Numerical and Experimental Studies of a Conical Striker Application for the Achievement of a True and Nominal Constant Strain Rate in SHPB Tests

Numerical and Experimental Studies of a Conical Striker Application for the Achievement of a True... The problem of ensuring both nominal and true constant strain rate in the split Hopkinson pressure bar experiment was considered through the application of the conical striker for 316 L steel specimen. The experimentally confirmed results from numerical analyses indicate that the application of a conical striker with the determined apex angle for the given experimental conditions is a good method for achieving a constant value of the strain rate. Moreover, the results of the study showed that the value of the striker apex angle has the greatest influence on the mechanical response of the specimen material. In turn, the impact velocity slightly affects the value of the striker apex angle. . . . Keywords Split Hopkinson pressure bar High-strain-rate testing Constant strain rate Numerical simulation Introduction pulse-shaping technique [7, 8], conical (tapered) striker method [9, 10], and a three-bar technique with a dum- The basic methodological requirement of a split my specimen [11]. Hopkinson pressure bar (SHPB) technique is that a In the current work, the attention is focused on the incident specimen needs to deform nearly uniformly at a con- pulse-forming technique with the use of a conical striker to stant strain rate under dynamically equilibrated stresses, achieve a constant strain rate. The literature contains a rela- and propagation of elastic waves through the input and tively large number of publications on the use of a shaped output bars is described using a one-dimensional wave striker in investigations of brittle materials such as rocks theory [1]. Strain acceleration, which is the effect of a [12–14], concrete [15] and even bones [9, 10]. However, it non-constant strain rate, can produce additional axial is difficult to find publications that investigate the use of a stress and radial stress in a specimen [2–5], which shaped striker for testing of metals and their alloys, particular- may influence the measurement results [6]. Several ly for materials with a high strain-hardening coefficient. Only methods are available for solving the problem of main- Sato and Takeyama published studies on this topic, however, taining the constant strain rate during SHPB tests: a in a narrow range [16, 17]. To achieve the aim of the work, the authors carried out numerical analysis using Ls-Dyna code [18]. The material and geometric parameters of the split Hopkinson pressure * R. Panowicz robert.panowicz@wat.edu.pl bar set-up were the same as those used in the authors’ previous experimental measurement system [19]. The numerical con- J. Janiszewski siderations were done for the specimens made of 316 L aus- jacek.janiszewski@wat.edu.pl tenitic steel described by the simplified Johnson-Cook model K. Kochanowski (JC) [18]. Material constants for this material were obtained krzy.kochanowski@gmail.com based on the authors’ research (Table 1). In turn, Coulomb’s law was used to predict the friction between the interacting Faculty of Mechanical Engineering, Military University of surfaces. A friction coefficient was assumed as 0.06 [20], Technology, Urbanowicz Street 2, 00-908 Warsaw, Poland whereas the striker impact velocity V values were within the Faculty of Mechatronics and Aviation, Military University of range of 15–25 m/s. The striker geometry was described in Technology, Urbanowicz Street 2, 00-908 Warsaw, Poland Exp Mech Table 1 Material ρ [kg/m]8000 A [MPa] 304 constants of 316 L austenitic steel E [GPa] 193 B [MPa] 1097 ν [−]0.27 n [−]0.492 C [−]0.014 Fig. 1. For clarity and simplicity of description, it is assumed that, in the case of the striker impact with the smaller-diameter end, the apex angle is positive, and in the other cases, it is negative (Fig. 1). Fig. 2 Influence of apex angle α on the incident pulse shape, red lines— Results and Discussion positive apex angles, blue lines—negative apex angles, black line— cylindrical striker, V = 20 m/s The influence of conical striker geometry with the given apex angles α on the incident pulse in the SHPB experiments is strain-hardening coefficient that affects the geometry of the illustrated in Fig. 2. As the apex angle increases (Fig. 1(a)), the striker, i.e. its mass and impact energy and consequently in- usable portion of the incident pulse, which corresponds to the fluences the strain rate of the specimen (Fig. 3(a)). cylindrical striker curve plateau of the pulse, grows