A bi-crystal aggregate model of pseudoelastic behaviour of shape-memory alloy polycrystals

A multi-scale model of stress-induced phase transformation and martensite variant reorientation in shape memory alloy (SMA) polycrystals is developed. It is proposed to include neighbouring-grain interaction in a simple manner by introducing an intermediate bi-crystal level into the sequential averaging scheme for SMA. The constitutive relationships are defined by specifying the free energy and dissipation functions. At the level of a single grain, the rate-independent dissipation function is used that incorporates the dissipation due to forward and reverse austenite-to-martensite transformation as well as reorientation of martensite variants. The global response of the model is simulated numerically by minimizing the total incremental energy supply. Specific examples are calculated for a NiTi polycrystal for proportional and non-proportional loading paths.     

含SMA约束层的复合材料矩形板的阻尼能力分析

研究由形状记忆合(shape memory alloy，简写为SMA)SMA约束层、SMA纤维混杂叠层材料构成的复合材料矩形板的阻尼性能。采用多胞模型和细观力学阻尼分析方法，分别预测叠层复合材料单层的弹性性能和阻尼性能，在叠层材料中计入横向剪切变形的影响。在导出矩形板的应变能和耗散能的基础上，根据最大应变能理论建立板的模态阻尼比的数学表达式。数值结果表明，文中提出的含有SMA约束层的SMA纤维叠层复合材料的集成阻尼设计方法，是一种有效的阻尼增强方案。     

Organic Polycrystalline Scintillators with Improved Characteristics

The properties of organic polycrystalline scintillators produced by different methods are studied. It is shown that polycrystals in the shape of plates, made by compacting powders of solution-grown organic crystals at premelting temperatures, exhibit better characteristics. Their energy resolution for and particles is higher by 40% and, for X-rays, by 20–25% than the resolution of polycrystals produced by other methods. The scintillation properties of such polycrystals are comparable to the characteristics of organic single crystals.     

Residual deformation of active structures with SMA actuators

In this paper, a three species thermomechanical constitutive model for Shape Memory Alloy (SMA) actuators, based on previous work by Boyd and Lagoudas (Proceedings of the 4th International Symposium on Plasticity and its Current Applications, Baltimore, MD, 19–23 July, 1993) is developed. The three species that contribute to the specific free energy of SMA are: self-accommodated martensite, detwinned martensite and austenite. The total martensitic volume fraction is decomposed into two parts: self-accommodated and detwinned martensite. The dissipation potentials, utilized for the evolution of the volume fractions of the two parts of martensite, are explicity given for 1-D. The concept of critical stress associated with detwinning of self-accommodated martensite, is introduced to incorporate the observed phenomenon during cooling of SMA actuators. The constitutive model described above is well suited for applications in active structures, because the maximum amount of the detwinned martensitic volume fraction is related to the current stress and temperature of the SMA actuator. This maximum amount of volume fraction can be reached during cooling in a constrained structural environment and is determined by the evolution of the internal variables. A prototype structural example, which is a flexible cantilever beam with an externally attached SMA actuator, is used to demonstrate the capability to predict the residual deformation and stress upon cooling.     

Elasto-plastic micromechanical model for determination of dynamic stiffness and real contact area from ultrasonic measurements

The interaction of ultrasonic waves with rough surfaces in contact is sensitive to the micromechanics of the contacts and to the topography of the surfaces. A continuous effort to develop a link between ultrasonic measurements and interfacial properties has evolved to the extent that elasto-plasticity occurring during loading can now be taken into account. Here, a state-of-the-art model is critically revisited in light of recent results on the micromechanics of elasto-plastic asperities in contact during unloading. A new probability density function of the asperity height is derived, which takes into account plastic deformation. This function is used to evaluate the pressure during unloading as a function of the relative approach between the mean planes of the surfaces. It is also shown that this relation can be cast in terms of the probability density function prior deformation, provided that a suitable transformation variable is utilized. These results are used to obtain a new expression for the dynamic stiffness of the elasto-plastic interface which determines the response of the latter to an incident wave. Finally, some results illustrating the behavior of the static and dynamic interfacial stiffness during a complete loading–unloading cycle are presented.     

Finite Element Method on Shape Memory Alloy Structure and Its Applications

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy(SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software.This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation.Two scalars,named by phase-transition modulus and equivalent stiffness,are defined to make it easy to establish and implement the finite element method for a SMA structure.An incremental constitutive equation is developed to formulate the relationship of stress,strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness.A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus,stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition.A finite element equation is established to express the incremental relationship of nodal displacement,external force and temperature change in a finite element discrete structure of SMA.The incremental constitutive equation,phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure.Two SMA structures,which undergo large and uneven deformation,are numerically simulated by the supposed finite element method.Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation,and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.     

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.     

