Characterisation and modelling of behaviour of a shape memory alloys

Shape memory alloys (SMAs) provide an attractive solid-state actuation alternative to engineers in various fields due to their ability to exhibit recoverable deformations while under substantial loads. This feature is of particular importance when utilising the smart composite materials reinforced by SMA. Many constitutive models describing this repeatable phenomenon have been proposed, where some models also capture the effects of rate-independent irrecoverable deformations in SMAs. This paper presents experimental investigations and numerical simulations on shape memory alloys. First, by consisting in determining the transformations of equiatomic Ti–Ni shape memory alloys by differential scanning calorimeter. Then, in order to validate a 3D numerical model of the pseudoelastic behaviour of SMA allowing a finite strain analysis, a set of experimental tests at various initial temperatures is proposed. Finally, the numerical simulations of uniaxial tests performed on shape memory alloys are presented and compared with experimental data, permitting the validation of the proposed modelling. Reasonably good correlation is obtained between the experimental and model predictions.     

含形状记忆合金(SMA)层柔性梁的振动频响特性

主要研究具有形状记忆合金（shape memory alloy,SMA）层的梁结构的动力响应特性，重点分析了应力诱发马氏体相变的影响。首先采用SMA超弹性分段线性的应力－应变模型表示SMA的超弹性本构特征；其次借助有关粘弹性材料结构动力学分析的复模量方法，推出简谐激励作用下SMA层的面内变形和应力之间的关系，提出具有SMA表层的简支梁横向稳态频率响应求解的数学模型。SMA超弹性非线性的影响使得结构产生复杂的动力学特征，如存在多值稳态解、跳跃性、周期3响应等。上述现象的发生与激振力幅值、温度的变化密切相关。     

柔性立管内衬层的非线性力学行为分析

由于聚合物材料的黏弹性，柔性立管内衬层易发生蠕变而"嵌入"至骨架层沟槽中，这一现象可能造成立管结构完整性缺失和骨架层撕裂等安全隐患，但现有的分析理论及有限元模型中，对材料的性质均是做了简单的线性假设，并未考虑聚合物材料的非线性黏弹性特性。基于PA11的试验测试结果，分别采用时间硬化非线性本构模型和考虑时温影响的多重积分非线性本构模型来表征材料性质，并对比两种模型与试验数据拟合情况。根据内衬层与骨架层的真实结构建立二维有限元数值模型，采用两种理论模型进行结构的非线性蠕变行为分析及对比。结果表明：非线性蠕变本构模型能够在在非稳态阶段和存在温度梯度的条件下，更加准确地预测的结构关键部位应变和应力，可为柔性立管内衬层的设计及评估提供借鉴和参考。     

A new hardening rule for metallic foam plasticity

Metallic foams are a class of porous materials widely used in the industry because of their advantages. In recent years, extensive studies on the behavior of these materials have been conducted. Several constitutive equations have also been presented and applied. This study proposes a new constitutive equation that predicts metallic foam behavior using the stress–strain curve in uniaxial compression. The proposed model offers a new functionality for work hardening and is evaluated for both isotropic and combined hardening. The constitutive equations are implemented in MATLAB and integrated using return mapping algorithm. The material parameters are identified using genetic algorithm and through a comparison of the experimental and numerical results. The aluminum foams discussed in this paper are the commercially available types, Foaminal and Alporas. The comparison of numerical and experimental results indicate that this new constitutive equation predicts foam behavior in a reasonable manner. Moreover, a good agreement is observed between the experimental and computational curves.     

搅拌摩擦焊中材料流动行为数值模拟的研究进展

搅拌摩擦焊是一种革命性的焊接技术。相比于熔化焊,搅拌摩擦焊在铝合金、镁合金等材料的焊接方面具有明显的优势。而搅拌摩擦焊过程中材料在熔化温度以下经历剧烈的塑性流动,这与传统焊接过程有着明显不同,因此非常有必要对搅拌摩擦焊过程中的材料流动行为进行研究。由于试验方法本身在空间与时间上的局限性,数值模拟成为研究搅拌摩擦焊过程中的材料流动行为的重要方法。分析搅拌摩擦焊过程中的物理过程,从数值方法、热源模型、边界摩擦模型、材料本构模型这四个方面介绍搅拌摩擦焊中材料流动行为的数值模拟的最新研究进展及相关应用。对当前搅拌摩擦焊材料流动模拟中存在的不足进行分析,提出未来研究中应关注的研究方向。     

A phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys

Shape memory alloys (SMAs) possess the distinctive ability to recover large mechanically-induced inelastic strains upon unloading, which is known as the pseudoelastic behavior. This paper deals with an extension of the phenomenological viscoplasticity theory, which has been developed by the author to depict the negative strain rate sensitivity, to model the macroscopic behavior of the phase transformation. Unlike most phenomenological models for the pseudoelasticity, the proposed model does not employ a kinetic law describing the evolution of the martensitic volume fraction and the transformation loading and unloading conditions but introduces two internal state variables concerned with the evolution of the elastic modulus and the back stress. The applicability of the constitutive model to SMAs is validated by comparing simulation results with experimental data on uniaxial and torsional loading reported in the literature. And then it is demonstrated that the same constitutive equations can be applied to model the highly nonlinear unloading behavior of solid polymer.     

功能梯度形状记忆合金梁纯弯曲的理论分析

功能梯度形状记忆合金(Functionally graded shape memory alloy, FG-SMA)是一种兼备功能梯度材料(Functionally graded material, FGM)和形状记忆合金(Shape memory alloy, SMA)特性的新型功能材料。根据复合材料力学和已有的SMA本构关系,通过充分考虑组分材料的应力应变关系,建立一个描述FG-SMA力学性能的宏观本构模型。应用该模型,对由弹性材料A和SMA组成的FG-SMA梁在纯弯曲载荷下的力学行为进行研究,详细讨论加载过程的弹性阶段和相变阶段,并给出相应的解析解。通过算例,对截面的应力分布、中性轴的位置和弯矩与曲率的关系进行详细讨论。结果表明,与普通FGM相比,FG-SMA可显著减小载荷作用下的最大应力,避免材料由于应力过大而导致的破坏。研究结果可为FG-SMA材料的设计和进一步研究提供一定的依据。     

Prediction of anisotropic material behavior based on multiresolution continuum mechanics in consideration of a characteristic length scale

New advanced materials have received more attention from many scientists and engineers because of their outstanding chemical, electrical, thermal, optical, and mechanical properties. Since the design of advanced material by experiments requires high cost and time, numerical approaches have always been of great interest. In this paper, finite element analysis of anisotropic material behavior has been carried out based on a multiresolution continuum theory. Gurson-Tvergaard-Needleman (GTN) damage model has been applied as a constitutive model at macroscale. Effects of plastic anisotropy on deformation behavior are assessed using Hill??s 48 yield function for anisotropic material and von Mises yield function for isotropic material, respectively. The material parameters for both isotropic and anisotropic damage models have systematically been determined from microstructure through unit cell modeling. The newly proposed linear approximation of local velocity gradient resolved the underdetermined problem of the previous homogenization process. Anisotropic material behaviors of a tensile specimen have been investigated by the proposed multiresolution continuum theory.     

An adjoint variable method for design sensitivity analysis of elastoplastic structures

Design sensitivity analysis of structural problems obeying an elastoplastic material behavior is developed using adjoint variable method. An elastoplastic constitutive equation with yield surface and kinematic hardening is considered to describe the material behavior. The traditional incremental procedure and its design variation need special treatments in order to predict the discontinuity of the structural response sensitivity because the contribution from the design sensitivity at the material transition point is lost during the calculation. In this study, discontinuities of the design variations at the material transition points are alleviated in the adjoint variable method. Analytical and numerical examples are used not only to demonstrate the developed sensitivity procedure but also to gain insights of numerical implementation for the design sensitivity analysis of the elastoplastic structure based on the adjoint variable method. The comparisons between adjoint variable and direct variation methods are also discussed.     

压电复合悬臂梁非线性模型及求解

基于功能材料的复合悬臂梁涉及多物理场耦合,其本构关系的非线性影响悬臂梁的输出及控制精度,采用Helmholtz Gibbs自由能关系建立压电材料的非线性本构模型。基于Boltzmann原理,该模型的内核函数由热能和Gibbs能量平衡决定。将模型与悬臂梁结构进行耦合,利用边界和初始条件导出压电复合悬臂梁的强解形式,并对强解进行弱化,采用Galerkin法对弱解进行离散化,利用三次B样条函数得到悬臂梁的数值解。研究结果表明,与已有文献的实验进行比较,所建立的压电材料非线性本构模型能够较好地预测复合悬臂梁的行为。     

Plastic continuum models for truss lattice materials with cubic symmetry

Analytical and numerical studies on continuum models for the elastic-plastic behavior of uniformly periodic lattice materials under multi-axial loading are presented in this paper. This study firstly investigates the basic topology of unit cell structures for three different lattice materials with cubic symmetry. By homogenizing the mechanical properties of these materials within the unit volume space, the equivalent continuum models are obtained with the internal variables which result in the mechanical and geometrical characteristics of discrete truss members at the micro-scale such as structural packing, axial stiffness, and material density. Therefore, in this study, the strain hardening was applied to the material model of individual truss members in a valuable effort to explain the plastic behavior of the homogenized lattice material. The expansion of pressure-dependent stress surface at the macro-scale level is estimated by analytical predictions, which are derived from the equivalent continuum models. Analytical predictions show good agreements with existing results obtained by finite element (FE) analyses.     