from the Since the process of plastic deformation of a sample under the smallest value proportional to α.However,the maximum SHPB test conditions is determined by, among others, the dimen- pulse level decreases with the increase of the striker apex sions of the specimen, numerical experiments were conducted to angle. In an analogous manner, the influence of the striker determine an influence of the sample geometry and striker impact apex angle on the incident wave pulse (Fig. 2, blue lines) velocity. The influence of both the diameter and the length of the was investigated for the case in which the striker maximum specimen on the history of the deformation curve was investigat- diameter end impacts the incident bar (Fig. 1(b)). ed in the case of strikers with apex angles optimized for the To obtain a constant strain rate with the use of the conical following experimental conditions: diameter and length of the strikers, numerical analyses, which resulted in obtaining the sample = 5 × 5 mm and impact velocity V = 20 m/s. striker apex angles of the 316 L steel and experimental condi- Figure 4(a) shows the influence of the sample diameter on tions, were carried out. The results were collected in Fig. 3 characteristics of the strain rate-time curve. The cases of spec- which shows a change in both the nominal (solid line) and the imens with diameters of 4, 5 and 6 mm (in which a specimen true (dashed line) strain rates. For comparative purposes, the with a 5-mm diameter is reference specimen for which the curves obtained from the cylindrical striker experiments striker apex angle is chosen) are considered. Based on Fig. (black lines) are also included. It was found that to obtain a 4(a), it can be concluded that an influence of the sample di- nominal constant strain rate, the striker apex angle should be ameter in the considered range does not significantly affect the α = 0.8°, whereas for the true strain rate, the angle is equal to strain-rate curve, i.e., plastic deformation of the specimens α = 0.55°. The abovementioned influence of the striker apex occurs at a nearly constant strain rate. However, it can be angle on the course of the strain rate curves is also reflected in noted that in the case of small-diameter specimens, the strain the profile of the stress-time curves (Fig. 3(b)). Based on Fig. rate obviously increases slightly with an increase in the spec- 3(b), the differences between the curves are visible for both imens deformation but decreases for larger ones. Hence, it can the nominal and true constant strain rate. These differences are be concluded that a conical striker can be used in studies in expressed in a different level of plastic flow stress (black and which the materials and the diameters of the specimens vary blue solid lines). This observation is due, as expected, to the considerably. sensitivity of steel to the strain rate and to the high value of the Fig. 1 Conical striker geometry; apex angle α is positive in the case of impact with the end of a smaller diameter (a), and negative in the other cases (b) Exp Mech Fig. 3 Nominal and true strain rate-time (a) and stress-time (b) curves of 316 L steel specimens V = 20 m/s based on Fig. 4(c), and at the same time, it reveals a nearly A significantly larger effect of α angle on εðÞ t can be ob- linear dependence of the striker apex angle on the striker im- served for specimens of different lengths (Fig. 4(b)). For the tested specimens corresponding to L/D = 0.5, 1, and 1.5, the pact velocity. Moreover, Fig. 5 clearly shows the dependence of the striker impact velocity on the optimal apex angle for effect of length is relatively large. However, it can be ob- served, as expected, that the strain rate of the short samples experiments with the true constant strain rate. A series of dynamic tests was conducted to verify the re- (L = 2.5 mm) decreases with an increase in strain, whereas in the case of long samples (L = 7.5 mm), the opposite relation- sults of numerical analyses. The experiments were performed using the setup shown in Fig. 6(a). The verification tests were ship is observed. Useful practical guidelines are also derived performed using four strikers with different apex angles. The from the analysis of the curves shown in Fig. 4(c). These strikers were made of the same steel as the input and output curves show that the conical striker with a given apex angle bars. can be used regardless of the accepted range of the striker The number of tests conducted, together with their markings impact velocity for nominal strain rates curves. and the experimental conditions, are listed in Table 