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Sound speed is of great importance for high velocity impact phenomena because it is a fundamental parameter to deduce the shear moduli, strengths and phase transitions of materials at high pressure. It has attracted much attention because of significant challenges to experiment and simulation. In practice, with the development of laser interferometer measurement system, one can obtain velocity-time histories of windowed-surfaces or free surfaces with high resolution in shock or ramp compression and unload experiments. This development provides a possible way to infer the sound speed from these velocity profiles. The key problem is to build valid analysis technique to extract the sound speed. Commonly used Lagrangian analysis methods include backward integration method, incremental impedance matching method, transfer function method and backward characteristic analysis method. However, all of these methods hardly infer the right results from the nonsymmetric impact and release experiment with only one depth of material due to the complex impedance mismatch among a flyer, sample and window. Some decreasing impedance mismatch techniques have been developed for the experiments including reverse impact or using a high strength flyer, but these techniques will limit the pressure range or need a newly designed gun with large caliber. In fact, the traditional backward characteristic analysis method only considers the sample/window interaction while bending of the incoming characteristics due to impedance difference between the flyer and sample is always ignored, which causes a distortion to the loading condition of samples. Thus in this work, we add forward characteristics to describe rarefaction wave reflection at the flyer/sample interface. Then a reasonable loading-releasing in-situ velocity profile of the interface can be derived from this improvement. We use the improved/tradition characteristics and incremental impedance matching method to analyze a synthetic nonsymmetric impact experiment in which the flyer, sample and window are of Al, Cu and LiF, respectively. Synthetic analyses suggest that the modified characteristic method can give more accurate results including sound speed-particle velocity and release path at high pressure. Compared with other methods, the new characteristic method just needs to know the release path of flyer and window that can be calibrated by well-developed technique, moreover, this method also does not need to know the form of equation of state and constitutive model of the sample. Calculation of this method is not complex and the iterative approach usually achieves convergence in less than 10 steps. All of these features will facilitate using this method to infer sound speed from the velocity profile of nonsymmetric impact experiments.
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Keywords:
- sound speed /
- characteristic method /
- shock compression
[1] Asay J R, Kerley G I 1987 Int. J. Impact Eng. 5 69
[2] Yu Y Y, Tan Y, Dai C D, Li X M, Li Y H, Tan H 2014 Acta Phys. Sin. 63 026202 (in Chinese) [俞宇颖, 谭叶, 戴诚达, 李雪梅, 李英华, 谭华 2014 物理学报 63 026202]
[3] Hu J B, Zhou X M, Tan H, Li J B, Dai C D 2008 Appl. Phys. Lett. 92 111905
[4] Huang H, Asay J R 2005 J. Appl. Phys. 98 033524
[5] Furnish M D, Alexander C S, Brown J L, Reinhart W D 2014 J. Appl. Phys. 115 033511
[6] Tan Y, Yu Y Y, Dai C D, Yu J D, Wang Q S, Tan H 2013 Acta Phys. Sin. 62 036401 (in Chinese) [谭叶, 俞宇颖, 戴诚达, 于继东, 王青松, 谭华 2013 物理学报 62 036401]
[7] Pan H, Hu X M, Wu Z H, Dai C D, Wu Q 2012 Acta Phys. Sin. 61 206401 (in Chinese) [潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 物理学报 61 206401]
[8] Asay J R, Lipkin J 1978 J. Appl. Phys. 49 4242
