TORSIONAL TESTING AT HIGH STRAIN RATES USING A KOLSKY BAR

Transcription

1 Technical Sciences 233 TORSIONAL TESTING AT HIGH STRAIN RATES USING A KOLSKY BAR Gigi Ionu NICOL ESCU nicolaescu_ionut@yahoo.com George Amado TEFAN amadostefan@yahoo.com Constantin ENACHE enache63@yahoo.com Marius Valeriu CÂRMACI mariusvaleriu@yahoo.com Military Technical Academy, Bucharest, Romania ABSTRACT The dynamic properties of materials are important in a variety of engineering problems such as forming operations or impact problems. Dynamic tests are usually performed using a Split Hopkinson Pressure Bar (SHPB) or a Torsional Split Hopkinson (Kolsky) Bar. The main advantage of torsional tests is that high strains can easily be reached without occurrence of instabilities (buckling in compression or necking in tension tests). The Torsional Split Hopkinson Bar (Kolsky) experimental technique has become a standard method to characterize the dynamic mechanical properties of materials that involve s -1 strain-rate regimes. This paper will present a technique to convert the torque-twist data obtained using a Torsional Split Hopkinson (Kolsky) Bar into true stress true strain curve. KEYWORDS: torsional Split Hopkinson (Kolsky) bar, high strain rate, large strains, CW614N brass 1. Introduction A first compression version of SHPB was constructed by Herbert Kolsky in 1949 based on studies of John Hopkinson, Bertram Hopkinson and Davies [1], [2]. He placed a specimen between two elastic bars and then struck one of them with a striker bar. A compressive wave is generated and will propagate through the first bar, named the input bar or the incident bar, will encounter the specimen when the wave will be divided into transmitted and reflected components. The first torsional Kolsky bar was introduced in 1966 by Baker and Yew and further was developed by other researchers

2 234 Technical Sciences [3]. The principle of this technique is to produce a torsional wave by releasing a stored torque using a clamp mechanism. 2. Specimen Geometry The test specimen is made from CW614N Brass and is a short thin-wall tube with hexagonal flanges (figure no.1) attached between the two bars [4]. It was fixed using a hexagonal socket because this technique is less time consuming than an adhesive fixation (figure no. 2). A disadvantage of this technique is that the specimen can rotate relative to the socket, but it can be removed by using small screws. Figure no. 1 Specimen geometry Figure no. 2 Fixing the specimen using a hexagonal socket The mechanical impedance of the hexagonal socket must be equal to that of the bars, otherwise the incident wave will be reflected due to impedance difference. 3. Description of Apparatus The torsional Kolsky bar is made up of two collinear bars (incident and transmitter bars) supported by bearings that allow them to rotate freely. Between them is placed a short specimen, usually is a thinwall tube specimen. The bars are made of titanium and they have a diameter of about 25 mm (figure no. 3). Figure no. 3 Schematic of a torsional Kolsky bar

3 Technical Sciences 235 The loading wave in the incident bar is produced by the release of a torque that is initially stored at the section of the bar between the clamp and the loading end. During the tests it is assumed that the specimen is under a state of pure and uniform shear stress and deformation. The stored torque is generated by first tightening the clamp with a hydraulic pump and then turning the end of the incident bar using a loading jack. The design of the clamp is very important because it must be able to hold the desired torque without slipping and release the torque rapidly enough to produce a rectangular stress pulse. Duffy clamping techniques was used to generate a torsional wave (figure no. 4 and 5). This method consists of two plates that are held together at the top by a fracture pin [5]. The clamp is tightened by a hydraulic pump that pushes the lower ends of the clamp arms (plates) together. After the desired torque is loaded between the loading end and the clamp, the hydraulic pressure is increased until the fracture pin is broken and the stored torque will be released. Fig. 4 Clamping system The fracture pin material and the geometry were chosen taking into account the ASTM standards and the reference articles specifications. For this purpose were performed a series of tests to get a torsion wave with a profile close to a rectangle shape. The material chosen for the fracture pin is an aluminum alloy T6165 [6]. a) Inadequate fracture b) Proper fracture Figure no. 5 Fracture pin To conduct a test, a torsional wave is generated in one of the bars (incident bar). The wave propagates toward the specimen, and, when it arrives, the specimen is loaded and the wave is partially reflected back to the incident bar and partially transmitted to the other bar (transmitter bar).

