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In order to better understand the fracture mechanism of body-centered-cubic (BCC) metal, the multiscale quasi-continuum method (QC) is employed to analyze the nano-sized mode I cracks of three kinds of BCC metal materials, i.e., Ta, Fe and W. The plastic deformation near the crack tip and the brittle cleavage process are both investigated. The simulation result shows that there are different ductile-brittle behaviors in the cracks of different BCC materials. In the same loading range, the plastic deformation, such as dislocation nucleation and emission, stacking faults and twinning, is the main phenomenon for the crack of BCC-Ta. For the crack of BCC-Fe, plastic deformation and brittle cleavage are observed successively. At the initial stage, plastic deformation is dominant, which is similar to the crack of Ta. As loading increases, the crack begins to propagate, which differs from the crack of Ta. At first, the crack propagates along the initial direction [001], but then turns to [01] as the surface energy of {110} is lower than that of {01}. With the crack propagating, the crack tip is blunted by the plastic deformation, which is consistent with experimental results. As for BCC-W, the crack is found to propagate as brittle cleavage without plastic deformation at first. And the brittle cleavage is dominant all the time, which is a significant difference between W and the other two materials. In addition to the atomistic simulation, some theoretical calculations are also performed to analyze the ductile-brittle behaviors of the cracks. By an atomic slip model, the generalized stacking fault curves of BCC Ta, Fe and W are generated, which exhibit the unstable stacking fault energies of these materials. Based on the unstable stacking fault energy, two theoretical ductile-brittle criterions are analyzed. For the Rice-criterion, the result shows that the dislocation condition is met before cleavage for Ta and Fe, while for W the cleavage occurs before dislocation. For the ductile-brittle-parameter criterion, the result shows that Ta is the most ductile one in the three materials, followed by Fe, and W is the least ductile but the most brittle one. The analysis results of the two theoretical criterions both coincide well with the atomic simulation result, which well validates the simulation and fracture mechanisms.
[1] Giffith A A 1924 Proceedings of the First Congress of Applied Mechanics Delft 1924 p55-63
[2] Miller R, Ortiz M, Phillips R 1998 Engineer. Fract. Mech. 61 427
[3] Cui C B, Beom H G 2014 Mater. Sci. Engineer. A 609 102
[4] Liu X B, Xu Q J, Liu J 2014 The Chinese J. Nonferrous Metals 24 1408 (in Chinese) [刘晓波, 徐庆军, 刘剑2014中国有色金属学报24 1408]
[5] Inga R V, Erling O, Christian T, Diana F 2011 Mater. Sci. Engineer. A 528 5122
[6] Wu Y F, Wang C Y, Guo Y F 2005 Prog. Nat. Sci. 15 206 (in Chinese) [吴映飞, 王崇愚, 郭雅芳2005自然科学进展15 206]
[7] Tadmor E B 1996 The Quasicontinuum Method (Rhode: Brown University Press) pp8-20
[8] Li Y, Siegel D J, Adams J B 2003 Phys. Rev. B 67 125101
[9] Mendelev M I, Han S, Srolovitz D J, Ackland G J, Sun D Y, Asta M 2003 Philosophical Magazine 83 3977
[10] Finnis M, Sinclair E 1984 Philosophical Magazine A 50 45
[11] Featherston F H, Neighbours J R 1963 Phys. Rev. 130 1324
[12] Michal L, Anna M, Alena U, Jaroslav P, Pavel L 2016 Int. J. Fatigue 87 63
[13] Rice J R, Beltz G E 1994 J. Mech. Phys. Solids 42 333
[14] Tadmor E B, Hai S 2003 Mech. Phys. Solids 51 765
[15] Vitek V 1968 Philosophical Magazine 18 773
[16] Zimmerman J A, Gao H J, Abraham F F 2000 Model. Simul. Mater. Sci. Engineer. 8 103
[17] Lu G, Kioussis 2000 Phys. Rev. B 62 3099
[18] Rice J R 1992 Mech. Phys. Solids 40 239
[19] Wang S G, Tian E K, Lung C W 2000 J. Phys. Chem. Solids 61 1295
[20] Mei J F, Ni Y S, Li J W 2011 Int. J. Solids Struct. 48 3054
[21] Wang Z Q, Chen S H 2009 Advanced Fracture Mechanics (Beijing: Science Press) p14-16(in Chinese) [王自强, 陈少华2009高等断裂力学(北京: 科学出版社)第14–16页]
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[1] Giffith A A 1924 Proceedings of the First Congress of Applied Mechanics Delft 1924 p55-63
[2] Miller R, Ortiz M, Phillips R 1998 Engineer. Fract. Mech. 61 427
[3] Cui C B, Beom H G 2014 Mater. Sci. Engineer. A 609 102
[4] Liu X B, Xu Q J, Liu J 2014 The Chinese J. Nonferrous Metals 24 1408 (in Chinese) [刘晓波, 徐庆军, 刘剑2014中国有色金属学报24 1408]
[5] Inga R V, Erling O, Christian T, Diana F 2011 Mater. Sci. Engineer. A 528 5122
[6] Wu Y F, Wang C Y, Guo Y F 2005 Prog. Nat. Sci. 15 206 (in Chinese) [吴映飞, 王崇愚, 郭雅芳2005自然科学进展15 206]
[7] Tadmor E B 1996 The Quasicontinuum Method (Rhode: Brown University Press) pp8-20
[8] Li Y, Siegel D J, Adams J B 2003 Phys. Rev. B 67 125101
[9] Mendelev M I, Han S, Srolovitz D J, Ackland G J, Sun D Y, Asta M 2003 Philosophical Magazine 83 3977
[10] Finnis M, Sinclair E 1984 Philosophical Magazine A 50 45
[11] Featherston F H, Neighbours J R 1963 Phys. Rev. 130 1324
[12] Michal L, Anna M, Alena U, Jaroslav P, Pavel L 2016 Int. J. Fatigue 87 63
[13] Rice J R, Beltz G E 1994 J. Mech. Phys. Solids 42 333
[14] Tadmor E B, Hai S 2003 Mech. Phys. Solids 51 765
[15] Vitek V 1968 Philosophical Magazine 18 773
[16] Zimmerman J A, Gao H J, Abraham F F 2000 Model. Simul. Mater. Sci. Engineer. 8 103
[17] Lu G, Kioussis 2000 Phys. Rev. B 62 3099
[18] Rice J R 1992 Mech. Phys. Solids 40 239
[19] Wang S G, Tian E K, Lung C W 2000 J. Phys. Chem. Solids 61 1295
[20] Mei J F, Ni Y S, Li J W 2011 Int. J. Solids Struct. 48 3054
[21] Wang Z Q, Chen S H 2009 Advanced Fracture Mechanics (Beijing: Science Press) p14-16(in Chinese) [王自强, 陈少华2009高等断裂力学(北京: 科学出版社)第14–16页]
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