Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 173 (217 ) 68 614 11th International Symposium on Plasticity and Impact Mechanics, Implast 216 The Effect of Specimen Dimension on the Results of the Split- Hopkinson Tension Bar Testing Dini A. Prabowo a, Muhammad A. Kariem a, *, Leonardo Gunawan a a Faculty of Mechanical and Aerospace Engineering, Bandung Institute of Technology, Ganesha Street no. 1 Street, Bandung, West Java 4132, Indonesia Abstract The split-hopkinson tension bar (SHTB) has been used widely to determine the dynamic characteristics of materials. Despite of its application, the tensile test specimen has not been standardised yet, whereas its dimension could affect the test results. Therefore, it is necessary to study the consistency of SHTB results by varying the dimension of its specimen. This paper examines whether consistent results can be achieved from three case studies of SHTB in a direct method. The study was conducted by numerical simulation using LS-DYNA. A dumbbell-shaped specimen was designed similar to the standard specimen on ASTM A37. Pressure bars were made of Maraging steel with 14 mm in diameter and a flange with thickness of 5 mm was used, while the specimen was made of 16 mild steel. The simplified Johnson-Cook was used as the constitutive material model. Three case studies were carried out. The first case study used a group of specimens with thesame gage length of 6 mm and varied diameters; the second case study used a group of specimens with the same diameter of 8 mm and varied lengths; and the third case study used a group of specimens with the same gage length of 8 mm and varied diameters. Based on the results of all case studies, the specimen s length-to-diameter ratio (L/D) of.75 generates a good stress-strain behavior. 217 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 216 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4./). Peer-review under responsibility of the organizing committee of Implast 216. Peer-review under responsibility of the organizing committee of Implast 216 Keywords: High-strain rate testing; split-hopkinson tension bar; dumbbell-shaped specimen standard. 1. Introduction The Hopkinson pressure bar technique has been commonly used for the dynamic characterisation of materials. This technique is classified into dynamic high-strain rates and can be conducted in several difference ways: compression, tension, torsion, shear and triaxial. The technique is named after the Hopkinson family (John and Bertram Hopkinson) [1-4] for their pioneering and major contribution to the research of high strain rate testing. In 1949, Kolsky [5] extended the Hopkinson bar technique for the dynamic characterisation of several materials: polythene, natural and * Corresponding author. Tel.: +62-22-25979; fax: +62-22-256361. E-mail address: kariem@edc.ms.itb.ac.id 1877-758 217 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4./). Peer-review under responsibility of the organizing committee of Implast 216 doi:1.116/j.proeng.216.12.114
Dini A. Prabowo et al. / Procedia Engineering 173 ( 217 ) 68 614 69 synthetic rubbers, polymethylmethacrylate (PMMA), copper and lead. Instead of one pressure bar, he promoted using two elastic bars where a specimen was sandwiched in between. Therefore, the technique has since been known as the split Hopkinson pressure bar (SHPB) or Kolsky bar. One of the popular techniques is the split-hopkinson tension bar (SHTB), which has been commonly used to determine the dynamic tensile stress-strain curve of materials. The basic principle of SHTB is similar to SHPB. The main differences between these two techniques are the method for generating the pulse, the specimen design and the method for attaching the specimen [6]. Similar to the SHPB, the SHTB has not been standardized yet. The SHTB technique used an apparatus with the dimensions and the materials chosen by its researcher without any specific explanation. Consequently, the results of the tests are slightly different one from another. Three methods of SHTB have been developed. The first methodis the direct method using a top-hat specimen developed by Lindholm and Yeakley [7] in 1968. A solid input bar is used, while the output bar is a hollow tube. The second method is the indirect method developed by Nicholas [8] in 198. A dumbbell-shaped specimen with threads on each end-side is used. A collar is applied to protect the specimen from the compressive pulse, thus it will propagate to the output bar, while the specimen will only receive pulse being reflected from the free-end of the output bar as a tension pulse. The third method is the direct method with striker tube developed by Nemat-Nasser [9] in 1991. In this method three kinds of specimen can be used: cylindrical, dumbbell-shaped, and flat. The later method