Thermomechanical modeling of nonlinear internal hysteresis due to incomplete phase transformation in pseudoelastic shape memory alloys

This paper presents a thermomechanical model for pseudoelastic shape memory alloys (SMAs) accounting for internal hysteresis effect due to incomplete phase transformation. The model is developed within the finite-strain framework, wherein the deformation gradient is multiplicatively decomposed into thermal dilation, rigid body rotation, elastic and transformation parts. Helmholtz free energy density comprises three components: the reversible thermodynamic process , the irreversible thermodynamic process and the physical constraints of both. In order to capture the multiple internal hysteresis loops in SMA, two internal variables representing the transition points of the forward and reverse phase transformation, \(\phi _s^f\) and \(\phi _s^r\), are introduced to describe the incomplete phase transformation process. Evolution equations of the internal variables are derived and linked to the phase transformation. Numerical implementation of the model features an Euler discretization and a cutting-plane algorithm. After validation of the model against the experimental data, numerical examples are presented, involving a SMA-based vibration system and a crack SMA specimen subjected to partial loading–unloading case. Simulation results well demonstrate the internal hysteresis and free vibration behavior of SMA.

     

Determination of the Johnson–Cook Material Parameters Using the SCS Specimen

This note addresses the determination of the Johnson-Cook material parameters using the shear compression specimen (SCS). This includes the identification of the thermal softening effect in quasi static and dynamic loading as well as and the strain rate hardening effect in dynamic loading. A hybrid experimental–numerical (finite element) procedure is presented to identify the constitutive parameters, with an application to Ti6Al4V alloy. The present results demonstrate the suitability of the SCS for constitutive testing.     

斜波压缩下锡的相变和层裂行为

获取不同热力学路径下锡的动态响应实验数据,是深入研究其相变和损伤物理过程的基础.利用小型磁驱装置CQ-4完成了金属锡的斜波加载实验,获取了锡含有相变和层裂损伤物理信息的实验数据.实验结果显示,在加载段锡依次经历了弹塑性转变和β-γ相变两种物理过程,屈服强度约0.194 GPa,相变压力随着锡厚度的增加从7.54 GPa减小到7.14 GPa.在卸载段出现了明显的层裂损伤,层裂强度约1.1 GPa,与相同加载压力下冲击实验结果有巨大差异,层裂片厚度约0.38 mm.结合由锡的多相Helmholtz自由能计算的多相状态方程、Hayes相变动力学方程和损伤度理论,对斜波压缩实验过程进行一维流体动力学数值模拟,计算结果可以很好描述锡的弹塑性转变、相变和层裂三个物理过程.     

TiNi合金冲击相变过程中温度变化规律的实验研究

针对初始SME(shape memory effect)和PE(pseudo-elastic)状态TiNi合金试样,采用带有红外测温系统的SHPB冲击压缩装置,实时测量了冲击相变过程中两种材料试样表面瞬态温度,并根据实验结果计算了相应的温度变化。实验结果表明,冲击加载相变过程中,温度随相变应变的增大而升高,当应变最大时,温度最高;卸载过程中,对初始PE状态试样,温度降低,对初始SME状态试样,温度保持最高温度不变或降低,这同加载最高温度有关;卸载完成后,两种试样温度均高于其初始温度。计算温度结果表明,相变耗散功对加、卸载相变过程中温度变化的作用不可忽略。     

低应变速率下形状记忆合金的特性实验研究

形状记忆合金以其特有的形状记忆效应和超弹性,被广泛应用于医学、航空和建筑防震。在耗能性机构中,需要形状记忆合金能够在变速率条件下工作。为了获得非静态条件下的行为特性,比较静态和非静态条件下形状记忆合金的行为特性的差异,本文采用一种新的分析方法,即以形状记忆合金的特性参数为对象,来分析不同应变速率对形状记忆合金特性的影响。在不同的应变速率(0.0005/s,0.001/s,0.005/s,0.01/s,0.05/s,0.1/s)下,对50.8at%-Ni-Ti记忆合金丝的形状记忆效应和超弹性特性进行了实验研究。在低应变速率范围内,由实验结果得到:随应变速率增大,两种特性行为中的各纯相的杨氏模量保持不变;拉伸过程相变起始和终了临界应力会增大,卸载过程相变起始和终了临界应力会减小,滞后环面积增大;相变硬化系数在形状记忆效应行为中会增大,而在超弹性行为中基本不变。     

