基于晶体塑性有限元法的316LN不锈钢单轴力学行为

doi:10.12068/j.issn.1005-3026.2024.06.012

摘要/Abstract

摘要：

为了更准确描述316LN不锈钢单轴力学行为，在率相关晶体塑性理论框架下，以Ahmadzadeh-Varvani （A-V）随动硬化准则为基础，构建了多晶循环塑性本构模型.通过程序UMAT将其移植到有限元软件ABAQUS中，并通过Voronoi图建立二维多晶有限元模型；分别模拟了不同加载率、应变循环和非对称应力循环条件下316LN不锈钢的变形行为.对比模拟结果与实验数据可知：单轴拉伸条件下，两者的应力误差在±0.9%附近波动，最大应力误差仅为1.9%；应变循环条件下，两者的最大应力误差出现在第5圈，拉伸和压缩阶段应力误差分别为11.4%和12.2%，循环稳定后，拉伸和压缩阶段应力误差分别为7.4%和7.9%；应力循环条件下，两者的误差主要体现在滞环宽度上，模拟的滞环面积相对较窄，但滞环演化趋势误差较小.

关键词: 晶体塑性理论, A-V随动硬化准则, 饱和硬化准则, Voronoi图, 棘轮效应

Abstract:

To describe the uniaxial mechanical behavior of 316LN stainless steel more accurately， a polycrystalline cyclic plasticity constitutive model is constructed based on the Ahmadzadeh-Varvani （A-V） kinematic hardening rule in the framework of the rate?dependent crystal plasticity theory. The constitutive model is implemented to the finite element software ABAQUS through the UMAT， and a two?dimensional polycrystalline finite element model is established through Voronoi diagrams. And then the deformation behavior of 316LN stainless steel is simulated under different loading rates， strain cycles and asymmetric stress cycles， respectively. The simulated results compared with the experimental data show that under the uniaxial tensile condition， the stress errors of both fluctuate around±0.9%， and the maximum stress error is only 1.9%； under the strain cycle condition， the maximum stress error between the two appears in the 5th cycle， with 11.4% and 12.2% errors in the tensile and compression phases， respectively， and 7.4% and 7.9% errors in the tensile and compression phases， respectively， after cycle stabilization. Under the asymmetric stress cycle condition， the errors of both mainly appear in the hysteresis loop width， the simulated hysteresis loop width is narrower， but the error of the hysteresis loop evolution trend is smaller.

Key words: crystal plasticity theory, A-V kinematic hardening rule, saturation hardening rule, Voronoi diagram, ratcheting effect

中图分类号:

TB 302.3

陈小辉, 陈天祥, 朱琳, 郎朗. 基于晶体塑性有限元法的316LN不锈钢单轴力学行为[J]. 东北大学学报（自然科学版）, 2024, 45(6): 843-849.

Xiao-hui CHEN, Tian-xiang CHEN, Lin ZHU, Lang LANG. Uniaxial Mechanical Behavior of 316LN Stainless Steel Based on Crystal Plasticity Finite Element Method[J]. Journal of Northeastern University(Natural Science), 2024, 45(6): 843-849.

图/表 7

图1 二维多晶有限元模型和边界条件

Fig.1 Two?dimensional polycrystalline finite element model and boundary conditions

表1 晶体本构模型参数

Table 1 Crystal constitutive model parameters

参数	值
$E$ /GPa	195
$v$	0.37
$n$	6.8
$k$ /MPa	48
$C$	4 200
$v 1$	130
$v 2$	10
$δ$	0.6
$g 0$ /MPa	64
$h s$ /MPa	25
$g s$ /MPa	420

表1 晶体本构模型参数

Table 1 Crystal constitutive model parameters

参数	值
$E$ /GPa	195
$v$	0.37
$n$	6.8
$k$ /MPa	48
$C$	4 200
$v 1$	130
$v 2$	10
$δ$	0.6
$g 0$ /MPa	64
$h s$ /MPa	25
$g s$ /MPa	420

图2 不同加载率下的单轴拉伸模拟

Fig.2 Uniaxial tensile simulation at different

图3 单轴拉伸后的应力和应变云图（a）—加载率1×10-5/s时X方向应力S11；（b）—加载率1×10-5/s时X方向应变LE11；（c）—加载率1×10-4/s时X方向应力S11；（d）—加载率1×10-4/s时X方向应变LE11；（e）—加载率1×10-3/s时X方向应力S11；（f）—加载率1×10-3/s时X方向应变LE11.

Fig.3 Stress and strain nephograms after uniaxial tensile

图4 应变幅值±1%时对称应变循环的结果（a）—第1圈应力-应变关系；（b）—前20圈的应力峰值与循环次数之间的关系.

Fig.4 Results of symmetrical strain cycle under strain amplitude ±1%

图5 应力-应变滞回曲线（a）—实验[12]；（b）—模拟.

Fig.5 Stress?strain hysteresis curve

图6 棘轮应变演化速度

Fig.6 Ratcheting strain evolution rate

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