has been commonly used due to its advantages such as the simplicity of the specimen geometry compared to those of Lindholm s and Yeakley s methods and the transmitted wave being recorded is clearer than Nicholas method. This paper examines the effect of specimen dimension on the results of SHTB testing. Three case studies of SHTB in Nemat-Nasser s method have been carried out. The first case study group used specimens with the same gage length of 6 mm and varied diameters; the second case study used specimens with the same diameter of 8 mm and varied lengths; and the third case study used specimens with the same gage length of 8 mm and varied diameters. Our purpose is to examine whether consistent results can be achieved from the three case studies or not. 2. Numerical Simulations The main purpose of the following numerical simulation is to predict the proper dimensions of specimen which will generate the best result in term of stress-strain behavior. The criteria used to define a better stress-strain behavior of all cases are the force equilibrium and stress-strain relation. Figure 1 shows the schematic of the SHTB apparatus. The specimen geometry was made similar to the standard specimen on ASTM A37 [1] for its proportionality of gage length, diameter, and fillet. Input bar Striker tube Output bar Flange Specimen Fig. 1. Schematic of split-hopkinson tension bar apparatus. Numerical simulations were conducted by using LS-DYNA. In this study, three sets of cases were investigated. The first case study used a group of specimens with the same gage length of 6 mm and varied diameters; the second case study used a group of specimens with the same diameter of 8 mm and varied lengths; and the third case study used a group of specimens with the same gage length of 8 mm and varied diameters. Detailed dimensions of the specimens are given in Table 1. Specimen A.3 is actually the same as B.2 and specimen C.3 is the same as B.2. Specimen C.4* is added in the analysis with the reason tobe explained later. Hence in total there were 1 specimens. Table 1. Three sets of cases studied. Specimen dimension Case I Case II Case III A.1 A.2 A.3 A.4 B.1 B.2 B.3 B.4 C.1 C.2 C.3 C.4* Diameter (mm) 4 6 8 1 8 8 8 8 6 8 1 1.6 Gage length (mm) 6 6 6 6 4 6 8 1 8 8 8 8
61 Dini A. Prabowo et al. / Procedia Engineering 173 ( 217 ) 68 614 2.1. Numerical Simulation Parameters The pressure bars and striker tube were assumed to be made of Maraging steel, while the specimen to be made of mild steel 16. Pressure bars and striker tube were assigned as elastic material models, MAT #1, while the specimen was assigned as a simplified Johnson-Cook material model, MAT #98. This decision of material models is based on the fact that the bars and striker tube experience an elastic deformation during the testing, while the specimen experiences elastic and plastic deformation. The mechanical properties for both materials and Johnson-Cook parameters for mild steel 16 are listed in Table 2, while the dimensions of all components are listed in Table 3. Mechanical properties Table 2. Mechanical properties and Johnson-Cook parameters of materials being used [11]. Density (kg/m 3 ) Young s modulus (GPa) Poisson s ratio Johnson-Cook parameters A (MPa) B (MPa) n C Maraging steel 8, 19.3 - - - - Mild steel 16 7,85 21.3 4 275.36.22 Table 3. Component dimensions. Components Diameter (mm) Length (mm) Outer: 18 Striker tube Inner: 14 3 Flange 18 Thickness: 5 Pressure bars 14 1,2 A 3D quarter-symmetric model was used in the numerical simulation, as shown in Fig. 2. The sampling rate of the numerical simulations was selected to be 1 μs with a time step formula based on the bar wave velocity. The termination time was selected to be 6 μs. 2.2. Contact, Boundary and Initial Conditions Fig. 2. Screen shot of 3D quarter-symmetric model for specimen area. A 3D tied nodes-to-surface contact was applied at the flange-input bar, the input bar-specimen and the specimenoutput bar, and a 3D automatic nodes-to-surface was applied at the striker tube-flange and the striker tube-input bar. Nodes along the neutral axes in all components and all nodes of the striker tube were restricted to translate in Y axes. For the 3D quarter-symmetric model, all nodes on X-Y plane were restricted to translate in X and Y axes, while all nodes on Y-Z plane were restricted to translate in Y and Z axes. Finally, all the boundary conditions mentioned above were also restricted to rotate about Y axes only. An initial velocity of 4 m/s was applied to all elements of the striker tube in the direction of the impact, here is to Y axes in negative value. In order to minimize the time of analysis, the initial distance of the striker tube and the flange was set to be just.1 mm. There was also a.1 mm clearance between the striker tube and the input bar.
