含损伤智能结构的性能表征与细观分析
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摘要
智能结构由于其兼具传统复合材料结构和功能复合材料结构的双重特性，已越来越受到人们的关注，并开始在航空航天、国防、建筑、医学等领域获得初步应用。尤其是SMA增强智能结构可用于结构的强度和形状自适应以及失效防范。围绕SMA智能结构，国内外学者做了许多研究工作，但基本上都是针对无损伤情况下的，而有关含损伤SMA增强智能结构的研究至今仍不多见。本文从细观角度出发，着重对含损伤智能结构的性能、力学行为表征及损伤检测进行研究，得到了一些有价值的结果，为智能结构的失效防范研究和完整性评估提供了相应的理论基础和实验准备。
本文主要创新点：
1)对NiTi合金性能进行了系统的实验研究，得出了一些有价值的结果。
2)基于滞后元方法，对NiTi合金的拉伸σ-ε关系进行表征，建立了物理模型，并将数值模拟结果与实验结果相比较，两者吻合较好。
3)基于对马氏体相变热流-温度实验曲线的唯象模拟，以及马氏体体积分数与热力势对温度偏导数之间的线性关系，建立了一种新的马氏体相变动力学模型，并与其他模型及实验结果进行了比较。比较结果表明，新模型的计算结果与实验结果最为接近。
4)研究了SMA热力学非线性方程的求解方法。由于该方程中变量之间相互嵌套，给方程求解带来许多困难。本文根据SMA热力学非线性方程的特点，提出了一种以马氏体百分数为切入点的求解方法，并进行了实例验算。与实验结果的比较表明，计算结果与实验结果基本吻合，说明了该求解方法的可行性与正确性，可应用于实际问题。
5)引入了纤维断裂损伤度ψ、纤维剥离损伤度η和界面影响系数C等表征损伤程度的物理量，并最终建立了考虑这些损伤影响的SMA增强智能结构的一维增量本构关系。用细观力学方法，研究了含损伤宿主材料的刚度退化和纵向热膨胀系数变化规律，并给出了相应的数学表达式。
6)运用剪滞模型和变分原理，对含损伤SMA增强智能结构的热、力学行为进行了分析，给出了含损伤典型单元体的细观位移场、应力应变场的数学描述，建立了SMA增强智能结构界面的失效判据，并通过算例对失效判据进行了直观的几何描述。
Smart structures have attracted more and more attention due to their dual properties of conventional composite structures and of functional composite structures, and are applying or to be applied in some fields such as aeronautics & astronautics, national defense, architecture, medicine. Among them, shape memory alloy (SMA) reinforced smart structures could be used to do self-adaptive structural shape and strength and to prevent structure failures. Although many researches on SMA smart structures without damages have been made, however, researches on SMA smart structures with damages have rarely reported thus far. In this dissertation, researches on material property, meso-mechanical behavior characterization, and damages detection have been emphatically made, and some valuable results have been obtained, with the aim of providing a theoretical basis and experimental data for further studying on failure prevention and integrity evaluation of smart structures.
The novel researches done in this dissertation include:
1) Experimental methods for NiTi-SMA are proposed based on the SMA material evaluation technology and requirement of adaptive structures, and experiments on NiTi wires have been performed. Some useful experimental results are presented herein.
2) Based on the method of hysteresis element, the a - e relation of NiTi-SMA has been obtained for tensile tests, and numerical simulations are in good agreement with experimental results.
3) A novel Martensitic transformation kinetics model for SMA is proposed based on the phenomenological description of the Martensitic transformation heat flow-temperature curve and on the linear relationship between the partial derivatives with respect to the temperature of Martensite fraction and of Gbbis free energy. Numerical simulations by utilizing the proposed model are closer to experimental results than those from other models.
4) As is noticed that the thermodynamics nonlinear equation of SMAs is very complicated and difficult to obtain the solution due to variables nested each other, a simple method starting from martensite fraction has been proposed to solve the equation. Numerical example indicates that the proposed method is simple and accurate, and may find its application in engineering applications.
5) A one- dimensional meso-mechanical model is developed to describe the longitudinal stiffness reduction and thermo-dilatation variation of the composites caused by fiber breaking or by fiber peeling off the base material. Incremental
constitutive relation is then established for SMA fiber reinforced smart structures with damages by introducing three parameters to describe the extents of fiber breaking, fiber peeling off the base material and interface weakening.
