形状记忆合金及其复合材料的本构关系
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摘要
智能材料的概念产生于二十世纪八十年代后期。形状记忆合金机敏复合材料一直是智能材料研究中的热点与重点之一，而形状记忆合金及其复合材料本构关系的研究是应用与发展这类机敏材料的关键基础性问题。本文从两个不同的角度建立了形状记忆合金的本构关系，并且将形状记忆合金的唯象模型应用于复合材料中，为智能复合材料材料的设计提供了有价值的参考意见。具体工作如下：
在Tanaka唯象模型中，相变的体积百分数与应力及温度之间存在指数关系，且形状记忆合金的四个特征相变温度与应力之间存在线性关系，因此，在材料为完全马氏体态时加载，Tanaka模型不可能反映形状记忆合金的马氏体重定向现象。因此，作者建立了自己的唯象模型，它仍然采用Tanaka的马氏体体积分数指数模型，应用Brinson的特征相变温度与应力之间的关系，对于不同的相变驱动采用不同的相变应变表达式，同时，将挛晶马氏体的去挛晶过程看作为相变，这样，当形状记忆合金为完全的挛晶马氏体态加载时就可以反映马氏体的重定向，进而利用等效应力的概念将一维模型推广至三维情况，由于在相变过程中只应用了一套马氏体体积百分数的动力学方程，因此构造的模型简单实用。计算结果表明，本模型预测的应力应变曲线与实验结果吻合。
利用Dvorak等的弹塑性长纤维复合材料本构关系理论框架，推导了SMAs长纤维复合材料在应力循环变化情况下的细观本构模型，考虑了基体材料的非线性，从复合材料界面的连续条件出发，分五种情况推导了复合材料在应力循环过程中的具体本构关系表达式，并且应用该模型分析了复合材料在应力循环变化情况下的宏观力学性能。这对于智能复合材料的设计提供了有价值的参考意见。
长纤维SMAs铝基复合材料经常应用热压法、压铸法和粉末烧结法来制备，因此必须考虑复合材料在温度变化的情况下复合材料中纤维和基体的应力变化情况，这直接关系到复合材料的整体宏观性能。利用作者的形状记忆合金的唯象模型推导了SMAs长纤维复合材料在温度循环变化情况下的细观本构模型，计算了基体及纤维中残余应力的变化，得出了定量的结论。这为
Abstr8Ct
智能复合材料的制各提供了参考意见。
应用形状记忆合金相变过程中的热力学原理构造了细观多变体本构
模型。不同晶粒间的相互作用通过Eshelby伽ner方法来表示，考虑到形
状记忆合金在相变过程中位错的增殖、吞并而引起塑性应变，将塑性应变
作为材料在相变过程中耗散内变量，将其引入到材料相变过程中耗散能和
自由余能的表达式中来表示材料在相变过程中的能量耗散及能量驱动。因
此，在材料的变形过程中，当不发生相变及涎相变时，塑性应变不发生任
何变化。并以理想两变体情况进行了数值计算，得到的结果完全模拟了形
状记忆合金的形状记忆效应及相变伪弹性。
The concept of intelligent materials came into being in the late 1980's. Shape memory Alloys(SMAs) smart composites have been one of the most absorbable things in the diversity of intelligent materials. The constitutive relations of shape memory alloys and its composites have been a crucial issue for application of the shape memory alloys smart composites. Two constitutive relations were constructed along two different direction, and the constitutive relations of composites reinforced by long shape memory alloys fibers were formed by using the phenomenological model of shape memory alloys, the work can be useful for smart composites design. The main works are as follows:
In the phenomenological model of Tanaka's, the volume fraction of transformation products is exponential to stresses and temperature, and the four characteristic transformation temperatures are linear to the stress, so when the shape memory alloys which morphology is full twinned martensite, was stretched, the model of Tanaka's can not reflect the reorientation of the martensite. The author constructed his own phenomenological model by using Tanaka's exponential model of transformation products, but Brinson's relations of transformation temperatures and stresses were adopted, different recoverable strains expressions were determined according to the applied load, meanwhile, the process which twinned martensite detwinned can be assumed as transformation, so the new model can reflect the reorientation of martensite, and it can be expanded to three dimensional easily by using the concept of equivalent stress. The model is simple because only one dynamic equation of martensite is adopted. The theoretical predictions of the model consist well with experiment.
The constitutive model of composites reinforced by long SMAs fiber was constructed by using the framework of Dvorak's elastoplastic fibrous composites theory. In the model, the elastoplastic matrix was considered, and the definite expressions of five subdivisions can be obtained from the continuous constraint of interface between the matrix and the fibers The macroscopic properties can be determined by the model, and it is useful for intelligent composites design.
Usually the long SMAs fiber reinforced aluminum matrix composite is made
by the method of casting with high pressure, or pressure with high temperature and agglomeration of powder, the internal stresses in the fibers and matrix of composites must be studied under the variation of temperature for the research does influence macroscopic properties of the composites. The micromechanical model of long SMAs fibrous composites was constructed by using the phenomenological model of SMAs, the residual stresses in the fibers and matrix were calculated by using the micromechanical model. The research is useful for manufacture of intelligent composites.
A multivariant model was produced by using the principle of thermodynamics in the phases of martensitic transformation and its reverse transformation. The interactions among different grains were calculated by Eshelby-Kroner method, the plastic strain can be introduced at the fact that the dislocations can be reproduced and merged in the phases of martensitic transformation and its reverse transformation, the plastic strain can be considered as a internal variable of dissipation, it should be noted that the plastic strain is only a part of expressions of energy dissipation and complementary free energy, so when the transformation and its reverse cannot occur the plastic strain cannot change. As an example, we selected an ideal SMAs with two completely self-accommodated martensite variants, the results of the calculations can be simulated well with the phenomena of shape memory effect and transformation pseudoelasticity.
