螺旋压缩弹簧应力松弛特性试验分析及其应用

本文通过应力松弛试验、理论推导及数值模拟研究了高温下螺旋压缩弹簧的应力松弛规律,并利用加速模型对工况下弹簧应力松弛服役寿命做出预测。首先,根据螺旋压缩弹簧的结构特点搭建了弹簧应力松弛连续动态测试装置,该装置不仅避免了传统测试方法存在的缺陷,而且能够保证试验过程中位移载荷恒定,并实时监测载荷变化。本文以某飞机舱门单锁机构中的螺旋压缩弹簧为试验对象进行了不同温度条件下的应力松弛试验,得到其松弛动力学曲线,并基于Arrhenius模型建立了弹簧在工况下的应力松弛服役寿命预测模型;其次,基于应力松弛和蠕变在本质上的一致性,结合金属材料蠕变规律并根据试验弹簧的受力特点,推导出用于描述试验材料松弛行为的蠕变本构方程,由试验结果获得该本构方程的材料常数;最后,通过该本构方程及材料常数,在ANSYS软件中对试验弹簧的松弛过程进行模拟,结果表明,模拟结果与试验结果误差不大于4%。因此,通过本文方法所建立的蠕变方程对弹簧在不同载荷条件下的应力松弛规律进行仿真分析具有一定的可行性与准确性。     

A GENERALIZED PIEZOELECTRIC-THERMOELASTIC THEORY WITH STRAIN RATE AND ITS APPLICATION 1)

工程中大量材料的形变介于弹性与黏性之间, 既具有弹性固体特性, 又具有黏性流体特点, 即为黏弹性. 黏弹性使得材料出现很多力学松弛现象, 如应变松弛、滞后损耗等行为. 在研究受热载荷作用的多场耦合问题的瞬态响应时, 考虑此类问题中的热松弛和应变松弛现象, 对准确描述其瞬态响应尤为重要. 针对广义压电热弹问题的瞬态响应, 尽管已有学者建立了考虑热松弛的广义压电热弹模型, 但迄今, 尚未计入应变松弛. 本文中, 考虑到材料变形时的应变松弛, 通过引入应变率, 在Chandrasekharaiah广义压电热弹理论的基础之上, 经拓展, 建立了考虑应变率的广义压电热弹理论. 借助热力学定律, 给出了理论的建立过程并得到了相应的状态方程及控制方程. 在本构方程中, 引入了应变松弛时间与应变率的乘积项, 同时, 分别在本构方程和能量方程中引入了热松弛时间因子. 其后, 该理论被用于研究受移动热源作用的压电热弹一维问题的动态响应问题. 采用拉普拉斯变换及其数值反变换, 对问题进行了求解, 得到了不同应变松弛时间和热源移动速度下的瞬态响应, 即无量纲温度、位移、应力和电势的分布规律, 并重点考察了应变率对各物理量的影响效应, 将结果以图形形式进行了表示. 结果表明: 应变率对温度、位移、应力和电势的分布规律有显著影响.     

岩石分形节理粗糙性对应力场影响的光弹模拟研究

节理的粗糙性是影响岩体力学特性的重要因素。现有的众多的研究结果表明：不规则的节理面具有很好的自相似特征，可以用分形几何去描述，节理面的分形维数是表征节理面粗糙度（ＪＲＣ）恰当的统计量。基于以上观点，为了能够精确地控制节理面的粗糙性，本文以Ｍａｎｄｅｌｂｒｏｔｗｅｉｅｒｓｔｒａｓｓ函数生成不同分维的分形曲线来模拟实际的粗糙节理面，制成光弹实验试样进行多组的单压和压剪实验，通过光弹条纹和接触点的变化来研究不规则的节理对于岩体变形，应力场的影响，得出了一些有益的结论．     

