Acta Polytechnica https://doi.org/10.14311/AP.2021.61.0552 Acta Polytechnica 61(4):552–561, 2021 © 2021 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague PERFORMANCE CHARACTERISTICS OF HOPKINSON’S SET-UP PNEUMATIC LAUNCHER Kamil Sobczyk, Leopold Kruszka∗, Ryszard Chmielewski, Ryszard Rekucki Military University of Technology, Faculty of Civil Engineering and Geodesy, Department of Military Engineering and Military Infrastructure, 2 Gen. Sylwester Kaliski Str., 00-908 Warsaw, Poland ∗ corresponding author: leopold.kruszka@wat.edu.pl Abstract. The paper presents a performance characteristics of a pneumatic launcher, which is an important element of the split Hopkinson bar set-up (SHPB) at the Department of Military Engineering and Infrastructure (the Military University of Technology in Warsaw) for the purpose of dynamic strength tests of construction materials. The process of experimental calibration of the launcher for selected loading bar-projectiles is shown. Two types of compression during direct impact tests were also used simultaneously to investigate the behaviour of metallic samples with the use of this launcher as well as the Hopkinson measuring bar: the first — a short cylindrical sample, including a miniature (small diameter) sample, and the second — a long cylindrical sample (Taylor test). The relationships describing the stress and strain state as a function of strain rate for the first type of the experiment and engineering empirical formulas for the second type of the research were given. Keywords: Pneumatic launcher, Hopkinson measuring bar, direct impact tests. 1. Introduction The beginnings of the development of gas launchers are related to a military technology. The design of the pneumatic guns used to launch large-diameter missiles was first presented by D. M. Medford in 1883 in Fort Hamilton (USA). However, the first land-based air cannons designed by the American inventor born in Kórnik (Poland), Major Edmund Żaliński, were installed in 1894 at Sandy Hook Fort in New Jersey. It was a three-gun battery of 15-inch (381 mm) coastal artillery guns operating in a similar way to an air gun: compressed air was used to fire a projectile (explosive charge) [1]. In 1900, Żaliński’s triple air gun was installed on the USS Vesuvius, and a twin 8.425 in (214 mm) on the Holland IV submarine, known as Zalinski Boat, designed by Edmund Żaliński and John Holland. The rapid development of fuel and missiles in the late 1890s and early 1900s led to the creation of gunpowder guns and caused pneumatic guns to be substantially phased out from the US Army starting in 1905. Currently, pneumatic guns are designed to carry out various research impact tests, with various energy possibilities, limited by the diameter and working pres- sure [2]. Small-diameter systems (up to 70 mm) allow for higher velocities for smaller-mass projectiles, while in medium-diameter solutions (70-150 mm) for objects with larger mass, the muzzle velocity is lower. The greatest drop in speed is recorded for large-diameter devices (over 200 mm). The small-diameter pneumatic launcher is an im- portant element of the stationary test stand called the split Hopkinson pressure bar SHPB [3]. This stand is intended for testing the behaviour of samples of construction materials, including construction mate- rials subjected to impact loads [4] and in the field metals [5–9] as well as for concretes [10], polymers, wood, soils [11–15] and other materials [16–18]. Under- standing the dynamic strength characteristics of these materials is important for the design of protective structures for buildings, especially in the conditions prone to industrial accidents [19], to ensure safety [20]. With the use of compressed air, the launcher on this test stand allows for throwing projectiles, such as a bar or Hopkinson measuring bars, directly load- ing the tested metallic sample, U. S. Lindholm used a spring and then a pneumatic 0.5 inch (12.7 mm) launcher in the SHPB test stand for the first time at the beginning of the 1960s [21]. Until then, blasting shots have been used to generate a stress pulse in Hopkinson measuring bars. The stationary pneumatic launcher, which is an el- ement of the SHPB, intended to test the behaviour of material samples subjected to dynamic (shock) loads, does not meet the statutory definitions of “firearms”, “gun” and “pneumatic weapons” [22]. This means that pursuant to the Act of June 13, 2019 on the perfor- mance of economic activity in the field of production and trade in explosives, weapons, ammunition, and products and technology for military or police pur- poses [23] it is not considered a weapon. However, if the pneumatic launcher in question was designed and intended solely for the production or certification, qualification or testing of products included