4 236 Technical Sciences At the release of the clamp, half of the torque stored between the clamp and the loading end will travel as a shear wave, at the shear wave speed of titanium, toward the specimen. Shear pulse of the same magnitude will travel at the same speed in the other direction unloading the torque that is stored at that end (figure no. 6). This unloading pulse will reflect completely at the loading end of the incident bar and travel toward the specimen releasing the torque to zero; therefore, the total length of the shear pulse that will twist the specimen is equal to the time taken by the unloading pulse to travel toward the loading end and back to the clamp. Figure no. 6 Position-time (X-t) diagram of the stress waves 4. Measuring the Elastic Waves in the Bars Shear stress pulses in the input and output bars are measured using a strain gage bridge. Each bridge consisting of two pairs, one pair attached diametrically opposite the other on the surface of the bar. The gages are oriented at a 45 deg. angle to the axis of the bars (fig. 7). The first strain gauge bridge is placed in the region of stored torque between clamp and loading end and is used only to measure the magnitude of the applied (stored) torque to the input bar. The second strain gauge is located on the input bar (incident bar) between clamp and specimen. This gauge will record the incident wave and the reflected wave. The third strain gauge is located on the transmitter bar and it will record only the transmitted wave [7].

5 Technical Sciences 237 y = = = Figure no. 7 Wheatstone quarter bridge circuit P = x The pure shear stress is equivalent to a biaxial state of equal tensile ( ) and compressive ( ) stresses oriented at 45 o to the pure shear axes (figure no. 8). The shear strain measured is [8]: (1) Figure no. 8 Pure shear stress A static calibration of the Kolsky bar is performed. For this method the input and output bars are joined and the output bar is fixed at one end using a small arm. A loading arm that is attached at the input bar is used to generate different torques by hanging up different weights (figure no. 9). The resulting gauge voltages for the input and output gauges are recorded as functions of torques. For each bridge a static calibration curve is generated. Figure no. 9 Kolsky bar calibration The relationship between torque and shear strain is: (2) where: is the shear strain recorded by gauges at the surface of titanium bars (input and output) is radius of titanium bar, is shear modulus of titanium. The equation (2) can be easily deduced from the relation between torque and shear strain of the outer surface of titanium bar, taking in consideration that the shear stress varies linearly with the radius. The shear stress in titanium bars has a linear distribution across the bar diameter, being zero at the center and maximum at the outer surface [9].

6 238 Technical Sciences 5. Results & Conclusions The waves recorded to each strain gauges bridge are converted easily in equivalent torques using the calibration curves (figure no. 10, figure no. 11): Figure no. 10 Shear strain[v] pulses at second and third gage locations Figure no. 11 Equivalent torque pulses at second and third gage locations The incident, reflected and transmitted waves are extracted (figure no. 12): Figure no. 12 Waves extraction The magnitude of stress, strain, and strain rate of the specimen can be computed form the measured shear strain records of the input and output bars. The shear strain rate of the specimen is computed using data recorded on reflected bar [10] (figure no. 13): where: (3) is the mean radius of specimen ( = 0.95 mm), is the length of the specimen ( = 3.8 mm), is the density of titanium ( ), J is the polar moment of inertia (J = cm 4 ), c is the torsional wave speed (c = 3152 m/s defined as ).

