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玻璃态材料非线性流变:简化的Maxwell模型

薛海峰 倪勇

薛海峰, 倪勇. 玻璃态材料非线性流变:简化的Maxwell模型[J]. 应用数学和力学, 2019, 40(1): 8-19. doi: 10.21656/1000-0887.390149
引用本文: 薛海峰, 倪勇. 玻璃态材料非线性流变:简化的Maxwell模型[J]. 应用数学和力学, 2019, 40(1): 8-19. doi: 10.21656/1000-0887.390149
XUE Haifeng, NI Yong. Nonlinear Rheology of Glassy Materials: a Simplified Maxwell Model[J]. Applied Mathematics and Mechanics, 2019, 40(1): 8-19. doi: 10.21656/1000-0887.390149
Citation: XUE Haifeng, NI Yong. Nonlinear Rheology of Glassy Materials: a Simplified Maxwell Model[J]. Applied Mathematics and Mechanics, 2019, 40(1): 8-19. doi: 10.21656/1000-0887.390149

玻璃态材料非线性流变:简化的Maxwell模型

doi: 10.21656/1000-0887.390149
基金项目: 国家自然科学基金(11672285)
详细信息
    作者简介:

    薛海峰(1990—),男,硕士(通讯作者. E-mail: yni@ustc.edu.cn).