Dini A. Prabowo et al. / Procedia Engineering 173 ( 217 ) 68 614 611 2.3. Validation Validation was conducted on the numerical simulations of bar apart and the results was then compared to the theoretical value. The theoretical value is given by: V (1) Apressurebar c 1 Astri kertube The bar apart simulation was conducted by impacting the striker tube on the flange attached to the input bar only. Figure 3 shows the strain wave of the bar apart, compared to the theoretical value in which = 3154 μm/m. This figure shows that the strain waves from the numerical simulation fits about well with the theoretical value. Thus it confirms that the numerical simulation is valid. Strain (μm/m) 5 4 3 2 1-1 -2-3 -4-5 1 2 3 4 5 6 2.4. Numerical Simulation Analysis Fig. 3. Numerical simulation on the bar apart validation. On the first case group, four specimens (specimens A.1, A.2, A.3 and A.4) with gage lengths of 6 mm were set to have varied diameters, i.e. 4, 6, 8 and 1 mm. This makes specimens L/D of 2.5, 1.,.75 and.6, respectively. On the second case group, four specimens (specimens B.1, B.2, B.3 and B.4) with diameters of 8 mm were set to have varied gage lengths, i.e. 4, 6, 8 and 1 mm. This makes specimens L/D of.5,.75, 1 and 1.25, respectively. On the third case group, three specimens (specimens C.1, C.2 and C.3) with gage lengths of 8 mm were set to have varied diameters, i.e. 6, 8 and 1 mm. This makes specimen s L/D of 1.3, 1 and.8, respectively. Figure 4 shows the dynamic force equilibrium for all cases being studied. is defined as the force at the input barspecimen interface, while is the force at the specimen-output bar interface. It is shown that the dynamic force equilibrium were reached for all cases after ringing-up periods. From Fig. 4 we can analyze the difference between the average forces, as listed in Table 4. The specimens deformations are shown in Fig. 5.
612 Dini A. Prabowo et al. / Procedia Engineering 173 ( 217 ) 68 614 3 2 1-1 -2 (a) 1 2 3 5 4 3 2 1-1 -2 (b) 1 2 3 6 4 2-2 (c) 1 2 3 8 6 4 2-2 (d) 1 2 3 6 4 2-2 -4 (e) 1 2 3 6 4 2-2 (f) 1 2 3 6 4 2-2 (g) 1 2 3 4 3 2 1-1 -2 (h) 1 2 3 8 6 4 2-2 (i) 1 2 3 8 6 4 2-2 (j) 1 2 3 Fig. 4. Numerical simulation results of dynamic force equilibrium for: (a) A.1; (b) A.2; (c) A.3 and B.2; (d) A.4; (e) B.1; (f) B.3 and C.2; (g) B.4; (h) C.1; (i) C.3 and (j) C.4*.
Dini A. Prabowo et al. / Procedia Engineering 173 ( 217 ) 68 614 613 Table 4. Forces difference percentage. Result A.1 A.2 A.3/B.2 A.4 B.1 B.3/C.2 B.4 C.1 C.3 C.4* average (kn) 6,629 15,73 27,627 44,368 28,43 27,762 27,576 15,471 43,61 48,957 average (kn) 6,76 14,876 27,61 43,986 28,216 27,291 27,15 14,96 43,5 48,46 Force difference (%) 9.1 1.33.6.87.66 1.72 1.57 3.41 1.3 1.2 (a) A.1 (b) A.2 (c) A.3/B.2 (d) A.4 (e) B.1 (f) B.3/C.2 (g) B.4 (h) C.1 (i) C.3 (j) C.4* Fig. 5. Numerical simulation results of specimen deformation for: (a) A.1; (b) A.2; (c) A.3 and B.2; (d) A.4; (e) B.1; (f) B.3 and C.2; (g) B.4; (h) C.1; (i) C.3; and (j) C.4*. Figures 6(a), 6(b) and 6(c) show the true stress-true strain curves of first case group, second case group and third case group, respectively, and Table 5 presents the numerical simulation results. These results show that different dimensions of specimen produce different final strain and also strain rate. True stress (MPa) 8 6 4 2 (a) Case I True stress (MPa) 1 8 6 4 2 (b) Case II 2 4 6 True strain (%) A.1 A.2 A.3 A.4 1 2 3 4 5 6 True strain (%) B.1 B.2 B.3 B.4 True stress (MPa) 8 6 4 2 (c) Case III 1 2 3 4 True strain (%) C.1 C.2 C.3 C.4* Fig. 6. Numerical simulation results of true stress-true strain for: (a) Case I; (b) Case II and (c) Case III