2. Additionally, to illustrate the influence of the striker impact velocity on the optimum striker apex angle, Fig. 5 is present- Experimental tests marked with letters A to D were performed under the experimental conditions required to ensure a constant ed. This figure confirms the earlier observations conducted Fig. 4 Influence of specimen parameters and striker velocity on strain rate-time: diameter (a), length (b), striker velocity (c) Exp Mech Table 2 Summary of verification test conditions Test V [m/s] α [°] Type of strain rate L D S S A 15.6 0.78 Nominal 4.95 4.81 B 15.6 0.78 Nominal 5.05 4.81 C 20.2 0.55 True 4.97 4.83 D 20.3 0.55 True 4.99 4.77 in real experimental conditions, the waveforms obtained in the usable range, i.e., the corresponding plateau, deviate from the constant value to a greater degree than in the case of the curves obtained based on numerical analyses (Fig. 6(b)). Fig. 5 Influence of conical striker velocity on the optimal striker apex The fact that the assumed constancy of the strain rate was angle for 316 L steel not achieved in the experimental conditions results from the discrepancy between the real conditions of the SHPB experi- strain rate, both nominal and true. The experimental strain rate- ment and the adopted conditions of the numerical experiment. time curves for these experiments are shown in Fig. 6(b). According to the authors, the above discrepancies are mainly a The results of experimental investigations on the selected consequence of using the JC constitutive model for the con- sidered materials and the friction model. For example, the conical strikers are coincident with the results of numerical anal- yses, which leads to the conclusion that the constant strain rate slight increase in the true strain rate in the plateau range ob- served in Fig. 6(b) is probably a result of using the JC model. (both true and nominal) can be obtained using the appropriately selected geometry of the conical striker. It should be noted that, It should be assumed that this model do not adequately Fig. 6 (a) Experimental set-up, and (b) nominal and true strain rate-time curves received with his aid (a) Exp Mech Acknowledgements The support of Military University of Technology describe the mechanical behaviour of the tested material. In grant PBS 23-937 is gratefully acknowledged. addition, a characteristic change (marked with a dotted ellipse) in the profile of the curves on the plateau section can be ob- Open Access This article is distributed under the terms of the Creative served. The probable cause of this phenomenon is variability Commons Attribution 4.0 International License (http:// of the friction forces occurring on the specimen-bar contact creativecommons.org/licenses/by/4.0/), which permits unrestricted use, surfaces during the dynamic deformation of the specimen. In distribution, and reproduction in any medium, provided you give appro- the initial stage, the friction forces are relatively small due to a priate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. lubricant layer between the contact surfaces. As a result, the initial increase in the strain rate is visible. Due to deformation of the specimen and the applied loading, the lubricant layer References decreases until it disappears entirely (time less than 60 μs). This effect on the strain rate-time curve is expressed by chang- 1. Chen W, Song B (2011) Split Hopkinson (Kolsky) bar: design, ing the curve trend from increasing to decreasing or approxi- testing and applications. Springer, Berlin mately constant. This phenomenon was not included in the 2. Malinowski JZ, Klepaczko JR (1986) A unified analytic and nu- numerical model because it was assumed that the coefficient merical approach to specimen behaviour in the split-Hopkinson of friction does not depend on the conditions of the pressure bar. Int J Mech Sci 28(6):381–391 experiment. 3. Gorham DA (1991) An effect of specimen size in the high strain rate compression test. J Phys D 24(8):1489–1492 4. Gray GT (2000) Classic split-Hopkinson pressure bar testing. American society for materials Handbook, 8th edn. American Society for Materials International, Materials Park, pp 462–476 Conclusion 5. Forrestal MJ, Wright TW, Chen W (2007) The effect of radial inertia on brittle samples during the split Hopkinson pressure bar test. Int J Impact Eng 34(3):405–411 The numerical and experimental analyses presented in this 6. Li QM, Meng H (2003) About the dynamic strength enhancement article showed that application of a conical striker is a good of concrete-like materials in a split Hopkinson pressure bar test. Int method for achieving a constant strain rate, both nominal and J Solids Struct 40(2):343–360 true, in SHPB experiments. However, this method requires the 7. Chen W, Luo H (2004) Dynamic compressive responses of intact and damaged ceramics from a single split Hopkinson pressure bar use of a numerical model of the SHPB experiment to deter- experiment. Exp Mech 44(3):295–299 mine the conical striker apex angle for a given specimen ma- 8. Lu YB, Li QM (2010) Appraisal of pulse-shaping technique in split terial, its geometry (diameter, length) and the impact velocity Hopkinson pressure bar tests for brittle materials. Int J Prot Struct of the projectile. 