形状记忆合金的本构模型及试验研究
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摘要
由于地震、台风等自然灾害或其它因素的影响,混凝土结构在长期的使用过程中,经常会出现裂缝等破坏现象,如何提高混凝土结构的抗震能力以及如何进行结构的修复和加固工作,都成为工程领域亟需解决的问题。因为形状记忆合金(Shape Memory Alloys,简称SMA)材料具有形状记忆效应、超弹性、高阻尼、电阻特性等特性而体现出自感知、自诊断和自适应能力,必将在结构振动控制和结构健康监测等领域,发挥不可忽视的作用。然而,SMA在本构模型特别是多维的本构模型方面,以及在振动控制及混凝土结构修复等方面还存在很多问题有待进一步研究。本文主要针对SMA的本构模型以及在土木工程中的应用,做了基础性的研究,具体内容如下：
(1)对不同直径的奥氏体相SMA丝进行加载和卸载试验,研究不同的循环次数、应变幅值、加载速率、温度等因素对SMA丝力学性能的影响；并且研究了SMA丝在不同加载条件下的电阻特性。试验结果显示,加载幅值、加载速率和环境温度均是影响SMA丝力学性能的重要参数。
(2)基于Kazuhiko Arai的理论,利用能量分析的方法,并考虑了SMA相变和应变率变量的影响建立了SMA的一维连续动力学模型。近几十年来,国内外的学者对SMA材料的本构模型做了大量的研究分析,并相继提出了多种模型,但传统的SMA一维模型,多数不考虑应变率的影响,而且加载和卸载阶段要分别用不同的关系式表达。为了证明所提出模型的实用性,利用该模型计算的结果与试验结果进行对比,结果吻合良好。
(3)利用了塑性力学中的屈服面方程,并结合了Brinsion的一维本构模型的思想和Boyd和Lagoudas模型的概念,提出了一种改进的SMA多维本构模型。该本构模型可以用来计算不同的应力和温度以及不同的加载过程下材料的变形。为了验证该多维模型的有效性,利用MATLAB软件编写程序,对三个不同的算例进行模拟计算,结果表明所提出的改进模型不仅可以很好的描述SMA一维情况的力学行为,也可以很好地定性描述SMA二维薄板的形状记忆效应和超弹性。
(4)完成了利用SMA形状记忆效应对混凝土梁进行修复的试验。将常温下为马氏体相的SMA丝和SMA绞线埋入混凝土梁中,制成SMA智能混凝土梁,并对试件进行四点弯曲试验,卸载后对SMA丝进行通电激励,利用SMA的形状记忆效应在相变过程中产生的恢复力来修复混凝土梁的裂缝宽度和挠度。观察实验结果可知,由于SMA丝会向周围混凝土散热的原因,使无粘结力SMA混凝土梁比有粘结力SMA混凝土梁修复效果要好；由于接触面积的问题,使配有SMA绞线的混凝土梁比配有单根SMA丝的混凝土梁的修复效果要好；由于配置在受拉区的钢筋阻碍了SMA的恢复,所以没有配置受拉区钢筋的混凝土梁比配置受拉区钢筋的混凝土梁的修复效果要明显。
(5)设计并制作出了一种新型的SMA-粘滞阻尼器,并完成相关力学性能试验。针对目前阻尼器耗能形式单一、无复位功能的问题,新研制的利用奥氏体状态SMA超弹性阻尼器不但具有高耗能,而且还具有自复位的性能。对该阻尼器进行了加载卸载试验,实验表明,随着加载频率和加载位移幅值的增大,阻尼器的耗能量显著增大；对一个八层简单钢框架结构模型应用复合阻尼器进行动力时程分析,模拟结果显示,复合阻尼器模型对结构的抗震作用明显,可以很好地降低结构的顶层位移和最大加速度。
Because of various disasters, such as earthquakes and Hurricane, etc., concrete structures often appear cracks and other damage phenomena in long-term use. How to improve the seismic capacity of concrete structures and how to repair and reinforce these structures become a much-needed engineering problem. Shape memory alloys (SMAs) have many characteristics such as shape memory effect, super-elasticity, high damping and resistance, etc., reflecting the properties of self-perception, self-diagnostics and adaptive capacity, and these properties are bound to make SMAs play a significant role in the field of vibration control and structural health monitoring. However, there are still many problems to be studied further about the SMAs, for instance, vibration control and concrete structure repair as well as constitutive models, especially the multi-dimensional constitutive model. In this paper, some basic researches about the constitutive model and applications in civil engineering for SMAs are conducted, and the main works of the paper are as follows:
(1) The basic mechanical properties of Austenite phase SMA wires with different diameters, different cycles, strain amplitudes, loading rates, temperature and other factors were studied by experimental method, and the resistance of the SMA wire at different imposed conditions were also studied. The results showed that loading magnitude, loading rate and temperature were the important parameters, which will affect the mechanical properties of SMA wires.
