留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于有限变形弹塑性模型模拟伪弹性合金全程变形行为

王晓明 肖衡

王晓明, 肖衡. 基于有限变形弹塑性模型模拟伪弹性合金全程变形行为[J]. 应用数学和力学, 2018, 39(3): 286-299. doi: 10.21656/1000-0887.380067
引用本文: 王晓明, 肖衡. 基于有限变形弹塑性模型模拟伪弹性合金全程变形行为[J]. 应用数学和力学, 2018, 39(3): 286-299. doi: 10.21656/1000-0887.380067
WANG Xiaoming, XIAO Heng. Comprehensive Simulation of Shape Memory Alloys Based on a Finite Elastoplastic Model[J]. Applied Mathematics and Mechanics, 2018, 39(3): 286-299. doi: 10.21656/1000-0887.380067
Citation: WANG Xiaoming, XIAO Heng. Comprehensive Simulation of Shape Memory Alloys Based on a Finite Elastoplastic Model[J]. Applied Mathematics and Mechanics, 2018, 39(3): 286-299. doi: 10.21656/1000-0887.380067

基于有限变形弹塑性模型模拟伪弹性合金全程变形行为

doi: 10.21656/1000-0887.380067
详细信息
    作者简介:

    王晓明(1987—),男,讲师,博士(通讯作者. E-mail: wangxiaoming.g@163.com).

  • 中图分类号: O343;O344

Comprehensive Simulation of Shape Memory Alloys Based on a Finite Elastoplastic Model

