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CN 34-1054/N

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Phase field simulation of an extended dislocation passing through void and inclusion under shear stress

  • Department of Modern Mechanics, School of Engineering Science, University of Science and Technology of China, Hefei 230027, China

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https://doi.org/10.3969/j.issn.0253-2778.2020.04.017
  • Received Date: 20 May 2019
  • Accepted Date: 30 May 2019
  • Rev Recd Date: 30 May 2019
  • Publish Date: 30 April 2020
    Abstract

  • Abstract

    The dynamics of the extended dislocation passing through the void and inclusion in the face-centered cubic (FCC) crystals of aluminum (Al) and copper (Cu) under shear stress were simulated by phase-field method combined with the phase-field microelasticity (PFM) theory and the Peierls-Nabarro (PN) model, respectively. The PFM theory was employed to calculate the long-range elastic interaction between the dislocation and the void (or the inclusion phase), the PN model was used to describe the structure of the extended dislocation based on the one-dimensional crystal energy function, and the Ginzburg-Landau dynamic equation was used to describe the movement of the dislocation. The simulated results showed that when the dislocation slips to the void, the dislocation is attracted to the edge of the void first and then pinned and finally depinned. When the dislocation slips to the inclusion phase, the dislocation is first bent by the inclusion and then passes through the inclusion with a dislocation loop left. Moreover, in the case that the stacking fault (SF) energy is relatively low, it was found that the SF narrows when the extended dislocation approaches the void (or the inclusion phase). While an extended dislocation passes through the void (or the inclusion phase), the leading partial dislocation passes through the void first, and then the trailing partial dislocation passes through the void, which is also accompanied by the phenomenon of SF broadening. Our simulation results are not only consistent with the previous atomic simulated results, but also further reveal the effects of stress amplitude and SF energy parameters on the dynamics of the extended dislocation passing through the void (or the inclusion) at a longer time scale.