基于虚拟制备的金属橡胶各向异性本构特性研究

金属橡胶是一种各向异性的多孔材料，其本构特性常靠人工经验或试验获得，内部复杂的螺旋网状结构无法通过测试手段弄清机理。为此，运用虚拟制备技术与数值动态重构等手段，深入探究金属橡胶内部空间几何拓扑结构和弹簧微元间接触摩擦机理，结合扫描电子显微镜（Scanning electron microscope，SEM）中材料的微观形态进一步解释金属橡胶在宏观上的各向异性力学行为。通过引入弹簧微元组合概率分布以及空间局域性孔隙分布的概念，有效表征金属橡胶材料内部弹簧微元无序式网格互穿结构。充分考虑金属橡胶细观上的空间拓扑结构与微观摩擦机理参量，以及包含了材料形状、相对密度、金属丝直径、螺旋卷螺距、金属丝弹性模量等宏观制备参数，构建能够反映金属橡胶细观结构特征与宏观性能相一致的各向异性本构模型。通过与材料准静态压缩试验结果对比分析，采用残差分析定量验证。结果表明，提出的金属橡胶各向异性的本构模型，能够有效地反映与预测金属橡胶材料的复杂各向异性力学行为，为材料的深入研究与应用普及提供一定的理论指导。     

Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method

This paper is concerned with the application of the element-free Galerkin method to simulate the superelastic behaviour of shape memory alloys (SMA). The meshfree shape functions are derived from a moving least-squares interpolation scheme. A thermomechanical SMA constitutive law is used to describe the superelastic effect. The incremental displacement-based formulation for large deformation is developed by employing the meshfree shape functions and the continuum tangent stiffness tensor in the weak form of the equilibrium equations. By eliminating the unknown constrained nodal variables from the discrete equations, an effective approach is developed for the imposition of the essential boundary conditions. The numerical tests show that the proposed meshfree scheme can successfully reproduce the superelastic behaviour of shape memory alloys.     

A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels)

The determination of residual stresses induced by welding or heat treatment operations requires the use of complex models taking into account thermal, metallurgical and mechanical phenomena. In this paper, we propose a mechanical model in which each phase can follow its own constitutive law. This model also takes into account phase transformation plasticity, which is treated independently of the behavior of each phase. This model has been implemented into the French FEM code Castem 2000. The interest of the proposed method is that it allows one to mix any type of nonlinear behavior using Taylor homogenization hypothesis. There is no need to develop a theory to get the equations of the homogenized material law. Two numerical examples demonstrate the efficiency and the flexibility of this approach. The results obtained are compared to experimental values for a typical welding situation and a high-temperature response. This comparison seems to indicate that viscous effects in the materials have a significative influence on the residual stresses produced by welding.     

Principes variationnels et exploitation de mesures de champs en élasticité

Sometimes parameters pertaining to constitutive materials or to the overall definition of a mechanical structure need to be identified in an indirect manner from experimental measurements. Field measurements provide rich data and, as such, are particularly well suited to material or structural parameter identification problems. In this article, identification techniques specifically devised for the exploitation of field measurements are presented. The identification of distributed elastic moduli is used as a model problem, but other identification problems can be treated along similar lines. This article emphasizes the fact that one is by no means limited to using output least-squares cost functions for solving such identification problems. Indeed, the availability of field measurements allow to define other criteria, well-suited to this type of data and directly linked to fundamental variational principles. Most of this article is devoted to two criteria of this family, namely the error in constitutive equation and the reciprocity gap functional. Various illustrative examples, generally of a synthetic (i.e., purely numerical) nature are provided.     

