Study on energy absorbing composite structure made of concentric NiTi spring and porous NiTi

An energy absorbing composite structure made of a concentric NiTi spring and a porous NiTi rod is investigated in this paper. Both NiTi spring and porous NiTi rod are of superelastic grade. Ductile porous NiTi cylindrical specimens are fabricated by spark plasma sintering. The composite structure exhibits not only high reversible force–displacement relation for small to intermediate loading but also high energy absorbing property when subjected to large compressive load. A model for the compressive force–displacement curve of the composite structure is presented. The predicted curve is compared to the experimental data, resulting in a reasonably good agreement.     

A numerical model based on Voronoi tessellation for the simulation of the mechanical response of porous shape memory alloys

In recent years, porous shape memory alloys have found several industrial applications. Thanks to biocompatibility, corrosion resistance, and superior mechanical properties, porous NiTi has been introduced as a promising candidate for being used as bone scaffolds. Since the mechanical response of a scaffold is of importance in order to prevent stress-shielding phenomena and trigger ossteointegration, predicting the mechanical response of these scaffolds before fabrication is inevitable. In this paper, a new mesoscale model based on Voronoi tessellation of three-dimensional space is presented for the simulation of porous shape memory alloys. To do so, after tessellating the space, some cells are selected randomly to be assigned as pores and a suitable constitutive model of dense SMA is attributed to the other cells. The model is validated against experimental findings reported in the literature demonstrating good agreement. In addition, the effects of number of cells, level of randomness, and the type of boundary conditions on the stress–strain response is assessed. The results show that in order to achieve desirable results, the number of cells and the value of randomness must be chosen greater than minimum corresponding values. As another result, the geometrically periodic model is more computationally efficient than the mechanically periodic one.     

多孔NiTi形状记忆合金的力学性能的实验研究

本文介绍了NiTi形状记忆合金的应用前景,利用MTS材料试验机研究经过热处理的多孔NiTi合金在压缩时的应力一应变曲线,结果表明,在一定的热处理后,多孔NiTi合金具有形状记忆效应,同样利用差热分析仪也证明了这一特性,因此,这种合金在一定程度上满足生物医用材料的医学使用条件。     

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.0005～15 s?1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。     

含电子相影响的多功能含能结构材料冲击压缩理论计算

为了更好地描述疏松态金属材料的冲击压缩特性,基于托马斯-费米原子统计模型,研究金属晶体中电子热行为对系统内粒子数、内能、压强等参数的影响,修改了描述疏松金属材料的Wu-Jing模型中的参数R的计算方法。结合混合物的冷能叠加原理,得到考虑电子相影响的疏松态混合物物态方程。并对不同配比的密实态W/Cu合金、不同疏松度的Al/Ni合金的典型多功能含能结构材料进行计算,获得其冲击压力-比容关系及冲击波速度-粒子速度关系,计算结果与实验结果吻合较好。结果表明,本文中模型对未反应条件下的金属材料冲击压缩特性预测较好;疏松材料的冲击压力-粒子速度关系并不呈现出密实材料的近似线性关系,其冲击压缩过程分为压实前和压实后2个明显的阶段;多功能含能结构材料的冲击压缩特性受材料孔隙率、材料配比等影响明显。     

Experimental characterization and micromechanical modeling of superelastic response of a porous NiTi shape-memory alloy

