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As a rare metal material with low density, high strength and high melting point, beryllium (Be) is widely utilized in many fields including aerospace and vehicles. Dynamic loadings such as impact and high-rate compression often happen in the applications of Be materials in these fields. However, the dynamic behaviors of Be materials under high pressure and high-rate loading have not been fully investigated, although they are valuable for better applications of Be materials. articularly, the effect of twinning on dynamic behaviors of Be material is very important for better understanding the plasticity deformation mechanism of Be material. In this paper, a thermoelastic-viscoplastic crystal plasticity model is developed for dynamic behaviors of Be material under high pressure and high strain-rate loading based on the physical mechanism of plasticity deformation. Besides, the dislocation motion and work hardening are considered within the constitutive framework by the Orowan relation and the Taylor equation respectively, and the contribution of twinning to the plasticity deformation is also considered via twinning fraction evolution and fragmentation of crystal due to twinning deformation. With the model, dynamic behaviors of Be material are investigated, including effect of pressure on the dynamic yield strength, the quasi-elastic unloading behavior, and evolution of twinning in shock loading and unloading. Compared with the classical SG model, the model developed in this paper accords better with the experimental results in predicting yield strength of Be material under impact loading, especially with high pressure. Moreover, it is revealed that the condition of yield strength of the Be material is divided into three cases, namely the non-twinning under low pressure, the twinning deformation under moderate pressure, and the twinning fragmentation under high pressure. The unloading behavior of Be material under impact loading is also studied with the model, and the quasi-elastic unloading behavior observed in experiments many times, is faithfully predicted. It is found that the quasi-elastic unloading phenomenon of the material is closely related to the variation of the shear velocity of shock wave with the shear strain, which suggests that the non-linear elastic property of the material is an important reason for this phenomenon. Finally, the evolution of twinning of Be material in the shock loading is studied, showing that the increasing of twinning friction happens not only in the loading process but also in the unloading process of the shock waves. Some crystals break up into sub-crystals due to the fact that the volume fraction of twinning exceeds the critical fraction in the evolution of twinning.
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Keywords:
- twinning /
- crystal fragmentation /
- crystal plasticity model /
- impact loading
[1] Zhang Y S, Qin Y J, Wu D Z, Xie Z Q 2001 Trans. China Welding Inst. 22 92 (in Chinese) [张友寿, 秦有钧, 吴东周, 谢志强 2001 焊接学报 22 92]
[2] Johnson W, Rice S L 1972 Impact Strength of Materials (London: Edward Arnold)
[3] Meyers M A 1994 Dynamic Behavior of Materials (New York: John wiley & Sons)
[4] Brown D W, Clausen B, Sisneros T A, Balogh I, Beyerlein I J 2013 Metall. Mater. Trans. A 44 5665
[5] Champman C L, Wise J L, Asay J R 1982 AIP Conference Proceedings 78 422
[6] Steinberg D, Breithaupt D, Honodel C 1986 Physica B+C 139 762
[7] Brown J L, Knudson M D, Alexander C S, Asay J R 2014 J. Appl. Phys. 116 033502
[8] Frahan M T H, Belof J L, Cavallo R M, Raevsky V A, Ignatova O N, Lebedev A, Ancheta D S, El-dasher B S, Florando J N, Gallegos G F, Johnsen E, LeBlanc M M 2015 J. Appl. Phys. 117 225901
