Farklı Kristalografik Yönelime Sahip Cu Nano Telindeki Bauschinger Etkisinin Moleküler Dinamik Benzetimi

Yıl 2024, Cilt: 19 Sayı: 1, 203 - 211, 28.03.2024

Sefa Kazanç , Canan Aksu Canbay

https://doi.org/10.55525/tjst.1358465

Öz

Bu çalışmada, Cu atomlarının <100>, <110> ve <111> yüksek simetrili kristalografik doğrultulara yerleştirilmesiyle elde edilen nano tellere uygulanan çekme-sıkıştırma deformasyonu sonucu oluşan Bauschringer Etkisi (BE) Moleküler Dinamik (MD) benzetim yöntemi kullanılarak incelendi. Çok cisim etkileşmelerini içeren Gömülmüş Atom Metodu (GAM) potansiyel fonksiyonunun gradientinden atomlar arasındaki kuvvetler belirlendi. Model sisteme uygulanan çekme ve sıkıştırma deformasyon işlemi sonucu elde edilen zor-zorlanma eğrileri arasında bir asimetri olduğu belirlendi. Bu asimetriden <100> kristalografik yönelime sahip nano tel için çekme işleminde elde edilen akma geriliminin sıkıştırma işlemi sonucu elde edilen akma geriliminden daha büyük olduğu belirlendi. Buna karşılık <110> ve <111> kristalografik yönelime sahip nano teller için tam tersi bir durum tespit edildi. Ayrıca model nano tel sistemine uygulanan çekme işlemi sonucu akma gerinim değeri aşıldıktan sonra farklı ön-gerinim değerlerinde sıkıştırma deformasyon işlemi uygulandı. Çekme işlemine karşılık gelen ileri yükleme sonucu akma dayanımı değerinin yüklenmenin kaldırıldığı sıkıştırma işlemi sonucu elde edilen akma değerinden küçük olması olarak ifade edilen Bauschinger Etkisi (BE)’nin varlığı belirlendi. BE’nin farklı kristalografik yönelimlere sahip Cu nano telleri üzerindeki etkisini açıklığa kavuşturmak için Bauschinger Stress parametresi (BSP) ve Bauschinger Parametresi (BP) değerleri hesaplandı.

Anahtar Kelimeler

Nano tel, Bauschinger etkisi, kristalografik yönelim, mekanik özellikler, moleküler dinamik

Molecular Dynamics Simulation of Bauschinger Effect in Cu Nanowire with Different Crystallographic Orientation

Öz

In this study, the Bauschringer Effect (BE) resulting from tension-compression deformation applied to nanowires obtained by placing Cu atoms in <100>, <110> and <111> highly symmetric crystallographic directions was investigated using the Molecular Dynamics (MD) simulation method. The forces between atoms were determined from the gradient of the Embedded Atom Method (EAM) potential function, which includes many-body interactions. It was determined that there is an asymmetry between the stress-strain curves obtained as a result of the tension and compression deformation process applied to the model system. From this asymmetry, it was determined that the yield stress obtained in the drawing process for nanowire with <100> crystallographic orientation was greater than the yield strain obtained as a result of the compression process. In contrast, the opposite was found for nanowires with crystallographic orientation <110> and <111>. In addition, after the yield strain value is exceeded as a result of the drawing process applied to the model nanowire system, compression deformation process was applied at different pre-strain values. The existence of the Bauschinger Effect (BE), which is expressed as the yield strength value as a result of forward loading corresponding to the tension operation, is smaller than the yield value obtained as a result of the compression process in which the loading is removed, was determined. To clarify the effect of BE on Cu nanowires with different crystallographic orientations, Bauschinger Stress parameter (BSP) and Bauschinger Parameter (BP) values were calculated.

Anahtar Kelimeler

Nanowire, Bauschinger effect, crystallographic orientation, mechanical properties, molecular dynamics.

