基于有理插值方法模拟SMAs循环加载下的变形行为

王晓明; 肖衡

doi:10.21656/1000-0887.430279

基于有理插值方法模拟SMAs循环加载下的变形行为

doi: 10.21656/1000-0887.430279

王晓明^1, ,,
肖衡^2,

1.
宁波职业技术学院应用力学研究所, 浙江宁波 315000
2.
暨南大学力学和建筑工程学院, 广州 510632

基金项目:

浙江省教育厅科研项目 Y202147389

浙江省教育厅科研项目 FG2022042

国家自然科学基金项目 1217020816

详细信息

作者简介:
肖衡(1963—)，男，教授，博士生导师(E-mail: hxiao@jnu.edu.cn)

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

中图分类号: O343;O345
计量
- 文章访问数: 312
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- PDF下载量: 33
- 被引次数: 0
出版历程
- 收稿日期: 2022-09-05
- 修回日期: 2022-10-27
- 刊出日期: 2023-06-01

Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation

WANG Xiaoming^{1
, ,},
XIAO Heng^2
,

1.
Institute of Applied Mechanics, Ningbo Polytechnic, Ningbo, Zhejiang 315000, P.R.China
2.
School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, P.R.China

摘要

摘要: 提出了一个有限弹塑性模型，用来模拟形状记忆合金(shape memory alloys, SMAs)在循环荷载下的变形行为. 首先，通过分析上下屈服阶段形函数的特点，利用有理插值方法给出循环荷载下的应力-应变形函数显式表达, 可以精确匹配任意形状的实验数据；其次，基于对数客观率，构建了有限弹塑性J2流模型，耦合了屈服中心的移动和屈服面的增大；再次，从单轴情况出发，推导得到了单个循环下的三个硬化函数显式表达，再引入局部因子和多轴扩展不变量，构造了光滑统一且多轴有效的硬化函数；最后，将模型得到的结果与经典实验结果比较，证明了新方法的有效性. 该文创新点如下：第一，通过改进传统的背应力演化方程，使得新模型产生强烈的Bauschinger效应，从而使新方法具备模拟SMAs特殊变形行为的能力；第二，新的光滑统一硬化函数在单个循环下会自动退化，得到精确符合实验数据的结果；第三，利用本构方程推导得到有效塑性功演化规律，而有理插值得到的形函数中包含依赖有效塑性功的参数，给出这些参数方程以后使得模型具备了预测变形的能力.
- J2流模型 /
- 形状记忆合金 /
- 对数客观率 /
- 屈服 /
- 硬化函数 /
- 形函数
Abstract: A finite elastoplasticity model was proposed to simulate deformation behaviors of SMAs under cyclic loading. First, the explicit formulations of shape functions were given with the rational interpolation method to exactly match any given experimental data. Second, a finite elastoplasticity J2 flow model based on the logarithmic objective rate was built to couple the moving of the yielding center and the expanding of the yielding surface. Third, 3 explicit hardening functions under the single loading cycle were deduced in the uniaxial case, to construct the smooth, unified and multiaxial hardening function through introduction of the local factor and the multiaxial extended invariant. Finally, the model results were compared with the classical test data to prove the effectiveness of the new model. The research results show that, the new model can produce intense Bauschinger effects and simulate the complex deformation of SMAs through improvement of the evolution equation of the back stress. The new smooth unified hardening function can automatically degenerate under the single loading cycle to give results exactly matching the test data. The effective plastic work evolution law deduced with the constitutional equation, and the parameter equations dependent on the effective plastic work contained in the shape functions through rational interpolation, enable the proposed model to predict deformations well.
- J2 flow model /
- SMAs /
- logarithmic objective rate /
- yielding /
- hardening function /
- shape function

HTML全文

图 1 循环荷载下的应力-应变示意图

Figure 1. Schematic of stress-strain curves under cyclic loading

下载: 全尺寸图片幻灯片

图 2 第i次循环下的应力-应变示意图

Figure 2. Schematic of stress-strain curve in the ith cycle

下载: 全尺寸图片幻灯片

图 3 第1、2、3、4、8、12和20次循环的模型结果和实验结果^[33]对比

Figure 3. Comparation between model results and experimental data^[33] for the 1st, 2nd, 3rd, 4th, 8th, 12th and 20th cycles

下载: 全尺寸图片幻灯片

图 4 第4至第8个循环的模型预测

Figure 4. Model predictions from the 4th to the 8th cycles

下载: 全尺寸图片幻灯片

表 1 形函数中关键点应力、应变和有效塑性功

Table 1. Stresses, strains and effective plastic works of key points in the shape function

points	τ	h	$ \vartheta$
P₀	0	h_i－1^p	$ \vartheta$_i－1
P₁	r₀	h_0i	$ \vartheta$_i－1
P₂	τ_i^*	h_i^*	$ \vartheta$^*
Q₁	τ_i^*	h_i^*	$ \vartheta$_i^*
Q₂	0	h_i^p	$ \vartheta$_i

下载: 导出CSV

表 2 p_i(τ)中固定参数值

Table 2. Values of fixed parameters in p_i(τ)

ξ₁	ξ₂	β₁	r₀/MPa
0.001 9	0	0.016	240

下载: 导出CSV

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