in Part IV — WT of the Annex to the Regulation [24], then it would be subject to regulation resulting from the provisions of the Act [25]. The contractor of such 552 https://doi.org/10.14311/AP.2021.61.0552 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 61 no. 4/2021 Performance characteristics of Hopkinson’s . . . Figure 1. General view of the SHPB test stand DMEI (MUT) – on the right side of the test stand, there is a pneumatic launcher (the pressure chamber with the barrel are marked with a red ellipse). a pneumatic launcher would have to have a license granted by the Minister of the Interior and Admin- istration, at least in the scope of manufacturing and trading in products for military or police purposes specified in WT XIII section 1 or 2 depending on: • a type of equipment specially designed or modified for the production of products covered by Part IV — WT, and specially designed components thereof; • the type of a specially designed facility for conduct- ing environmental tests and the type of specially designed equipment for the purpose of certification, qualification or testing of products included in the list contained in Part IV — WT. At present, the disadvantages of split Hopkinson bars, such as the high air operating pressures to obtain high strain rates, the noise due to the instantaneous air expansion, and a large overall station length, have been eliminated in the electromagnetic Hopkinson bar. It uses the intense pressure created in the magnetic field created by the passage of an electric current pulse through a series of coils. The magnetic field behaves like the release of air from a high-pressure vessel and can impart a high initial velocity to the bar-projectile to obtain very high compressive and strain rates of metallic materials, more than 104 1/s. However, for low and medium impact velocities of this projectile, pneumatic launchers are still useful for conducting physical experiments in the range of deformation rates 102 – 103 1/s. They ensure a good reproducibility of obtaining the value of the impact velocity for indi- vidual set values of the deformation rate. However, from the point of view of objectivity of dynamic tests, it is necessary to conduct preliminary tests to vali- date the pneumatic launcher, a so-called calibration procedure, before a series of physical experiments to obtain empirical relationships between the working pressure and the impact velocity for the geometric parameters of the bar-projectile used in further tests, which characterize the performance of this launcher. This is especially important during various schemes for material impact tests with the use of the pneu- matic launcher. The subject of this work is devoted to these issues. 2. Characteristics of the pneumatic launcher of the SHPB stand The subject of the work is a pneumatic launcher in- cluded in the split Hopkinson bar testing stand (shown in Figure 1), which is located at the Department of Military Engineering and Infrastructure (DMEI) of the Military University of Technology (MUT) in War- saw. The pneumatic launcher consists of a pressure cham- ber with a capacity of 10 dm3 with a smooth barrel with a diameter of 20 mm and a length of 2700 mm. Figure 2 shows a general view of the launcher and shows the valve with a digital pressure gauge that feeds the launcher chamber and the valve supplying the space behind the bar-projectile in the barrel. The launcher in question is fed with compressed air from a compressor to a maximum working pres- sure pmax=8 bar. The important elements of this pneumatic system are: • air compressor type Specair HL 275/50 (Figure 3); • filter-reducer with a pressure gauge, connected by flexible spiral hoses with the compressor and the pneumatic launcher (Figure 4). The launcher in question throws bar-projectiles of different lengths, it depends on the conditions of the physical experiment that is carried out on this test stand. Typical bar-projectiles are 100, 200 and 250 mm in length (Figure 5). Detailed parameters of these bar-projectiles are presented in the Table 1. 553 K. Sobczyk, L. Kruszka, R. Chmielewski, R. Rekucki Acta Polytechnica Figure 2. General view of the pressure chamber of the pneumatic launcher: 1 – valve with a digital pressure gauge that feeds the launcher chamber, 2 – valve supplying the space behind the bar-projectile in the barrel. Figure 3. Air compressor type Specair HL 275/50. Bar-projectile Type 1 Type 2 Type 3 Length Lbp [mm] 99.10 199.40 249.80 Weight mbp [g] 234.91 353.72 491.04 Diameter Dbp [mm] 19.92 19.97 19.96 Material Steel C350 Modulus of longitudinal elasticity material E [GPa] 200 Wave propagation velocity c0 [m·s−1] 5000 Table 1. Detailed parameters of typical bar-projectiles. 