含损伤热粘塑性本构数值算法和铝锂合金动态响应研究
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摘要
本文紧密结合国家自然科学基金项目“复合冲击载荷下铝锂合金应力波传播特性及层裂准则研究”(基金号：10272097)，在实验研究的基础上通过理论分析和数值模拟等多种手段相结合的方法，系统地研究了国产新型铝锂合金的动态力学性能、应力波传播和层裂问题。全文包括热力率耦合的含损伤热粘塑性动态本构关系及本构算法研究，高压状态方程研究，损伤演化及层裂准则研究，数值计算程序开发及数值模拟方法研究，复合应力波传播及层裂特性研究。其主要内容包括以下几个方面：
1、含损伤的热粘塑性本构关系及本构的数值算法研究。以冲击动力学中的粘塑性本构计算的需要为背景，分析了多耦合因素含损伤热粘塑性本构关系的一般形式和几种典型常用形式，给出了本构关系严格的增量型计算公式及相应的计算流程；提出了适用于一般的多耦合因素非线性本构关系的计及弹性应变影响的半径回归本构算法，并比较和分析了半径回归算法与严格增量算法之间的计算流程和特点；以理论和实验相结合的方法建立了新型铝锂合金材料的热、力、率、损伤耦合型的动态本构关系，并以不同温度不同应变率下MTS和SHPB实验结果为基础，采用新的拟合方法确定了铝锂合金材料的本构参数；研究了铝锂合金绝热熵增型Hugoniot状态方程，并根据铝锂合金靶板撞击实验结果得到了状态方程的材料参数。
2、材料的损伤演化方程和层裂准则研究。以损伤力学和波动力学为指导，通过细观统计和唯象分析相结合的手段并采用新的推导方法建立了基于材料微观损伤的材料损伤演化方程和微观层裂准则，并以此为依据推导了工程上几种常用的宏观层裂准则，并分析了各参数的物理意义；给出了一种以实验、理论和计算相结合，通过系统地数值模拟由实验测量得到的自由面速度时程曲线确定材料损伤演化方程和层裂准则参数的方法；提出了一种新的评价层裂计算结果与实验结果吻合度的指标，并通过损伤演化方程各参数对层裂信号影响的详细分析，建立了一种确定损伤演化方程参数的优选原则；利用所提出的方法和优选原则确定了铝锂合金材料损伤演化方程和层裂准则的有关材料参数，从而也得到了几种工程层裂准则中的有关参数，并根据不同撞击速度的计算结果得出了一些关于层裂效应的有工程指导意义的结论。
3、一维复合应力波及层裂的数值模拟研究。从研究铝锂合金平板在压剪联合作用下的复合应力波层裂效应入手，建立了包括三种不同本构算法的一维复合应力波有限差分计算程序；首次尝试性地将切应力项嵌入到损伤演化方程内研究了切应力对损伤演化和层裂的影响，并运用数值模拟的方法，通过采用不同的切
This paper is correlative with "Research on stress wave propagation characteristics and spallation criterion of Al-Li Alloys under combined impact loadings" which is supported by the National Nature Science Foundation of China (10272097). Because of their special impact ductility and good high-temperture bearing propeterities, the Al-Li alloys have been getting into wider and wider uses as a primary material in the field of spaceflight and avigation. This paper has carried out the research on the dynamic mechanical behavior and properties of AL-LI alloys by the experimental, theoretical and numerical ways. The paper mainly include: thermal-mechanical-rate-damage coupling dynamic constitutive relation, high pressure state equation, the damage evolution equation and the spallation criterion, numerical simulations and combined stress wave propagation rules.
About constitutive relation and numerical method. Firstly, on the modified Drucker's postulate and theory of internal variables in the constitutive relations, the universal form of the damaged thermo-visco-plastic incremental constitutive relations and the computational routine are established. This constitutive relation can cover various kinds of plastic hardening (softening) behaviors, thermo-softening behaviors, damage-softening behaviors and their coupling effects between each other. Secondly, a strictly theoretical testification of the better method of radius regression is given. Thirdly, this paper has researched into the thermal-mechanical-rate-damage coupling propeties of Al-li alloys under combined impact loadings. Especailly the limit strain rate softening effect(negative sensitivity of the materials to strain rate) is found, and the scientific concept of the limit strain rate softening is presented. Lastly, We have established the high pressure state eqution and dynamic constitutive relation with limit strain rate softening and temperature softening effects.