1(3):363–390 9. Cloete TJ, van der Westhuizen A, Kok S, Nurick GN (2009) A Contrary to the initial predictions, the use of the striker with tapered striker pulse shaping technique for uniform strain rate dy- a specific geometry does not limit its use to the given exper- namic compression of bovine bone. DYMAT-international confer- imental conditions. For a given material group, preparation of ence on the mechanical and physical behaviour of materials under a several conical strikers set (3–4 pieces) is sufficient for ad- dynamic loading 1:901–907 justment of the experimental conditions to achieve a constant 10. Bekker A, Cloete TJ, Chinsamy-Turan A et al (2015) Constant strain rate compression of bovine cortical bone on the split- strain rate. The results of this research showed that the me- Hopkinson pressure bar. Mater Sci Eng C 46:443–449 chanical response of the specimen materials has the greatest 11. Ellwood S, Griffiths LJ, Parry DJ (1982) Materials testing at high influence on the value of the striker apex angle, whereas the constant strain rates. J Phys [E] 15(3):280–282 dimensions of the disk sample storage affect it to a lesser 12. Li XB, Lok TS, Zhao J, Zhao PJ (2000) Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic extent, with the exception of short samples, i.e., those with stress-strain curves for rocks. Int J Rock Mech Min Sci 37(7): an L/D ratio lower than 1. Similarly, the impact velocity has a 1055–1060 small effect on the value of the striker apex angle. In the case 13. Zhou YX, Xia K, Li XB et al (2015) Suggested methods for deter- of a nominal strain rate, this angle is nearly independent of the mining the dynamic strength parameters and mode-I fracture tough- striker velocity, whereas for the true strain rate, it depends on ness of rock materials. In: Ulusay R (ed) The ISRM suggested methods for rock characterization, testing and monitoring: 2007– this velocity and is nearly a linear function. 2014. Springer, Cham, pp 35–42 Based on the observations from the experimental studies, it 14. Christensen RJ, Swanson SR, Brown WS (1972) Split-Hopkinson- can be concluded that guaranteeing a constant strain rate re- bar tests on rocks under confining pressure. Exp Mech 12(11):508– quires the development of a more complex numerical model 15. Hao Y, Hao H, Huang X (2015) Dynamic behaviours of spiral- that considers the physics of the specimen dynamic deforma- shaped steel fibre reinforced concrete under splitting tension: ex- tion. In such a case, striker geometry may deviate from the perimental and numerical study. In: Dilum F, Jin-Guang T, Jose LT shape of the cone with a complex contour which is more (eds) Proceedings of the second international conference on difficult to develop and probably has a limited range of the performance-based and life-cycle structural engineering Brisbane, QLD, Australia, pp 868–876 use compared with conical strikers. Exp Mech 16. Sato Y, Takeyama H (1982) The use of the split Hopkinson 19. Panowicz R, Janiszewski J, Traczyk M (2017) Strain measuring accuracy with splitting-beam laser extensometer technique at split pressure bar to deform a metal specimen at a predetermined strain rate history - a constant strain-rate testing using the Hopkinson compression bar experiment. Bull Pol Acad Sci Tech compression SHPB system I. J JSTP (in Japanese) 23(254): Sci 65(2):163–169 252–258 20. Hartley RS, Cloete TJ, Nurick GN (2007) An experimental 17. Sato Y, Yamashita M, Hattori T, Suzuki S (2009) Standardization of assessment of friction effects in the split Hopkinson pressure split Hopkinsao pressure bar compression system without frictional bar using the ring compression test. Int J Impact Eng effects for metal plate specimens. J Solid Mech Mater Eng 3(3): 34(10):1705–1728 584–595 18. Hallquist JO (2006) Ls-Dyna. Theoretical manual. Livermore Software Technology Corporation, California http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experimental Mechanics Springer Journals

