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

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

王晓明¹,
肖衡²

¹宁波职业技术学院, 浙江宁波 315800;²暨南大学力学与建筑工程学院, 广州 510632

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
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- 文章访问数: 1096
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- 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

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

WANG Xiaoming¹,
XIAO Heng²

¹Ningbo Polytechnic, Ningbo, Zhejiang 315800, P.R.China;²School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, P.R.China

摘要

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.
- J2流 /
- 弹塑性本构 /
- 伪弹性 /
- 塑性 /
- 软化破坏
Abstract: A new elastoplastic J2 flow model was proposed for shape memory alloys to comprehensively simulate the pseudo-elastic stage with perfect strain recovery, the plastic stage with partial strain recovery and the softening stage up to failure. To this end, a new explicit method based on any given uniaxial data was introduced to obtain the multi-axial expression for the constitutive quantities incorporated in this model. The advantage of this model lies in avoiding the usual complicated numerical procedures in treating nonlinear rate constitutive equations with a number of phase transition conditions and micro-macro averaging methods. Numerical examples give results in good accordance with experiment data.
- J2 flow /
- elastoplastic constitution /
- pseudo-elasticity /
- plasticity /
- softening

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参考文献(31)

[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.