[9] Hayes D B, Hall C A, Asay J R, Knudson M D 2004 J. Appl. Phys. 96 5520
[10] Rothman S D, Davis J P, Maw J, Robinson C M, Parker K, Palmer J 2005 J. Phys. D 38 733
[11] Brown J L, Alexander C S, Asay J R, Vogler T J, Ding J L 2013 J. Appl. Phys. 114 223518
[12] Brown J L, Alexander C S, Asay J R, Vogler T J, Dolan D H, Belof J L 2014 J. Appl. Phys. 115 043530
[13] Rothman S, Edwards R, Vogle, T J, Furnish M D 2012 Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter Chicago, United States, June 26-July 1, 2011 p104
[14] Pan H, Hu X M, Wu Z H 2015 EPJ Web Conf. 94 01007
[15] Lowe M R, Rothman S D, Chapman D, Robinson C 2014 J. Phys. Conf. Series 500 112043
[16] Rothman S D, Davis J P, Gooding S, Knudson M D, Ao T 2014 J. Phys. Conf. Series 500 032016
[17] Tan H 2006 Introduction to Experimental Shock-Wave Physics (Beijing: National Defense Industry Press) p160 (in Chinese) [谭华 2006 实验冲击波物理导引(北京:国防工业出版社) 第160页]
[18] Duffy T S, Ahrens T J 1995 J. Geophys. Res. 100 529
[19] Casem D T, Dandekar D P 2012 J. Appl. Phys. 111 063508
[20] Li W X 2003 One-Dimensional Nonsteady Flow and Shock Waves (Beijing: National Defense Industry Press) p98, p215 (in Chinese) [李维新 2003 一维不定常流与冲击波(北京:国防工业出版社) 第 98, 215 页]
[21] Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
[22] Fratanduono D E, Boehly T R, Barrios M A, Meyerhofer D D, Eggert J H, Smith R F, Hicks D G, Celliers P M, Braun D G, Collins G W 2011 J. Appl. Phys. 109 123521
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[1] Asay J R, Kerley G I 1987 Int. J. Impact Eng. 5 69
[2] Yu Y Y, Tan Y, Dai C D, Li X M, Li Y H, Tan H 2014 Acta Phys. Sin. 63 026202 (in Chinese) [俞宇颖, 谭叶, 戴诚达, 李雪梅, 李英华, 谭华 2014 物理学报 63 026202]
[3] Hu J B, Zhou X M, Tan H, Li J B, Dai C D 2008 Appl. Phys. Lett. 92 111905
[4] Huang H, Asay J R 2005 J. Appl. Phys. 98 033524
[5] Furnish M D, Alexander C S, Brown J L, Reinhart W D 2014 J. Appl. Phys. 115 033511
[6] Tan Y, Yu Y Y, Dai C D, Yu J D, Wang Q S, Tan H 2013 Acta Phys. Sin. 62 036401 (in Chinese) [谭叶, 俞宇颖, 戴诚达, 于继东, 王青松, 谭华 2013 物理学报 62 036401]
[7] Pan H, Hu X M, Wu Z H, Dai C D, Wu Q 2012 Acta Phys. Sin. 61 206401 (in Chinese) [潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 物理学报 61 206401]
[8] Asay J R, Lipkin J 1978 J. Appl. Phys. 49 4242
[9] Hayes D B, Hall C A, Asay J R, Knudson M D 2004 J. Appl. Phys. 96 5520
[10] Rothman S D, Davis J P, Maw J, Robinson C M, Parker K, Palmer J 2005 J. Phys. D 38 733
[11] Brown J L, Alexander C S, Asay J R, Vogler T J, Ding J L 2013 J. Appl. Phys. 114 223518
[12] Brown J L, Alexander C S, Asay J R, Vogler T J, Dolan D H, Belof J L 2014 J. Appl. Phys. 115 043530
[13] Rothman S, Edwards R, Vogle, T J, Furnish M D 2012 Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter Chicago, United States, June 26-July 1, 2011 p104
[14] Pan H, Hu X M, Wu Z H 2015 EPJ Web Conf. 94 01007
[15] Lowe M R, Rothman S D, Chapman D, Robinson C 2014 J. Phys. Conf. Series 500 112043
[16] Rothman S D, Davis J P, Gooding S, Knudson M D, Ao T 2014 J. Phys. Conf. Series 500 032016
[17] Tan H 2006 Introduction to Experimental Shock-Wave Physics (Beijing: National Defense Industry Press) p160 (in Chinese) [谭华 2006 实验冲击波物理导引(北京:国防工业出版社) 第160页]
[18] Duffy T S, Ahrens T J 1995 J. Geophys. Res. 100 529
[19] Casem D T, Dandekar D P 2012 J. Appl. Phys. 111 063508
[20] Li W X 2003 One-Dimensional Nonsteady Flow and Shock Waves (Beijing: National Defense Industry Press) p98, p215 (in Chinese) [李维新 2003 一维不定常流与冲击波(北京:国防工业出版社) 第 98, 215 页]
[21] Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
[22] Fratanduono D E, Boehly T R, Barrios M A, Meyerhofer D D, Eggert J H, Smith R F, Hicks D G, Celliers P M, Braun D G, Collins G W 2011 J. Appl. Phys. 109 123521
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