554 vol. 61 no. 4/2021 Performance characteristics of Hopkinson’s . . . Figure 4. Filter-reducer with connections and manometer: 1 – pressure regulator, 2 – pressure gauge, 3 – filter, 4 – spiral tube (connected to the compressor), 5 – spiral tube (connected to the launcher chamber), 6 – spiral tube connected to the barrel part behind the bar-projectile. Figure 5. Typical bar-projectiles are 100, 200 and 250 mm in length. 3. Pneumatic launcher calibration procedure The pneumatic launcher was calibrated for the bar- projectiles used. This procedure included measure- ments of the velocity v0 of the bar-projectile at the moment of leaving the barrel for different lengths Lbp of the bar-projectile (Lbp1 = 100 mm; Lbp2 = 200 mm; Lbp3 = 250 mm) in a cycle of five experiments (i = measurement projectile number) in three variants of the operating pressure p0 of the pneumatic launcher (p01 = 0,5 bar; p02 = 1,0 bar; p03 = 1,5 bar). The standard deviation for each cycle of five exper- iments was calculated according to the formula: σ = √√√√ 1 n · n∑ i=1 (xi − x)2 (1) The results of the calibration of the launchers are shown in Table 2. The results contained in Table 2 are presented graphically as diagrams of the muzzle velocity v0 of the bar-projectile depending on: a) the working pressure p0 of the pneumatic launcher and b) the number of the experimental attempt in three variants of the initial pressure p0 for the length Lbp of the bar-projectile: • Lbp1=100 mm — Figure 6a and 6b; • Lbp2 = 200 mm — Figure 7a and 7b; • Lbp3 = 250 mm — Figure 8a and 8b. 4. Impact tests with the use of an SHPB pneumatic launcher Using the SHPB pneumatic launcher, it is possible to use the schemes of two types of compression im- pact tests for the purpose of testing the behaviour of 555 K. Sobczyk, L. Kruszka, R. Chmielewski, R. Rekucki Acta Polytechnica Length Lbp of the bar-projectile [mm] The velocity v0i of the bar-projectile at the moment of exiting the barrel [m/s] Attempt number p01 = 0.5 bar p02 = 1.0 bar p03 = 1.5 bar (0.05 MPa) (0.10 MPa) (0.15 MPa) 100 1) 4.2728 14.4931 22.0418 2) 4.6167 11.6163 21.1648 3) 2.7173 14.1429 22.3073 4) 4.0480 15.2419 21.9018 5) 3.8620 13.8606 20.6063 Average velocity values v0i 3.9034 13.8709 21.6044 Standard deviation σ0i 0.6442 1.2185 0.6266 200 1) 6.5917 14.3951 19.0846 2) 7.4256 14.8395 19.0956 3) 8.1195 14.6096 19.2573 4) 7.6029 13.7991 19.9091 5) 8.0451 13.7009 20.1823 Average velocity values v0i 7.5569 14.2688 19.5058 Standard deviation σ0i 0.5488 0.4474 0.4534 250 1) 6.6579 11.9606 16.6895 2) 7.9015 12.7004 16.7397 3) 7.6272 12.8853 16.5981 4) 8.3620 12.1925 16.2739 5) 9.0590 11.5410 16.5953 Average velocity values v0i 7.9215 12.2560 16.5793 Standard deviation σ0i 0.7964 0.4891 0.1623 Table 2. Summary of the obtained muzzle velocities v0i of the bar-projectiles for different variants of the length Lbp of the bar-projectile and the working pressure p0 of the pneumatic launcher. (a). (b). Figure 6. Dependency graph a) v0(p0) and b) v(0,i) (i – number of the experimental attempt) for Lbp1 = 100 mm. 556 vol. 61 no. 4/2021 Performance characteristics of Hopkinson’s . . . (a). (b). Figure 7. Dependency graph a) v0(p0) and b) v(0,i) (i – number of the experimental attempt) for Lbp2 = 200 mm. (a). (b). Figure 8. Dependency graph a) v0(p0) and b) v(0,i) (i – number of the experimental attempt) for Lbp3 = 250 mm. metallic samples: the first — a short cylindrical sam- ple, including a miniature (small diameter) sample, and the second — a long cylindrical sample (Taylor test). Along with the diagrams, the formulas for both variants of direct compression are presented to deter- mine the stress σs, strain εs and strain rate ε̇s in the engineering (nominal) measure, and for the Taylor impact test - empirical formulas for calculating the initial dynamic yield stress proposed by Taylor σT y and Wilkins and Guinana σW G y [26] are presented. (1.) Two variants of direct compression of the first type: (a) variant I of a miniature sample — with the use of a loading bar-projectile, which, at the moment of impact, has accumulated kinetic energy many times greater than the work of elasto-plastic de- formation of this sample; in this case, the speed of the bar-projectile is constant or changes slowly during the entire process of elasto-plastic deforma- tion of the sample on the front of the Hopkinson measuring bar (Figure 9); vs(t) = c0,H · εt(t) (2) ε̇s(t) = 1 L1 · [v0 − vs(t)] (3) εs(t) = 1 L1 · [ v0 · t − c0,H · ∫ t 0 εt(t)dt ] (4) σs(t) = EH · ( DH D1 )2 · εt(t) (5) where: • L1 is initial length of the short cylindrical spec- imen; 557 K. Sobczyk, L. Kruszka, R. Chmielewski, R. Rekucki Acta Polytechnica Figure 9. Scheme of direct compression in variant I – miniature short cylindrical sample. • εt(t) is elastic positive incident strain pulse in the measuring Hopkinson bar, registered by a strain gauge after passing the compressive