Thermomechanical coupling in shape memory alloys under cyclic loadings: Experimental analysis and constitutive modeling

In this paper, we examine the influence of thermomechanical coupling on the behavior of superelastic shape memory alloys subjected to cyclic loading at different loading rates. Special focus is given to the determination of the area of the stress-strain hysteresis loop once the material has achieved a stabilized state. It is found that this area does not evolve monotonically with the loading rate for either transient or asymptotic states. In order to reproduce this observation analytically, a new model is developed based on the ZM model for shape memory alloys which was modified to account for thermomechanical coupling. The model is shown to predict the non-monotonic variation in hysteresis area to good accord. Experimentally observed variations in the temperature of SMA test samples are also correctly reproduced for lower strain rates.     

A decoupled modal analysis for nonlinear dynamics of an orthotropic thin laminate in a simply supported boundary condition subject to thermal mechanical loading

In this paper, we analyze the nonlinear dynamic response of an orthotropic laminate in a simply supported boundary condition subject to thermal and mechanical loading. The equation of motion for the laminate’s deflection is obtained in a decoupled Duffing equation by means of a Galerkin-type method without Berger’s approximations. The Duffing equation incorporates an arbitrary thermal field, with both the in-plane and transverse temperature variations in a steady-state and a transient state. The formulation indicates that the transverse temperature variation produces an additional pressure load, while the in-plane temperature variation affects the system frequency. The equation allows for characterization of the laminate behaviors in nonlinear thermal buckling, thermal vibration and thermal mechanical response.     

Infrared temperature sensing of mechanically loaded specimens: Thermal analysis

Infrared temperature-sensing techniques have the major advantages of virtually no interference of the sensor with the sensed phenomenon and fast inherent response. On the other hand, infrared temperature sensing, as a superficial measurement technique, does not indicate the specimen's core temperatures, and hence a complementary thermal analysis is required. A thermal analysis of surface temperature measurements of a mechanically loaded cylindrical specimen is presented. The specimen is modeled as an infinite cylinder, suddenly exposed to a uniformly distributed volumetric heat source. This heat source results from the conversion of mechanical energy into thermal energy. A closed-form solution is obtained and numerical examples are given for metallic and polymeric specimens. The current analysis provides the upper boundaries for temperature differences between the core and the surface temperatures when compared with the actual problem of a finite specimen. It is shown that surface temperature measurement is a good indication of the core temperature for metallic specimens but may lead to some poor results in the case of polymeric specimens. It is found that the transient thermal response of the infinite cylinder to sudden heating behaves like a first-order process. In the case of cyclic loading, the typical time scale of loading is found to be at least two orders of magnitude shorter than the typical time scale of heat transfer. Hence, the specimen is affected by the average power of heat generation, and not by the instantaneous effect of heating within a single loading cycle.     

Fast prediction of the fatigue behavior of short-fiber-reinforced thermoplastics based on heat build-up measurements: application to heterogeneous cases

Short-fiber-reinforced thermoplastics components for structural applications are usually very complex parts as stiffeners, ribs and thickness variations are used to compensate the quite low material intrinsic stiffness. These complex geometries induce complex local mechanical fields but also complex microstructures due to the injection process. Accounting for these two aspects is crucial for the design in regard to fatigue of these parts, especially for automotive industry. The aim of this paper is to challenge an energetic approach, defined to evaluate quickly the fatigue lifetime, on three different heterogeneous cases: a classic dog-bone sample with a skin-core microstructure and two structural samples representative of the thickness variations observed for industrial components. First, a method to evaluate dissipated energy fields from thermal measurements is described and is applied to the three samples in order to relate the cyclic loading amplitude to the fields of cyclic dissipated energy. Then, a local analysis is detailed in order to link the energy dissipated at the failure location to the fatigue lifetime and to predict the fatigue curve from the thermomechanical response of one single sample. The predictions obtained for the three cases are compared successfully to the Wöhler curves obtained with classic fatigue tests. Finally, a discussion is proposed to compare results for the three samples in terms of dissipation fields and fatigue lifetime. This comparison illustrates that, if the approach is leading to a very relevant diagnosis on each case, the dissipated energy field is not giving a straightforward access to the lifetime cartography as the relation between fatigue failure and dissipated energy seems to be dependent on the local mechanical and microstructural state.     