在Tanaka唯象模型中，相变的体积百分数与应力及温度之间存在指数关系，且形状记忆合金的四个特征相变温度与应力之间存在线性关系，因此，在材料为完全马氏体态时加载，Tanaka模型不可能反映形状记忆合金的马氏体重定向现象。因此，作者建立了自己的唯象模型，它仍然采用Tanaka的马氏体体积分数指数模型，应用Brinson的特征相变温度与应力之间的关系，对于不同的相变驱动采用不同的相变应变表达式，同时，将挛晶马氏体的去挛晶过程看作为相变，这样，当形状记忆合金为完全的挛晶马氏体态加载时就可以反映马氏体的重定向，进而利用等效应力的概念将一维模型推广至三维情况，由于在相变过程中只应用了一套马氏体体积百分数的动力学方程，因此构造的模型简单实用。计算结果表明，本模型预测的应力应变曲线与实验结果吻合。
利用Dvorak等的弹塑性长纤维复合材料本构关系理论框架，推导了SMAs长纤维复合材料在应力循环变化情况下的细观本构模型，考虑了基体材料的非线性，从复合材料界面的连续条件出发，分五种情况推导了复合材料在应力循环过程中的具体本构关系表达式，并且应用该模型分析了复合材料在应力循环变化情况下的宏观力学性能。这对于智能复合材料的设计提供了有价值的参考意见。
长纤维SMAs铝基复合材料经常应用热压法、压铸法和粉末烧结法来制备，因此必须考虑复合材料在温度变化的情况下复合材料中纤维和基体的应力变化情况，这直接关系到复合材料的整体宏观性能。利用作者的形状记忆合金的唯象模型推导了SMAs长纤维复合材料在温度循环变化情况下的细观本构模型，计算了基体及纤维中残余应力的变化，得出了定量的结论。这为
Abstr8Ct
智能复合材料的制各提供了参考意见。
应用形状记忆合金相变过程中的热力学原理构造了细观多变体本构
模型。不同晶粒间的相互作用通过Eshelby伽ner方法来表示，考虑到形
状记忆合金在相变过程中位错的增殖、吞并而引起塑性应变，将塑性应变
作为材料在相变过程中耗散内变量，将其引入到材料相变过程中耗散能和
自由余能的表达式中来表示材料在相变过程中的能量耗散及能量驱动。因
此，在材料的变形过程中，当不发生相变及涎相变时，塑性应变不发生任
何变化。并以理想两变体情况进行了数值计算，得到的结果完全模拟了形
状记忆合金的形状记忆效应及相变伪弹性。
The concept of intelligent materials came into being in the late 1980's. Shape memory Alloys(SMAs) smart composites have been one of the most absorbable things in the diversity of intelligent materials. The constitutive relations of shape memory alloys and its composites have been a crucial issue for application of the shape memory alloys smart composites. Two constitutive relations were constructed along two different direction, and the constitutive relations of composites reinforced by long shape memory alloys fibers were formed by using the phenomenological model of shape memory alloys, the work can be useful for smart composites design. The main works are as follows:
In the phenomenological model of Tanaka's, the volume fraction of transformation products is exponential to stresses and temperature, and the four characteristic transformation temperatures are linear to the stress, so when the shape memory alloys which morphology is full twinned martensite, was stretched, the model of Tanaka's can not reflect the reorientation of the martensite. The author constructed his own phenomenological model by using Tanaka's exponential model of transformation products, but Brinson's relations of transformation temperatures and stresses were adopted, different recoverable strains expressions were determined according to the applied load, meanwhile, the process which twinned martensite detwinned can be assumed as transformation, so the new model can reflect the reorientation of martensite, and it can be expanded to three dimensional easily by using the concept of equivalent stress. The model is simple because only one dynamic equation of martensite is adopted. The theoretical predictions of the model consist well with experiment.
The constitutive model of composites reinforced by long SMAs fiber was constructed by using the framework of Dvorak's elastoplastic fibrous composites theory. In the model, the elastoplastic matrix was considered, and the definite expressions of five subdivisions can be obtained from the continuous constraint of interface between the matrix and the fibers The macroscopic properties can be determined by the model, and it is useful for intelligent composites design.
Usually the long SMAs fiber reinforced aluminum matrix composite is made
by the method of casting with high pressure, or pressure with high temperature and agglomeration of powder, the internal stresses in the fibers and matrix of composites must be studied under the variation of temperature for the research does influence macroscopic properties of the composites. The micromechanical model of long SMAs fibrous composites was constructed by using the phenomenological model of SMAs, the residual stresses in the fibers and matrix were calculated by using the micromechanical model. The research is useful for manufacture of intelligent composites.
A multivariant model was produced by using the principle of thermodynamics in the phases of martensitic transformation and its reverse transformation. The interactions among different grains were calculated by Eshelby-Kroner method, the plastic strain can be introduced at the fact that the dislocations can be reproduced and merged in the phases of martensitic transformation and its reverse transformation, the plastic strain can be considered as a internal variable of dissipation, it should be noted that the plastic strain is only a part of expressions of energy dissipation and complementary free energy, so when the transformation and its reverse cannot occur the plastic strain cannot change. As an example, we selected an ideal SMAs with two completely self-accommodated martensite variants, the results of the calculations can be simulated well with the phenomena of shape memory effect and transformation pseudoelasticity.
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