Kaynakça

• Wang JF, Gudiksen MS, Duan XF, Cui Y, Lieber CM. Highly polarized photoluminescence and photodetection from single indium phosphide nanowires. Science 2001; 293: 1455-1457.
• Joyce HJ, Gao Q, Tan HH, Jagadish C, Kim Y, Zou J. et.al. III-V semiconductor nanowires for optoelectronic device applications. Prog Quant Electron 2011; 35: 23-75.
• Cui Y, Zhong ZH, Wang DL, Wang WU, Lieber CM. High performance silicon nanowire field effect transistors. Nano Lett 2003; 3: 149-152.
• Huang Y, Duan XF, Lieber CM. Nanowires for integrated multicolor nanophotonics. Small 2005;1: 142-147.
• Diao J, Gall K, Dunn ML. Yield Strength Asymmetry in Metal Nanowires. Nano Letters 2004; 4: 1863-1867.
• Park HS, Zimmerman JA. Modeling inelasticity and failure in gold nanowires. Physical Review B 2005; 72: 054106.
• Park HS, Gall K, Zimmerman JA. Deformation of FCC nanowires by twinning and slip. J. Mech. Phys. Solids 2006; 54: 1862-1881.
• Mahato JK, De PS, Sarkar A, Kundu A, Chakraborti PC. Effect of deformation mode and grain size on Bauschinger behavior of annealed copper. International Journal of Fatigue 2016; 83: 42-52.
• Paul JDH, Hoppe R, Appel F. On the Bauschinger effect in TiAl alloys. Acta Materialia 2016; 104: 101-108
• Stoltz RE, Pelloux RM. The Bauschinger effect in precipitation strengthened aluminum alloys. Metall Trans A 1976; 7: 1295-1306.
• Pedersen OB, Brown LM, Stobbs WM. The bauschinger effect in copper. Acta Metall 1981; 29: 1843-1850.
• Waheed S, Hao R, Bhowmik A, Balint DS, Giuliani F. A unifying scaling for the Bauschinger effect in highly confined thin films: a discrete dislocation plasticity study. Model Simulat Mater Sci Eng 2017; 25: 54003.
• Han K, Van Tyne CJ, Levy BS. Effect of strain and strain rate on the bauschinger effect response of three different steels. Metall Mater Trans A 2005; 36: 2379-2384.
• Gui HL, Li Q, Huang QX. The influence of Bauschinger effect in straightening process. Math. Probl. Eng 2015; 2015; 1-5.
• Chun BK, Kim HY, Lee JK. Modeling the Bauschinger effect for sheet metals, part II: applications. Int. J. Plast. 2002; 18: 597–616.
• Chun BK, Jinn JT, Lee JK. Modeling the Bauschinger effect for sheet metals, part I: theory, Int. J. Plast. 2002; 18: 571–595.
• Srivatsan TS, Al-Hajri M, Troxell JD. The tensile deformation, cyclic fatigue and final fracture behavior of dispersion strengthened copper. Mech. Mater. 2004; 36: 99–116.
• Tang CY, Li DY, Wen GW. Bauschinger's effect in wear of materials. Tribol. Lett. 2010; 41: 569–572.
• Tang C, Wang JM, Wen GW, Wang Y, Li DY. Bauschinger effect in wear of Cu–40Zn alloy and its variations with the wear condition. Wear 2011; 271(9): 1237–1243.
• Xiaoyu H, Chao W, Margolin H, Nourbakhsh S. The Bauschinger effect and the stresses in a strained single crystal. Scr. Metall. Mater. 1992; 27: 865–870.
• Gao Y, Wang H, Zhao J, Sun C, Wang F. Anisotropic and temperature effects on mechanical properties of copper nanowires under tensile loading. Computational Materials Science 2011; 50: 3032-3037.
• Sainath G, Choudhary BK. Orientation dependent deformation behaviour of bcc iron nanowires. Computational Materials Science 2016; 111: 406-415.
• Lieber CM. Nanoscale science and technology: building a big future from small things MRS Bull. 2003; 28: 486–491.
• Mughrabi H. Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals. Acta Metall. 1983; 31: 1367–1379.
• Liu X, Yuan F, Zhu Y, Wu X. Extraordinary Bauschinger effect in gradient structured copper. Scr. Mater. 2018; 150: 57–60.
• Tsuru T. Origin of tension-compression asymmetry in ultrafine-grained fcc metals. Phys. Rev. Mater. 2017; 1: 2–4.
• Park HS, Zimmerman JA. Modeling inelasticity and failure in gold nanowires. Phys. Rev. B 2005; 72: 054106.
• Olsson PAT, Melin S, Persson C, Atomistic simulations of tensile and bending properties of single-crystal bcc iron nanobeams. Phys. Rev. B 2007; 76: 224112.
• Sainath G, Choudhary BK, Jayakumar T. Molecular dynamics simulation studies on the size dependent tensile deformation and fracture behaviour of body centred cubic iron nanowires. Comput. Mater. Sci. 2015; 104: 76–83.
• Zhou M, Liang W. Response of copper nanowires in dynamic tensile deformation. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2004; 218(6): 599–606.
• Park HS, Gall K, Zimmerman JA. Deformation of FCC nanowires by twinning and slip. J. Mech. Phys. Solids 2006; 54: 1862–1881.
• Xie H, Yin F, Yu T, Lu G, Zhang Y. A new strain-rate-induced deformation mechanism of Cu nanowire: Transition from dislocation nucleation to phase transformation. Acta Mater. 2015; 85: 191–198.
• Norskov JK. Covalent effects in the effective-medium theory of chemical binding: Hydrogen heats of solution in the 3d metals. Phys. Rev. B 1982; 26: 2875.
• Cleri F, Rosato V. Tight-binding potentials for transition metals and alloys. Phys. Rev. B 1993; 48: 22.