比例/非比例加载路径下5754O汽车用铝合金板各向异性变形行为的精确解析

随着越来越高的汽车轻量化需求,铝合金板在现代汽车工业中的应用越来越广。在不同加载路径下,包括比例和非比例加载,5754O铝合金板在塑性成形过程中具有复杂的各向异性规律。试验表明5754O铝合金板的各向异性规律随变形量的增加会发生改变,因此在常参数屈服准则理论框架下,基于传统的单一曲线假设难以对5754O铝合金板在整个塑性变形过程中的各向异性行为进行精确描述。鉴于上述问题,并同时考虑到大变形过程中材料变形的稳定性,对Yld2000-2d屈服准则进行改进。基于改进的Yld2000-2d屈服准则和单一曲线假设推导不同方向的单向拉伸应力应变曲线,并与试验结果进行了对比。结果表明,与原始的Yld2000-2d屈服准则不同,基于改进的Yld2000-2d屈服准则,传统的单一曲线假设仍然适用于5754O铝合金板各向异性问题。给出不同强化方式在比例加载路径下的统一性和非比例加载路径下的分散性证明。基于改进的Yld2000-2d屈服准则和等向强化和混合两种强化方式,推导非比例加载路径下板料的应力应变曲线。基于试验结果,验证了推导的理论曲线的精度。实现了5754O铝合金板在比例和非比例加载路径下变形行为的精确描述,为其工业应用提供了重要的理论支撑。     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

Imaging dislocations in ice

Three techniques have been used to study dislocations in ice: etch pitting-replication, transmission electron microscopy, and X-ray topography (XT). It is shown that, because ice is a weak absorber of X-rays and can be produced with a low dislocation density, allowing relatively thick specimens to be studied, the most useful technique is XT. The observations that have been made with conventional XT are briefly outlined. However, the introduction of high-intensity synchrotron radiation, with its concomitant short exposure times, showed that images obtained through conventional XT observations were of dislocations that had undergone recovery. The important dynamic observations and measurements that have been made using synchrotron X-ray topography are presented. Dynamic synchrotron X-ray topography observations of ice single crystals undergoing deformation in situ have shown that slip mainly occurs by the movement of screw and 60 degrees (1/3) [1120] dislocations on the basal plane, although non-basal slip by edge dislocations can also occur. The operation of Frank-Read and other dislocation multiplication sources have been clearly demonstrated and dislocation velocities have been measured. In contrast, in polycrystals, dislocation generation occurred at grain boundaries where there are stress concentrations before lattice dislocation generation mechanisms operate. Faulted dislocation loops have been determined to be mainly interstitial in both polycrystals and single crystals.     

Anomalous dynamic elastic-plastic response of a galerkin beam model

A study of the anomalous motion of an elastic—plastic beam under short pulse loading is presented. The geometric nonlinearity due to axial end constraints is taken into account. We apply the Galerkin method to the governing partial differential equation of the transverse motion to obtain a general model of n degrees of freedom (nDoF). The results of elastic—plastic deformation analysis and dynamic response for the 2DoF model of a pin-ended beam are presented. The regular and irregular motions of the 2DoF model for the pin-ended beam are examined by various methods including time history, phase diagram, Lyapunov characteristic exponent and power spectral density.     

SMA丝缠绕角对扭力驱动器驱动性能影响的试验研究

在智能结构的驱动系统研究中,形状记忆合金(SMA)以其独特的力学性能倍受关注。将含有预拉伸变形的SMA丝与薄壁圆管复合,能够构成具有扭转变形输出或转矩输出功能的驱动器,为飞行器翼面操纵系统等提供新的设计思路。在SMA扭力驱动器中,SMA丝的缠绕角是影响驱动器驱动能力的一个重要参数。针对缠绕角分别为40°、45°、55°、60°和75°的一组驱动器,采用试验手段,获得了自由状态、完全约束状态和弹性约束等三种状态下,上述驱动器的温度－缠绕角－扭转角(或转矩)等多组关系曲线,得到了当缠绕角为60°时,驱动器有最大扭转角和最大转矩的试验结果。研究结果对深入探索SMA扭力驱动器的力学模型和驱动器结构参数的优化具有重要的参考价值。     

The effect of crystallographic orientation on fatigue and fretting-initiated fatigue of copper single crystals

The effect of varying the crystallographic orientation of copper single crystals on their fatigue and fretting-initiated fatigue behavior was studied. Single crystal fatigue specimens were tested under both uniaxial fatigue loading and uniaxial fatigue loading with superimposed fretting. The results show the extreme degree of anisotropy of the individual grains and the strong dependence of both fatigue life and fretting-fatigue life on crystallographic orientation and they help to provide a base on which further models can be built, in order to understand the complexities involved in polycrystalline materials. It is suggested that surface deformation characteristics, slip mode and slip character are extremely important variables in the frettingfatigue process.     

Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells

In this paper, an analytical solution is provided for the postbuckling behaviour of moderately thick plates and shallow shells made of functionally graded materials (FGMs) under edge compressive loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell, according to a power law distribution of the volume fraction of the constituents. The fundamental equations for moderately thick rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection and high-order shear deformation theory for moderately thick plates. The solution is obtained in terms of mixed Fourier series and the obtained results are compared with those of the Reissner–Mindlin's theory for moderately thick plates and the classical theory ignoring transverse shear deformation. The effect of material properties, boundary conditions and thermomechanical loading on the buckling behaviour and the associated stress field are determined and discussed. The results reveal that thermomechanical coupling effects and the boundary conditions play a major role in dictating the response of the functionally graded plates and shells under the action of edge compressive loads.     