两种缓冲材料的应力松弛实验分析

 用逐次残余法分析了聚乙烯和聚苯乙烯缓冲材料的应力松弛试验数据．结果表明可用有限个并联的Ｍａｘｗｅｌ模型来表示这两种材料的应力松弛试验曲线．     

甘肃北山地质处置库围岩节理抗剪强度经验估算

节理抗剪强度参数是地质处置库预选地段工程地质对比和围岩稳定性分析的重要指标。本文在旧井地段英云闪长岩节理分组的基础上,运用定向统计测量方法估测节理粗糙度系数,通过评价节理粗糙度系数的尺寸效应,确定节理抗剪强度经验估算有效长度,由JRC-JCS模型求得各组节理4个方向的抗剪强度参数,并评价了地质处置库围岩节理抗剪强度的各向异性特征。     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程 ,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率 ,并给出了前三阶复频率与流速的关系 .计算结果表明 ,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响 .     

岩石非弹性特性的内时理论模型

针对岩石的非弹性特性,将内时理论引入到岩石特性的研究中来。首先对内时理论的方程作了简要推导和说明。将核函数作四阶的Prony展开,将积分方程用一组微分方程来代替,最后得出可以进行数值运算的内时方程。在MTS压机上进行了砂岩、花岗岩等不同岩石样品的多种循环加卸载实验,得到一系列应力—应变曲线。根据滞回曲线的拐点,用最小二乘拟合法来具体确定内时方程中的有关参数。将理论产生的各种滞回曲线与实验滞回曲线作比较,可以看出在滞回曲线和残余应变这二个岩石非弹性特性最明显的标志上,非常一致。说明在中等应变强度时,利用内时理论可以对岩石非弹性特性作很好的研究。与塑性理论比较,可以免去确定屈服面的困难。最后对岩石滞回特性的微观机制用P-M模型作了简要讨论和分析。     

岩石蠕变的应力-应变比分析

对岩石蠕变的应力-应变比分析方法进行了探索。蠕变是岩石重要的力学性质之一。岩石在各个应力水平下的蠕变曲线具有几何相似性。根据岩石蠕变的应力-应变比曲线可以近一步分析得到等时模量曲线。在岩石蠕变本构描述十分复杂、至今没有成熟的理论的情况下,应力-应变比分析方法具有十分重要的现实意义。     

Constitutive relationships for polymeric materials with power-law distributions of relaxation times

The linear relaxation modulus of polydisperse polymer melts and solutions can often be approximated by a power law,ct ^–m over some range of time,t. If, in addition, the nonlinear rheology is given by a separable integral equation, with a strain-dependent factor typical of those observed experimentally, then some commonly observed empirical rules and equations can be readily derived as approximations, namely the Cox-Merz relationship between complex viscosity and steady-state shear viscosity, Bersted's predictions of steady shear stress and first normal-stress difference from a truncated spectrum of linear relaxation times, and the observation of Koyama and coworkers that the ratio of the nonlinear to the linear time-dependent elongational viscosity is independent of strain rate, over a range of strain rates outside the linear regime.     

液晶高分子各向异性粘弹性流体本构方程理论

将液晶高分子－各向异性流体的本构方程,建立在Oldroyd随体导数观点基础上。推广上随机Oldroyd B流体模型,提出共转OldroydB流体模型,同时将微观结构的影响通过宏观参数表示出来,使在宏观理论中包含微观结构的贡献,即引入取向物质函数,非线性各向异性黏度函数和各向异性松弛时间及推迟时间等,表征取向运动对黏度和松弛及推迟现象的影响,在此基础上开展了一类新的液晶高分子－Oldroyd型本构方程理论,由该类型本构方程得出的物质函数,液晶高分子流体的第一、第二法向应力差与实验结果一致,解释了液晶高分子溶液的第一、第二法向应力差的特殊流变学行为。     

边坡预应力锚杆蠕变的数值分析

运用非线性蠕变分析理论模型,采用MSC.MARC软件重点研究了锚杆的应力指数、蠕变系数和几何参数的变化对于锚杆应力松弛的影响.通过对预应力锚杆支护的边坡进行数值分析,探讨了锚杆的蠕变规律以及锚杆预应力松弛现象.锚杆的参数取不同数值时,比较数值模拟结果发现:锚杆的轴力和剪力主要分布在锚固段的前端;随着锚杆应力指数及蠕变系数的增加,蠕变应变增大,应力松弛加快.     