• Finnis MW, Sinclair JE. A Simple Empirical N- body Potential for Transition Metals. Philos. Mag. A-Phys. Condens. Matter Struct. Defect Mech. Prop. 1984; 50: 45.
• Daw MS, Baskes M. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 1984; 29: 6443.
• Nam HS, Hwang NM, Yu BD, Yoon JK. Formation of an Icosahedral Structure during the Freezing of Gold Nanoclusters: Surface-Induced Mechanism. Phys. Rev. Lett. 2002; 89: 275502.
• Cagin T, Dereli G, Uludogan M, Tomak M. Thermal and mechanical properties of some fcc transition metals. Phys. Rev. B 1999; 59: 3468.
• Koh SJA, Lee HP, Lu C, Cheng QH. Molecular dynamics simulation of a solid platinum nanowire under uniaxial tensile strain: Temperature and strain-rate effects. Phys. Rev. B 2005; 72: 085414.
• Sturgeon JB, Laird BB. Adjusting the melting point of a model system via Gibbs-Duhem integration: Application to a model of aluminum. Phys. Rev. B 2000; 62: 14720.
• http://lammps.sandia.gov/.LAMMPS Molecular Dynamics Simulator (Erişim Tarihi:02.04.2021).
• Stukowski A. Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modelling and Simulation in Materials Science and Engineering 2010; 18(1): 015012.
• Kazanc S. The effects on the lattice dynamical properties of the temperature and pressure in random NiPd alloy. Can. J. Phys. 2013; 91(10): 833-838.
• Kazanc S, Ozgen S, Adiguzel O. Pressure effects on martensitic transformation under quenching process in a molecular dynamics model of NiAl alloy. Physica B 2003; 334(3-4): 375-381.
• Saitoh KI, Liu WK. Molecular dynamics study of surface effect on martensitic cubic-to-tetragonal transformation in Ni-Al alloy. Computational Materials Science 2009; 46: 531-544.
• Jacobus K, Sehitoglu H, Balzer M. Effect of stress state on the stress-induced martensitic transformation in polycrystalline Ni-Ti alloy. Metallurgical and Materials Transactions A 1996; 27(A): 3066-3073.
• Guellil AM, Adams JB. The application of the analytic embedded atom method to bcc metals and alloys. J Mater Res 1992; 7: 639–652.
• Foiles SM, Baskes MI, Daw MS. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 1986; 33: 7983.
• Setoodeh AR, Attariani H, Khosrownejad,M. Nickel nanowires under uniaxial loads: A molecular dynamics simulation study. Computational Materials Science 2008; 44: 378-384.
• Wang P, Chou W, Nie A, Huang Y, Yao H, Wang H. Molecular dynamics simulation on deformation mechanisms in bodycentered-cubic molybdenum nanowires. J Appl Phys 2011; 093521:110.
• Zhou J, Shen J, Essa FA, Yu J. Twins and grain boundaries-dominated the reverse Bauschinger effect and tensioncompression asymmetry. journal of materials research and technology 2022; 18: 15 -28.
• Wu HA. Molecular dynamics study of the mechanism of metal nanowires at finite temperature. European Journal of Mechanics A/Solids 2006; 25: 370-377.
• Setoodeh AR, Attariani H. Nanoscale simulations of Bauschinger effects on a nickel nanowire. Materials Letters 2008; 62: 4266–4268.
• Jordon JB,Horstemeyer MF,Solanki K,Xue Y. Damage and stress state influence on the Bauschinger effect in aluminum alloys. Mechanics of Materials 2007; 39: 920–931.
• Abel A, Muir H. The Bauschinger effect and discontinuous yielding. Phil Mag 1972; 26: 489–504.
• Brown LM. Orowan’s explanation of the Bauschinger effect. Scr Metall 1977; 11: 127–131.
• Zhu D, Zhang H, Li DY. Influence of Nanotwin Boundary on the Bauschinger’s Effect in Cu: A Molecular Dynamics Simulation Study.Metallurgical and Materials Transactions A 2013; 44A: 2013-4207-4217.
• Abel A. Historical perspectives and some of the main features of the Bauschinger effect. Mater. Forum 1987; 10(1): 11– 26.
• Horstemeyer MF. Damage influence on Bauschinger effect of a CAST A356 alluminum alloy. Scripta Mater. 1998; 39: 1491–1495.
• Caceres CH, Griffiths JR, Reiner P. Influence of microstructure on the Bauschinger effect in an Al Si–Mg alloy. Acta Metall. 1996; 44: 15–23.
• Prinz F, Argon AS. Dislocation cell formation during plastic deformation of copper single crystals. Phys. Status Solidi A 1980; 57: 741-753.
• Rzychoñ T, Rodak K. Microstructure characterization of deformed copper by XRD line broadening. Arch. Mater. Sci. Eng. 2007; 28: 605-608.
• Novak V, Sittner P. Stability of dislocation structure. Acta Universities Caroline-Math et Phys 1990; 22: 89–94.
• Sohn SS, Han SY, Shin SY, Bae JH, Lee S. Effect of microstructure and pre-strain on Bauschinger effect in API X70 and X80 line pipe steel. Met Mater Int 2013; 19: 423–431.
• Han SY, Sohn SS, Shin SY, Bae JH, Kim HS, Lee S. Effect of microstructure and yield ratio on strain hardening and Bauschinger effect in two API X80 linepipe steels. Mat Sci Engg A 2012; 551: 192–199.
• De PS, Kundu A, Chakraborti PC. Effect of prestrain on tensile properties and ratcheting behavior of Ti-stabilised interstitial free steel. Mat Des 2013; 87–97