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。     

Temperature analysis of one-dimensional NiTi shape memory alloys under different loading rates and boundary conditions

Superelastic polycrystalline NiTi shape memory alloys under tensile loading accompany the strain localization and propagation phenomena. Experiments showed that the number of moving phase fronts and the mechanical behavior are very sensitive to the loading rate due to the release/absorption of latent heat and the material’s inherent temperature sensitivity of the transformation stress. In this paper, the moving heat source method based on the heat diffusion equation is used to study the temperature evolution of one-dimensional superelastic NiTi specimen under different loading rates and boundary conditions with moving heat sources or a uniform heat source. Comparisons of temperature variations with different boundary conditions show that the heat exchange at the boundaries plays a major role in the nonuniform temperature profile that directly relates to the localized deformation. Analytical relation between the front temperature of a single phase front, the inherent Clausius–Clapeyron relation (sensitivity of the material’s transformation stress with temperature), heat transfer boundary conditions and the loading rate is established to analyze the nucleation of new phase fronts. Finally, the rate-dependent stress hysteresis is also simply discussed by using the results of temperature analyses.     

纳米晶钽在单向拉伸载荷下的分子动力学模拟

利用分子动力学方法模拟了纳米晶钽在单轴拉伸载荷作用下的微观结构演化情况. 结果表明纳米晶钽在塑性变形过程中可以发生从BCC到FCC, HCP结构的应力诱导相变. FCC 结构原子百分比的最大值和试样的抗拉强度成线性关系,据此可推出一个相变发生的临界应 力值. 应变率越大,相变滞后于应力越严重. 当应变达到一定值时,试样会发生晶间断裂现 象,定量分析发现纳米晶钽晶间裂纹初始形成应变不受平均晶粒尺寸的影响,而与应变率和 模拟温度有着密切的关系.     

Solution of The Double-Coupled Problem of Buckling of a Shape Memory Alloy Rod Due to The Direct Thermoelastic Phase Transformation

Problems of the stability of a shape memory alloy rod during the direct martensitic phase transformation under constant compressive loading are solved taking into account the effect of stresses on the phase transition and the effect of the phase transition on the temperature regime using various statements. A comparison of the results of the obtained solutions is made.     

PBX-1炸药的力学性能和本构关系

PBX的力学行为对其安全性有重要影响。为研究PBX-1的力学性能,以PBX-1为研究对象,进行准静态力学实验和SHPB(分离式霍普金森压杆)实验研究。结果表明,准静态压缩实验中,试样的裂纹出现在与加载方向大约成45°的最大剪应力方向。SHPB实验中,在应变率100~1 500 s^-1范围内,随着应变率的提高,PBX-1炸药的动态屈服强度、动态压缩强度和破坏应变不断提高。动态屈服强度逐渐从静态的2.77 MPa增加至16.1 MPa;压缩强度从7.46 MPa增加至16.1 MPa,破坏应变从6.23%增加到26.4%。同时,基于Z-W-T模型,建立了一种含损伤的动态黏弹性本构模型,在330~1 500 s^-1应变率范围内具有较高的精度,可以较好地描述PBX-1炸药在达到破坏前的动态力学行为。     

Constitutive model of discontinuous plastic flow at cryogenic temperatures

FCC metals and alloys are frequently used in cryogenic applications, nearly down to the temperature of absolute zero, because of their excellent physical and mechanical properties including ductility. Some of these materials, often characterized by the low stacking fault energy (LSFE), undergo at low temperatures three distinct phenomena: dynamic strain ageing (DSA), plastic strain induced transformation from the parent phase (γ) to the secondary phase (α′) and evolution of micro-damage. The constitutive model presented in the paper is focused on the discontinuous plastic flow (serrated yielding) and takes into account the relevant thermodynamic background. The discontinuous plastic flow reflecting the DSA effect is described by the mechanism of local catastrophic failure of Lomer–Cottrell (LC) locks under the stress fields related to the accumulating edge dislocations (below the transition temperature from the screw dislocations to the edge dislocations mode T₁). The failure of LC locks leads to massive motion of released dislocations accompanied by the step-wise increase of the strain rate. The response of stress is defined in terms of four stages within each serration cycle. In the fourth stage, the strain rate sensitivity model with temperature playing the role of relaxation parameter is applied. Identification of parameters of the constitutive model is based on the experimental data collected during a campaign of tensile tests carried out on copper and stainless steel samples immersed in liquid helium (4.5 K), by means of a unique equipment developed at CERN.     