Porous shape-memory alloys are usually brittle due to the presence of various nickel-titanium intermetallic compounds that are produced in the course of most commonly used synthesizing techniques. We consider here a porous NiTi shape-memory alloy (SMA), synthesized by spark-plasma sintering, that is ductile and displays full shape-memory effects over the entire appropriate range of strains. The porosity however is only 12% but the basic synthesizing technique has potential for producing shape-memory alloys with greater porosity that still are expected to display superelasticity and shape-memory effects. The current material has been characterized experimentally using quasi-static and dynamic tests at various initial temperatures, mostly within the superelastic strain range, but also into the plastic deformation regime of the stress-induced martensite phase. To obtain a relatively constant strain rate in the high strain-rate tests, a novel pulse-shaping technique is introduced. The results of the quasi-static experiments are compared with the predictions by a model that can be used to calculate the stress-strain response of porous NiTi shape-memory alloys during the austenite-to-martensite and reverse phase transformations in uniaxial quasi-static loading and unloading at constant temperatures. In the austenite-to-martensite transformation, the porous shape-memory alloy is modeled as a three-phase composite with the parent phase (austenite) as the matrix and the product phase (martensite) and the voids as the embedded inclusions, reversing the roles of austenite and martensite during the reverse transformation from fully martensite to fully austenite phase. The criterion of the stress-induced martensitic transformation and its reversal is based on equilibrium thermodynamics, balancing the thermodynamic driving force for the phase transformation, associated with the reduction of Gibbs’ free energy, with the resistive force corresponding to the required energy to create new interface surfaces and to overcome the energy barriers posed by various microstructural obstacles. The change in Gibbs’ free energy that produces the driving thermodynamic force for phase transformation is assumed to be due to the reduction of mechanical potential energy corresponding to the applied stress, and the reduction of the chemical energy corresponding to the imposed temperature. The energy required to overcome the resistance imposed by various nano- and subnano-scale defects and like barriers, is modeled empirically, involving three constitutive constants that are then fixed based on the experimental data. Reasonably good correlation is obtained between the experimental and model predictions.     

Mechanically alloyed nanocrystalline iron and copper mixture: behavior and constitutive modeling over a wide range of strain rates

A comprehensive study on the response of a nanocrystalline iron and copper mixture (80% Fe and 20% Cu) to quasi-static and dynamic loading is performed. The constitutive model developed earlier by Khan, Huang & Liang (KHL) is extended to include the responses of nanocrystalline metallic materials. The strain rate and grain size dependent behaviors of porous nanocrystalline iron-copper mixture were determined experimentally for both static and dynamic loading. A viscoplastic model is formulated by associating the modified KHL model (representing the fully dense matrix behavior), and Gurson's plastic potential which provides the yield criteria for porous material. Simulations of uniaxial compressive deformations of iron-copper mixture with different initial porosity, grain size and at a wide range of strain rate (10⁻⁴ to 10³ s⁻¹) are made. The numerical results correlate well with the experimental observations.     

A multivariant micromechanical model for SMAs Part 1. Crystallographic issues for single crystal model

A general 3-D multivariant model for shape memory alloy constitutive behavior is further developed in this paper. The model is based on the habit planes and transformation directions for variants of martensite and uses a thermodynamic and micromechanics approach to develop the governing equations for thermomechanical response. The model accounts for the self-accomodating group structure exhibited during martensitic plate formation and utilizes this concept in its calculation of the interaction energy between variants. In this paper, we expand the multivariant model to consider the impact of inclusion shape on model predictions. A direction selection scheme is proposed for penny shaped inclusions and is based on the fact that several habit plane variants tend to cluster about one of the {011} or {001} poles. We also explore in detail the crystallographic basis of material response and the impact of specific crystallographic changes on the macroscopic single crystal constitutive response. Differences between type I and type II twinning are examined and it is shown that choice of the proper twinning type is essential to capture experimental data. The grouping structure is examined and several different options published for a NiTi alloy are implemented and results compared. Several concepts, i.e. artificial merging, exclusive and non-exclusive grouping, are raised to assist exploration of NiTi grouping possibilities. The anisotropy of the single crystal material response is illustrated and implications on higher level modeling are discussed. It is noted that properly representing the details of the crystallographic microstructure is crucial to obtaining accurate macroscopic stress–strain predictions.     

Identification of Drag Parameters of Flow in High Permeability Materials by U-Tube Method

The identification procedure of linear and nonlinear drag parameters of flow of liquid in high permeability materials by U-tube method is presented. The experimental technique is based on control of pressure in liquid oscillating in the U-tube including porous material and direct computer data acquisition. The macroscopic model which takes into account inertial forces, gravity, and interaction of oscillating liquid with porous material and U-tube walls is elaborated. The drag parameters are determined numerically for porous foams by fitting model predictions to experimental data. The methodology incorporates calibration of the U-tube system without sample of porous material, which is a necessary step to determine independently parameters of interaction of liquid with tube walls.     