(2) Based on Kazuhiko Arai's theory for which the method of energy analysis was used, one-dimensional continuous dynamic model for the SMAs was established by taking into account the affects of the transformation of SMA and the variables of strain rate. In recent decades, scholars at home and abroad had made a great deal of research and analysis for the constitutive model of the SMA material. However, the most of the researched models were not pay attention to the influence of the strain rate, and use different relationship to express the process of loading and unloading. In order to prove the usefulness of the proposed model, the results calculated by using the proposed model were compared with the results by experiments, and the results were in good agreement.
(3) An improved three-dimensional constitutive model of the SMAs was established by using the yield surface equation of plasticity, combining with the idea of Brinsion's one-dimensional constitutive model and the concept of Boyd and Lagoudas model. The proposed constitutive model can be used to calculate the deformation of the SMAs under different temperatures, different stresses and different loading paths. In order to verify the validity of the three-dimensional model, the MATLAB software was used for programming and the simulation of three different examples, and the simulation results showed that the improved model can not only well describe the SMA's mechanical behavior under one-dimensional situation, but also be very well to qualitatively describe the SMA shape memory effect and superelasticity of two-dimensional sheet.
(4) A validation test for repairing cracks and deformation of concrete beams by using shape memory effect was conducted in a laboratory. The SMA smart concrete beams were made by embedding the SMA wires and SMA strands in the concrete beams, which all the SMAs were under martensite phase at room temperature. The specimens used for the four-point bending experiment were experimentally developed. After completely unloading, the embedded SMAs were drived by Joule heating to repair the cracks width and deflection in concrete beams by using the restoring force which generated in the process of phase transformation. The experimental results showed that the repairing effect for the damaged concrete beams without bond strength was better than those with bond strength because of the easy heat transmission from the SMA wires to the surrounding concrete. The repairing effect of the concrete beam with the SMA strands was better than that with a single SMA wire for the different contact areas. The repairing effect of the concrete beams without tension reinforcement was better than that with tension reinforcement for the tension reinforcement hindered the recovery of the SMAs.
(5) A novel type of SMA-viscous damper was designed and manufactured and the corresponding mechanical property test was conducted. At present, the damper has only a single form of energy consumption and no self-centrical function. The developed damper by using the superelastic of the austenitic SMAs has not only highly energy-consuming but also the performance of self-reset. The proposed damper was tested by loading and unloading, and experimental results showed that the energy consumption capacity of the damper could increase significantly by increasing the loading frequency and load displacement amplitude. A dynamic time-history analysis for a model of simple eight storey steel frame structure installed the proposed SMA dampers under earthquake excitations was carried out and the simulation results showed that the new SMA damper can well reduce the displacement and maximum acceleration at the top of the structure. This can be proved that the developed SMA damper can significantly reduce the vibration of this structure.
(1)对不同直径的奥氏体相SMA丝进行加载和卸载试验,研究不同的循环次数、应变幅值、加载速率、温度等因素对SMA丝力学性能的影响；并且研究了SMA丝在不同加载条件下的电阻特性。试验结果显示,加载幅值、加载速率和环境温度均是影响SMA丝力学性能的重要参数。
(2)基于Kazuhiko Arai的理论,利用能量分析的方法,并考虑了SMA相变和应变率变量的影响建立了SMA的一维连续动力学模型。近几十年来,国内外的学者对SMA材料的本构模型做了大量的研究分析,并相继提出了多种模型,但传统的SMA一维模型,多数不考虑应变率的影响,而且加载和卸载阶段要分别用不同的关系式表达。为了证明所提出模型的实用性,利用该模型计算的结果与试验结果进行对比,结果吻合良好。
(3)利用了塑性力学中的屈服面方程,并结合了Brinsion的一维本构模型的思想和Boyd和Lagoudas模型的概念,提出了一种改进的SMA多维本构模型。该本构模型可以用来计算不同的应力和温度以及不同的加载过程下材料的变形。为了验证该多维模型的有效性,利用MATLAB软件编写程序,对三个不同的算例进行模拟计算,结果表明所提出的改进模型不仅可以很好的描述SMA一维情况的力学行为,也可以很好地定性描述SMA二维薄板的形状记忆效应和超弹性。
(4)完成了利用SMA形状记忆效应对混凝土梁进行修复的试验。将常温下为马氏体相的SMA丝和SMA绞线埋入混凝土梁中,制成SMA智能混凝土梁,并对试件进行四点弯曲试验,卸载后对SMA丝进行通电激励,利用SMA的形状记忆效应在相变过程中产生的恢复力来修复混凝土梁的裂缝宽度和挠度。观察实验结果可知,由于SMA丝会向周围混凝土散热的原因,使无粘结力SMA混凝土梁比有粘结力SMA混凝土梁修复效果要好；由于接触面积的问题,使配有SMA绞线的混凝土梁比配有单根SMA丝的混凝土梁的修复效果要好；由于配置在受拉区的钢筋阻碍了SMA的恢复,所以没有配置受拉区钢筋的混凝土梁比配置受拉区钢筋的混凝土梁的修复效果要明显。
(5)设计并制作出了一种新型的SMA-粘滞阻尼器,并完成相关力学性能试验。针对目前阻尼器耗能形式单一、无复位功能的问题,新研制的利用奥氏体状态SMA超弹性阻尼器不但具有高耗能,而且还具有自复位的性能。对该阻尼器进行了加载卸载试验,实验表明,随着加载频率和加载位移幅值的增大,阻尼器的耗能量显著增大；对一个八层简单钢框架结构模型应用复合阻尼器进行动力时程分析,模拟结果显示,复合阻尼器模型对结构的抗震作用明显,可以很好地降低结构的顶层位移和最大加速度。