614 Dini A. Prabowo et al. / Procedia Engineering 173 ( 217 ) 68 614 It is shown in Fig. 6 that on Case I a consistent curve was achieved on A.2 and A.3; on Case II and Case III a consistent curve was achieved on all cases. On case A.1 the curve has a different shape compared to another cases which was caused by a large specimen s length-to-diameter ratio. Thus, for Case I a good curve was achieved when specimen s L/D.75; for Case II it was achieved when specimen s L/D.5; and for Case III it was achieved when L/D.8. Therefore we cannot recommend the range of good L/D based on the former result, thus we still need to conduct a numerical simulation for.75 L/D.5 on Case III. Apparently for the real testing, a specimen with diameter of 1.6 mm (which makes an L/D =.75) or greater could not be conducted since its cross-sectional area will be greater than the pressure bars. But the numerical simulation still could be conducted, which defined as case C.4*. The result shows that the curve is still consistent with another cases on Case III. Table 5. Numerical simulation results. Result A.1 A.2 A.3/B.2 A.4 B.1 B.3/C.2 B.4 C.1 C.3 C.4* L/D 2.5 1..75.6.5 1. 1.25 1.3.8.75 Strain rate (μm/ μm) 4,99 4,526 3,82 2,921 5,622 2,892 2,31 3,35 2,227 1,996 Final strain (%) 44.3 4.8 35.4 28. 49. 27.9 22.9 32.1 22.1 2 4. Conclusions Numerical simulations of three sets of SHTB cases have been successfully conducted, i.e. specimens with gage length of 6 mm and diameters of 4, 6, 8 and 1 mm; specimens with diameter of 8 mm and gage lengths of 4, 6, 8 and 1 mm; specimens with gage length of 8 mm and diameters of 6, 8 and 1 mm. The dumbbell-shaped specimen was made of mild steel 16 and its geometry was made similar to standard specimen on ASTM A37. The striker bar velocity is 4 m/s. In summary, three sets of SHTB cases generated comparable results, namely true stress-true strain curve, final strain and strain rate for some specimen s length-to-diameter ratio. From all cases, a specimen s length-to-diameter ratio of L/D =.75 always gives a good true stress-true strain curve which indicates the possibility of SHTB standardization for specimen dimension in the future. Acknowledgements This research was supported by Kementerian Riset Teknologi dan Pendidikan Tinggi Republik Indonesia (Ministry of Research, Technology and Higher Education of the Republic of Indonesia) under the program of Sistem Informasi Manajemen Penelitian dan Pengabdian Kepada Masyarakat (Title: Pengembangan Split Hopkinson Tension Bar Guna Karakterisasi Sifat Mekanik Material Pada Laju Regangan Tinggi, contract no. FTMD.PN-7-3-216). This research was also supported by LSTC by providing the education licenses of LS-DYNA. References 1. Hopkinson, J. On the rupture of iron wire by a blow. in Proceedings of the Manchester Literary and Philosophical Society. 1872. 2. Hopkinson, J. Further experiments on the rupture of iron wire. in Proceedings of the Manchester Literary and Philosophical Society. 1872. 3. Hopkinson, B., The effects of momentary stresses in metals, Proceedings of the Royal Society of London, 74 (194) 498-56 4. Hopkinson, B., A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 213 (1914) 437-456 5. Kolsky, H., An investigation of the mechanical properties of materials at very high rates of loading, Proceedings of the Physical Society. Section B, 62 (1949) 676-7 6. Gray, G.T., Classic Split-Hopkinson Pressure Bar Testing, Materials Park, OH: ASM International, 2., (2) 462-476 7. Lindholm, U. and L. Yeakley, High strain-rate testing: tension and compression, Experimental Mechanics, 8 (1968) 1-9 8. Nicholas, T., Dynamic tensile testing of structural materials using a split Hopkinson bar apparatus. 198, DTIC Document. 9. Nemat-Nasser, S., J.B. Isaacs, and J.E. Starrett. Hopkinson techniques for dynamic recovery experiments. in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 1991: The Royal Society. 1. ASTM A37-16, Standard Test Methods and Definitions for Mechanical Testing of Steel Products. 216, ASTM International: West Conshohocken, PA. 11. Kariem, M.A., Reliable Materials Performance Data from Impact Testing, in Faculty of Engineering and Industrial Sciences. 212, Swinburne University of Technology: Melbourne.