静动组合载荷下混凝土率效应机理及强度准则

混凝土结构在受到动载荷作用之前,通常已承受着初始静载荷的作用.大量关于混凝土应变率效应的研究均没有考虑初始静载荷对动强度的影响,会导致过高地估计混凝土的动强度,使混凝土结构设计偏于危险.本文通过分析混凝土材料在静动组合载荷下的率效应机理,给出了初始静载荷的定义.在此基础上,推导了混凝土材料参数与初始静载荷和应变率的表达式,提出了建立静动组合强度准则的一般方法.通过材料参数反映初始静载荷与应变率的联合影响,给出了由初始有效静载荷、动态黏聚强度和摩擦强度共同组成的混凝土动态强度,将广义非线性强度准则发展为静动组合多轴强度准则.建立的强度面在相同初始静载荷下随应变率的增大向外扩张,在相同应变率下随初始静载荷的增大向里收缩,即混凝土的强度在相同初始静载荷下随应变率的增大而增大,在相同应变率下随初始静载荷的增大而减小.此外,当初始静载荷和应变率不变时,加载路径对混凝土材料的应变率效应无影响,但会影响混凝土材料的静水压力效应,即当初始静载荷和应变率固定不变时,静动组合强度面的位置和大小即可确定,不同加载路径下强度的不同是由于静水压力效应导致的.最后利用多组混凝土材料静动组合强度试验对建立的静动组合强度准则进行了验证.     

Experimental investigation and modeling of the tension behavior of polycarbonate with temperature effects from low to high strain rates

The effects of strain rate and temperature on the tension stress–strain responses of polycarbonate are experimentally investigated over a wide range of strain rates (0.001–1700 s⁻¹) and temperatures (0–120 °C). A modified split Hopkinson tension bar is used for high-rate uniaxial tension tests. Experimental results indicate that the stress–strain responses of polycarbonate at high strain rates exhibit the nonlinear characteristics including the obvious yielding and strain softening. The tension behavior is strongly dependent on the strain rate and temperature. The values of yield stress and strain at yield present a dramatic increase at higher strain rates and decrease with the increase in temperature. Moreover, there exists a significant rate-sensitivity transition in the polycarbonate tension yield behavior. Based on the experimental investigation, a physically based three-dimensional elastoplastic constitutive model for the finite deformation of glassy polymers is used to characterize the rate-temperature dependent yield and post-yield behavior of polycarbonate when subjected to tension loading. The model results are shown close to the experimental data within the investigated strain-rate and temperature ranges.     

Investigating the transient response of a shear thickening fluid using the split Hopkinson pressure bar technique

The split Hopkinson pressure bar (SHPB) technique is implemented to evaluate the transient response of a colloidal suspension exhibiting shear thickening at strain rates and timescales never before explored in a laboratory instrument. These suspensions are shown to exhibit a discontinuous transition from fluid-like (shear thinning) to solid-like (shear thickening) behavior when evaluated using rotational rheometry. The effect of loading rate on this transition time is studied for a particle volume fraction of 0.54 using the SHPB technique. It is shown that the time required for transition to occur decreases logarithmically with loading rate. From these results, we conclude that transition is not triggered by a characteristic shear rate, but rather a critical shear strain is required. Results from SHPB experiments performed up to Peclet numbers of order 10⁷ are presented and discussed for 0.50, 0.52, and 0.54 particle volume fraction suspensions.     

Modeling of macroscopic response of phase transforming materials under quasi-static loading

Based on a continuum model of solid-solid phase transformations, the macroscopic response of a bar of a thermoelastic phase transforming material loaded quasistatically is investigated. A critical loading rate is identified for the evolution of a single phase boundary in the bar during an isothermal process. It is shown that, when the loading rate is larger than this critical loading rate, nucleation occurs either continuously or at multiple sites; when the loading rate is lower than this critical loading rate, the size of the hysteresis loop increases with increasing loading rate, and decreases with an increase in the mobility of the phase boundary. The heat conduction due to the heat generated by the latent heat of the phase transformation is considered for a special case.     