6) The thermo-mechanical behaviors of SMA fiber reinforced smart structures with damages have been analyzed by utilizing the shear lag model and variational principle. Mathematical expressions on meso-displacement field, stress-strain field of typical element with damages have been presented, and a failure criterion of interface between SMA wires and base material is established. A geometric characterization on the failure criterion has also been made via an example.
本文主要创新点：
1)对NiTi合金性能进行了系统的实验研究，得出了一些有价值的结果。
2)基于滞后元方法，对NiTi合金的拉伸σ-ε关系进行表征，建立了物理模型，并将数值模拟结果与实验结果相比较，两者吻合较好。
3)基于对马氏体相变热流-温度实验曲线的唯象模拟，以及马氏体体积分数与热力势对温度偏导数之间的线性关系，建立了一种新的马氏体相变动力学模型，并与其他模型及实验结果进行了比较。比较结果表明，新模型的计算结果与实验结果最为接近。
4)研究了SMA热力学非线性方程的求解方法。由于该方程中变量之间相互嵌套，给方程求解带来许多困难。本文根据SMA热力学非线性方程的特点，提出了一种以马氏体百分数为切入点的求解方法，并进行了实例验算。与实验结果的比较表明，计算结果与实验结果基本吻合，说明了该求解方法的可行性与正确性，可应用于实际问题。
5)引入了纤维断裂损伤度ψ、纤维剥离损伤度η和界面影响系数C等表征损伤程度的物理量，并最终建立了考虑这些损伤影响的SMA增强智能结构的一维增量本构关系。用细观力学方法，研究了含损伤宿主材料的刚度退化和纵向热膨胀系数变化规律，并给出了相应的数学表达式。
6)运用剪滞模型和变分原理，对含损伤SMA增强智能结构的热、力学行为进行了分析，给出了含损伤典型单元体的细观位移场、应力应变场的数学描述，建立了SMA增强智能结构界面的失效判据，并通过算例对失效判据进行了直观的几何描述。
Smart structures have attracted more and more attention due to their dual properties of conventional composite structures and of functional composite structures, and are applying or to be applied in some fields such as aeronautics & astronautics, national defense, architecture, medicine. Among them, shape memory alloy (SMA) reinforced smart structures could be used to do self-adaptive structural shape and strength and to prevent structure failures. Although many researches on SMA smart structures without damages have been made, however, researches on SMA smart structures with damages have rarely reported thus far. In this dissertation, researches on material property, meso-mechanical behavior characterization, and damages detection have been emphatically made, and some valuable results have been obtained, with the aim of providing a theoretical basis and experimental data for further studying on failure prevention and integrity evaluation of smart structures.
The novel researches done in this dissertation include:
1) Experimental methods for NiTi-SMA are proposed based on the SMA material evaluation technology and requirement of adaptive structures, and experiments on NiTi wires have been performed. Some useful experimental results are presented herein.
2) Based on the method of hysteresis element, the a - e relation of NiTi-SMA has been obtained for tensile tests, and numerical simulations are in good agreement with experimental results.
3) A novel Martensitic transformation kinetics model for SMA is proposed based on the phenomenological description of the Martensitic transformation heat flow-temperature curve and on the linear relationship between the partial derivatives with respect to the temperature of Martensite fraction and of Gbbis free energy. Numerical simulations by utilizing the proposed model are closer to experimental results than those from other models.
4) As is noticed that the thermodynamics nonlinear equation of SMAs is very complicated and difficult to obtain the solution due to variables nested each other, a simple method starting from martensite fraction has been proposed to solve the equation. Numerical example indicates that the proposed method is simple and accurate, and may find its application in engineering applications.
5) A one- dimensional meso-mechanical model is developed to describe the longitudinal stiffness reduction and thermo-dilatation variation of the composites caused by fiber breaking or by fiber peeling off the base material. Incremental
constitutive relation is then established for SMA fiber reinforced smart structures with damages by introducing three parameters to describe the extents of fiber breaking, fiber peeling off the base material and interface weakening.
6) The thermo-mechanical behaviors of SMA fiber reinforced smart structures with damages have been analyzed by utilizing the shear lag model and variational principle. Mathematical expressions on meso-displacement field, stress-strain field of typical element with damages have been presented, and a failure criterion of interface between SMA wires and base material is established. A geometric characterization on the failure criterion has also been made via an example.
引文
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