基于分数阶微分流变模型的非晶合金黏弹性行为及流变本构参数研究

近年来, 基于非晶合金名义弹性区的流变力学行为探索其结构及形变机理是非晶合金领域研究的热点之一. 本文根据非晶合金结构不均匀性的特征, 提出能够比拟树状分形网络结构的分数阶微分流变模型研究非晶合金的黏弹性行为. 通过室温纳米压痕实验, 对三种不同泊松比和玻璃化转变温度的非晶合金的黏弹性变形行为进行了研究. 实验结果表明: 在表观弹性区, 非晶合金的变形表现出与加载速率相关的线性黏弹性性质. 根据Riemann-Liouville分数阶微积分定义, 分别由分数阶微分及整数阶Kelvin模型对实验结果进行了分析. 分析结果表明, 相对于整数阶流变模型, 分数阶微分流变模型能更精细地表征材料的黏弹性变形特征; 在流变模型参数中, 黏性系数η_A和分数阶次α反映出材料的流变特性和流动趋势, 流变参数与玻璃转变温度、泊松比之间具有较好的相关性, 上述相关性有助于从微观结构角度理解材料塑性与泊松比的关联.     

应变率相关的橡胶本构模型研究

为研究橡胶在不同应变率下的响应特性,建立应变率相关的橡胶黏超弹性本构模型,分别采用超弹性本构模型和黏弹性本构模型表征其非线性弹性行为和应变率相关的弹性行为。首先,对于超弹性模型,基于最小二乘法,对比了Mooney-Rivlin模型、修正的Mooney-Rivlin模型、Yeoh模型、修正的Yeoh模型、Ogden模型和Arruda-Boyce模型等超弹性本构模型的拟合能力。结果表明,经修正的Mooney-Rivlin模型和Yeoh模型的拟合优度与Ogden模型和Arruda-Boyce模型接近。在此基础上,基于一种参数较少且拟合效果良好的修正Mooney-Rivlin模型和应变率相关的Maxwell模型,建立了橡胶黏超弹性本构模型,考察了该黏超弹性本构模型在单轴拉伸和单轴压缩情况下中高应变率时的拟合能力。结果表明,对于这两种受力情况下的应变率相关的实验数据,该黏超弹性本构模型的拟合优度均在0.95以上。研究结果为大应变率范围内单轴拉伸和单轴压缩下橡胶的本构模型选择提供了参考。     

基于剪切模量和热分析数据研究Zr_(50–x)Cu_(34)Ag_8Al_8Pd_x(x=0,2)非晶合金缺陷浓度演化

非晶合金具有独特物理和力学性能,如何建立非晶合金微观结构非均匀性与物理/力学性能之间的关联是非晶固体的重要研究课题之一.微合金化是调控非晶合金微观结构有效手段之一.本研究以玻璃形成能力优异的Zr_(50–x)Cu_(34)Ag_8Al_8Pd_x(x=0, 2)非晶合金为模型合金,借助差示扫描量热仪和电磁声转换设备,研究非晶合金铸态、弛豫态和结晶态热流和剪切模量随温度的演化规律,以及物理时效(低于玻璃转变温度)过程剪切模量的变化随时间演化规律.基于自间隙原子理论,利用热流曲线表征非晶合金在相同热历史剪切模量热效应.通过分析铸态和弛豫态自间隙缺陷浓度和激活能谱,发现结构弛豫导致自间隙缺陷浓度减小,诱导剪切模量随温度演化偏离软化过程,并伴随体系放热.与此同时,研究发现添加微量Pd元素可抑制模型合金体系原子迁移,增加特征弛豫时间.本研究从非晶合金模量热效应角度进一步理解非晶合金微观结构非均匀性.     

铁基块体非晶合金在纳米压痕过程中的蠕变行为研究

利用纳米压痕技术研究了{［（Fe_0.6Co_0.4）_0.75B_0.2Si_0.05］_0.96Nb_0.04}₉₆Cr₄铁基块体非晶合金的室温蠕变行为及不同的加载速率对该块体非晶合金蠕变变形的影响.{［（Fe_0.6Co_0.4）_0.75B_{0.2< 关键词： 块体非晶合金 蠕变 EVEV模型 蠕变速率敏感指数}     

不同力学激励形式探索La基非晶合金微观结构非均匀性

非晶合金力学行为与其微观结构非均匀性之间本征关联,是固体力学研究领域至今未能很好解决的重要科学问题之一.单一力学激励形式并不能有效地描述非晶合金微观结构非均匀性,特别是结构与动力学的关联.如何探索非晶合金结构信息,须将诸多因素综合,在不同力学激励下研究非晶合金微观结构非均匀性与变形机理.本研究以La₆₂Cu₁₂Ni₁₂Al₁₄非晶合金为模型体系,利用动态力学分析仪研究非晶合金动态弛豫行为.基于准点缺陷模型,对模型合金体系α弛豫和β弛豫进行了分离.借助于拉伸应变率跳实验,探索非晶合金高温流变行为.确定非晶合金塑性流变过程中弹性、滞弹性以及塑性变形的贡献.本研究从非晶合金动态力学弛豫行为和宏观塑性流变行为出发,尝试揭示微观非均匀性对非晶合金在不同激励形式中缺陷的激活、扩展和融合的物理本质.     

