A non-linear uniaxial integral constitutive equation incorporating rate effects,creep and relaxation

A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.     

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。     

Fracture criteria under creep with strain history taken into account,and long-term strength modelling

In the present paper, we continue to study the nonlinear constitutive relation (CR) between the stress and strain proposed in [1] to describe one-dimensional isothermal rheological processes in the case of monotone variation of the strain (in particular, relaxation, creep, plasticity, and superplasticity). We show that this CR together with the strain fracture criterion (FC) leads to theoretical long-term strength curves (LSC) with the same qualitative properties as the typical experimental LSC of viscoelastoplastic materials. We propose two parametric families of fracture criteria in the case of monotone uniaxial strain, which are related to the strain fracture criterion (SFC) but take into account the strain increase history and the dependence of the critical strain on the stress. Instead of the current strain, they use other measures of damage related to the strain history by time-dependent integral operators. For any values of the material parameters, analytic studies of these criteria allowed us to find several useful properties, which confirm that they can be used to describe the creep fracture of different materials. In particular, we prove that, together with the proposed constitutive relations, these FC lead to theoretical long-term strength curves (TLSC) with the same qualitative properties as the experimental LSC. It is important that each of the constructed families of FC forms a monotone and continuous scale of criteria (monotonously and continuously depending on a real parameter) that contains the SFC as the limit case. Moreover, the criteria in the first family always provide the fracture time greater than that given by the SFC, the criteria in the second family always provide a smaller fracture time, and the difference can be made arbitrarily small by choosing the values of the control parameter near the scale end. This property is very useful in finding a more accurate adjustment of the model to the existing experimental data describing the fracture time dependence on the stress, temperature, radiation, and other factors: if these data are poorly described by the SFC, then one can choose a more appropriate criterion from the constructed families by varying the value of the control parameter smoothly and monotonously.     

Asymptotic behavior of creep curves in the Rabotnov nonlinear heredity theory under piecewise constant loadings and memory decay conditions

Some minimal prior constraints are imposed on the two material functions used in the Rabotnov nonlinear constitutive relation. The asymptotic dependence of creep curves on the characteristics of these material functions and on the parameters of loading programs is analytically studied in the case of stepped loadings. Some conditions are obtained for the case when these curves tend to the creep curve under instantaneous loading as t→∞. The importance of the limit value of the creep function derivative at infinity is analyzed for the plastic strain accumulation. A number of distinctions and additional possibilities are found compared to the linear integral relation of viscoelasticity.     

一般加载规律的弹塑性本构关系

将有关文献给出一般加载规律一维全量理论的简单模型推广到一般加载规律的一维增量理论,进而推广到一般加载规律的多维增量理论,在此基础上,建立了推导一般加载规律的多维增量理论的本构关系的一种途径。应用这种途径,从应力空间的加载函数和应变空间的加载函数出发,推导了等向强化材料和被加热的等向强化材料的一般加载规律的弹塑性本构关系的两种表示形式。理论和实例均表明,这种途径对等向强化材料、随动强化材料和理想弹塑性材料均适用。     

Finite ramp time correction method for non-linear viscoelastic material model

In this paper, a simple formula for the prediction of stress (strain) in the relaxation (creep) period is derived for a non-linear viscoelastic material model which takes into account the finite ramp time. Usually, it is assumed that the ramp time is small and, therefore, loading can be described via Heaviside step function. This assumption, when applied to the material parameters identification process, can lead to a large errors in the values of the approximated material parameters. Especially, for the materials which undergo significant stress decay in the beginning of relaxation the assumption of infinite small ramp time can induce severe errors. With the help of the derived formula more reliable material parameter identification can be accomplished. The proposed method is tested with numerical simulations and compared with analytical results, Heaviside step loading case and method described by Nordin and Varna. Simulations show good agreement with analytical results.     

Properties of a nonlinear viscoelastoplastic model of Maxwell type with two material functions

General qualitative properties of quasistatic curves for creep, relaxation, strain, and others are studied analytically. These curves are obtained on the basis of a one-dimensional constitutive relation of Maxwell type. Some constraints are proposed for the material functions to adequately describe the typical properties of experimental curves for a wide class of viscoelastoplastic materials. The applicability of the proposed model to describe, in particular, the superplastic deformation is analyzed. The effects that cannot be described in the framework of this model are found and its applicability range is revealed.     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

家兔肌腱的蠕变变形行为的实验研究

研究了家兔肌腱的蠕变规律，测定了稳定蠕变速率等力学参量，通过对试验结果的分析，建立了肌腱的蠕变本构关系，结果表明，蠕变应变与瞬时应力和时间有关，在一定的瞬时应力作用下，稳定蠕变速率近似为常数，稳定蠕变速率与瞬时应力近似成指数关系。     

Thermovisco-hyperelastic behavior of elastomeric materials modified by filler nanoparticles

We present the results of experimental studies of hyperelastic and relaxation properties of polymer composites with elastomeric matrix made of hydrogenated nitrile butadiene rubber filled with nanoparticles of technical carbon in the temperature range 19–150° C. We present typical experimental diagrams of deformation of the material with constant strain rate and the stress relaxation curves at different strain levels under tension and compression conditions. We consider a possible version of constitutive relations for describing some singularities of the behavior of the material under study. We developed a method for determining all the parameters of the accepted relations on the basis of the results of uniaxial tests. We found a nonmonotone dependence of the relaxation modulus on the temperature and proposed a formula for describing this dependence in the temperature range under study. To justify the possible use of the considered constitutive relations to perform calculations under conditions of arbitrary compound stress state, we performed numerical modeling of the compression experiment for cylindrical samples. A rather satisfactory agreement between the computational results and experimental data was obtained.     

