【作者】 薛立军；

【导师】 兑关锁；

【作者基本信息】 北京交通大学 ， 固体力学， 2014， 博士

【摘要】 功能梯度形状记忆合金(Functionally Graded Shape Memory Alloy,简称FG-SMA)是一种新兴的功能材料,其不仅具有功能梯度材料(Functionally Graded Material,简称FGM)的连续变化的材料特性,能够消除普通层合材料中的应力集中,还具有形状记忆合金(Shape Memory Alloy,简称SMA)的独特的形状记忆效应和超弹性。FG-SMA以其独特的物理力学性能引起了材料界的广泛关注和研究,并开始被应用到许多不同的实际工程领域,这些实际应用必须以该材料的物理力学性能为前提。本文对不同载荷作用下的不同结构形式的FG-SMA的力学性能进行了研究,主要内容如下：首先对由弹性材料和弹塑性材料组成的FGM简支梁受均布载荷作用的弹塑性变形行为进行分析,得到这种FGM梁受力变形的理论解。文中采用幂函数来描述FGM梁中组分材料体积分数的变化情况,应用细观力学平均化的方法确定材料的整体性能。这种方法可以避免直接假设FGM的整体性能的变化,而且可以考虑不同材料的泊松比的影响。此外,对于本文研究的FGM梁,只有一相材料(弹塑性材料)发生屈服,屈服函数完全由弹塑性材料的应力确定,而非FGM的整体应力。这种方法更加接近材料的真实情况,而已有的直接假设FGM整体性能变化的方法无法真实模拟该情况。通过充分考虑组分材料各自的本构关系,本文给出了FG-SMA复合材料梁在纯弯曲载荷作用下的受力变形行为的理论解。其中SMA的本构关系由分段线性模型确定,这种方法可以避免直接考虑马氏体体积分数的复杂的变化形式,有效的简化计算,并考虑了SMA的拉压不对称特性。数值计算结果显示,与普通FGM(不含SMA)梁相比,FG-SMA梁能显著降低梁内的最大应力。通过与实验数据对比可知,上述方法能够较好的模拟FG-SMA复合材料的力学行为。将热传导的理论与复合材料力学的理论相结合,本文对受梯度温度载荷作用的FG-SMA复合材料板的热力学性能进行了研究,给出了确定板内某位置处相变状态的相变函数和计算板内热应力的方法。研究结果表明,在不同的上下表面温度作用下,板内的温度场呈非线性的分布；由于温度和材料性能的不同,板内首先发生马氏体相变的位置和区域并不固定,需要研究特定温度下的相变函数来确定板内某位置处的相变状态。与已有文献对比显示,本文给出的研究FG-SMA执力学性能的方法是准确有效的。功能梯度多孔形状记忆合金(Functionally Graded Porous Shape Memory Alloy,简称FGP-SMA)是一种特殊的多孔SMA,其材料内部的孔隙率沿着梯度方向不断变化。本文应用细观力学的理论,充分考虑材料的微观组成和组分材料之间的相互作用,建立了一个FGP-SMA的细观力学本构模型,该模型可预测FGP-SMA在外力和温度等复杂载荷作用下的力学行为。应用该模型对FGP-SMA圆柱在单轴压缩下的力学行为进行了研究。通过对多孔SMA的相变机理进行研究,本文提出了一个新的考虑了静水压力的相变势函数,建立了一个FGP-SMA的宏观唯象模型。此外,针对FGP-SMA材料的内部结构特点,介绍了一种能够用于研究FGP-SMA力学性能的有限元建模方法。数值计算结果显示,与单一孔隙率多孔sMA的应力应变关系曲线类似,FGP-SMA的平均应力随着应变的增大而平滑的增大,没有明显的相变转折点。此外,有限元分析结果显示,材料内部的马氏体相变首先发生在孔隙周围的高应力集中区域,并逐渐向其它区域扩展。文中建立的细观力学模型、宏观唯象模型和有限元模型均能较好的模拟FGP-SMA的力学行为,其中细观力学模型的结果比宏观唯象模型的结果更接近实验数据,但宏观唯象模型在应用时更加简便,计算简单,无需迭代。更多还原

