Johnson-Cook本构模型和Steinberg本构模型的比较研究
摘要
极端条件下的物理学是21世纪物理学研究的一个重要方向，高温和高压复合环境，特别是借助强冲击波技术产生的高温高压复合环境下材料物性的研究，不仅是凝聚态物理领域的一个重要的基础性研究问题，而且在航天飞行器安全防护、武器物理、新能源及工程爆破等技术和工程科学研究中也有广泛的应用背景。
强击波高温高压作用下金属材料的力学运动可用流体动力学方程组描述，材料特性方程采用流体弹塑性模型，并把流体部分和弹塑性部分作解耦处理。前者可以归结为对物态方程的研究，表示球量应力贡献部分；后者可以归结为对本构方程的研究，表示偏量应力贡献部分。高温高压下固体材料本构关系的研究其实质性问题是对高温高压环境下固体材料剪切模量G和屈服强度Y的精密测量问题，所涉及的物理难题主要有：(1)由于所关心的压力范围大多在几十吉帕以上，与传统弹塑形力学研究的低应力区的情形不同，静水压(球量应力)和温度对G、Y有显著影响，须利用高压物理方法来进行研究；(2)现有的高压物理实验方法中，对高温高压环境下G值的测量技术相对成熟，较易实现，但对Y值的测量成功率不高，而且测量值的不确定度也比较大。
本文的研究思路是，选取铝、铜、钨三种材料作为低、中、高阻抗材料的代表(而且三种材料的晶体结构也不一样，铝和铜为面心立方结构，钨为体心立方结构)，综合分析其一维应力和一维应变下的实验数据，以期获得三种材料的Johnson-Cook模型和Steinberg模型的本构参数，重点关注由冲击波加载下材料波剖面测量中表现出来的本构行为，对这两种本构模型的适用性进行比较研究。主要的研究成果包括以下几个方面：
1．用低应力下的SHPB(Split Hopkinson Pressure Bar)动态压缩实验和MTS(Mechanical Test System)准静态压缩实验，测量了LY12铝的温度在25℃～400℃和应变率在10~(-4)／s～10~3／s范围的应力-应变曲线，并结合公开文献新近发表的10~(-4)／s～10~5／s应变率范围内实验数据，综合优选了铝、铜、钨的Johnson-Cook本构模型的材料参数和Steinberg本构模型中的有关材料参数。
2．综合分析了公开文献发表的关于铝、铜、钨在4 GPa～200 GPa冲击压力范围内的波剖面测量结果，并进行了少量的验证实验，利用高压声速结果和对波剖面
Research of physics under extreme conditions is an important direction of physics study in 21st century. Material properties at high-pressure and high-temperature environments, especially induced by strong shock wave, are not only a fundamental problem of condensed matter physics, but also have comprehensive applications in safe protection of space aircraft, weapon physics, new energy, and engineering explosion, etc.
Mechanical movement of metals subjected to strong shock wave is controlled by hydrodynamics equations. The elastic-plastic-flow model is adopted to characterize the dynamic behavior of metals. The hydro part is come down to EOS (equation of state) research field, and the elastic-plastic part belongs to constitutive equation research field. The substantial question of high-pressure and high-temperature constitutive equation research is how to measure shear modulus G and yield strength Y precisely. The following are puzzles: (1) because the pressure range is exceed to tenths of GPa, the effects of pressure and temperature to G and Y are considerably large, and the high-pressure physics technique must be utilized to study the G and Y ; (2) the measurement of Y is difficult and the measurement uncertainty is large, although the measurement of G under high-pressure and high-temperature is easy to realize relatively.
In this paper, we selected Al, Cu and W as the representations of low, medium and high impedance materials (in addition, Al, Cu are FCC metal, and W is BCC metal). Then experimental data of one-dimensional stress experiments and one-dimensional strain experiments were systematically analyzed in order to obtain the material parameters of Johnson-Cook model and Steinberg model. The applicability of these two constitutive models is comparatively studied by means of numerical simulation method. The principle results are as follows:
1. The stress-strain curves of aluminum under temperature ranging from 25 ℃ to 400 ℃ and strain-rate ranging from 10~(-4)/s to 10~3 /s were measured via SHPB (Split Hopkinson Pressure Bar) dynamic compression and MTS (Mechanical Test System) quasi-static compression experiments. Combined with the experimental data of literatures, the material parameters of Johnson-Cook model and Steinberg model for Al, Cu and W were educed.