A constitutive model for shape memory alloys accounting for thermomechanical coupling

This paper presents a generalized Zaki-Moumni (ZM) model for shape memory alloys (SMAs) [cf. Zaki, W., Moumni, Z., 2007a. A three-dimensional model of the thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 55, 2455-2490 accounting for thermomechanical coupling. To this end, the expression of the Helmholtz free energy is modified in order to derive the heat equation in accordance with the principles of thermodynamics. An algorithm is proposed to implement the coupled ZM model into a finite element code, which is then used to solve a thermomechanical boundary value problem involving a superelastic SMA structure. The model is validated against experimental data available in the literature. Strain rate dependence of the mechanical pseudoelastic response is taken into account with good qualitative as well as quantitative accuracy in the case of moderate strain rates and for mechanical results in the case of high strain rates. However, only qualitative agreement is achieved for thermal results at high strain rates. It is shown that this discrepancy is mainly due to localization effects which are note taken into account in our model. Analyzing the influence of the heat sources on the material response shows that the mechanical hysteresis is mainly due to intrinsic dissipation, whereas the thermal response is governed by latent heat. In addition, the variation of the area of the hysteresis loop with respect to the strain rate is discussed. It is found that this variation is not monotonic and reaches a maximum value for a certain value of strain rate.     

Assessment of Non-Adiabatic Behaviour in Thermoelastic Stress Analysis of Small Scale Components

The classical thermoelastic equation and the generalized heat conduction equation are developed to deal with a non-adiabatic response in thermoelastic stress analysis. A FE simulation procedure is set up to solve the heat conduction equation over a range of loading frequencies. A small disc (20 mm diameter) loaded under three-point diametric compression is used to examine the effect of in-plane heat conduction. As the disc has regions of zero, moderate and high stress gradients it is an ideal component for this analysis. A regime is developed that provides a basis for an assessment of the nature of the response and allows a minimum loading frequency to be identified so that adiabatic behaviour is obtained. This validity of this approach is demonstrated on steel disc of 20 mm diameter. A special loading device has been designed to obtain the three-point loading and a recently introduced Instron Electropuls test machine is used to achieve the high levels of cyclic loading required for the adiabatic conditions.     

一种考虑非比例附加损伤的多轴低周疲劳模型

在实际工作环境中,机械结构往往承受着多轴非比例循环载荷.相比多轴比例循环加载,多轴非比例循环加载由于产生了附加强化现象,造成机械结构疲劳寿命下降.通过分析薄壁圆筒管件在非比例加载工况下应力应变变化规律和发生破坏位置,本文基于临界面法提出一种考虑多轴非比例附加损伤的疲劳模型.该模型将最大剪切应变幅平面作为临界面,提出一个新的附加强化因子,结合临界面上切应变幅和正应变幅组成新的多轴疲劳损伤参量.此参量不仅考虑了非比例加载下临界面上正应变幅和切应变幅对材料造成的疲劳损伤,还考虑到应变路径的变化和材料非比例加载敏感特性对材料疲劳寿命的影响.考虑到实际情况下模型所需材料附加强化系数有时难以获得的情况,给出了材料附加强化系数的有关近似计算公式.只需要材料基本力学参数便可得到材料附加强化系数,方便工程实际应用.采用8种材料的多轴疲劳寿命数据对提出的新模型进行检验,结果表明所提出的新模型与传统多轴疲劳模型相比预测寿命精度更高.      

A decoupled modal form Duffing equation for an orthotropic laminate in a clamped boundary condition with thermal diffusion

The non-linear thermo-elasticity response of an orthotropic laminate in a clamped boundary condition is analyzed by means of the method of weighted residuals for its behaviors subject to thermal and mechanical loading. The equation of motion for the laminate's deflection is obtained in the form of a decoupled modal form Duffing equation, without Berger's approximation. The thermal field, with both the in-plane and transverse temperature variations, is incorporated in both a steady-state and transient state. The formulation indicates that a transverse thermal field with a temperature rise produces a load onto the laminate, while the in-plane temperature variation affects the system frequency and stability. We demonstrate the numerical results of the modal response of an isotropic laminate for the thermal buckling and vibration.     