7 Technical Sciences 239 Figure no. 13 Shear strain rate as a function of time The shear strain in the specimen is obtained by integrating the shear strain rate (figure no. 14): (4) Figure no. 14 Shear strain as a function of time The shear stress is given by the transmitted wave (figure no. 15): (5) where: is the thickness of the specimen is the average radius of the specimen Figure no. 15 Shear stress as a function of shear strain

8 240 Technical Sciences Using the von Mises yield criterion the data are converted into equivalent stress, strain and strain rate using the relations: (7) (6) the final relationships being: (5) (4) (8) The true strain, true stress and true strain rate are obtained by making the assumption that the volume of the specimen is constant during the test [11], [12]: (7) (6) (2) (3) The dynamic behavior of the material is characterized by the true strain time, true strain rate time and true stress true strain curves (figure no. 16, 17, 18): Figure no. 16 True strain vs. Time Figure no. 17 True strain rate vs. Time

9 Technical Sciences 241 Figure no. 18 True stress vs. true strain In the dynamic test the maximum values for shear strain rate and shear stress were 613 s -1 respectively 615 Mpa. The static compression tests were performed on cylindrical specimens at room temperature on an INSTRON 8802 servohydraulic testing machine. Acknowledgement This paper has been financially supported within the project entitled Horizon Doctoral and Postdoctoral Studies: Promoting the National Interest through Excellence, Competitiveness and Responsibility in the Field of Romanian Fundamental and Applied Scientific Research, contract number POSDRU/159/1.5/S/ This project is co-financed by European Social Fund through Sectoral Operational Programme for Human Resources Development Investing in people! REFERENCES 1. Weinong Chen, Bo Song, Split Hopkinson (Kolsky) Bar. Design, Testing and Applications, (New York: Springer, 2011), 3-4, Florin Ilie, Contributions on the calculus and attempts of materials used for bulletproof protection equipment creating, Doctoral thesis, Military Technical Academy, 2010, Weinong Chen, Bo Song, 3-4, ASM International, ASM HandBook, Volume 8, Mechanical Testing and Evaluation, (Ohio: ASM International, 2000), 1125, 1120, 1122, Ibidem. 6. Ibidem. 7. Weerasooriya Tusit, The MTL torsional split Hopkinson bar, (U.S. Army Materials Technology Laboratory, 1990), Cornel Bia, Vasile Ille, Mircea V. Soare, Rezisten a materialelor i teoria elasticit ii, (Bucharest: Didactic i Pedagogic Publishing House, 1983), 228, Ibidem, p. 228, ASM International, ASM HandBook, Volume 8, Mechanical Testing and Evaluation, (Ohio: ASM International, 2000), 1125, 1120, 1122, Marc Andre Meyers, Dynamic Behavior of Materials, (New York: John Wiley & Sons, 1994), Iman Faridmehr, Mohd Hanim Osman, Azlan Bin Adnan, Ali Farokhi Nejad, Reza Hodjati, Mohammadamin Azimi, Correlation between Engineering Stress-Strain and True Stress-Strain Curve, 5.

10 242 Technical Sciences BIBLIOGRAPHY ASM International, ASM HandBook, Volume 8, Mechanical Testing and Evaluation. Ohio: ASM International, Bia, Cornel, Vasile Ille, Mircea V. Soare. Rezisten a materialelor i teoria elasticit ii. Bucharest: Editura Didactic i Pedagogic Publishing House, Chen, Weinong, Song Bo, Split Hopkinson (Kolsky) Bar. Design, Testing and Applications. New York: Springer, Faridmehr, Iman, Osman Mohd Hanim, Bin Adnan Azlan, Nejad Ali Farokhi, Hodjati Reza, Azimi Mohammadamin, Correlation between Engineering Stress-Strain and True Stress-Strain Curve, Ilie, Florin, Contributions on the calculus and attempts of materials used for bulletproof protection equipment creating, Doctoral thesis, Military Technical Academy, Meyers, Marc Andre. Dynamic Behavior of Materials New York: John Wiley & Sons, Tusit, Weerasooriya. The MTL torsional split Hopkinson bar. U.S. Army Materials Technology Laboratory, 1990.