULATION VALIDATION
In order to validate the new experimental technique, the SHPB test simulation was performed in LS-DYNA. The material of bar and shutters was aluminum alloy (material density of 2.78 g/cm3 and elastic modulus of 72 GPa). The lengths of the bars were 2000 mm, 1200 mm, and 300 mm for the incident, transmission, and striker bars, respectively. The sample was a low-strength and brittle material (sample density of 1.86 g/cm3 and elastic modulus of 7.5 GPa). The dimensions of shutters were as same as stated above. The 3D finite element model was shown in Fig. 3. There were two important questions to answer by simulation validation. One was that whether the velocity of reflector slices designed can replace the interfacial velocity between the bars and specimen, the other was that whether the stressstrain response deduced by the velocity of reflector slices can factually characterize the dynamic behavior of sample. This was discussed with the simulation and experimental results below.
FIG. 3. Simulation model of SHPB. The points In1 and In2 were gauges on the interfaces between shutters and specimen. The points Re1 and Re2 were gauges on the end of reflector slices.
FIG. 4. The velocity curves of reflector slices and interfaces between the bars and specimen in simulation.
V. RESULTS
To show the rationality of reflector slices designed, the velocity of reflector slices and interface of the shuttersspecimen were given and shown in Fig. 4. The closeness of the slices and interfaces velocity curves was evident. From this, it was concluded that the velocity of reflector slices could replace the interfacial velocity between the bars and specimen. In addition, the non-uniform velocity distribution on the end surface of the bar due to mismatch of cross-sectional area would be neglected. In order to answer the second question, the stress-strain curve calculated by the new technique was compared with the stress-strain curve predefined by an elastic modulus parameter. Two curves were shown in Fig. 5. One (dotted curve) was the stress-strain trace calculated from the velocity of reflector slices by Eqs. (5) and (7). The other (real line) was a known curve given by an elastic modulus as simulation parameter in sample. The good agreement with two curves indicated that the new technique described in this paper can be applied to determine the dynamic behavior of sample.
FIG. 5. The comparison of elastic stress-strain curves.
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045120-4
Fu et al.
FIG. 6. The original signal of FMDISAR.
The dynamic test of a brittle explosive material was performed using the new technique. The dimension of the aluminum alloy bars and shutters was described as simulation. The velocity signals from the two reflector slices were recorded using a Tektronix 7054 digital storage oscilloscope. The brittle material was a kind of Plastic Bonded Explosives (PBXs). The sample was a composite material consisted of 87% HMX, 7% TATB, and 6% Estane binder by weight (sample density of 1.86 g/cm3 , diameter of 10 mm, and thickness of 5 mm). When the striker impacted the incident bar, there was a compressive wave transmitting through all the bars. The moving information of reflector slices were sent to opticfiber probe by laser and finally recorded by digital oscillograph. The original signal was shown in Fig. 6. After the experimental data were processed, the velocity of the reflector slices v(t) was obtained. In order to compare the new technique with conventional technique, the SHPB test including reflector slices and semiconductor strain gauge was performed without sample, the two velocity curves deduced from different technique were compared and shown in Fig. 7. There
FIG. 7. The comparison of velocity curves.
Rev. Sci. Instrum. 85, 045120 (2014)
FIG. 8. The velocity curves of two reflector slices.
was an evident difference between this work and the conventional technique. The velocity amplitude of the conventional technique before amendment was lower than that of the new technique because of its limitations. After amendment according to the new technique, they were in good agreement. The pulse-shaper technique was also used for increasing the rise time of the incident pulse to ensure stress equilibrium in specimen. Once the velocity of two reflector slices v1 (t) and v2 (t) were captured, the stress-strain curves of sample could be determined by Eqs. (5) and (7). The velocity curves were shown in Fig. 8. The two stress-strain curves of explosive sample were shown in Fig. 9. The explosive sample was a typical brittle material. There was a direct correlation between the dynamic behavior of explosive and loading strain rate. The explosive occurred elastic deformation and no failure when strain rate was about 80 s−1 . The explosive was in failure state when strain rate was about 200 s−1 , failure stress was 61.5 MPa, and failure strain was 0.146. The explosive tended to behave elastically, while heavily loaded may yield, and then rapidly strain soften.
FIG. 9. The stress-strain curves of the explosive.
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045120-5
Fu et al.