锆基非晶合金的动态弛豫和应力松弛

非晶合金动态弛豫、变形和微观结构非均匀性之间的关联是非晶态物理领域重要研究内容之一.本文选取玻璃形成能力优良,热稳定性好的Zr₄₈(Cu_5/6Ag_1/6)₄₄Al₈块体非晶合金作为研究载体,借助于动态力学分析及应力松弛实验探究了温度和结构弛豫对非晶合金动态弛豫和变形行为的影响.研究结果表明非晶合金动态弛豫行为对温度极其敏感,随温度升高表现为等构型、老化、玻璃转变和晶化4个阶段.基于玻璃转变温度之下等温测试,结构弛豫行为导致非平衡高能量状态非晶合金向低能量状态迁移,内耗随时间演化规律可用Kohlrausch-Williams-Watts (KWW)扩展指数方程描述.此外,基于KWW方程和激活能谱等方法分析了模型合金应力松弛过程中非均匀结构激活,该过程涉及弹性变形向非弹性变形的转变.由于非晶合金存在微观尺度的结构非均匀性与能量起伏,变形单元的激活并非为单一特征时间,而是服从一定分布.通过考虑对数时间尺度和变形单元激活的特征时间分布分别为对称Gauss分布和非对称Gumbel分布,可...     

分数阶Oldroyd-B黏弹性Poiseuille流的Laplace数值反演分析

采用Laplace数值反演的Stehfest算法研究了分数阶Oldroyd-B粘弹性流体在两平板间非定常的Poiseuille流动问题.首先,通过数值解与近似解析解的比较验证了Stehfest算法的有效性.其次,运用Stehfest算法对平板Poiseuille流动进行了研究,揭示了分数阶黏弹性平板流的速度过冲和应力过冲现象,指出这些现象对分数导数的阶数存在明显的依赖性.同时,数值结果表明,整数阶本构方程仅仅是分数阶本构方程的特例,分数阶本构方程较整数阶本构方程具有更广泛的适用性。     

电动扬声器悬置系统蠕变效应建模

对电动扬声器悬置系统的蠕变效应进行了分数阶建模。通过将标准线性固体模型中的牛顿黏壶替换为分数阶Abel黏壶,提出了悬置系统分数阶标准线性固体力顺模型。使用Klippel扬声器单元电阻抗激光测量系统,测量了2只具有不同橡胶折环的中频扬声器单元的电阻抗和传递函数(振膜输出位移/输入声压),并采用最小二乘法拟合实测曲线,得到了模型参数。通过与已有的考虑蠕变效应的4参数对数模型和标准线性固体模型拟合结果的对比,结果表明:分数阶标准线性固体模型能够准确描述力顺损耗因数随频率的变化规律,对蠕变效应具有更好的模拟精度。      

反应等离子喷涂纳米TiN涂层的显微硬度及微观结构研究

阐述了反应等离子喷涂(RPS)方法的基本思想.利用气体隧道等离子喷枪，通过RPS方法在Q23 5钢基底上成功制备了氮化钛涂层.检测了TiN涂层在不同载荷下的显微硬度，结果显示TiN涂层具有明显的硬度压痕尺寸效应，在高载荷下加工硬化效应较弱.XRD,TEM及HRTEM等分析 表明,通过RPS方法制备得到了纳米TiN涂层，涂层由直径约为50—70nm的TiN晶粒及非晶Ti N所组成. 关键词： 反应等离子喷涂 纳米 氮化钛 微观结构     

穆斯堡尔谱学研究非晶TM_(80)M_(20)~1)合金的微观结构

在室温下和4.2K下测定了非晶Fe_(80)B_(20-x)M_x合金(M=P,C)的穆斯堡尔吸收谱。利用分布参数拟合程序得到了超精细内场H_i和同质异能移IS同类金属成份的变化关系。利用这些结果考察了非晶合金的微观结构,比较了两类结构模型:Bernal-Polk模型和微晶模型。对比非晶合金和它们的相应晶相的行为得知,这类非晶合金中不存在微晶近程序,Bernal-Polk模型对描述TM-M类非晶合金的微观结构优于微晶模型。     

A modified fractional model to describe the viscoelastic behavior of solid amorphous polymers: The effect of physical aging

Amorphous polymers are viscoelastic materials. When they are subjected to dynamical loads, their behavior can be modeled by transform functions of stress and strain in the complex plane. In our work, a model based on the fractional calculus concept is proposed in order to predict the viscoelastic behavior of polymethylmethylacrylate (PMMA) over a wide temperature range between (T_g -190°C) and (T_g +15°C). The extended fractional solid model is shown to be capable of describing experimentally observed dynamic viscoelastic behavior over a wide temperature range, including multiple relaxations, using a limited number of free parameters. Structural recovery of PMMA was studied by dynamic mechanical spectrometry, and its effect on the different parameters is also discussed. Furthermore, from the fractional differential and fractional integral formulations. most of the relevant viscoelastic functions that quantify the degree of molecular mobility of amorphous polymers, like E(t), E?(τ). and H(t), can be derived analytically.     