【Abstract】 Functionally Graded Shape Memory Alloy (FG-SMA) is a new kind of functional materials which possesses the excellent properties of both Functionally Graded Materials (FGM) and Shape Memory Alloys (SMA), such as the property of FGM to eliminate the stress singularity and the shape memory effect and pseudoelasticity of SMA. Due to its particular properties of physics and mechanics, FG-SMA has attracted wide attention and investigations. FG-SMA has potential applications in many fields, and all these applications should base on the mechanical properties of this material. In this article, the mechanical behaviors of FG-SMA with different structures under different loads are investigated in detail, and the main works are as follows:The elastoplastic behavior of a FGM simply supported beam consisting of elastic and elastoplastic materials under uniformly distributed load is investigated, and the theoretical solutions are obtained. A power function is used to describe the volume fractions of constituent materials, and the average property of the FGM is obtained by using the averaging method of micromechanics. This method can avoid the assumption of the varing properties of the whole material, and can consider the different Possion’s ratios of different constituent materials. What’s more, only the elastoplastic material in the FGM beam will yield, and the yield function is determined by the stress of the elastoplastic material only, rather than the average stress of the FGM. The method used in this work is closer to real material, while the method by assuming the variation of the whole properties of FGM can not describe this status really.Considering the constitutive relations of each constituent, theoretical results of the mechanical behavior of a FG-SMA beam under pure bending are given out. The constitutive relation of SMA is described by a piecewise linear model. This method can simplify the calculation effectively by avoiding directly considering the complex form of the martensite volume fraction. It can be studied that compared to common FGM, FG-SMA can decrease the maximum stress greatly. Compared to experimental results, it can also be learned that this method can describe the mechanical behaviors of FG-SMA very well.By combining the heat conduction theory with the theory of the mechanics of composite materials, the thermomechanical properties of a FG-SMA plate under graded temperature load is investigated, and a transformation function which can be used to determine the transformation status of a position in the plate is given out, as well as the method to calculate the thermal stress in the plate. The numerical results show that under different surface temperatures, the temperature in the plate distributes nonlinearly along the thickness direction. The position at which the martensite transformation takes place first is not fixed due to the difference of the temperature and material properties at different position of the plate, so it needs to consider the transformation function under certain surface temperatures to determine the transformation areas. Compared to the existing results, it can be learned that the method provided in this work is valid to study the thermal properties of FG-SMA.Functionally Graded Porous Shape Memory Alloy (FGP-SMA) is a new kind of porous SMA, in which the porosity varies along the gradient direction. According to the theory of mesomechanics, considering the interaction of the components, a mesomechanical constitutive model of FGP-SMA is established, which can be used to describe the mechanical behavior of FGP-SMA under complex loads, including stress and temperature. With this model, the mechanical behavior of a FGP-SMA cylinder under uniaxial compression is investigated.By investigating the transformation mechanism of porous SMA, a new transformation function considering the effect of hydrostatic stress is provided, as well as a macro phenomenological model of FGP-SMA. What’s more, a new method for creating the finite element model of FGP-SMA is also given out. It can be studied from the numerical results that similar to common porous SMA, the average stress of FGP-SMA increases smoothly with the increase of strain, without an obvious turning point of transformation. Furthermore, the finite element results show that the transformation starts from the areas around the porous where the stress singularity is high, and then expand to other areas.The mesomechanical model, the macro phenomenological model and the finite element model provided in this work all can describe the mechanical behaviors of FGP-SMA very well, and the results of the mesomechanical model have more in common with the experimental data than the results of the macro model, while the macro model can simplify the calculation, avoiding iteration.更多还原