VI. CONCLUSIONS
As stated above, the new experimental technique of SHPB was presented. The two shutters with reflector slices were designed and mounted on the end of bars to directly measure interfacial velocity using FMDISAR. The integrated stress-strain responses of specimen could be obtained from the velocity of reflector slices. ACKNOWLEDGMENTS
This work was supported by the Natural Science Foundation of China (NSFC) through Grant Nos. 11272294 and 110722271, National Key Laboratory Fund through Grant No. 2012-Z-05.
Rev. Sci. Instrum. 85, 045120 (2014) 1 H.
Kolsky, Proc. Phys. Soc., London, Sect. B 62, 676–700 (1949). M. Davis, Proc. R. Soc. London, Ser. A 240, 375–457 (1948). 3 T. Nicholas, Exp. Mech. 21, 177–188 (1981). 4 E. Cadoni, G. Solomos, and C. Albertini, Concr. Res. 61, 221–228 (2009). 5 H. D. Espinosa, A. Patanella, and M. Fisher, Exp. Mech. 40, 138–153 (2000). 6 H. Huang and R. Feng, Int. J. Solids Struct. 41, 2821–2835 (2004). 7 P. D. Zhao, F. Y. Lu, R. Chen, Y. L. Lin, J. L. Li, L. Lu, and G. L. Sun, Rev. Sci. Instrum. 82, 035110 (2011). 8 W. Chen, F. Lu, and B. Zhou, Exp. Mech. 40, 1–6 (2000). 9 D. J. Frew, M. J. Forrestal, and W. Chen, Exp. Mech. 42, 93–106 (2002). 10 L. J. Griffiths and D. J. Martin, J. Phys. D: Appl. Phys. 7(17), 2329–2344 (1974). 11 K. T. Ramesh and S. Narasimhan, Int. J. Solids Struct. 33(25), 3723–3738 (1996). 12 R. Chen, S. Huang, K. Xia, and F. Lu, Rev. Sci. Instrum. 80, 076108 (2009). 2 R.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 129.105.215.146 On: Wed, 24 Dec 2014 07:16:17
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 045120 (2014)
An experimental technique of split Hopkinson pressure bar using fiber micro-displacement interferometer system for any reflector H. Fu,1 X. R. Tang,1 J. L. Li,1,2 and D. W. Tan1 1 National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, Sichuan, China 2 National University of Defense Technology, Changsha, Hunan 410071, China
(Received 6 November 2013; accepted 8 April 2014; published online 28 April 2014) A novel non-contact measurement technique had been developed for the mechanical properties of materials in Split Hopkinson Pressure Bars (SHPB). Instead of the traditional strain gages mounted on the surfaces of bars, two shutters were mounted on the end of bars to directly measure interfacial velocity using Fiber Micro-Displacement Interferometer System for Any Reflector. Using the new technique, the integrated stress-strain responses could be determined. The experimental technique was validated by SHPB test simulation. The technique had been used to investigate the dynamic response of a brittle explosive material. The results showed that the new experimental technique could be applied to the dynamic behavior in SHPB test. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4871955] I. INTRODUCTION
Since Hopkinson contrived original impacting bars system in 1914, the Split Hopkinson Pressure Bars (SHPB) had been developed by Kolsky1 and Davies2 to investigate the dynamic compressive behavior of engineering materials in the strain rate range of 102 –104 s−1 . Nowadays, SHPB had been widely used due to its ability to resolve the time evolution of material response and the simplicity of its operation. Over these decades, the system had also been extended for tensile,3, 4 torsion,5, 6 and shear7 responses of materials. An excellent review of the experimental technique was provided. It had been widely accepted that SHPB was a standard tool for dynamic response testing. In conventional SHPB experiment, the strain gauge and quartz-crystal transducer had been widely used.8 The strain gauges which were mounted on the surfaces of bars utilized the elasticity of the bars to deduce the properties of the material. The coefficients of strain gauges were very important for data analysis. However, the coefficients were easily influenced by ambient temperature and humidity. The situations may get more serious when semiconductor strain gauges were applied to the low-impedance, low-strength, and small strain failure brittle materials, such as rock, concrete, and explosive.9 The quartz-crystal transducers could be employed to determine the weak stress signals and examine the process of dynamic stress equilibrium for low-impedance materials during testing, but the strain of samples could not be measured. New experimental techniques for SHPB have never stopped being explored. With the development of optical technique, researchers had dedicated to the application of non-contact optical measurement techniques in SHPB. Griffith and Martin10 adopted the white light to measure the displacement of specimen end surfaces. Ramesh and Narasimhan11 investigated the radial dilatation of specimen using linear laser. Chen et al.12 used a laser gap gauge to measure the deformation of ultra soft sample directly. Those optical techniques were usually employed to determine the strain or deformations of samples, but the stress response in the 0034-6748/2014/85(4)/045120/5/$30.00
sample could not be obtained due to measuring displacement of the two ends. In this paper, we presented an optical experimental technique of SHPB using Fiber Micro-Displacement Interferometer System for Any Reflector (FMDISAR). Applying the new technique, the integrated stress-strain responses of brittle materials could be determined. In Sec. II, the conventional experimental technique of SHPB was briefly described. In Sec. III, the new experimental technique that we had developed was described. Finally, the results of simulation validation and SHPB test were presented.