Numerical and Experimental Studies of a Conical Striker Application for the Achievement of a True and Nominal Constant Strain Rate in SHPB Tests

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Abstract

The problem of ensuring both nominal and true constant strain rate in the split Hopkinson pressure bar experiment was considered through the application of the conical striker for 316 L steel specimen. The experimentally confirmed results from numerical analyses indicate that the application of a conical striker with the determined apex angle for the given experimental conditions is a good method for achieving a constant value of the strain rate. Moreover, the results of the study showed that the value of the striker apex angle has the greatest influence on the mechanical response of the specimen material. In turn, the impact velocity slightly affects the value of the striker apex angle. . . . Keywords Split Hopkinson pressure bar High-strain-rate testing Constant strain rate Numerical simulation Introduction pulse-shaping technique [7, 8], conical (tapered) striker method [9, 10], and a three-bar technique with a dum- The basic methodological requirement of a split my specimen [11]. Hopkinson pressure bar (SHPB) technique is that a In the current work, the attention is focused on the incident specimen needs to deform nearly uniformly at a con- pulse-forming technique with the use of a conical striker to stant strain rate under dynamically equilibrated stresses, achieve a constant strain rate. The literature contains a rela- and propagation of elastic waves through the input and tively large number of publications on the use of a shaped output bars is described using a one-dimensional wave striker in investigations of brittle materials such as rocks theory [1]. Strain acceleration, which is the effect of a [12–14], concrete [15] and even bones [9, 10]. However, it non-constant strain rate, can produce additional axial is difficult to find publications that investigate the use of a stress and radial stress in a specimen [2–5], which shaped striker for testing of metals and their alloys, particular- may influence the measurement results [6]. Several ly for materials with a high strain-hardening coefficient. Only methods are available for solving the problem of main- Sato and Takeyama published studies on this topic, however, taining the constant strain rate during SHPB tests: a in a narrow range [16, 17]. To achieve the aim of the work, the authors carried out numerical analysis using Ls-Dyna code [18]. The material and geometric parameters of the split Hopkinson pressure * R. Panowicz robert.panowicz@wat.edu.pl bar set-up were the same as those used in the authors’ previous experimental measurement system [19]. The numerical con- J. Janiszewski siderations were done for the specimens made of 316 L aus- jacek.janiszewski@wat.edu.pl tenitic steel described by the simplified Johnson-Cook model K. Kochanowski (JC) [18]. Material constants for this material were obtained krzy.kochanowski@gmail.com based on the authors’ research (Table 1). In turn, Coulomb’s law was used to predict the friction between the interacting Faculty of Mechanical Engineering, Military University of surfaces. A friction coefficient was assumed as 0.06 [20], Technology, Urbanowicz Street 2, 00-908 Warsaw, Poland whereas the striker impact velocity V values were within the Faculty of Mechatronics and Aviation, Military University of range of 15–25 m/s. The striker geometry was described in Technology, Urbanowicz Street 2, 00-908 Warsaw, Poland Exp Mech Table 1 Material ρ [kg/m]8000 A [MPa] 304 constants of 316 L austenitic steel E [GPa] 193 B [MPa] 1097 ν [−]0.27 n [−]0.492 C [−]0.014 Fig. 1. For clarity and simplicity of description, it is assumed that, in the case of the striker impact with the smaller-diameter end, the apex angle is positive, and in the other cases, it is negative (Fig. 1). Fig. 2 Influence of apex angle α on the incident pulse shape, red lines— Results and Discussion positive apex angles, blue lines—negative apex angles, black line— cylindrical striker, V = 20 m/s The influence of conical striker geometry with the given apex angles α on the incident pulse in the SHPB experiments is strain-hardening coefficient that affects the geometry of the illustrated in Fig. 2. As the apex angle increases (Fig. 1(a)), the striker, i.e. its mass and impact energy and consequently in- usable portion of the incident pulse, which corresponds to the fluences the strain rate of the specimen (Fig. 3(a)). cylindrical striker curve plateau of the pulse, grows from the Since the process of plastic deformation of