General properties of relaxation curves in the case of the initial stage of strain with a constant rate in the linear heredity theory

Qualitative properties of relaxation curves are analytically studied in the case of linear-time strain at the initial stage. These curves are induced by an integral constitutive relation of viscoelasticity with an arbitrary relaxation function. Among these properties are the intervals of monotonicity and convexity, jumps, breaks, the asymptotics of curves, their dependence on the parameters of the initial stage of strain and on the properties of a relaxation function, the convergence type of a family of relaxation curves when the duration of the initial stage tends to zero, etc.     

长期荷载作用下CFST界面粘结损伤试验研究

为考察在役钢管混凝土界面粘结性能与荷载作用时间的关系,以荷载作用时间段为基本参数,完成了7根圆钢管混凝土试件的推出试验.试验结果表明,钢管混凝土界面粘结力随荷载作用时间的延长而减小.根据试验结果,得出各个试件的荷载—滑移曲线.基于ANSI/ACI308-1992混凝土养护规程,得出每个试件在荷载作用下的混凝土徐变应变.从损伤力学的角度出发,定义界面损伤变量,推导了混凝土徐变应变与损伤的关系.通过回归得出含损伤变量的界面粘结—滑移本构关系.     

Interrelation of creep and relaxation for nonlinearly viscoelastic materials: application to ligament and metal

Creep and stress relaxation are known to be interrelated in linearly viscoelastic materials by an exact analytical expression. In this article, analytical interrelations are derived for nonlinearly viscoelastic materials which obey a single integral nonlinear superposition constitutive equation. The kernel is not assumed to be separable as a product of strain and time dependent parts. Superposition is fully taken into account within the single integral formulation used. Specific formulations based on power law time dependence and truncated expansions are developed. These are appropriate for weak stress and strain dependence. The interrelated constitutive formulation is applied to ligaments, in which stiffness increases with strain, stress relaxation proceeds faster than creep, and rate of creep is a function of stress and rate of relaxation is a function of strain. An interrelation was also constructed for a commercial die-cast aluminum alloy currently used in small engine applications.     

Cyclic stress-softening model for the Mullins effect in compression

This paper models the cyclic stress softening of an elastomer in compression. After the initial compression the material is described as being transversely isotropic. We derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain, and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These equations are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular a carbon-filled rubber vulcanizate. To establish the validity of the model we compare it with two test samples, one for filled vulcanized styrene–butadiene rubber and the other for filled vulcanized natural rubber. The model is found to fit this experimental data extremely well.     

高应力高水压下砂岩三轴蠕变特性试验研究

对砂岩进行高围压高水压条件下的三轴压缩蠕变试验。试验表明,在整个加载过程中,孔隙水压力主要起到增强轴向变形和横向变形的作用;但在加载的初始阶段,孔隙水压力在一定程度上抑制了轴向变形。当应力水平高于屈服应力时,横向蠕变速率明显大于轴向蠕变速率,且横向蠕变率先进入加速蠕变阶段。本文提出一个新的非线性黏性元件,并引入一个能判断是否进入加速蠕变阶段的计时器元件,组建一个非线性黏塑性加速蠕变启动模型,将该黏塑性模型与Burgers模型串联,构建一个新的非线性黏弹塑性蠕变模型,推导了该模型在常规三轴应力状态下的本构方程。基于试验结果,通过对非线性优化算法(BFGS)的Matlab编程,实现对本文提出蠕变模型的参数识别,识别效果比较理想。对比试验曲线与拟合曲线,二者相当吻合,验证了新提出的非线性黏弹塑性蠕变模型的正确性。     

黄土固结蠕变特性试验研究

基于杨凌地区黄土的单向固结试验资料,分别研究了加载条件下原状黄土和扰动黄土的固结蠕变特性,由试验数据整理分析出不同含水率、不同固结压力下的固结蠕变曲线簇,根据蠕变曲线形态特征,推导出单向固结条件下黄土的应变-时间关系并拟合得到该关系中的参数,在分析参数与固结压力之间关系的基础上推导出黄土的一维固结蠕变本构关系,经试验证明,该关系能较好的描述杨凌地区黄土的固结蠕变特性。另外,基于试验资料以及Buisman次固结系数的概念,分析出次固结系数与固结压力之间的定量关系,为确定固结压力对黄土次固结特性的影响提供了一种新途径。     

A fractional non-linear creep model for coal considering damage effect and experimental validation

Accurate prediction of coal׳s creep behavior is of great significance to coalbed methane extraction. In this study, taking into account the visco-elastic–plastic characteristics and the damage effect, a fractional non-linear model is proposed to describe the creep behavior of coal. The constitutive and creep equations of the proposed fractional non-linear model are derived via the Boltzmann superposition principle and discrete inverse Laplace transform. Furthermore, uniaxial creep tests under different axial stress conditions were carried out to validate the proposed model. It is found that the present model can describe the experimental data from creep tests with better accuracy than classical models. Particularly, the present model can predict the accelerating creep deformation of coal which classical models fail to reproduce. Finally, the parametric sensitivity analysis is performed to investigate the effects of model parameters on the creep strain. It is verified that the introduction of fractional parameters and damage factor in the present model is essential to accurate prediction of the full creep stage of coal.