Cyclic loading of beams based on the Prager and Frederick–Armstrong kinematic hardening models

The kinematic hardening theory of plasticity based on the Prager and Frederick–Armstrong models are used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. The beam material is assumed to follow non-linear strain hardening property. The material's strain hardening curves in tension and compression are assumed to be both identical for the isotropic material and different for the anisotropic material. A numerical iterative method is used to calculate the stresses and plastic strains in the beam due to cyclic loadings. The results of the analysis are checked with the known experimental tests. It is concluded that the Prager kinematic hardening theory under deformation controlled conditions, excluding creep, results into reversed plasticity. The load controlled cyclic loading under the Prager kinematic hardening model with isotropy assumption results into reversed plasticity. Under anisotropy assumption of tension/compression curve, this model predicts ratcheting. On the other hand, the Frederick–Armstrong model predicts ratcheting behavior of the beam under load controlled cyclic loading with non-zero mean load. This model predicts reversed plasticity under the load controlled cyclic loading with zero mean load, and deformation controlled cyclic loading.     

Fatigue resistance of SMA-martensite bars subjected to flexural bending

The fatigue resistance of Ni–Ti shape memory alloy (SMA)-martensite bars in bending subjected to large deformation cycles has been experimentally evaluated. Firstly, fatigue tests under constant displacement amplitude have been carried out, at two different frequencies of loading. Then, the cumulative fatigue damage and fatigue life prediction of specimens loaded under variable load conditions have been investigated. Finally, the effect of low-cycle-fatigue (LCF) and plastic deformations on subsequent high-cycle-fatigue (HCF) has been studied.The experimental results point out that the frequency of loading (i.e. temperature) significantly affects the fatigue life of the specimens. The damage accumulation process seems to follow the “Miner” linear damage theory for low-to-high (L–H) loading sequences, while the same does not hold for high-to-low (H–L) loading sequences. Surprisingly, a small fraction of LCF life consumption seems to enhance the subsequent HCF limits.     

Polycrystalline behavior analysis of pure magnesium by the homogenization method

In this study, mechanical behaviors of pure magnesium polycrystals are numerically investigated. The homogenization method, which combines the crystal and macroscopic scales, is introduced to include the effect of crystalline scale behaviors. The polycrystal plasticity model modified for pure magnesium, in which twinning is considered as asymmetric slip-like deformation, is utilized as a constitutive equation. Within this framework, numerical convergence analyses are conducted, and a representative volume element to present realistic deformation of pure magnesium is investigated. Second, polycrystalline behaviors of pure magnesium are investigated. The present approach is shown to reproduce the typical phenomena induced by crystalline scale structure in pure magnesium: nonuniform strain distribution, asymmetric crystal lattice orientation, strength differential effect, and strongly anisotropic initial and subsequent yield surfaces.     

Numerical analysis of phase transformations and residual stresses in steel cone-shaped elements hardened by induction and flame methods

Numerical model simulations of induction and flame hardening and hardening after furnace heating are presented in the paper. In the models the coupling between electromagnetic, thermal field, phase transformations field and stress field are considered. The electromagnetic field is calculated from Maxwell's equations taking into account changes in the conductivity and permeability of the material during the process. The thermal field in the conducting materials is calculated on the basis of Fourier—Kirchhoff equation. The kinetics of diffusion-dependent phase transformation and martensitic transformations are coupled to the transient heat flow. The fractions of phases created during the phase transformations are calculated by use of TTT-heating diagrams and TTT-cooling diagrams. Thermoplasticity theory with isotropic hardening was applied to calculate the internal stresses resulting from phase changes as well as temperature variations. The changes in the thermomechanical parameters of the material, as a function of phase content and thermal field, were considered in the stress calculations. The numerical calculations have been made for surface-hardened cone-shaped steel machine parts.     

Elastoplastic buckling of rectangular plates in biaxial compression/tension

This paper examines the elastoplastic buckling of a rectangular plate, with various boundary conditions, under uniform compression combined with uniform tension (or compression) in the perpendicular direction. The analysis is based on the standard linear buckling equations and material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity. A detailed parametric study has been made for Al 7075 T6 over a range of plate geometries (a/b=0.25–4,a/h≈20–100) and with three sets of boundary conditions (four simply supported boundaries and the symmetric combinations of clamped/simply supported sides). For sufficiently thin plates we recover with both theories the classical elastic results. However, for thicker plates there is a remarkable difference in the buckling loads predicted by these two theories. Apart from the expected observation that deformation theory gives lower critical stresses than those obtained from the flow theory, we report on the existence of an optimal loading path for the deformation theory model. Buckling loads attained along the optimal path—specified by particular compression/tension ratios—are the highest possible over the entire space of loading histories. By contrast, no similar optimum has been found with the flow theory. This discrepancy in the buckling behaviour, obtained from the two competing plastic theories, provides a possibly new illustration of the plastic buckling paradox.