    Abstract

    The dynamics of the extended dislocation passing through the void and inclusion in the face-centered cubic (FCC) crystals of aluminum (Al) and copper (Cu) under shear stress were simulated by phase-field method combined with the phase-field microelasticity (PFM) theory and the Peierls-Nabarro (PN) model, respectively. The PFM theory was employed to calculate the long-range elastic interaction between the dislocation and the void (or the inclusion phase), the PN model was used to describe the structure of the extended dislocation based on the one-dimensional crystal energy function, and the Ginzburg-Landau dynamic equation was used to describe the movement of the dislocation. The simulated results showed that when the dislocation slips to the void, the dislocation is attracted to the edge of the void first and then pinned and finally depinned. When the dislocation slips to the inclusion phase, the dislocation is first bent by the inclusion and then passes through the inclusion with a dislocation loop left. Moreover, in the case that the stacking fault (SF) energy is relatively low, it was found that the SF narrows when the extended dislocation approaches the void (or the inclusion phase). While an extended dislocation passes through the void (or the inclusion phase), the leading partial dislocation passes through the void first, and then the trailing partial dislocation passes through the void, which is also accompanied by the phenomenon of SF broadening. Our simulation results are not only consistent with the previous atomic simulated results, but also further reveal the effects of stress amplitude and SF energy parameters on the dynamics of the extended dislocation passing through the void (or the inclusion) at a longer time scale.
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    • References(33)
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    韩恩厚. 核电站关键材料在微纳米尺度上的环境损伤行为研究：进展与趋势[J]. 金属学报, 2011, 47(7): 769-776.
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    GROH S. Transformation of shear loop into prismatic loops during bypass of an array of impenetrable particles by edge dislocations[J]. Materials Science and Engineering: A, 2014, 618: 29-36.
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    DUTTA A, BHATTACHARYA M, GAYATHRI N, et al. The mechanism of climb in dislocation-nanovoid interaction[J]. Acta Materialia, 2012, 60(9): 3789-3798.
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    ASARI K, HETLAND O S, FUJITA S, et al. The effect of stacking fault energy on interactions between an edge dislocation and a spherical void by molecular dynamics simulations[J]. Journal of Nuclear Materials, 2013, 442(1-3): 360-364.
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    HUANG Minsheng, ZHU Yaxin, LI Zhenhuan. Dislocation dissociation strongly influences on Frank-Read source nucleation and microplasticy of materials with low stacking fault energy[J]. Chinese Physics Letters, 2014, 31(4): 046102.
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    KEYHANI A, ROUMINA R. Dislocation-precipitate interaction map[J]. Computational Materials Science, 2018, 141: 153-161.
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    [23]
    WANG Y, LI J. Phase field modeling of defects and deformation[J]. Acta Materialia, 2010, 58(4): 1212-1235.
    [24]
    HUNTER A, BEYERLEIN I J, GERMANN T C, et al. Influence of the stacking fault energy surface on partial dislocations in fcc metals with a three-dimensional phase field dislocations dynamics model[J]. Physical Review B, 2011, 84(14): 144108.
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    HUNTER A, ZHANG R F, BEYERLEIN I J, et al. Dependence of equilibrium stacking fault width in fcc metals on the γ-surface[J]. Modelling and Simulation in Materials Science and Engineering, 2013, 21(2): 025015.
    [26]
    SHEN C, WANG Y. Phase field model of dislocation networks[J]. Acta Materialia, 2003, 51(9): 2595-2610.
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    SHEN C, WANG Y. Incorporation of γ-surface to phase field model of dislocations: Simulating dislocation dissociation in fcc crystals[J]. Acta Materialia, 2004, 52(3): 683-691.
    [28]
    ZHENG S, ZHENG D, NI Y, et al. Improved phase field model of dislocation intersections[J]. npj Computational Materials, 2018, 4(1): 20.
    [29]
    ZHENG S L, NI Y, HE L H. Alternative transmission mode and long stacking fault formation during a dissociated screw dislocation across a coherent sliding interface[J]. Journal of Physics D: Applied Physics, 2015, 48(39): 395301.
    [30]
    ZHENG S, NI Y, HE L. Phase field modeling of a glide dislocation transmission across a coherent sliding interface[J]. Modelling and Simulation in Materials Science and Engineering, 2015, 23(3): 035002.
    [31]
    LIU H, GAO Y, QI L, et al. Phase-field simulation of Orowan strengthening by coherent precipitate plates in an aluminum alloy[J]. Metallurgical and Materials Transactions A, 2015, 46(7): 3287-3301.
    [32]
    WANG Y U, JIN Y M, KHACHATURYAN A G. Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid[J]. Journal of Applied Physics, 2002, 92(3): 1351-1360.
    [33]
    CHEN L Q, SHEN J. Applications of semi-implicit Fourier-spectral method to phase field equations[J]. Computer Physics Communications, 1998, 108(2-3): 147-158.
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    [1]
    韩恩厚. 核电站关键材料在微纳米尺度上的环境损伤行为研究：进展与趋势[J]. 金属学报, 2011, 47(7): 769-776.
    HAN Enhou. Research trends on micro and nano-scale materials degradation in nuclear power plant[J]. Acta Metallurgica Sinica, 2011, 47(7): 769-776.
    [2]
    肖厦子, 宋定坤, 楚海建, 等. 金属材料力学性能的辐照硬化效应[J]. 力学进展, 2015, 45(1): 141-178.
    XIAO Xiazi, SONG Dingkun, CHU Haijian, et al. Irradiation hardening for metallic materials[J].Advances in Mechanics, 2015, 45(1): 141-178.