A Study on the Evaluation of the Fracture Process Zone in CCNBD Rock Samples

The safety of many civil and mining concrete and rock structures including pre-existing crack networks is fundamentally affected by the mechanical behaviour of the material under static and cyclic loading. In cyclic loading case, cracks can grow at a lower load level compared to the monotonic case. This phenomenon is called fatigue due to subcritical crack propagation and depends on the behaviour of the fracture process zone (FPZ). This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I (tensile) fracture toughness response to static and cyclic loading and relevant FPZ. The FPZ and fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (K _IC ) of 42 % was obtained for the highest amplitude increasing cyclic loading test. Detailed scanning electron microscope (SEM) examinations were performed on the surfaces of the tips of the chevron notch cracks, revealing that both loading methods cause FPZ development in the CCNBD specimens. When compared with monotonic FPZ development, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, while smooth and bright cracks along cleavage planes were formed under static loading. Further, the SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular and transgranular subcritical fracturing.     

FINITE ELEMENT ANALYSIS OF CARDIAC MYOCYTE DEBONDING AND REORIENTATION DURING CYCLIC SUBSTRATE STRETCH EXPERIMENTS

The substrate stretch experiment, which is carried out on several kinds of adherent cells, is usually used to catch the physiological variation and morphological response to cyclic substrate deformation. In this paper, stretch loading was exerted on cardiac myocytes cultured on silica substrates using a custom-made substrate stretch device. The effect of stretch on the alignment orientation of cardiac myocytes was studied through morphocytological statistics. Under cyclic stretch stimulus, the long axes of cardiac myocytes oriented perpendicularly to the stretch direction for continuous stretch acting. However, the mechanism underlying these behaviors is not well understood from such in vitro tests. Finite element （FE） model was developed in the analysis to investigate these behaviors. Xu-Needleman formulation was used to define the interaction behavior for contact surfaces between cell and substrate. The role of cell viscoelasticity nature is studied in adherent cell debonding with the substrate and aligning perpendicular to the stretch direction during long time cyclic stretch stimulation. There were four different strain magnitudes considered in the simulation to find out the cell debonding affected by the cyclic strains. The potential role of cyclic strain frequency in regulating cell debonding and alignment was also studied using FE analysis.     

NiTi形状记忆合金裂纹尖端热力耦合行为研究

本文对NiTi形状记忆合金I型裂纹尖端热力耦合行为进行了数值仿真分析和实验验证。建立了包含相变和热力耦合的本构模型,通过有限元计算得到了裂纹尖端附近的纵向应变、马氏体体积分数和温度场分布,依据马氏体相变情况对裂纹尖端有效应力强度因子进行了修正,揭示了加载速率对形状记忆合金裂纹尖端有效应力强度影子的影响规律。参数研究表明,随着加载频率的增加,裂纹尖端附近温度逐渐升高,马氏体相变区域逐渐缩小,有效应力强度因子呈下降趋势,形状记忆合金表现出增韧效应,有助于减缓裂纹扩展。本研究结果对于揭示热力耦合作用下超弹性形状记忆合金疲劳裂纹扩展规律具有重要参考意义。     

磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.      

THREE-DIMENSIONAL ANALYSIS OF A MAGNETOELECTROELASTIC HALF-SPACE UNDER AXISYMMETRIC TEMPERATURE LOADING 1)

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.     

Influence of Cyclic Stretch on Mechanical Properties of Endothelial Cells

The aim of this study was to investigate effects of cyclic stretch on the mechanical properties of Endothelial cells (ECs). Human Umbilical Vein Endothelial Cells were cultured and exposed to uniaxial cyclic stretch with two amplitude (10 % and 20 %) and different time duration (2, 4, 6 and 8 h). Micropipette aspiration technique coupled with the generalized Maxwell model was used to evaluate the mechanical properties of the ECs. Effects of cyclic stretch on the cell cytoskeleton were analyzed by actin filament staining. Results confirmed viscoelastic behavior of ECs in the micropipette aspiration experiment. The present results confirmed that increased stretch amplitude and duration led to lower deformation and further stiffening of ECs. Actin fibers were shown to align and bundle in response to the cyclic stretch. The results were compared statistically among test and control groups and it was concluded that cyclic loading causes significant alteration in mechanical properties of ECs due to remodeling of cell cytoskeleton.     