强击波高温高压作用下金属材料的力学运动可用流体动力学方程组描述，材料特性方程采用流体弹塑性模型，并把流体部分和弹塑性部分作解耦处理。前者可以归结为对物态方程的研究，表示球量应力贡献部分；后者可以归结为对本构方程的研究，表示偏量应力贡献部分。高温高压下固体材料本构关系的研究其实质性问题是对高温高压环境下固体材料剪切模量G和屈服强度Y的精密测量问题，所涉及的物理难题主要有：(1)由于所关心的压力范围大多在几十吉帕以上，与传统弹塑形力学研究的低应力区的情形不同，静水压(球量应力)和温度对G、Y有显著影响，须利用高压物理方法来进行研究；(2)现有的高压物理实验方法中，对高温高压环境下G值的测量技术相对成熟，较易实现，但对Y值的测量成功率不高，而且测量值的不确定度也比较大。
本文的研究思路是，选取铝、铜、钨三种材料作为低、中、高阻抗材料的代表(而且三种材料的晶体结构也不一样，铝和铜为面心立方结构，钨为体心立方结构)，综合分析其一维应力和一维应变下的实验数据，以期获得三种材料的Johnson-Cook模型和Steinberg模型的本构参数，重点关注由冲击波加载下材料波剖面测量中表现出来的本构行为，对这两种本构模型的适用性进行比较研究。主要的研究成果包括以下几个方面：
1．用低应力下的SHPB(Split Hopkinson Pressure Bar)动态压缩实验和MTS(Mechanical Test System)准静态压缩实验，测量了LY12铝的温度在25℃～400℃和应变率在10~(-4)／s～10~3／s范围的应力-应变曲线，并结合公开文献新近发表的10~(-4)／s～10~5／s应变率范围内实验数据，综合优选了铝、铜、钨的Johnson-Cook本构模型的材料参数和Steinberg本构模型中的有关材料参数。
2．综合分析了公开文献发表的关于铝、铜、钨在4 GPa～200 GPa冲击压力范围内的波剖面测量结果，并进行了少量的验证实验，利用高压声速结果和对波剖面
Research of physics under extreme conditions is an important direction of physics study in 21st century. Material properties at high-pressure and high-temperature environments, especially induced by strong shock wave, are not only a fundamental problem of condensed matter physics, but also have comprehensive applications in safe protection of space aircraft, weapon physics, new energy, and engineering explosion, etc.
Mechanical movement of metals subjected to strong shock wave is controlled by hydrodynamics equations. The elastic-plastic-flow model is adopted to characterize the dynamic behavior of metals. The hydro part is come down to EOS (equation of state) research field, and the elastic-plastic part belongs to constitutive equation research field. The substantial question of high-pressure and high-temperature constitutive equation research is how to measure shear modulus G and yield strength Y precisely. The following are puzzles: (1) because the pressure range is exceed to tenths of GPa, the effects of pressure and temperature to G and Y are considerably large, and the high-pressure physics technique must be utilized to study the G and Y ; (2) the measurement of Y is difficult and the measurement uncertainty is large, although the measurement of G under high-pressure and high-temperature is easy to realize relatively.
In this paper, we selected Al, Cu and W as the representations of low, medium and high impedance materials (in addition, Al, Cu are FCC metal, and W is BCC metal). Then experimental data of one-dimensional stress experiments and one-dimensional strain experiments were systematically analyzed in order to obtain the material parameters of Johnson-Cook model and Steinberg model. The applicability of these two constitutive models is comparatively studied by means of numerical simulation method. The principle results are as follows:
1. The stress-strain curves of aluminum under temperature ranging from 25 ℃ to 400 ℃ and strain-rate ranging from 10~(-4)/s to 10~3 /s were measured via SHPB (Split Hopkinson Pressure Bar) dynamic compression and MTS (Mechanical Test System) quasi-static compression experiments. Combined with the experimental data of literatures, the material parameters of Johnson-Cook model and Steinberg model for Al, Cu and W were educed.
引文
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