loading wave through the specimen; • DH and D1 are initial diameters of the measur- ing Hopkinson bar and the specimen, respec- tively; • EH is Young’s modulus of the measuring Hop- kinson bar; • cH is sound velocity in the measuring Hopkin- son bar; • σs is engineering stress in the specimen ob- tained as a function of time in the assumption of equality of forces at the ends of the specimen during the entire deformation process; • εs is engineering strain in the specimen tested; • dotεs is engineering strain rate of the specimen tested. (b) variant II - with the use of a bar-projectile with a much lower mass than in variant I (about 50 % mass of a bar-projectile in variant I); the process of dynamic loading of the sample is wave- like in the case of the bar-projectile – sample – Hopkinson measuring bar system (Figure 10); vs(t) = v0(t) − 2 · c0,H · εt(t) (6) ε̇s(t) = 1 L2 · [v0 − 2 · c0,H · εt(t)] (7) εs(t) = 1 L2 · [ v0 · t − 2 · c0,H · ∫ t 0 εt(t)dt ] (8) σs(t) = EH · ( DH D2 )2 · εt(t) (9) where: signs and symbols as in point ((1.).a.). (2.) Taylor impact test — a long cylindrical sample- projectile fired by a pneumatic launcher hits di- rectly on the front of a Hopkinson measuring bar and undergoes an inhomogeneous elastic-plastic de- formation (Figure 11). σT y = (L0 − Lpl) · ρ · v0 2 2 · (L0 − L1) · ln ( L0 Lpl ) [12] (10) σW G y = ρ · v0 2 2 · ln ( (L0−Lpl (L1−Lpl ) [12] (11) ε̇s = v0 2 · (L0 − Lel) (12) where: • L0 is initial length of specimen; • L1 is compressed (final) length of specimen; • Lpl is length of a section of the specimen along its axis where only plastic deformation occurred; • Lel is length of a section of the specimen along its axis where only elastic deformation occurred; • σy is engineering yield stress (upper index T — according to the Taylor formula, upper index WG — according to the Wilkins and Guinan formulation); • v0 is impact velocity; • ρ is mass density of specimen. The above formulas describing the real (true) measures of stress σt, strain εt and strain rate ε̇t of the tested samples in variants I and II have the following forms, respectively: ε̇t(t) = ε̇e 1 + εe(t) (13) εt(t) = ln [1 + εe(t)] (14) σt(t) = σe(t) · [1 + εe(t)] (15) 558 vol. 61 no. 4/2021 Performance characteristics of Hopkinson’s . . . Figure 10. Scheme of direct compression in variant II – short cylindrical sample. Figure 11. The scheme of the Taylor test - a long cylindrical sample before and after the test (isolines of permanent plastic deformations are marked on the longitudinal section of the sample). 559 K. Sobczyk, L. Kruszka, R. Chmielewski, R. Rekucki Acta Polytechnica Figure 12. A typical course of the elastic strain impulse in the Hopkinson measuring bar for the deter- mination of the yield strength of the tested metal for a dynamic loading σL y and unloading σUL y [27]. The direct compression test of a short cylindrical sample (variant II) also allows to determine the dynamic Bauschinger effect δ of the tested metal. The paper [20] presents a method of determining the measure of this effect using this shock test, using the registration of the compressive elastic deformation in time in the Hopkinson measuring bar for this purpose. Figure 12 shows a typical course of an elastic strain pulse in this measuring rod. From this dia- gram, the initial dynamic yield limits can be deter- mined: σL y during loading and σUL y during unload- ing – the differences between the points: between 0 and B, and between B and C. The calculation of the dynamic Bauschinger effect δ is determined from the relationship: δ = σUL y σL y . (16) 5. Conclusions The characteristics of the operation of a pneumatic launcher for the purpose of conducting direct impact tests with the use of a bar-projectile and a Hopkinson measuring bar are presented. The obtained results of the experimental calibration of the pneumatic launcher — loading bar-projectiles characterize the performance of a given essential el- ement of the SHPB set-up, which is significant for conducting various impact direct tests, including the Taylor one. Schemes of two impact tests with the use of the pneumatic launcher and the Hopkinson measuring bar are presented as noteworthy for dynamic testing of metals in various typical compression modes, which allow to determine their real impact resistance — two variants of direct compression of a short cylindrical sample, including miniature, and a long cylindrical samples, which can also be used as projectiles in the Taylor test. For these tests, relationships were given that allow to determine the nominal (engineering) and real (true) values of stress σ, strain ε and strain rate ε̇ as well as the initial dynamic yield strength σy in the version proposed by Taylor σT y and Wilkins and Guinan σW G y . 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