II. CONVENTIONAL EXPERIMENTAL TECHNIQUE OF SHPB
As shown in Fig. 1, a conventional SHPB consisted of a striker bar, an incident bar, a transmission bar, and a sample placed between the incident and transmission bars. When the striker bar impacted the incident bar, an elastic compressive stress pulse, referred to as the incident pulse, was generated and propagates along the incident bar toward the specimen. When the incident pulse reached the specimen, part of the pulse was reflected backward into the incident bar due to the impedance mismatch at the bar-specimen interface. The remaining part of the pulse was transmitted into the specimen and, eventually, into the transmission bar. Axial strain gages mounted on the surfaces of the incident and transmission bars provided time-resolved measures of the elastic strain pulses in the bars. If the sample was in dynamic stress equilibrium, the stress, strain, and strain rate in sample were given by
85, 045120-1
σs =
ε=
EA εt (t), As
−2c u1 − u2 = l0 l0
(1) t
εr (t)dt,
(2)
0
© 2014 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 129.105.215.146 On: Wed, 24 Dec 2014 07:16:17
045120-2
Fu et al.
Rev. Sci. Instrum. 85, 045120 (2014)
FIG. 1. Schematic of a conventional SHPB.
v1 − v2 −2c ε˙ = = εr (t), l0 l0
(3)
where E, A, and c were the Young’s modulus, cross-sectional area, and wave speed of the bars, respectively. As and l0 were the initial cross-sectional area and initial length of specimen. εr (t) and εt (t) were reflected strain pulse and transmitted strain pulse measured by strain gages. u1 and u2 were the displacements at the sample-bar interfaces. v1 and v2 were the velocities at the sample-bar interfaces. We took subscripts 1 and 2 to represent the locations of the ends of the sample. Thus, the strain rate and strain in the specimen could be determined from the reflected pulse, and the stress in the specimen could be determined from the transmitted pulse, the above pulses were commonly obtained by strain gauges mounted on the surfaces of bars. The conventional experimental technique using strain gages had some limitations. The coefficients of strain gauge were difficult to determine accurate value. Since the resistance of strain gauges would be easily influenced by itself deformation, ambient temperature, and humidity. Furthermore, the conventional calibration work of the coefficients were carried out using laser-beam measurement velocity equipment before the formal test. However, the traditional laser-beam system was not accurate enough to measure the speed of striker. The striker would slow down and incline when getting out of the gun barrel. The measured speed was an average velocity of the striker moving through the laser-beam equipment, the velocity value would be bigger than the instantaneous velocity of striker impacting incident bar. Therefore, the obtained coefficients of strain gauges were not so accurate, these factors resulted in some uncertainty, especially for semiconductor strain gauges. III. A NEW EXPERIMENTAL TECHNIQUE OF SHPB
The main characteristic of the new technique was that the interfacial velocity profiles between the bars and specimen were determined instead of the reflected and transmitted strain pulse in the middle of bars. Schematic diagram of the new technique was shown in Fig. 2. Since the experimental operation was inconvenient to determine the interfaces velocity of original bars and specimen directly due to the limitations of space, the shutters with reflector slices were designed. Two 2.5 mm thick shutters, made of the same material with the bars, were attached at the front and back ends of the sample. The diameter of shutter was the same size with the bar (D = 20 mm), the radius of reflector slice R was the tenth of the diameter, R = 2 mm. As a part of shutter, a small step (0.2 mm thickness) was against the contact surface of sample.