    [3]
    DUNDURS J, MURA T. Interaction between an edge dislocation and a circular inclusion[J]. Journal of the Mechanics and Physics of Solids, 1964, 12(3): 177-189.
    [4]
    KEER L M. Interaction between an edge dislocation and a rigid elliptical inclusion[J]. Journal of Applied Mechanics, 1986, 53(2): 383.
    [5]
    SROLOVITZ D J, PETKOVIC-LUTON R A, LUTON M J. Edge dislocation-circular inclusion interactions at elevated temperatures[J]. Acta Metallurgica, 1983, 31(12): 2151-2159.
    [6]
    MURA T. Micromechanics of Defects in Solids[M]. New York: Springer Science & Business Media, 2013.
    [7]
    FANG Q H, LIU Y W. Size-dependent interaction between an edge dislocation and a nanoscale inhomogeneity with interface effects[J]. Acta Materialia, 2006, 54(16): 4213-4220.
    [8]
    WANG X, PAN E. Interaction between an edge dislocation and a circular inclusion with interface slip and diffusion[J]. Acta Materialia, 2011, 59(2): 797-804.
    [9]
    DUDAREV S L, SUTTON A P. Elastic interactions between nano-scale defects in irradiated materials[J]. Acta Materialia, 2017, 125: 425-430.
    [10]
    PROVILLE L, BAKO B. Dislocation depinning from ordered nanophases in a model fcc crystal: From cutting mechanism to Orowan looping[J]. Acta Materialia, 2010, 58(17): 5565-5571.
    [11]
    XU S, XIONG L, CHEN Y, et al. Edge dislocations bowing out from a row of collinear obstacles in Al[J]. Scripta Materialia, 2016, 123: 135-139.
    [12]
    GROH S. Transformation of shear loop into prismatic loops during bypass of an array of impenetrable particles by edge dislocations[J]. Materials Science and Engineering: A, 2014, 618: 29-36.
    [13]
    DUTTA A, BHATTACHARYA M, GAYATHRI N, et al. The mechanism of climb in dislocation-nanovoid interaction[J]. Acta Materialia, 2012, 60(9): 3789-3798.
    [14]
    ASARI K, HETLAND O S, FUJITA S, et al. The effect of stacking fault energy on interactions between an edge dislocation and a spherical void by molecular dynamics simulations[J]. Journal of Nuclear Materials, 2013, 442(1-3): 360-364.
    [15]
    OKITA T, ASARI K, FUJITA S, et al. Effect of the stacking fault energy on interactions between an edge dislocation and a spherical void in fcc metals at various spatial geometries[J]. Fusion Science and Technology, 2014, 66(1): 289-294.
    [16]
    DOIHARA K, OKITA T, ITAKURA M, et al. Atomic simulations to evaluate effects of stacking fault energy on interactions between edge dislocation and spherical void in face-centred cubic metals[J]. Philosophical Magazine, 2018, 98(22): 2061-2076.
    [17]
    ZHU B, HUANG M, LI Z. Atomic level simulations of interaction between edge dislocations and irradiation induced ellipsoidal voids in alpha-iron[J]. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2017, 397: 51-61.
    [18]
    DOS REIS M L, PROVILLE L, SAUZAY M. Modeling the climb-assisted glide of edge dislocations through a random distribution of nano-sized vacancy clusters[J]. Physical Review Materials, 2018, 2(9): 093604.
    [19]
    DRS J, PROVILLE L, MARINICA M C. Dislocation depinning from nano-sized irradiation defects in a bcc iron model[J]. Acta Materialia, 2015, 99: 99-105.
    [20]
    HUANG Minsheng, ZHU Yaxin, LI Zhenhuan. Dislocation dissociation strongly influences on Frank-Read source nucleation and microplasticy of materials with low stacking fault energy[J]. Chinese Physics Letters, 2014, 31(4): 046102.
    [21]
    KEYHANI A, ROUMINA R. Dislocation-precipitate interaction map[J]. Computational Materials Science, 2018, 141: 153-161.
    [22]
    WANG Y U, JIN Y M, CUITINO A M, et al. Nanoscale phase field microelasticity theory of dislocations: Model and 3D simulations[J]. Acta Materialia, 2001, 49(10): 1847-1857.
    [23]
    WANG Y, LI J. Phase field modeling of defects and deformation[J]. Acta Materialia, 2010, 58(4): 1212-1235.
    [24]
    HUNTER A, BEYERLEIN I J, GERMANN T C, et al. Influence of the stacking fault energy surface on partial dislocations in fcc metals with a three-dimensional phase field dislocations dynamics model[J]. Physical Review B, 2011, 84(14): 144108.
    [25]
    HUNTER A, ZHANG R F, BEYERLEIN I J, et al. Dependence of equilibrium stacking fault width in fcc metals on the γ-surface[J]. Modelling and Simulation in Materials Science and Engineering, 2013, 21(2): 025015.
    [26]
    SHEN C, WANG Y. Phase field model of dislocation networks[J]. Acta Materialia, 2003, 51(9): 2595-2610.
    [27]
    SHEN C, WANG Y. Incorporation of γ-surface to phase field model of dislocations: Simulating dislocation dissociation in fcc crystals[J]. Acta Materialia, 2004, 52(3): 683-691.
    [28]
    ZHENG S, ZHENG D, NI Y, et al. Improved phase field model of dislocation intersections[J]. npj Computational Materials, 2018, 4(1): 20.
    [29]
    ZHENG S L, NI Y, HE L H. Alternative transmission mode and long stacking fault formation during a dissociated screw dislocation across a coherent sliding interface[J]. Journal of Physics D: Applied Physics, 2015, 48(39): 395301.
    [30]
    ZHENG S, NI Y, HE L. Phase field modeling of a glide dislocation transmission across a coherent sliding interface[J]. Modelling and Simulation in Materials Science and Engineering, 2015, 23(3): 035002.
    [31]
    LIU H, GAO Y, QI L, et al. Phase-field simulation of Orowan strengthening by coherent precipitate plates in an aluminum alloy[J]. Metallurgical and Materials Transactions A, 2015, 46(7): 3287-3301.
    [32]
    WANG Y U, JIN Y M, KHACHATURYAN A G. Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid[J]. Journal of Applied Physics, 2002, 92(3): 1351-1360.
    [33]
    CHEN L Q, SHEN J. Applications of semi-implicit Fourier-spectral method to phase field equations[J]. Computer Physics Communications, 1998, 108(2-3): 147-158.
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