Study on the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy based on a new crystal plasticity constitutive model

In this paper, a crystal plasticity based constitutive model (Yu et al., 2013) is extended to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy by considering the internal heat production. Two sources of internal heat productions are included in the proposed model, i.e., the mechanical dissipations of inelastic deformation and the transformation latent heat in the NiTi shape memory alloy. With an assumption of uniform temperature field in the alloy specimen, a simplified evolution law of temperature field is obtained by the first law of thermodynamics and the heat boundary conditions. An explicit scale-transition rule is adopted to extend the proposed single crystal model to the polycrystalline version. The capability of the extended polycrystalline model to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy is verified by comparing the predictions with the corresponding experimental ones. The comparison demonstrates that the proposed constitutive model considering the internal heat production predicts the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy fairly well.     

多孔材料填充薄壁结构吸能的相互作用效应

研究多孔材料填充薄壁结构的相互作用效应产生的机理，并建立了表征模型. 以泡沫 铝填充帽形结构为例，发现压溃的填充物分为致密区、过致密区和未变形区3个区域. 基于 理想可压缩假设建立了填充多孔材料分析模型，获得各区域体积变化和等效应变等关系；结 合薄壁结构超叠缩单元模型，对填充结构各组分的能量吸收进行了拆分. 研究表明，薄壁结 构的吸能略有增加，多孔材料的吸能增加40{\%}左右. 过致密区的形成是相互作用效应的 主要原因.     

The origin of nucleation peak in transformational plasticity

A typical stress-strain relation for martensitic materials exhibits a mismatch between the nucleation and propagation thresholds leading to the formation of the nucleation peak. We develop an analytical model of this phenomenon and obtain specific relations between the macroscopic parameters of the peak and the microscopic characteristics of the material. Although the nucleation peak appears in the model as an interplay between discreteness and nonlocality, it does not disappear in the continuum limit. We verify the quantitative predictions of the model by comparison with experimental data for cubic to monoclinic phase transformation in NiTi.     

Localization in NiTi tubes under bending

Nearly equiatomic NiTi can exhibit pseudoelastic behavior due to reversible solid-to-solid stress induced phase transformation at room level temperatures. In tension, the transformation leads to localized deformation of several percent that tends to spread at nearly constant stress. The deformation is recovered upon unloading while again localized deformation is exhibited. Under compression, while still pseudoelastic, the transformation strains are smaller, the stress is higher, the response is monotonic, and the deformation is essentially homogeneous. This study examines how this texture-driven, complex material asymmetry affects a simple structure: the bending of a tube. To this end, NiTi tubes are bent in a custom four-point bending facility under rotation control and isothermal conditions. The phase transformations lead to a closed moment-rotation hysteresis comprised of loading and unloading moment plateaus. During loading, localized nucleation of martensite results in a high curvature for the transformed sections of the tube and low curvature for the untransformed. Martensite, which corresponds to the higher curvature regime, spreads gradually while the moment remains nearly constant. The nucleation of martensite is in the form of bands inclined to the axis of the tube that organize themselves into diamond shaped deformation patterns on the tensioned side of the structure. The patterns are similar to those observed in bending of steel tubes with Lüders bands, however, for NiTi they develop only on the tensioned side due to the material asymmetry. A lower moment plateau is traced upon unloading with similar localized bending and the erasure of the diamond deformation patterns. This complex behavior was found to repeat for a number of temperatures in the pseudoelastic regime of NiTi with the moment-rotation hysteresis moving to higher or lower moment levels depending on the temperature.     