Micromechanical modeling of stress-induced phase transformations. Part 2. Computational algorithms and examples

Based on the theory developed in Part 1 of this paper [Levitas, V.I., Ozsoy, I.B., 2008. Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation. Int. J. Plasticity. doi:10.1016/j.ijplas.2008.02.004], various non-trivial examples of microstructure evolution under complex multiaxial loading are presented. For the case without interface rotation, the effect of the athermal thresholds for austenite (A)–martensite (M) and martensitic variant M_I–variant M_II interfaces and loading paths on stress–strain curves and phase transformations was studied. For coupled interface propagation and rotation, two types of numerical simulations were carried out. The tetragonal–orthorhombic transformation has been studied under general three-dimensional interface orientation and zero athermal threshold. The cubic–tetragonal transformation was treated with allowing for an athermal threshold and interface reorientation within a plane. The effect of the athermal threshold, the number of martensitic variants and an interface orientation in the embryo was studied in detail. It was found that an instability in the interface normal leads to a jump-like interface reorientation that has the following features of the energetics of a first-order transformation: there are multiple energy minima versus interface orientation that are separated by an energy barrier; positions of minima do not change during loading but their depth varies; when the barrier disappears (i.e. one of the minima transforms to the local saddle or maximum points), the system rapidly evolves toward another stable orientation. Depending on the loading and material parameters, we observed a large continuous change in interface orientation, a jump in interface reorientation, a jump in volume fractions and stresses, an expected stress relaxation during the phase transition and unexpected stress growth during the transition because of large change in elastic moduli.     

Dynamic Tensile Response of a Microwave Damaged Granitic Rock

Background

Understanding the dynamic tensile response of microwave damaged rock is of great significance to promote the development of microwave-assisted hard rock breakage technology. However, most of the current research on this issue is limited to static loading conditions, which is inconsistent with the dynamic stress circumstances encountered in real rock-breaking operations.

Objective

The objective of this work is to investigate the effects of microwave irradiation on the dynamic tensile strength, full-field displacement distribution and average fracture energy of a granitic rock.

Methods

The split Hopkinson pressure bar (SHPB) system combined with digital image correlation (DIC) technique is adopted to conduct the experiments. The overload phenomenon, which refers to the strength over-estimation phenomenon in the Brazilian test, is validated using the conventional strain gauge method. Based on the DIC analysis, a new approach for calculating the average fracture energy is proposed.

Results

Experimental results show that both the apparent and true tensile strengths increase with the loading rate while decreasing with the increase of the irradiation duration; and the true tensile strength after overload correction is lower than the apparent strength. Besides, the overload ratio and fracture energy also show the loading rate and irradiation duration dependency.

Conclusions

Our findings prove clearly that microwave irradiation significantly weakens the dynamic tensile properties of granitic rock.

     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

Numerical simulation and experimental investigation of the elastocaloric cooling effect in sputter-deposited TiNiCuCo thin films

The exploitation of the elastocaloric effect in superelastic shape memory alloys (SMA) for cooling applications shows a promising energy efficiency potential but requires a better understanding of the non-homogeneous martensitic phase transformation. Temperature profiles on sputter-deposited superelastic \({\mathrm {Ti_{55.2}Ni_{29.3}Cu_{12.7}Co_{2.8}}}\) shape memory alloy thin films show localized release and absorption of heat during phase transformation induced by tensile deformation with a strong rate dependence. In this paper, a model for the simulation of the thermo-mechanically coupled transformation behavior of superelastic SMA is proposed and its capability to reproduce the mechanical and thermal responses observed during experiments is shown. The procedure for experiment and simulation is designed such that a significant temperature change from the initial temperature is obtained to allow potential cooling applications. The simulation of non-local effects is enabled by the use of a model based on the one-dimensional Müller–Achenbach–Seelecke model, extended by 3D mechanisms such as lateral contraction and by non-local interaction, leading to localization effects. It is implemented into the finite element software COMSOL Multiphysics, and comparisons of numerical and experimental results show that the model is capable of reproducing the localized transformation behavior with the same strain rate dependency. Additionally to the thermal and the mechanical behavior, the quantitative prediction of cooling performance with the presented model is shown.     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。