  • 中图分类号: O373

Nonlinear Rheology of Glassy Materials: a Simplified Maxwell Model

Funds: The National Natural Science Foundation of China(11672285)
  • 摘要: 玻璃态材料在不同的加载条件下,其力学行为表现出很大的差异性.该文提出了一个简化的Maxwell模型结合速率方程,研究了应变率、温度和老化时间对自由体积缺陷演化控制的玻璃态材料非线性力学响应的影响.研究表明,一定范围内应变率越大、温度越低、老化时间越长,应力峰值越大,且应力峰值和临界应变对于老化时间具有对数依赖性.这些结论与前人分子动力学模拟得到的结果相一致.
  • [1] SCHUH C A, HUFNAGEL T C, RAMAMURTY U. Mechanical behavior of amorphous alloys[J]. Acta Materialia,2007,55(12): 4067-4109.
    [2] WANG W H. The elastic properties, elastic models and elastic perspectives of metallic glasses[J]. Progress in Materials Science,2012,57(3): 487-656.
    [3] DYRE J C. Colloquium: the glass transition and elastic models of glass-forming liquids[J]. Reviews of Modern Physics,2006,78(3): 953-972.
    [4] BERTHIER L, BIROLI G. Theoretical perspective on the glass transition and amorphous materials[J]. Reviews of Modern Physics,2011,83(2): 587-645.
    [5] PUOSI F, ROTTLER J, BARRAT J L. Time-dependent elastic response to a local shear transformation in amorphous solids[J]. Physical Review E,2014,89(4): 042302. DOI: 10.1103/PhysRevE.89.042302.
    [6] NICOLAS A, PUOSI F, MIZUNO H, et al. Elastic consequences of a single plastic event: towards a realistic account of structural disorder and shear wave propagation in models of flowing amorphous solids[J]. Journal of the Mechanics and Physics of Solids,2015,78: 333-351.
    [7] SPAEPEN F. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses[J]. Acta Metallurgica,1977,25(4): 407-415.
    [8] ARGON A S. Plastic-deformation in metallic glasses[J]. Acta Metallurgica,1979,27(1): 47-58.
    [9] FALK M L, LANGER J S. Dynamics of viscoplastic deformation in amorphous solids[J]. Physical Review E,1998,57(6): 7192-7205.
    [10] SOLLICH P. Rheological constitutive equation for a model of soft glassy materials[J]. Physical Review E,1998,58: 738-759.
    [11] FIELDING S M, CATES M E, SOLLICH P. Shear banding, aging and noise dynamics in soft glassy materials[J]. Soft Matter,2009,5(12): 2378-2382.
    [12] LU J, RAVICHANDRAN G, JOHNSON W L. Deformation behavior of the Zr41.2Ti13.8Cu12.5Ni10-Be22.5 bulk metallic glass over a wide range of strain-rates and temperatures[J]. Acta Materialia,2003,51(12): 3429-3443.
    [13] MA G C, ZHU Z W, WANG Z, et al. Deformation behavior of the Zr53.5Cu26.5Ni5Al12Ag3 bulk metallic glass over a wide range of strain rate and temperatures[J]. Journal of Materials Science & Technology,2015,31(9): 941-945.
    [14] VARNIK F, BOCQUET L, BARRAT J L. A study of the static yield stress in a binary Lennard-Jones glass[J]. Journal of Chemical Physics,2004,120(6): 2788-2801.
    [15] SHRIVASTAV G P, CHAUDHURI P, HORBACH J. Heterogeneous dynamics during yielding of glasses: effect of aging[J]. Journal of Rheology,2016,60(5): 835-847.
    [16] JIANG M Q, WILDE G, DAI L H. Origin of stress overshoot in amorphous solids[J]. Mechanics of Materials,2015,81: 72-83.
    [17] STRUIK L C E. Physical aging in amorphous glassy polymers[J]. Annals of the New York Academy of Sciences,1976,279(1): 78-85.
    [18] HODGE I M. Physical aging in polymer glasses[J]. Science,1995,267(5206): 1945-1947.
    [19] UTZ M, DEBENEDETTI P G, STILLINGER F H. Atomistic simulation of aging and rejuvenation in glasses[J]. Physical Review Letters,2000,84(7): 1471-1474.
    [20] DEBENEDETTI P G, STILLINGER F H. Supercooled liquids and the glass transition[J]. Nature,2001,410(6825): 259-267.
    [21] PICARD G, AJDARI A, LEQUEUX F, et al. Slow flows of yield stress fluids: complex spatiotemporal behavior within a simple elastoplastic model[J]. Physical Review E,2005,71(1): 010501. DOI: 10.1103/PhysRevE.71.010501.
    [22] MARTENS K, BOCQUET L, BARRAT J L. Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter[J]. Soft Matter,2012,8(15): 4197-4205.
    [23] WISITSORASAK A, WOLYNES P G. Dynamical theory of shear bands in structural glasses[J]. Proceedings of the National Academy of Sciences of the United States of America,2017,114(6): 1287-1292.
    [24] DEREC C, AJDARI A, LEQUEUX F. Rheology and aging: a simple approach[J]. The European Physical Journal E,2001,4(3): 355-361.
    [25] DEREC C, DUCOURET G, AJDARI A, et al. Aging and nonlinear rheology in suspensions of polyethylene oxide-protected silica particles[J]. Physical Review E,2003,67(6): 061403. DOI:10.1103/PhysRevE.67.061403.
    [26] NGUYEN V B, DARNIGE T, BRUAND A,et al. Creep and fluidity of a real granular packing near jamming[J]. Physical Review Letters,2011,107(13): 138303. DOI:10.1103/PhysRevLett.107.138303.
    [27] KATO H, KAWAMURA Y, INOUE A, et al. Modeling of stress-strain curves for Pd40Ni10Cu30-P20 glass alloy under constant strain-rate deformation[J]. Materials Science and Engineering: A,2001,304/306: 758-762.
    [28] ROTTLER J, MAASS P. Aging in the shear-transformation-zone theory of plastic deformation[J]. Physical Review E,2008,78(5): 056109. DOI:10.1103/PhysRevE.78.056109.
    [29] FIELDING S M, SOLLICH P, CATES M E. Aging and rheology in soft materials[J]. Journal of Rheology,2000,44(2): 323-369.
    [30] JAGLA E A. Strain localization driven by structural relaxation in sheared amorphous solids[J]. Physical Review E,2007,76(4): 046119. DOI:10.1103/PhysRevE.76.046119.
    [31] DOOLITTLE A K. Studies in Newtonian flow II, the dependence of the viscosity of liquids on free-space[J]. Journal of Applied Physics,1951,22(12): 1471-1475.
    [32] COHEN M H, TURNBULL D. Molecular transport in liquids and glasses[J]. Journal of Chemical Physics,1959,31(5): 1164-1169.
    [33] VAN AKEN B, DE HEY P, SIETSMA J. Structural relaxation and plastic flow in amorphous La50Al25Ni25[J]. Materials Science and Engineering: A,2000,278(1/2): 247-254.
    [34] MUKHERJEE S, SCHROERS J, ZHOU Z, et al. Viscosity and specific volume of bulk metallic glass-forming alloys and their correlation with glass forming ability[J]. Acta Materialia,2004,52(12): 3689-3695.
    [35] EVENSON Z, BUSCH R. Equilibrium viscosity, enthalpy recovery and free volume relaxation in a Zr44Ti11Ni10Cu10Be25 bulk metallic glass[J]. Acta Materialia,2011,59(11): 4404-4415.
    [36] DE HEY P, SIETSMA J, VAN DEN BEUKEL A. Structural disordering in amorphous Pd40Ni40-P20 induced by high temperature deformation[J]. Acta Materialia,1998,46(16): 5873-5882.
    [37] SESTAK J, BERGGRENN G. Study of the kinetics of the mechanism of solid-state reactions at increasing temperature[J]. Thermochim Acta,1971,3(1): 1-12.
    [38] KHAWAM A, FLANAGAN D R. Solid-state kinetic models: basics and mathematical fundamentals[J]. Journal of Physical Chemistry B,2006,110(35): 17315-17328.
    [39] PROUT E G, TOMPKINS F C. The thermal decomposition of potassium permanganate[J]. Transactions of the Faraday Society,1944,40: 488-497.
    [40] BOUCHAUD J P. Weak ergodicity breaking and aging in disorderedsystems[J]. Journal de Physique I,1992,2(9): 1705-1713.
    [41] LUO P, LU Z, LI Y Z, et al. Probing the evolution of slow flow dynamics in metallic glasses[J]. Physical Review B,2016,93(10): 104204. DOI: 10.1103/PhysRevB.93.104204.
    [42] ZHANG M, LIU L, WU Y. Facilitation and correlation of flow in metallic supercooled liquid[J]. Journal of Chemical Physics,2013,139(16): 164508. DOI: 10.1063/1.4826318.
    [43] ROTTLER J, ROBBINS M O. Unified description of aging and rate effects in yield of glassy solids[J]. Physical Review Letters,2005,95(22): 225504. DOI: 10.1103/PhysRevLett.95.225504.
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出版历程
  • 收稿日期:  2018-05-21
  • 修回日期:  2018-05-28
  • 刊出日期:  2019-01-01

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