  • 摘要: 提出一个J2流的有限弹塑性本构方程来显式、全面地模拟了形状记忆合金(SMAs)在3个不同阶段加载并卸载所表现出来的应力-对数应变关系.这3个阶段包括变形完全恢复的伪弹性阶段、变形部分恢复的塑性阶段以及软化破坏阶段.该文的主要思想在于从实验数据的形函数出发,得到用形函数表达的多轴硬化函数,进而代入到本构方程,建立一个能模拟任意形状应力-对数应变关系,多轴有效的本构方程.该文方法的优势在于避免考虑微观到宏观的平均方法、相变条件等一系列复杂处理,大大减少了计算量.所得到的数值结果可以精确匹配实验数据.
  • [1] PATOOR E, EBERHARDT A, BERVEILLER M. Micromechanical modelling of superelasticity in shape memory alloys[J]. Journal de Physique IV,1996,6: C1-277-C1-292.
    [2] GAO X, BRINSON L C. A simplified multivariant SMA model based on invariant plane nature of martensitic transformation[J]. Journal of Intelligent Material Systems and Structures,2002,13(12): 795-810.
    [3] TOKUDA M, YE M, TAKAKURA M, et al. Thermomechanical behavior of shape memory alloy under complex loading conditions[J]. International Journal of Plasticity,1999,15(2): 223-239.
    [4] GALL K, LIM T J, MCDOWELL D L, et al. The role of intergranular constraint on the stress-induced martensitic transformation in textured polycrystalline NiTi[J]. International Journal of Plasticity,2000,16(10/11): 1189-1214.
    [5] ANAND L, GURTIN M E. Thermal effects in the superelasticity of crystalline shape-memory materials[J]. Journal of the Mechanics & Physics of Solids,2003,51(6): 1015-1058.
    [6] TANAKA K. A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior[J]. Res Mechanica,1986,18(3): 251-263.
    [7] BRINSON L C. One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable[J]. Journal of Intelligent Material Systems and Structures,1993,4: 229-242.
    [8] 朱祎国, 吕和详, 杨大智. 一个新的形状记忆合金模型[J]. 应用数学和力学, 2002,23(9): 896-902.(ZHU Yiguo, L Hexiang, YANG Dazhi. A new model of shape memory alloys[J]. Applied Mathematics and Mechanics,2002,23(9): 896-902.(in Chinese))
    [9] 霍永忠. 内变量和伪弹性的热力学模型[J]. 应用数学和力学, 1996,17(10): 909-917.(HUO Yongzhong. Internal variables and thermodynamic modeling of pseudoelasticity[J]. Applied Mathematics and Mechanics,1996,17(10): 909-917.(in Chinese))
    [10] 曾忠敏, 彭向和. 计及相变与塑性的NiTi形状记忆合金循环伪弹性特性描述[J]. 应用数学和力学, 2014,38(8): 850-862.(ZENG Zhongmin, PENG Xianghe. A constitutive description of cyclic pseudoelasticity for the NiTi SMAs involving coupled phase transformation and plasticity[J]. Applied Mathematics and Mechanics,2014,38(8): 850-862.(in Chinese))
    [11] ABEYARATNE R, KIM S J. Cyclic effects in shape-memory alloys: a one-dimensional continuum model[J]. International Journal of Solids & Structures,1997,34(25): 3273-3289.
    [12] LAGOUDAS D C, ENTHEV P B. Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys, part I: constitutive model for fully dense SMAs[J]. Mechanics of Materials,2004,36(9): 865-892.
    [13] ZAKI W, MOUMNI Z. A 3D model of the cyclic thermomechanical behavior of shape memory alloys[J]. Journal of the Mechanics and Physics of Solids,2007,55(11): 2427-2454.
    [14] KAN Qianhua, KANG Guozheng. Constitutive model for uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy at room temperature[J]. International Journal of Plasticity,2010,26(3): 441-465.
    [15] LAGOUDAS D C, ENTCHEV P B, POPOV P, et al. Shape memory alloys, part II: modeling of polycrystals[J]. Mechanics of Materials,2006,38(5/6): 430-462.
    [16] AURICCHIO F, TAYLOR R L. Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior[J]. Computer Methods in Applied Mechanics and Engineering,1997,143(1/2): 175-194.
    [17] BATTACHARYA K. Microstructure of Marytensite: Why It Forms and How It Gives Rise to the Shape Memory Effect [M]. Oxford: Oxford University Press, 2003.
    [18] LAGOUDAS D C. Shape Memory Alloys: Modeling and Engineering Applications [M]. New York: Springer, 2008.
    [19] CISSE C, ZAKI W, ZINEB T B. A review of constitutive models and modeling techniques for shape memory alloys[J]. International Journal of Plasticity,2016,76: 244-284.
    [20] CHAO Yu, KANG Guozheng, KAN Qianhua. A micromechanical constitutive model for anisotropic cyclic deformation of super-elastic NiTi shape memory alloy single crystals[J]. Journal of the Mechanics & Physics of Solids,2015,82: 97-136.
    [21] QIAN Hui, LI Hongnan, SONG Gangbing, et al. A constitutive model for superelastic shape memory alloys considering the influence of strain rate[J]. Mathematical Problems in Engineering,2017, 2013,2013: 206-226.
    [22] WANG Jun, MOUMNI Z, ZHANG Weihong, et al. A thermomechanically coupled finite deformation constitutive model for shape memory alloys based on Hencky strain[J].International Journal of Engineering Science,2017,117: 51-77.
    [23] WANG Xiaoming, WANG Zhaoling, XIAO Heng. SMA pseudo-elastic hysteresis with tension-compression asymmetry: explicit simulation based on elastoplasticity models[J]. Continuum Mechanics and Thermodynamics,2014,27(6): 959-970. DOI: 10.1007/s00161-014-0394-1.
    [24] XIAO Heng. Pseudoelastic hysteresis out of recoverable finite elastoplastic flows[J]. International Journal of Plasticity,2013,41: 82-96.
    [25] XIAO H. An explicit, straightforward approach to modeling SMA pseudoelastic hysteresis[J]. International Journal of Plasticity,2014,53: 228-240.
    [26] XIAO H, BRUHNS O T, MEYERS A. Elastoplasticity beyond small deformations[J]. Acta Mechanica,2006,182(1/2): 31-111.
    [27] XIAO H, BRUHNS O T, MEYERS A. Thermodynamic laws and consistent Eulerian formulations of finite elastoplasticity with thermal effects[J]. Journal of the Mechanics and Physics of Solids,2007,55(2): 338-365.
    [28] XIAO H, BRUHNS O T, MEYERS A. The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate[J]. Proceedings: Mathematical, Physical and Engineering Sciences,2000,456(2000): 1865-1882.
    [29] XIAO H, BRUHNS O T, MEYERS A. A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient[J]. International Journal of Plasticity,2000,16(2): 143-177.
    [30] XIAO H, BRUHNS O T, Meyers A. Logarithmic strain, logarithmic spin and logarithmic rate[J]. Acta Mechanica,1997,124(1/4): 89-105.
    [31] SHAW J A, KYRIAKIDES S. Thermomechanical aspects of NiTi[J]. Journal of the Mechanics and Physics of Solids,1995,43(8): 1243-1281.
  • 加载中
计量
  • 文章访问数:  881
  • HTML全文浏览量:  77
  • PDF下载量:  857
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-03-24
  • 修回日期:  2017-12-27
  • 刊出日期:  2018-03-15

目录

    /

    返回文章
    返回