About the damage evolution equation and the spallation criterion. We present a new kind form of damage evolution equation by the method of phenomenological analysis and microscopic statistics, and on the basis of this we have established several spallation criterion that is used easily in engineering. We present a method by which the damage evolution equation and the spallation criterion can be established by the combination of experiment, theory and numerical simulations. With our method the damage evolution equation and spallation criterion of Al-Li alloys has been estabished. By the numerical simulations of the free surface velocity histories
1、含损伤的热粘塑性本构关系及本构的数值算法研究。以冲击动力学中的粘塑性本构计算的需要为背景，分析了多耦合因素含损伤热粘塑性本构关系的一般形式和几种典型常用形式，给出了本构关系严格的增量型计算公式及相应的计算流程；提出了适用于一般的多耦合因素非线性本构关系的计及弹性应变影响的半径回归本构算法，并比较和分析了半径回归算法与严格增量算法之间的计算流程和特点；以理论和实验相结合的方法建立了新型铝锂合金材料的热、力、率、损伤耦合型的动态本构关系，并以不同温度不同应变率下MTS和SHPB实验结果为基础，采用新的拟合方法确定了铝锂合金材料的本构参数；研究了铝锂合金绝热熵增型Hugoniot状态方程，并根据铝锂合金靶板撞击实验结果得到了状态方程的材料参数。
2、材料的损伤演化方程和层裂准则研究。以损伤力学和波动力学为指导，通过细观统计和唯象分析相结合的手段并采用新的推导方法建立了基于材料微观损伤的材料损伤演化方程和微观层裂准则，并以此为依据推导了工程上几种常用的宏观层裂准则，并分析了各参数的物理意义；给出了一种以实验、理论和计算相结合，通过系统地数值模拟由实验测量得到的自由面速度时程曲线确定材料损伤演化方程和层裂准则参数的方法；提出了一种新的评价层裂计算结果与实验结果吻合度的指标，并通过损伤演化方程各参数对层裂信号影响的详细分析，建立了一种确定损伤演化方程参数的优选原则；利用所提出的方法和优选原则确定了铝锂合金材料损伤演化方程和层裂准则的有关材料参数，从而也得到了几种工程层裂准则中的有关参数，并根据不同撞击速度的计算结果得出了一些关于层裂效应的有工程指导意义的结论。
3、一维复合应力波及层裂的数值模拟研究。从研究铝锂合金平板在压剪联合作用下的复合应力波层裂效应入手，建立了包括三种不同本构算法的一维复合应力波有限差分计算程序；首次尝试性地将切应力项嵌入到损伤演化方程内研究了切应力对损伤演化和层裂的影响，并运用数值模拟的方法，通过采用不同的切
This paper is correlative with "Research on stress wave propagation characteristics and spallation criterion of Al-Li Alloys under combined impact loadings" which is supported by the National Nature Science Foundation of China (10272097). Because of their special impact ductility and good high-temperture bearing propeterities, the Al-Li alloys have been getting into wider and wider uses as a primary material in the field of spaceflight and avigation. This paper has carried out the research on the dynamic mechanical behavior and properties of AL-LI alloys by the experimental, theoretical and numerical ways. The paper mainly include: thermal-mechanical-rate-damage coupling dynamic constitutive relation, high pressure state equation, the damage evolution equation and the spallation criterion, numerical simulations and combined stress wave propagation rules.
About constitutive relation and numerical method. Firstly, on the modified Drucker's postulate and theory of internal variables in the constitutive relations, the universal form of the damaged thermo-visco-plastic incremental constitutive relations and the computational routine are established. This constitutive relation can cover various kinds of plastic hardening (softening) behaviors, thermo-softening behaviors, damage-softening behaviors and their coupling effects between each other. Secondly, a strictly theoretical testification of the better method of radius regression is given. Thirdly, this paper has researched into the thermal-mechanical-rate-damage coupling propeties of Al-li alloys under combined impact loadings. Especailly the limit strain rate softening effect(negative sensitivity of the materials to strain rate) is found, and the scientific concept of the limit strain rate softening is presented. Lastly, We have established the high pressure state eqution and dynamic constitutive relation with limit strain rate softening and temperature softening effects.
About the damage evolution equation and the spallation criterion. We present a new kind form of damage evolution equation by the method of phenomenological analysis and microscopic statistics, and on the basis of this we have established several spallation criterion that is used easily in engineering. We present a method by which the damage evolution equation and the spallation criterion can be established by the combination of experiment, theory and numerical simulations. With our method the damage evolution equation and spallation criterion of Al-Li alloys has been estabished. By the numerical simulations of the free surface velocity histories
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