金属材料的率-温耦合响应与动态本构关系综述

袁康博; 姚小虎; 王瑞丰; 莫泳晖

doi:10.11883/bzycj-2021-0416

金属材料的率-温耦合响应与动态本构关系综述

doi: 10.11883/bzycj-2021-0416

1.
华南理工大学工程力学系，广东广州 510641
2.
西北工业大学航空学院，陕西西安 710072

基金项目: 中央高校基本科研业务费专项资金（x2tjD2220850）；国家自然科学基金（12202149）；国家杰出青年科学基金（11925203）；中国博士后科学基金（2022M711198）

详细信息

作者简介:
袁康博（1992－　），女，博士，kangboyuan0528@scut.edu.cn

通讯作者:
姚小虎（1974－　），男，博士，教授，博士生导师，yaoxh@scut.edu.cn

中图分类号: O347.3
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出版历程
- 收稿日期: 2021-10-08
- 录用日期: 2022-05-13
- 修回日期: 2022-01-04
- 网络出版日期: 2022-05-19
- 刊出日期: 2022-09-29

A review on rate-temperature coupling response and dynamic constitutive relation of metallic materials

1.
Department of Engineering Mechanics, South China University of Technology, Guangzhou 510641, Guangdong, China
2.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China

摘要

摘要: 金属材料在冲击、爆炸等高应变率加载下的塑性流动行为具有不同于静载下的率-温耦合性和微观机制。航空航天、航海、能源开采、核工业、公共安全、灾害防治等方面的金属结构设计与性能评估需要进行大量的动载实验和数值模拟，建立准确的材料动态本构模型是结构数值模拟可靠性的基础和关键。本文中，总结了金属材料的率-温耦合变形行为及内在机理，回顾了金属动态本构关系研究的起源与发展脉络，分别针对唯象模型、具有物理基础的模型和人工神经网络模型进行了详细介绍和横向比较。唯象模型和人工神经网络模型分别因易应用和高预测精度而受到青睐，基于物理概念的宏观连续介质模型可以描述体现内部演化的真实物理量，从而涵盖更大的应变范围，更好地反映应变率、温度和应变的影响机制。
- 金属材料 /
- 高应变率 /
- 塑性变形 /
- 动态本构模型
Abstract: Different from static loading conditions, the plastic flow behavior of metallic materials under high strain rate loadings, such as impact and explosion, exhibits special rate-temperature coupling effect and deformation micro-mechanism. The design and evaluation of metallic structures used in aerospace and navigation, energy mining, nuclear industry, public safety, disaster prevention, etc. require a large number of experiments under dynamic loadings. In recent years, the rapid-developing computational mechanics can be used to analyze the structural mechanical response under complex loading, evaluate the structural safety and optimize the structural design, and can also save the experimental costs. Accurate dynamic constitutive description of materials is the basis for the reliability of structural numerical simulation. In this paper, the dynamic plastic deformation behavior and micro-mechanism of metals, as well as the origin and development of the dynamic constitutive relationship of metals are reviewed and summarized. Over wide ranges of strain rate and temperature, the metals exhibit complex rate-temperature coupling effect, such as dynamic strain aging and segmented strain rate sensitivity. The high strain rate may lead to dynamic recrystallization, deformation twinning and shock-induced phase transition. The existing constitutive models can be divided into three types: phenomenological models, physically based models and artificial neural network models. Phenomenological models refer to the constitutive models established merely by describing experimental phenomena without considering the internal physical mechanism. Physically based macro-scale continuum models can represent true physical quantities for documenting and tracking the evolution which takes place within metallic materials. Artificial neural network models are good at reproducing the plastic flow behavior as function of many factors, such as strain rate, temperature and plastic strain, without the need of identifying complex logic relationships and parameters within the system. The developments, prediction capabilities, and application scopes of the three types of dynamic constitutive models are illustrated in detail and compared horizontally. In addition, some objective suggestions for the further development of dynamic constitutive descriptions for metals are proposed. Phenomenological models are favored for their ease in application, artificial neural network models are favored for their high prediction accuracy. Recent trend has increased the focus on physically based models. This type of model extends application to a wider strain range and more clearly represents the influence mechanism of strain rate, temperature and strain.
- metallic material /
- high strain rate /
- plastic deformation /
- dynamic constitutive model

HTML全文

图 1 低碳钢的屈服应力在不同温度和应变率区域内的应变率效应

Figure 1. Strain rate effect on yield stress of low-carbon steelin different temperature and strain rate regions

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图 2 金属的典型温度敏感性

Figure 2. Typical temperature sensitivity of metal

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图 3 Q235B钢在0.1应变下流动应力随温度和应变率的变化^[19]

Figure 3. Variation of flow stress with temperatureand strain rate for Q235B steel^[19]

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图 4 不同热处理状态下Inconel 718镍基高温合金的流动应力随温度变化曲线^[16]

Figure 4. Flow stress-temperature curves of Inconel 718 superalloyunder different heat-treatment conditions^[16]

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图 5 塑性流动曲线的4个阶段和绝热剪切引起的动态再结晶微观图片

Figure 5. Four stages of plastic flow curve and micro image of DRX caused by adiabatic shear

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图 6 不锈钢的绝热剪切局部化引起的变形孪晶^[44]

Figure 6. Deformation twinning in the stainless steel by adiabatic shear localization^[44]