[9] van Houtte P 1978 Acta Metar. 26 591
[10] Tomé C N, Lebensohn R A, Kocks U F 1991 Acta Mater. 39 2667
[11] Lebensohn R A, Tomé C N 1993 Acta Mater. 41 2611
[12] Kalidindi S R, Bronkhorst C A, Anand L 1992 J. Mech. Phys. Solids 40 537
[13] Winey J M, Gupta Y M 2014 J. Appl. Phys. 116 033505
[14] Pan H 2017 Ph. D. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [潘昊 2017 博士学位论文 (绵阳：中国工程物理研究院)]
[15] Salem A A, Kalidindi S R, Doherty R D 2002 Scripta Mater. 46 419
[16] Wang J, Beyerlein I J, Tomé C N 2010 Scripta Mater. 63 741
[17] Wu X, Kalidindi S R, Necker C, Salem A A 2007 Acta Mater. 55 423
[18] Salem A A, Kalidindi S R, Doherty R D 2003 Acta Mater. 51 4225
[19] Brown D W, Beyerlein I J, Sisneros T A, Clausen B, Tomé C N 2012 Int. J. Plast. 29 120
[20] Knezevic M, Beyerlein I J, Brown D W, Sisneros T A, Tomé C N 2013 Int. J. Plast. 49 185
[21] Kalidindi S R 1998 J. Mech. Phys. Solids 46 267273
[22] Johnson J N, Rohde R W 1971 J. Appl. Phys. 42 4171
[23] Wang H, Wu P D, Wang J, Tomé C N 2013 Int. J. Plast. 49 36
[24] Proust G, Tomé C N, Jain A, Agnew S R 2009 Int. J. Plast. 25 861
[25] Borodin E N, Mayer A E 2015 Int. J. Plast. 74 141
[26] Chhabildas L C, Wise J L, Asay J R 1982 AIP Confer. Proceed. 78 422
[27] Igonin V V 2014 Report on Task 3 Agreement# B590737 LLNL Livermore, CA
[28] Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
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[1] Zhang Y S, Qin Y J, Wu D Z, Xie Z Q 2001 Trans. China Welding Inst. 22 92 (in Chinese) [张友寿, 秦有钧, 吴东周, 谢志强 2001 焊接学报 22 92]
[2] Johnson W, Rice S L 1972 Impact Strength of Materials (London: Edward Arnold)
[3] Meyers M A 1994 Dynamic Behavior of Materials (New York: John wiley & Sons)
[4] Brown D W, Clausen B, Sisneros T A, Balogh I, Beyerlein I J 2013 Metall. Mater. Trans. A 44 5665
[5] Champman C L, Wise J L, Asay J R 1982 AIP Conference Proceedings 78 422
[6] Steinberg D, Breithaupt D, Honodel C 1986 Physica B+C 139 762
[7] Brown J L, Knudson M D, Alexander C S, Asay J R 2014 J. Appl. Phys. 116 033502
[8] Frahan M T H, Belof J L, Cavallo R M, Raevsky V A, Ignatova O N, Lebedev A, Ancheta D S, El-dasher B S, Florando J N, Gallegos G F, Johnsen E, LeBlanc M M 2015 J. Appl. Phys. 117 225901
[9] van Houtte P 1978 Acta Metar. 26 591
[10] Tomé C N, Lebensohn R A, Kocks U F 1991 Acta Mater. 39 2667
[11] Lebensohn R A, Tomé C N 1993 Acta Mater. 41 2611
[12] Kalidindi S R, Bronkhorst C A, Anand L 1992 J. Mech. Phys. Solids 40 537
[13] Winey J M, Gupta Y M 2014 J. Appl. Phys. 116 033505
[14] Pan H 2017 Ph. D. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [潘昊 2017 博士学位论文 (绵阳：中国工程物理研究院)]
[15] Salem A A, Kalidindi S R, Doherty R D 2002 Scripta Mater. 46 419
[16] Wang J, Beyerlein I J, Tomé C N 2010 Scripta Mater. 63 741
[17] Wu X, Kalidindi S R, Necker C, Salem A A 2007 Acta Mater. 55 423
[18] Salem A A, Kalidindi S R, Doherty R D 2003 Acta Mater. 51 4225
[19] Brown D W, Beyerlein I J, Sisneros T A, Clausen B, Tomé C N 2012 Int. J. Plast. 29 120
[20] Knezevic M, Beyerlein I J, Brown D W, Sisneros T A, Tomé C N 2013 Int. J. Plast. 49 185
[21] Kalidindi S R 1998 J. Mech. Phys. Solids 46 267273
[22] Johnson J N, Rohde R W 1971 J. Appl. Phys. 42 4171
[23] Wang H, Wu P D, Wang J, Tomé C N 2013 Int. J. Plast. 49 36
[24] Proust G, Tomé C N, Jain A, Agnew S R 2009 Int. J. Plast. 25 861
[25] Borodin E N, Mayer A E 2015 Int. J. Plast. 74 141
[26] Chhabildas L C, Wise J L, Asay J R 1982 AIP Confer. Proceed. 78 422
[27] Igonin V V 2014 Report on Task 3 Agreement# B590737 LLNL Livermore, CA
[28] Steinberg D J, Cochran S G, Guinan M W 1980 J. Appl. Phys. 51 1498
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