The velocity of reflector slices were measured and used as the interfacial velocity between the bars and specimen. The velocity of two reflector slices were measured using a non-contact optical method, called Optical FMDISAR. The FMDISAR was based on the selected frequency character of the optical resonant cavity to measure the displacement or velocity history of the moving object. The laser beam from the light source was past-through a fiber circular and directed to the optic probe. The reflected light by the probe was as reference beam. The transmission light illuminates the moving surface by means of the optic probe. The signal beam, which carried the Doppler-shifted information of the object, would transmit again through the fiber circulator and enter the fiber magnifier. Finally, the signal beam interfered with the reference beam and outputs signals, which would be detected by photodetector and recorded by digital oscillograph. It was easy to calculate the moving displacement or velocity of the moving object from output signal by Fourier transformation. In comparison with other traditional methods, the FMDISAR was a non-contact, stable, reliable, and high accuracy velocity measurement system. It could be applied in the field of verberation, ultrasonic, micro-displacement, and so on, the displacement resolution could reach to 0.1 μm. Once the velocity of two reflector slices were determined using FMDISAR, the engineering strain rate and strain of specimen were determined directly from these signals: ε˙ (t) = ε(t) = 0
t
v1 (t) − v2 (t) , l0
(4)
v1 (t) − v2 (t) dt, l0
(5)
where v1 (t) and v2 (t) were the measurement velocity of reflector slices attached at the ends of incident and transmission bars, respectively. Since there was relationship between the
FIG. 2. Schematic of a new experimental technique.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 129.105.215.146 On: Wed, 24 Dec 2014 07:16:17
045120-3
Fu et al.
Rev. Sci. Instrum. 85, 045120 (2014)
velocity and strain in bars: εt (t) =
v2 (t) . c0
(6)
Specimen stress may be determined using the velocity of reflector slices mounted on the end of the transmission bar, the stress of specimen was given from Eq. (1): σ =
EAv2 (t) . A0 c0
(7)
Accordingly, the integrated stress-strain response of specimen was obtained directly by Eqs. (5) and (7). There was no need to account for dispersion or the propagation of stress wave in bars because the measurement was made exactly at the point of interest. The primary disadvantage of this technique was that there was no way to measure the stress at the incident bar-specimen interface and the dynamic stress equilibrium in sample could not be examined. However, for the reasons discussed above, this was not usually a serious drawback. In cases when this was important, a technique involving measurement of the incident stress pulse can be employed, such as quartz-crystal transducers embedded in the end of incident bars. IV. SIMULATION VALIDATION
In order to validate the new experimental technique, the SHPB test simulation was performed in LS-DYNA. The material of bar and shutters was aluminum alloy (material density of 2.78 g/cm3 and elastic modulus of 72 GPa). The lengths of the bars were 2000 mm, 1200 mm, and 300 mm for the incident, transmission, and striker bars, respectively. The sample was a low-strength and brittle material (sample density of 1.86 g/cm3 and elastic modulus of 7.5 GPa). The dimensions of shutters were as same as stated above. The 3D finite element model was shown in Fig. 3. There were two important questions to answer by simulation validation. One was that whether the velocity of reflector slices designed can replace the interfacial velocity between the bars and specimen, the other was that whether the stressstrain response deduced by the velocity of reflector slices can factually characterize the dynamic behavior of sample. This was discussed with the simulation and experimental results below.
FIG. 3. Simulation model of SHPB. The points In1 and In2 were gauges on the interfaces between shutters and specimen. The points Re1 and Re2 were gauges on the end of reflector slices.
FIG. 4. The velocity curves of reflector slices and interfaces between the bars and specimen in simulation.
V. RESULTS
To show the rationality of reflector slices designed, the velocity of reflector slices and interface of the shuttersspecimen were given and shown in Fig. 4. The closeness of the slices and interfaces velocity curves was evident. From this, it was concluded that the velocity of reflector slices could replace the interfacial velocity between the bars and specimen. In addition, the non-uniform velocity distribution on the end surface of the bar due to mismatch of cross-sectional area would be neglected. In order to answer the second question, the stress-strain curve calculated by the new technique was compared with the stress-strain curve predefined by an elastic modulus parameter. Two curves were shown in Fig. 5. One (dotted curve) was the stress-strain trace calculated from the velocity of reflector slices by Eqs. (5) and (7). The other (real line) was a known curve given by an elastic modulus as simulation parameter in sample. The good agreement with two curves indicated that the new technique described in this paper can be applied to determine the dynamic behavior of sample.