Simulations of localized thermo-mechanical behavior in a NiTi shape memory alloy

Previous experiments have shown that stress-induced martensitic transformation in certain polycrystalline NiTi shape memory alloys can lead to strain localization and propagation phenomena when loaded in uniaxial tension. The number of nucleation events and kinetics of transformation fronts were found to be sensitive to the nature of the ambient media and imposed loading rate due to the release/absorption of latent heat and the material's inherent temperature sensitivity of the transformation stress. A special plasticity-based constitutive model used within a 3-D finite element framework has previously been shown to capture the isothermal, purely mechanical front features seen in experiments of thin uniaxial NiTi strips. This paper extends the approach to include the thermo-mechanical coupling of the material with its environment. The simulations successfully capture the nucleation and evolution of fronts and the corresponding temperature fields seen during the experiments.     

Material instabilities of anisotropic saturated multiphase porous media

This paper analyses the material instability of fully saturated multiphase porous media. On account of the fact that anisotropic mechanical behaviours are widely observed in saturated and partially saturated geomaterials, the anisotropic constitutive model developed by Rudnicki for geomaterials is used to model the anisotropic mechanical behaviour of the solid skeleton of saturated porous geomaterials in axisymmetric compression test. The inertial coupling effect between solid skeleton and pore fluid is also taken into account in dynamic cases. Conditions for static instability (strain localisation) and dynamic instability (stationary discontinuity and flutter instability) of fully saturated porous media are derived. The critical modulus, shear band angle for strain localisation, and the bound within which flutter instability may occur are given in explicit forms. The effects of material parameters on material instability are investigated in detail by numerical computations.     

Micromechanical quantification of elastic,twinning, and slip strain partitioning exhibited by polycrystalline,monoclinic nickel–titanium during large uniaxial deformations measured via in-situ neutron diffraction

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffraction data of tensile and compressive deformations of monoclinic NiTi to ~18% true strain. A deeper understanding of tension–compression asymmetry in NiTi is gained by connecting crystallographic calculations of polycrystalline twinning strains with in situ diffraction measurements. Our analyses culminate in empirical, micromechanical quantification of individual elastic, accommodation twinning, deformation twinning, and slip contributions to the total macroscopic stress–strain response of a monoclinic material subjected to large deformations. From these results, we find that 20–40% of the total plastic response at high strains is due to deformation twinning and 60–80% due to slip.     

Removal of Small Particles from a Porous Material by Ultrasonic Irradiation

A study has been made of the removal of small particles from a porous material by means of ultrasonic irradiation. To that purpose a microscopic theoretical model has been developed to calculate the force of a traveling acoustic wave on a spherical particle attached to the wall of a smooth, cylindrical pore inside the porous material. This force was compared with the adhesion force between a small particle and a pore wall. From the comparison between the two forces the conditions were found, at which particles are detached from pore walls and removed from the porous material. The transformation of the results gained from the microscopic model to macroscopic property (permeability) of the porous material was made by means of the Kozeny relation. The aim is to be able to understand and predict qualitatively the influence of relevant parameters on the ultrasonic cleaning process. Predictions made with the theoretical model were compared with data from experiments carried out with ultrasound to remove particles from Berea sandstone. The agreement is reasonable.     

Rate-dependent domain spacing in a stretched NiTi strip

Superelastic fine-grained Nickel–Titanium (NiTi) polycrystalline shape memory alloys under tensile loading deform collectively via the nucleation and growth of macroscopic martensite domains. Recent experiments on a stretched NiTi strip showed that the number of nucleated domains (or the domain spacing) increased (decreased) with increasing applied stretching rate. It is also shown that the rate dependence of the domain formation is due to the coupling between the transfer of the locally released heat and the temperature dependence of the transformation stress. In this paper, a simple one-dimensional model is developed to quantify this effect of thermo-mechanical coupling on the observed domain spacing. Analytical relationship between the domain number, thermo-mechanical properties of the material, heat transfer boundary conditions and the externally applied strain rate is established. It is found that for the case of strong heat convection the domain spacing is inversely proportional to the applied stretching rate, while for the case of weak convection, the domain spacing is dictated by a power-law scaling with exponent ?0.5. The latter theoretical prediction agrees well quantitatively with the experimental data in stagnant air.