a sample under the smallest value proportional to α.However,the maximum SHPB test conditions is determined by, among others, the dimen- pulse level decreases with the increase of the striker apex sions of the specimen, numerical experiments were conducted to angle. In an analogous manner, the influence of the striker determine an influence of the sample geometry and striker impact apex angle on the incident wave pulse (Fig. 2, blue lines) velocity. The influence of both the diameter and the length of the was investigated for the case in which the striker maximum specimen on the history of the deformation curve was investigat- diameter end impacts the incident bar (Fig. 1(b)). ed in the case of strikers with apex angles optimized for the To obtain a constant strain rate with the use of the conical following experimental conditions: diameter and length of the strikers, numerical analyses, which resulted in obtaining the sample = 5 × 5 mm and impact velocity V = 20 m/s. striker apex angles of the 316 L steel and experimental condi- Figure 4(a) shows the influence of the sample diameter on tions, were carried out. The results were collected in Fig. 3 characteristics of the strain rate-time curve. The cases of spec- which shows a change in both the nominal (solid line) and the imens with diameters of 4, 5 and 6 mm (in which a specimen true (dashed line) strain rates. For comparative purposes, the with a 5-mm diameter is reference specimen for which the curves obtained from the cylindrical striker experiments striker apex angle is chosen) are considered. Based on Fig. (black lines) are also included. It was found that to obtain a 4(a), it can be concluded that an influence of the sample di- nominal constant strain rate, the striker apex angle should be ameter in the considered range does not significantly affect the α = 0.8°, whereas for the true strain rate, the angle is equal to strain-rate curve, i.e., plastic deformation of the specimens α = 0.55°. The abovementioned influence of the striker apex occurs at a nearly constant strain rate. However, it can be angle on the course of the strain rate curves is also reflected in noted that in the case of small-diameter specimens, the strain the profile of the stress-time curves (Fig. 3(b)). Based on Fig. rate obviously increases slightly with an increase in the spec- 3(b), the differences between the curves are visible for both imens deformation but decreases for larger ones. Hence, it can the nominal and true constant strain rate. These differences are be concluded that a conical striker can be used in studies in expressed in a different level of plastic flow stress (black and which the materials and the diameters of the specimens vary blue solid lines). This observation is due, as expected, to the considerably. sensitivity of steel to the strain rate and to the high value of the Fig. 1 Conical striker geometry; apex angle α is positive in the case of impact with the end of a smaller diameter (a), and negative in the other cases (b) Exp Mech Fig. 3 Nominal and true strain rate-time (a) and stress-time (b) curves of 316 L steel specimens V = 20 m/s based on Fig. 4(c), and at the same time, it reveals a nearly A significantly larger effect of α angle on εðÞ t can be ob- linear dependence of the striker apex angle on the striker im- served for specimens of different lengths (Fig. 4(b)). For the tested specimens corresponding to L/D = 0.5, 1, and 1.5, the pact velocity. Moreover, Fig. 5 clearly shows the dependence of the striker impact velocity on the optimal apex angle for effect of length is relatively large. However, it can be ob- served, as expected, that the strain rate of the short samples experiments with the true constant strain rate. A series of dynamic tests was conducted to verify the re- (L = 2.5 mm) decreases with an increase in strain, whereas in the case of long samples (L = 7.5 mm), the opposite relation- sults of numerical analyses. The experiments were performed using the setup shown in Fig. 6(a). The verification tests were ship is observed. Useful practical guidelines are also derived performed using four strikers with different apex angles. The from the analysis of the curves shown in Fig. 4(c). These strikers were made of the same steel as the input and output curves show that the conical striker with a given apex angle bars. can be used regardless of the accepted range of the striker The number of tests conducted, together with their markings impact velocity for nominal strain rates curves. and the experimental conditions, are listed in Table 2. Additionally, to illustrate the influence of the striker