FIG. 5. The comparison of elastic stress-strain curves.
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045120-4
Fu et al.
FIG. 6. The original signal of FMDISAR.
The dynamic test of a brittle explosive material was performed using the new technique. The dimension of the aluminum alloy bars and shutters was described as simulation. The velocity signals from the two reflector slices were recorded using a Tektronix 7054 digital storage oscilloscope. The brittle material was a kind of Plastic Bonded Explosives (PBXs). The sample was a composite material consisted of 87% HMX, 7% TATB, and 6% Estane binder by weight (sample density of 1.86 g/cm3 , diameter of 10 mm, and thickness of 5 mm). When the striker impacted the incident bar, there was a compressive wave transmitting through all the bars. The moving information of reflector slices were sent to opticfiber probe by laser and finally recorded by digital oscillograph. The original signal was shown in Fig. 6. After the experimental data were processed, the velocity of the reflector slices v(t) was obtained. In order to compare the new technique with conventional technique, the SHPB test including reflector slices and semiconductor strain gauge was performed without sample, the two velocity curves deduced from different technique were compared and shown in Fig. 7. There
FIG. 7. The comparison of velocity curves.
Rev. Sci. Instrum. 85, 045120 (2014)
FIG. 8. The velocity curves of two reflector slices.
was an evident difference between this work and the conventional technique. The velocity amplitude of the conventional technique before amendment was lower than that of the new technique because of its limitations. After amendment according to the new technique, they were in good agreement. The pulse-shaper technique was also used for increasing the rise time of the incident pulse to ensure stress equilibrium in specimen. Once the velocity of two reflector slices v1 (t) and v2 (t) were captured, the stress-strain curves of sample could be determined by Eqs. (5) and (7). The velocity curves were shown in Fig. 8. The two stress-strain curves of explosive sample were shown in Fig. 9. The explosive sample was a typical brittle material. There was a direct correlation between the dynamic behavior of explosive and loading strain rate. The explosive occurred elastic deformation and no failure when strain rate was about 80 s−1 . The explosive was in failure state when strain rate was about 200 s−1 , failure stress was 61.5 MPa, and failure strain was 0.146. The explosive tended to behave elastically, while heavily loaded may yield, and then rapidly strain soften.
FIG. 9. The stress-strain curves of the explosive.
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VI. CONCLUSIONS
As stated above, the new experimental technique of SHPB was presented. The two shutters with reflector slices were designed and mounted on the end of bars to directly measure interfacial velocity using FMDISAR. The integrated stress-strain responses of specimen could be obtained from the velocity of reflector slices. ACKNOWLEDGMENTS
This work was supported by the Natural Science Foundation of China (NSFC) through Grant Nos. 11272294 and 110722271, National Key Laboratory Fund through Grant No. 2012-Z-05.
Rev. Sci. Instrum. 85, 045120 (2014) 1 H.
Kolsky, Proc. Phys. Soc., London, Sect. B 62, 676–700 (1949). M. Davis, Proc. R. Soc. London, Ser. A 240, 375–457 (1948). 3 T. Nicholas, Exp. Mech. 21, 177–188 (1981). 4 E. Cadoni, G. Solomos, and C. Albertini, Concr. Res. 61, 221–228 (2009). 5 H. D. Espinosa, A. Patanella, and M. Fisher, Exp. Mech. 40, 138–153 (2000). 6 H. Huang and R. Feng, Int. J. Solids Struct. 41, 2821–2835 (2004). 7 P. D. Zhao, F. Y. Lu, R. Chen, Y. L. Lin, J. L. Li, L. Lu, and G. L. Sun, Rev. Sci. Instrum. 82, 035110 (2011). 8 W. Chen, F. Lu, and B. Zhou, Exp. Mech. 40, 1–6 (2000). 9 D. J. Frew, M. J. Forrestal, and W. Chen, Exp. Mech. 42, 93–106 (2002). 10 L. J. Griffiths and D. J. Martin, J. Phys. D: Appl. Phys. 7(17), 2329–2344 (1974). 11 K. T. Ramesh and S. Narasimhan, Int. J. Solids Struct. 33(25), 3723–3738 (1996). 12 R. Chen, S. Huang, K. Xia, and F. Lu, Rev. Sci. Instrum. 80, 076108 (2009). 2 R.
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