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图 7 BP神经网络的结构示意图

Figure 7. Schematic structure of BP neural network

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表 1 唯象动态本构模型之间的比较

Table 1. Comparison among phenomenological dynamic constitutive models

发表时间	模型名称	应变率/s⁻¹	温度/℃	待定参数/个	主要特点
1976	Voce-Kocks (VK)^[80]	10⁻¹	−173～327	7	饱和应力${\sigma }_{\rm{s}}$为温度和应变率的函数
1983	Johnson-Cook (JC)^[77]	对数应变率的线性函数，可达10⁴	温度的幂函数	5	兼顾温度和应变率效应参数少，形式简单
1992	Khan-Huang (KH)^[82]	10⁻⁵～10⁴	不考虑	5	未考虑温度效应将总应变率分解为弹性和塑性分量
1999	Khan-Huang-Liang (KHL)^[83]	10⁻⁶～10⁴	25～316	7	在KH模型基础上增加温度效应
2009	Khan-Liang-Farrokh (KLF)^[115]	10⁻²～3×10⁴	−50～250	9	基于KHL模型兼顾温度和应变率效应考虑晶粒尺寸
2008	Improved Fields-Backofen (FB) model by Cheng^[107]	10⁻¹～10⁻⁴	150～300	5	兼顾温度和应变率效应参数少，形式简单
2005	Molinari-Ravichandran (MR)^[81]	10⁻²～10⁶	−196～200	9	基于微观结构的特征尺度考虑温度、应变率和晶粒尺寸
2010	Lin-Liu (LL)^[117]	10⁻²～10	850～1150	8	可描述热成形过程达到应力峰值的应力-应变曲线
2010	Toros-Ozturk (TO)^[118]	0.0016～0.16	室温～300	9	可描述大塑性应变下的软化行为

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表 2 具有物理基础的动态本构模型之间的比较

Table 2. Comparison among physically based dynamic constitutive models

年份	模型名称	建模思想	主要特点
1975	Bodner-Partom (BP)^[93]	基于不可逆热力学，位错动力学和内变量理论	采用塑性功度量变形抗力无需屈服函数参数较少（不多于10），应用广泛
1987	Zerilli-Armstrong (ZA)^[45]	位错动力学理论 BCC和FCC晶体结构的塑性变形微观机制不同	考虑温度、应变率和平均晶粒尺寸不同晶体结构具有不同表达式描述热激活区域的塑性流动行为
1980	Steinberg-Guinan (SG)^[94]	剪切模量和屈服应力具有相同的温度和压强依赖性，将流体与冲击下的固体等效	考虑温度、压强效应未考虑应变率效应（认为高应变率下应变率效应不明显）
1989	Steinberg-Lund (SL)^[96]	流动应力等于热分量和非热分量之和，压强通过影响剪切模量影响流动应力	考虑温度、应变率和压强效应适用于10⁻⁴～10⁶ s⁻¹宽应变率范围
1981	Mecking-Kocks (MK)^[95]	针对FCC金属位错累积是塑性变形主要障碍	流动应力是应变硬化和率-温效应的乘积在应变硬化项中考虑动态回复
1988	Mechanical Threshold Stress (MTS)^[91]	采用力学阈值应力作为内部结构参量，不存在应变率效应的突然增大	考虑温度、应变率和应变历史的影响需要较多实验结果确定本构参数
1998	Nemat-Nasser-Li (NN)^[98]	位错动力学热激活理论	考虑FCC金属的应变历史对热激活行为的影响
1999	Nemat-Nasser-Guo (NN)^[100]	位错动力学热激活理论高应变率下的黏性拖曳机制	考虑高应变率加载下，金属塑性变形具有黏性拖曳导致的强化
2015	Guo-Wang (GW)^[19]	位错动力学热激活理论动态应变时效经典理论	描述第三型应变时效及其应变率效应
2021	Guo-Yuan (GY)^[16]	沉淀强化理论动态应变时效经典理论	考虑晶粒尺寸、位错密度和沉淀相体积分数及尺寸描述不同晶体结构的多相合金的塑性流动行为的区别
2005	Voyiadjis-Abed (VA)^[128]	位错动力学	考虑FCC和BCC金属热激活行为的区别
2008	Voyiadjis-Almasri (VA)^[17]	热激活理论（热激活能与温度、应变率和应变之间的关系）	针对FCC金属，考虑应变历史的影响
2018–2020	Voyiadjis-Song (VS)^[130-132]	动态应变时效发生符合韦伯概率分布	考虑动态应变时效，并结合韦伯分布进行描述
2001 2009 2010	Rusinek-Klepaczko (RK)^[133-135]	流动应力为描述应变强化的内应力和描述率-温效应的有效应力之和	考虑杨氏模量的温度效应考虑动态应变时效引起的负应变率效应^[134] 考虑FCC金属在高应变率下的黏性拖曳^[135]
2003	Preston-Tonks-Wallace (PTW)^[137]	针对应变率效应机制的不同，分为3个区：热激活控制的位错滑移区、过渡区和超高应变率区	应变率范围涵盖15个数量级基于量纲分析法建模考虑强冲击下非线性位错拖曳效应在塑性变形机制中占主导地位
1998	Cellular Automaton (CA)^[139]	物理冶金原理针对动态再结晶中的微观组织演化	不同温度（高温）和应变率的动态再结晶反向方法

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