impact velocity on the optimum striker apex angle, Fig. 5 is present- Experimental tests marked with letters A to D were performed under the experimental conditions required to ensure a constant ed. This figure confirms the earlier observations conducted Fig. 4 Influence of specimen parameters and striker velocity on strain rate-time: diameter (a), length (b), striker velocity (c) Exp Mech Table 2 Summary of verification test conditions Test V [m/s] α [°] Type of strain rate L D S S A 15.6 0.78 Nominal 4.95 4.81 B 15.6 0.78 Nominal 5.05 4.81 C 20.2 0.55 True 4.97 4.83 D 20.3 0.55 True 4.99 4.77 in real experimental conditions, the waveforms obtained in the usable range, i.e., the corresponding plateau, deviate from the constant value to a greater degree than in the case of the curves obtained based on numerical analyses (Fig. 6(b)). Fig. 5 Influence of conical striker velocity on the optimal striker apex The fact that the assumed constancy of the strain rate was angle for 316 L steel not achieved in the experimental conditions results from the discrepancy between the real conditions of the SHPB experi- strain rate, both nominal and true. The experimental strain rate- ment and the adopted conditions of the numerical experiment. time curves for these experiments are shown in Fig. 6(b). According to the authors, the above discrepancies are mainly a The results of experimental investigations on the selected consequence of using the JC constitutive model for the con- sidered materials and the friction model. For example, the conical strikers are coincident with the results of numerical anal- yses, which leads to the conclusion that the constant strain rate slight increase in the true strain rate in the plateau range ob- served in Fig. 6(b) is probably a result of using the JC model. (both true and nominal) can be obtained using the appropriately selected geometry of the conical striker. It should be noted that, It should be assumed that this model do not adequately Fig. 6 (a) Experimental set-up, and (b) nominal and true strain rate-time curves received with his aid (a) Exp Mech Acknowledgements The support of Military University of Technology describe the mechanical behaviour of the tested material. In grant PBS 23-937 is gratefully acknowledged. addition, a characteristic change (marked with a dotted ellipse) in the profile of the curves on the plateau section can be ob- Open Access This article is distributed under the terms of the Creative served. The probable cause of this phenomenon is variability Commons Attribution 4.0 International License (http:// of the friction forces occurring on the specimen-bar contact creativecommons.org/licenses/by/4.0/), which permits unrestricted use, surfaces during the dynamic deformation of the specimen. In distribution, and reproduction in any medium, provided you give appro- the initial stage, the friction forces are relatively small due to a priate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. lubricant layer between the contact surfaces. As a result, the initial increase in the strain rate is visible. Due to deformation of the specimen and the applied loading, the lubricant layer References decreases until it disappears entirely (time less than 60 μs). This effect on the strain rate-time curve is expressed by chang- 1. Chen W, Song B (2011) Split Hopkinson (Kolsky) bar: design, ing the curve trend from increasing to decreasing or approxi- testing and applications. Springer, Berlin mately constant. This phenomenon was not included in the 2. Malinowski JZ, Klepaczko JR (1986) A unified analytic and nu- numerical model because it was assumed that the coefficient merical approach to specimen behaviour in the split-Hopkinson of friction does not depend on the conditions of the pressure bar. Int J Mech Sci 28(6):381–391 experiment. 3. Gorham DA (1991) An effect of specimen size in the high strain rate compression test. J Phys D 24(8):1489–1492 4. Gray GT (2000) Classic split-Hopkinson pressure bar testing. American society for materials Handbook, 8th edn. American Society for Materials International, Materials Park, pp 462–476 Conclusion 5. Forrestal MJ, Wright TW, Chen W (2007) The effect of radial inertia on brittle samples during the split Hopkinson pressure bar test. Int J Impact Eng 34(3):405–411 The numerical and experimental analyses presented in this 6. Li QM, Meng H (2003) About the dynamic strength enhancement article showed that application of a conical striker is a good of concrete-like materials in a split Hopkinson pressure bar test. Int method for achieving a constant strain rate, both nominal and J Solids Struct 40(2):343–360 true, in SHPB experiments. However, this method requires the 7. Chen W, Luo H (2004) Dynamic compressive responses of intact and damaged ceramics from a single split Hopkinson pressure bar use of a numerical model of the SHPB experiment to deter- experiment. Exp Mech 44(3):295–299 mine the conical striker apex angle for a given specimen ma- 8. Lu YB, Li QM (2010) Appraisal of pulse-shaping technique in split terial, its geometry (diameter, length) and the impact velocity Hopkinson pressure bar tests for brittle materials. Int J Prot Struct of the projectile. 