断层内破碎岩石渗透性的实验研究

断层破碎带岩石的渗透性是影响地下工程中由渗流失稳而引发灾害事故的重要影响因素之一。利用一种专门的破碎岩石压实渗透仪,在MTS815.02岩石力学伺服试验系统上测试了取自断层内的破碎灰岩、破碎砂岩、破碎泥岩的渗透系数,得到并分析了轴向压力、岩样粒径、水流速度与渗透系数的关系曲线。研究表明:破碎岩石渗透系数与其压实状态密切相关,随着轴压的增加,渗透系数都相应降低;在相同的轴向压力状态下,岩样粒径越小,其渗透系数也越小,因此,挤压程度和充填程度都较低的小断层导水性好,容易导致突水;破碎岩石的渗透系数随着水流速度的增大呈减小趋势,但水流速度对破碎岩石渗透系数的影响程度有限;在相同的压力、粒径情况下,破碎泥岩的渗透系数比破碎灰岩、破碎砂岩的要小1～2个量级,说明当断层上下盘为坚硬岩石时,断层带渗透性好、易导水。研究结果可为采动过程中评价断层的导水性提供参考。     

A constitutive equation derived from Lodge's network theory

A constitutive equation is presented, derived from Lodge's molecular network theory. The equation is of a form similar to the one presented previously by Carreau. The rate of creation of junctions and the probability of loss of junctions depend here also on the second invariant of the rate-of-strain tensor. The dependence, however, is through simple exponential functions, resulting in easy-to-use equations.Material functions are presented for the viscosity, the primary normal stress coefficient, the complex viscosity, the stress relaxation after cessation of steady simple shear, the stress growth after onset of steady simple shear and for elongational flow. The usefulness of the simplified (series truncated) equations is discussed and the model is evaluated with typical viscoelastic data.     

岩石三轴蠕变试验黏弹性解析及参数识别

基于岩石三轴蠕变试验,推导了相应的黏弹性解析解,并对三参量H-K流变模型给出 了黏弹性解析解的显式以及流变参数的识别方法. 在此基础上,针对花岗岩及片岩两种岩石 的室内蠕变分级加载试验曲线进行了流变参数的识别与反演. 分析表明,同一岩样在不同加 载级别下的弹性及黏弹性参数在量值上均有所不同,其中黏弹性模量和黏滞系数的量值随 载荷的增加出现损伤衰减,基于试验反演所获参数的解析蠕变曲线与试验蠕变曲线吻合较好.     

Relaxation and retardation functions of the Maxwell model with fractional derivatives

A four-parameter Maxwell model is formulated with fractional derivatives of different orders of the stress and strain using the Riemann-Liouville definition. This model is used to determine the relaxation and retardation functions. The relaxation function was found in the time domain with the help of a power law series; a direct solution was used in the Laplace domain. The solution can be presented as a product of a power law term and the Mittag-Leffler function. The retardation function is determined via Laplace transformation and is solely a power law type.The investigation of the relaxation function shows that it is strongly monotonic. This explains why the model with fractional derivatives is consistent with thermodynamic principles.This type of rheological constitutive equation shows fluid behavior only in the case of a fractional derivative of the stress and a first order derivative of the strain. In all other cases the viscosity does not reach a stationary value.In a comparison with other relaxation functions like the exponential function or the Kohlrausch-Williams-Watts function, the investigated model has no terminal relaxation time. The time parameter of the fractional Maxwell model is determined by the intersection point of the short- and long-rime asymptotes of the relaxation function.     