Couette flows of rigid/plastic solids: analytical examples of the interaction of constitutive and frictional laws

The exact analytical solution under plane strain conditions is found for a hollow circular cylinder subjected to rotational friction on the inner surface and an uniform pressure on the outer surface. Two constitutive laws, a rigid/plastic hardening model with a saturation stress (Voce-Palm material) and a rigid/viscoplastic model (Bingham material), are considered as well as three interfacial laws, sticking, Coulomb sliding friction and Tresca shearing friction. The study focuses on general behavior of the solutions for various pairs of constitutive and interfacial models, such as existence and uniqueness and qualitative differences in solution. For the Voce-Palm material, it is shown that solutions do not exist for certain boundary conditions if only sticking or Coulomb friction are permitted. On the other hand, multiple solutions exist for certain boundary conditions if only sticking and Tresca friction are permitted. Existence is achieved under all boundary conditions if sticking and both frictional laws permitted simultaneously. Uniqueness and unambiguity are achieved if two interface selection principles are invoked: (1) sticking must occur if it is possible and (2) Coulomb sliding must occur if it is possible and sticking is not. Geometrical interpretation of results in the form of friction maps is provided to illustrate possible regimes of interfacial behavior for different boundary conditions.     

An Improved Approach for 3D Rolling Contact Fatigue Simulations with Microstructure Topology

Several 2D and 3D numerical models have been developed to investigate rolling contact fatigue (RCF) by employing a continuum damage mechanics approach coupled with an explicit representation of microstructure topology. However, the previous 3D models require significant computational effort compared to 2D models. This work presents a new approach wherein efficient computational strategies are implemented to accelerate the 3D RCF simulation. In order to reduce computational time, only the volume that is critically stressed during a rolling pass is modeled with an explicit representation of microstructure topology. Furthermore, discontinuities in the subsurface stress calculation in the previously developed models for line and circular contact loading are removed. Additionally, by incorporating a new integration algorithm for damage growth, the fatigue damage simulations under line contact are accelerated by a factor of nearly 13. The variation in fatigue lives and progression of simulated fatigue spalling under line contact obtained using the new model were similar to the previous model predictions and consistent with empirical observations. The model was then extended to incorporate elastic–plastic material behavior and used to investigate the effect of material plasticity on subsurface stress distribution and shear stress–strain behavior during repeated rolling Hertzian line contact. It is demonstrated that the computational improvements for reduced solution time and enhanced accuracy are indispensable in order to conduct investigations on the effects of advanced material behavior on RCF, such as plasticity.     

正交各向异性有限变形下材料的粘塑性力学行为的研究

给出正交各向异性有限变形下的统一粘塑性理论中的 Walker模型的本构表达并成功地利用参数控制法(GPM方法 )对其进行数值计算 ,推导出 Walker模型的隐式应力积分过程。在计算的基础上 ,研究了温度、应变率对材料的应力应变关系的影响 ,以及蠕变 ,应力松弛 ,热恢复及循环塑性这些高温下材料的粘塑性力学行为。     

Analyzing mechanical properties and nondestructive characteristics of brazed joints of NiTi shape memory alloys to carbon steel rods

Research is being conducted on the use of shape memory alloys, in particular NiTi, in civil engineering, due to the superelastic behavior of NiTi which can be used for damping. In this particular application, NiTi has to be joined to steel, which constitutes a major difficulty due to the considerably different properties of materials involved and the poor weldability of NiTi. Brazing was investigated for this application, since it is an economic and efficient process to joint dissimilar materials. This paper presents a study on the mechanical behavior in the superelastic regime of dissimilar NiTi/steel joints and the feasibility of a nondestructive method based on eddy currents to characterize the weld metal. Brazed joints in lap configuration were produced with a 20 % Ag braze alloy and tested under fatigue conditions in the superelastic regime. Lap joints of steel rods to NiTi ribbons have undergone up to 60 cycles of load/unload without rupture at a maximum load of the superelastic plateau close to the pull-out load of the joint. Measurements of the electrical impedance, with a helicoidal cylindrical coil along the lap joint, allowed the identification of the location of the joint, with a good spatial resolution characterizing the morphology of the brazed joints.     

SMA-based tension control block for metallic tendons

Metallic tendons are frequently used in arches and vaults to absorb the lateral thrusting forces due to gravity loads or inertial forces caused by an earthquake. Traditional tendons, however, have some limitations (e.g. sensitivity to temperature variations, buckling under compression, etc.). Shape memory alloys (SMAs) can be used to enhance the performances of metallic tendons both in service and seismic conditions. This is achieved with the tensioning control block (TCB) system. The basic components of TCB are pre-strained superelastic SMA wires, in series with the metallic tendon. The number and diameter of the SMA wires is selected based on the force levels to reach. The length is optimised with respect to the thermal behavior of the system. A number of theoretical and experimental studies have been conducted to fully understand the thermal and mechanical behavior of TCB. In the paper, the main outcomes of these studies are described.