1(3):363–390 9. Cloete TJ, van der Westhuizen A, Kok S, Nurick GN (2009) A Contrary to the initial predictions, the use of the striker with tapered striker pulse shaping technique for uniform strain rate dy- a specific geometry does not limit its use to the given exper- namic compression of bovine bone. DYMAT-international confer- imental conditions. For a given material group, preparation of ence on the mechanical and physical behaviour of materials under a several conical strikers set (3–4 pieces) is sufficient for ad- dynamic loading 1:901–907 justment of the experimental conditions to achieve a constant 10. Bekker A, Cloete TJ, Chinsamy-Turan A et al (2015) Constant strain rate compression of bovine cortical bone on the split- strain rate. The results of this research showed that the me- Hopkinson pressure bar. Mater Sci Eng C 46:443–449 chanical response of the specimen materials has the greatest 11. Ellwood S, Griffiths LJ, Parry DJ (1982) Materials testing at high influence on the value of the striker apex angle, whereas the constant strain rates. J Phys [E] 15(3):280–282 dimensions of the disk sample storage affect it to a lesser 12. Li XB, Lok TS, Zhao J, Zhao PJ (2000) Oscillation elimination in the Hopkinson bar apparatus and resultant complete dynamic extent, with the exception of short samples, i.e., those with stress-strain curves for rocks. Int J Rock Mech Min Sci 37(7): an L/D ratio lower than 1. Similarly, the impact velocity has a 1055–1060 small effect on the value of the striker apex angle. In the case 13. Zhou YX, Xia K, Li XB et al (2015) Suggested methods for deter- of a nominal strain rate, this angle is nearly independent of the mining the dynamic strength parameters and mode-I fracture tough- striker velocity, whereas for the true strain rate, it depends on ness of rock materials. In: Ulusay R (ed) The ISRM suggested methods for rock characterization, testing and monitoring: 2007– this velocity and is nearly a linear function. 2014. Springer, Cham, pp 35–42 Based on the observations from the experimental studies, it 14. Christensen RJ, Swanson SR, Brown WS (1972) Split-Hopkinson- can be concluded that guaranteeing a constant strain rate re- bar tests on rocks under confining pressure. Exp Mech 12(11):508– quires the development of a more complex numerical model 15. Hao Y, Hao H, Huang X (2015) Dynamic behaviours of spiral- that considers the physics of the specimen dynamic deforma- shaped steel fibre reinforced concrete under splitting tension: ex- tion. In such a case, striker geometry may deviate from the perimental and numerical study. In: Dilum F, Jin-Guang T, Jose LT shape of the cone with a complex contour which is more (eds) Proceedings of the second international conference on difficult to develop and probably has a limited range of the performance-based and life-cycle structural engineering Brisbane, QLD, Australia, pp 868–876 use compared with conical strikers. Exp Mech 16. Sato Y, Takeyama H (1982) The use of the split Hopkinson 19. Panowicz R, Janiszewski J, Traczyk M (2017) Strain measuring accuracy with splitting-beam laser extensometer technique at split pressure bar to deform a metal specimen at a predetermined strain rate history - a constant strain-rate testing using the Hopkinson compression bar experiment. Bull Pol Acad Sci Tech compression SHPB system I. J JSTP (in Japanese) 23(254): Sci 65(2):163–169 252–258 20. Hartley RS, Cloete TJ, Nurick GN (2007) An experimental 17. Sato Y, Yamashita M, Hattori T, Suzuki S (2009) Standardization of assessment of friction effects in the split Hopkinson pressure split Hopkinsao pressure bar compression system without frictional bar using the ring compression test. Int J Impact Eng effects for metal plate specimens. J Solid Mech Mater Eng 3(3): 34(10):1705–1728 584–595 18. Hallquist JO (2006) Ls-Dyna. Theoretical manual. Livermore Software Technology Corporation, California

Journal

Experimental MechanicsSpringer Journals

Published: Jun 1, 2018

References

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