Fatigue behaviour of coke drum materials under thermal-mechanical cyclic loading

Coke drums are vertical pressure vessels used in the delayed coking process in petroleum refineries. Significant temperature variation during the delayed coking process causes damage in coke drums in the form of bulging and cracking. There were some studies on the fatigue life estimation for the coke drums, but most of them were based on strain-fatigue life curves at constant temperatures, which do not consider simultaneous cyclic temperature and mechanical loading conditions. In this study, a fatigue testing system is successfully developed to allow performing thermal-mechanical fatigue (TMF) test similar to the coke drum loading condition. Two commonly used base and one clad materials of coke drums are then experimentally investigated. In addition, a comparative study between isothermal and TMF lives of these materials is conducted. The experimental findings lead to better understanding of the damage mechanisms occurring in coke drums and more accurate prediction of fatigue life of coke drum materials.     

超磁致伸缩材料的擦除特性和同余特性实验研究

超磁致伸缩材料在力磁耦合作用下具有复杂的迟滞响应。Preisach模型可有效描述物理过程中的滞后现象,它具有两个重要特性,即擦除特性和同余特性。擦除特性是指输入局部极大值擦除了加载过程中小于该值的所有极大值,或输入局部极小值擦除了加载过程中大于该值的所有极小值,同时,与这些历史极值相应的加载历史也被擦除,不再影响之后的输出。同余特性是指输入极大值与极小值相同的所有闭合曲线一致。本文通过实验系统地研究了超磁致伸缩材料在多轴力磁耦合场作用下的磁致伸缩曲线、磁滞回线和应力应变的迟滞行为,发现其在力磁耦合下的非线性滞后行为具有擦除特性和同余特性。这满足了Preisach模型描述滞后现象的两个基本要求,验证了利用Preisach模型描述超磁致伸缩材料迟滞行为的可行性,为超磁致伸缩材料的非线性理论和器件设计提供了依据。     

Comparison of isotropic hardening and kinematic hardening in thermoplasticity

A coupled thermo-mechanical problem is presented in this paper. The constitutive model is based on thermoplastic model for large strains where both kinematic and isotropic hardening are included. It is shown that a non-associated plasticity formulation enables thermodynamic consistent heat generation to be modeled, which can be fitted accurately to experimental data. In the numerical examples the effect of heat generation is investigated and both thermal softening and temperature-dependent thermal material parameters are considered. The constitutive model is formulated such that pure isotropic and pure kinematic hardening yield identical uniaxial mechanical response and mechanical dissipation. Thus, differences in response due to hardening during non-proportional loading can be studied. Thermally triggered necking is studied, as well as cyclic loading of Cook’s membrane. The numerical examples are solved using the finite element method, and the coupled problem that arises is solved using a staggered method where an isothermal split is adopted.     

Thermoelastic state of a half-space having a thermally active crack parallel to its boundary

Using the boundary integral equation method, the problem of stationary heat conduction and thermoelasticity for a semi-infinite body with a crack parallel to its boundary is solved. Temperature or heat flow on the crack is prescribed. The body boundary is heat-insulated or is at zero temperature. The dependence of the stress intensity factor on the depth of occurrence of a circular crack at a constant temperature or under a constant heat flow is studied. In contrast to mechanical loading, thermal loading shows less SIF values than in an infinite body __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 46–54, April 2007.     

Prediction of fatigue life improvement in natural rubber using configurational stress

To some extent, continua can no longer be considered as free of defects. Experimental observations on natural rubber revealed the existence of distributed microscopic defects which grow upon cyclic loading. However, these observations are not incorporated in the classical fatigue life predictors for rubber, i.e. the maximum principal stretch, the maximum principal stress and the strain energy. Recently, Verron et al. [Verron, E., Le Cam, J.B., Gornet, L., 2006. A multiaxial criterion for crack nucleation in rubber. Mech. Res. Commun. 33, 493–498] considered the configurational stress tensor to propose a fatigue life predictor for rubber which takes into account the presence of microscopic defects by considering that macroscopic crack nucleation can be seen as the result of the propagation of microscopic defects. For elastic materials, it predicts privileged regions of rubber parts in which macroscopic fatigue crack might appear. Here, we will address our interest to a broader context. Rubber is assumed to exhibit inelastic behavior, characterized by hysteresis, under fatigue loading conditions. The configurational mechanics-based predictor is modified to incorporate inelastic constitutive equations. Afterwards, it is used to predict fatigue life. The emphasis of the present work is laid on the prediction of the well-known fatigue life improvement in natural rubber under tension–tension cyclic loading.