Dispersion curves for a viscoelastic Timoshenko beam with fractional derivatives

The Kramers–Kronig dispersion relation, often used as a viscoelastic constitutive law for polymeric materials, is based on purely mathematical properties of linearity, convergence of improper integrals, and causality; thus, it may also be valid as a viscoelastic constitutive law for general structural materials. Accordingly, the motion equation of a Timoshenko beam composed of conventional elastic structural materials is extended to one composed of viscoelastic materials. From the derived governing equation, a dispersive equation is derived for a viscoelastic Timoshenko beam. By plotting phase velocity curves and group velocity curves for a beam of solid circular cross-section composed of a viscoelastic material (polyvinyl chloride foam), the influence of the fractional order of viscoelasticity is examined. As a result, it is found that, in the high frequency range, only the first mode of a Timoshenko beam converged to the propagation velocity of the Rayleigh wave, which takes account of the fractional order of viscoelasticity. In addition, the phase velocity and the group velocity were found to increase as the fractional order approaches 0, and to decrease as the fractional order approaches 1. Furthermore, the rate of velocity change becomes greater as the fractional order approaches 0, and becomes smaller as the fractional order approaches 1.     

Preliminarily modeling of creep effect in electro-dynamic loudspeaker suspensions

The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid(FSLS) model was presented by substituting the Abel dashpot for Newton dashpot in Standard Linear Solid(SLS) model.The electrical impedance as well as the transfer function between diaphragm displacement and input voltage of the two tested midrange loudspeakers was measured by Klippel laser analyzer system,and the model parameters were identified by the least-mean-square method.By comparing the fitting results of FSLS model with the other two classical models- 4 Parameter Logarithmic model and SLS model,the results show that the FSLS model can rightly predict the frequency dependent compliance loss factor and yield higher accuracy for modeling the creep effect in loudspeaker suspensions.     

Softening micromechanical constitutive model of stress induced martensite transformation for NiTi single crystal shape memory alloy

Based on the assumption of laminated microstructure, a micromechanical model of stress induced martensite transformation for NiTi shape memory alloys single crystal is proposed. Elasticity anisotropy and different proper-ties for two phases are considered. Martensite volume fraction is chosen as the internal variable that controls the phase transformation quantitatively. An effective macroscopic elasticity matrix based on the different elasticity characteristics of each phase and the martensite volume fraction are obtained with the help of the perfect interfa-cial relationships. A phase transformation driving force is derived to construct the transformation criterion. The model corresponds to a non-convexity free energy function during phase transformation, so softening behavior can be well simulated by the model. A numerical simulation is implemented for the uniaxial loading of NiTi single crystal alloy according to the model, and simulation results are proved by experimental results of polycrystal with strong {111} texture. Superelasticity, Anisotropy, the evolution of microstructure and softening behavior can be well simulated.     

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler–Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler–Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor–corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.     

A Brief Review of Elasticity and Viscoelasticity for Solids

There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion.     

Damage evaluation of reinforced concrete frame based on a combined fiber beam model

In order to analyze and simulate the impact collapse or seismic response of the reinforced concrete(RC)structures,a combined fiber beam model is proposed by dividing the cross section of RC beam into concrete fiber and steel fiber.The stress-strain relationship of concrete fiber is based on a model proposed by concrete codes for concrete structures.The stress-strain behavior of steel fiber is based on a model suggested by others.These constitutive models are implemented into a general finite element program ABAQUS through the user defined subroutines to provide effective computational tools for the inelastic analysis of RC frame structures.The fiber model proposed in this paper is validated by comparing with experiment data of the RC column under cyclical lateral loading.The damage evolution of a three-dimension frame subjected to impact loading is also investigated.     

基于八面体理论的岩石循环加-卸载本构模型及修正

探究岩石的受力特点及破坏特性是研究岩石地下工程安全性的关键,诸多学者都期望能在岩石本构模型的研究上取得突破性进展。在此背景下,提出了一种能够描述循环加-卸载条件下岩石的本构模型。首先,假设岩石的微元强度服从八面体剪应力理论并且微元破坏服从Weibull概率公式,将岩石本构中的损伤变量以及岩石微元强度表达式里包含的损伤因子进行本构变换,得到关于应力、应变等其他表现加-卸载下岩石损伤本构模型的参数,表示出岩石微元强度和损伤变量,再将得到的岩石微元强度和损伤变量代入所提出的岩石本构模型中,并进行等式变换得到一个函数表达式。通过将其与实验数据进行拟合对比分析,得出修正后的拟合参数,将其代入函数式中,得到损伤本构模型的修正式。最后将拟合参数进行必要的敏感性分析,得出各拟合参数的实际物理意义。