Because of various disasters, such as earthquakes and Hurricane, etc., concrete structures often appear cracks and other damage phenomena in long-term use. How to improve the seismic capacity of concrete structures and how to repair and reinforce these structures become a much-needed engineering problem. Shape memory alloys (SMAs) have many characteristics such as shape memory effect, super-elasticity, high damping and resistance, etc., reflecting the properties of self-perception, self-diagnostics and adaptive capacity, and these properties are bound to make SMAs play a significant role in the field of vibration control and structural health monitoring. However, there are still many problems to be studied further about the SMAs, for instance, vibration control and concrete structure repair as well as constitutive models, especially the multi-dimensional constitutive model. In this paper, some basic researches about the constitutive model and applications in civil engineering for SMAs are conducted, and the main works of the paper are as follows:
(1) The basic mechanical properties of Austenite phase SMA wires with different diameters, different cycles, strain amplitudes, loading rates, temperature and other factors were studied by experimental method, and the resistance of the SMA wire at different imposed conditions were also studied. The results showed that loading magnitude, loading rate and temperature were the important parameters, which will affect the mechanical properties of SMA wires.
(2) Based on Kazuhiko Arai's theory for which the method of energy analysis was used, one-dimensional continuous dynamic model for the SMAs was established by taking into account the affects of the transformation of SMA and the variables of strain rate. In recent decades, scholars at home and abroad had made a great deal of research and analysis for the constitutive model of the SMA material. However, the most of the researched models were not pay attention to the influence of the strain rate, and use different relationship to express the process of loading and unloading. In order to prove the usefulness of the proposed model, the results calculated by using the proposed model were compared with the results by experiments, and the results were in good agreement.
(3) An improved three-dimensional constitutive model of the SMAs was established by using the yield surface equation of plasticity, combining with the idea of Brinsion's one-dimensional constitutive model and the concept of Boyd and Lagoudas model. The proposed constitutive model can be used to calculate the deformation of the SMAs under different temperatures, different stresses and different loading paths. In order to verify the validity of the three-dimensional model, the MATLAB software was used for programming and the simulation of three different examples, and the simulation results showed that the improved model can not only well describe the SMA's mechanical behavior under one-dimensional situation, but also be very well to qualitatively describe the SMA shape memory effect and superelasticity of two-dimensional sheet.
(4) A validation test for repairing cracks and deformation of concrete beams by using shape memory effect was conducted in a laboratory. The SMA smart concrete beams were made by embedding the SMA wires and SMA strands in the concrete beams, which all the SMAs were under martensite phase at room temperature. The specimens used for the four-point bending experiment were experimentally developed. After completely unloading, the embedded SMAs were drived by Joule heating to repair the cracks width and deflection in concrete beams by using the restoring force which generated in the process of phase transformation. The experimental results showed that the repairing effect for the damaged concrete beams without bond strength was better than those with bond strength because of the easy heat transmission from the SMA wires to the surrounding concrete. The repairing effect of the concrete beam with the SMA strands was better than that with a single SMA wire for the different contact areas. The repairing effect of the concrete beams without tension reinforcement was better than that with tension reinforcement for the tension reinforcement hindered the recovery of the SMAs.
(5) A novel type of SMA-viscous damper was designed and manufactured and the corresponding mechanical property test was conducted. At present, the damper has only a single form of energy consumption and no self-centrical function. The developed damper by using the superelastic of the austenitic SMAs has not only highly energy-consuming but also the performance of self-reset. The proposed damper was tested by loading and unloading, and experimental results showed that the energy consumption capacity of the damper could increase significantly by increasing the loading frequency and load displacement amplitude. A dynamic time-history analysis for a model of simple eight storey steel frame structure installed the proposed SMA dampers under earthquake excitations was carried out and the simulation results showed that the new SMA damper can well reduce the displacement and maximum acceleration at the top of the structure. This can be proved that the developed SMA damper can significantly reduce the vibration of this structure.
引文
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