From dynamic modulus via different relaxation spectra to relaxation and creep functions

The main goal of the paper is to compare predictive power of relaxation spectra found by different methods of calculations. The experimental data were obtained for a new family of propylene random copolymers with 1-pentene as a comonomer. The results of measurements include flow curves, viscoelastic properties, creep curves and rubbery elasticity of copolymer melts. Different relaxation spectra were calculated using independent methods based on different ideas. It lead to various distributions of relaxation times and their “weights”. However, all of them correctly describe the frequency dependencies of dynamic modulus. Besides, calculated spectra were used for finding integral characteristics of viscoelastic behaviour of a material (Newtonian viscosity, the normal stress coefficient, steady-state compliance). In this sense all approaches are equivalent, though it appears impossible to estimate instantaneous modulus. The most crucial arguments in estimating the results of different approaches is calculating the other viscoelastic function and predicting behaviour of a material in various deformation modes. It is the relaxation and creep functions. The results of relaxation curve calculations show that all methods used give rather similar results in the central part of the curves, but the relaxation curves begin to diverge when approaching the high-time (low-frequency) boundary of the relaxation curves. The distributions of retardation times calculated through different approaches also appear very different. Meanwhile, predictions of the creep curves based on these different retardation spectra are rather close to each other and coincide with the experimental points in the wide time range. Relatively slight divergences are observed close to the upper boundary of the experimental window. All these results support the conclusion about a rather free choice of the relaxation time spectrum in fitting experimental data and predicting viscoelastic behaviour of a material in different deformation modes. Received: 15 March 2000 Accepted: 18 September 2000     

Time-Dependent Diffusion and Surface-Enhanced Relaxation in Stochastic Replicas of Porous Rock

Understanding the connection between pore structure and NMR behavior of fluid-saturated porous rock is essential in interpreting the results of NMR measurements in the field or laboratory and in establishing correlations between NMR parameters and petrophysical properties. In this paper we use random-walk simulation to study NMR relaxation and time-dependent diffusion in 3D stochastic replicas of real porous media. The microstructures are generated using low-order statistical information (porosity, void–void autocorrelation function) obtained from 2D images of thepore space. Pore size distributions obtained directly by a 3D pore space partitioning method and indirectly by inversion of NMR relaxation data are compared for the first time. For surface relaxation conditions typical of reservoir rock, diffusional coupling between pores of different size is observed to cause considerable deviations between the two distributions. Nevertheless, the pore space correlation length and the size of surface asperity are mirrored in the NMR relaxation data for the media studied. This observation is used to explain the performance of NMR-based permeability correlations. Additionally, the early time behavior of the time-dependent diffusion coefficient is shown to reflect the average pore surface-to-volume ratio. For sufficiently high values of the self-diffusion coefficient, the tortuosity of the pore space is also recovered from the long-time behavior of the time-dependent diffusion coefficient, even in the presence of surface relaxation. Finally, the simulations expose key limitations of the stochastic reconstruction method, and allow suggestions for future development to be made.     

Composite viscoelasticity in glassy,transitional and molten states

As part of a study of viscous and elastic behaviors, over a range of temperatures from below the glass transition up to the hot melt, we here report steady-shear viscosities at 0.007 to 13 s^?1 and at 160 to 220 °C of polystyrene containing 0 to 60% by mass of 0.18-micron diameter titanium dioxide particles. The materials were shearthinning without a yield stress, with a constant activation energy at constant stress, but having a shear-dependent activation energy at constant shear rate — proportional to the volume fraction of the polymer matrix. Superposition of the flow curves at different temperatures for the unfilled and filled systems was possible. All the data were represented by one equation with four parameters: 1) a shear stress coefficient (units Pa · s²); 2) a characteristic stress level for non-Newtonian behavior, independent of temperature and composition; 3) an activation energy at constant stress; and 4) an Einstein coefficient (or intrinsic viscosity of the filler). Other equations also fitted the data, but the others diverged widely when extrapolated.     

Pulsatory Turbulent Compressible Fluid Flow and Propagation of Pressure Waves in a Channel

The properties of the damping coefficient and phase velocity of propagation of small-amplitude pressure waves as functions of the oscillation frequency are investigated for the turbulent flow of a weakly compressible fluid in a circular pipe. The wall friction is found by solving numerically the equation of motion and the relaxation equations for the turbulent shear stress and viscosity which provide the basis for a turbulent transfer model developed for unsteady conditions. The properties are explained in terms of an analysis of the calculated data on turbulent transfer. The results obtained are compared with experiments.