Comparison between the dynamic moduli of fully non-linear and quasilinear viscoelastic materials

This paper deals with the non-linear viscoelastic model with multiple hereditary integrals (MHI) in the frequency domain and the conditions that it reduces to single hereditary integral or the quasilinear viscoelastic (QLV) model. It is shown that when the higher order complex moduli are related to the first-order modulus as the MHI model reduces to the QLV model. The coefficients of quasilinearity should be real and independent of amplitude and frequency.     

Rate dependent finite strain constitutive model of polyurea

Continuous loading and unloading experiments are performed at different strain rates to characterize the large deformation behavior of polyurea under compressive loading. In addition, uniaxial compression tests are carried out with multistep strain history profiles. The analysis of the experimental data shows that the concept of equilibrium path may not be applied to polyurea. This finding implies that viscoelastic constitutive models of the Zener type are no suitable for the modeling of the rate dependent behavior of polyurea. A new constitutive model is developed based on a rheological model composed of two Maxwell elements. The soft rubbery response is represented by a Gent spring while nonlinear viscous evolution equations are proposed to describe the time-dependent material response. The eight material model parameters are identified for polyurea and used to predict the experimentally-measured stress-strain curves for various loading and unloading histories. The model provides a good prediction of the response under monotonic loading over wide range of strain rates, while it overestimates the stiffness during unloading. Furthermore, the model predictions of the material relaxation and viscous dissipation during a loading-unloading cycle agree well with the experiments.     

A technique for measuring the dynamic behavior of materials at high temperatures

A new experimental technique has been developed for the performance of high temperature, high-strain-rate experiments in the compression Kolsky bar (split-Hopkinson pressure bar or SHPB). The new technique (referred to as the High-Temperature Compression Kolsky Bar or HTCKB) uses an infra-red spot-heater to rapidly heat the specimen to the desired temperature, a!nd an electropneumatic actuation system to minimize the development of temperature gradients in the sample. The technique is cheap and relatively easy to implement and yet provides accurate, repeatable results. As an illustration of the application of the technique, we have examined the high-temperature response of the BCC metal vanadium at high-strain rates. Stress–strain curves are obtained for the material at strain rates of 4 × 10³ s⁻¹ and at temperatures ranging from 300 to 1100 K (27–800°C). Quasistatic (10⁻³ s⁻¹) experiments have also been performed on vanadium over a slightly smaller range of temperatures, and the results are compared with the new high-temperature, high-strain-rate data. It is observed that the rate of thermal softening is a function of the strain rate. These results illustrate the importance of including the coupling between temperature and strain r!ate in thermoviscoplastic constitutive models.     

A dynamic flow rule for viscoplasticity in polycrystalline solids under high strain rates

For visco-plasticity in polycrystalline solids under high strain rates, we introduce a dynamic flow rule (also called the micro-force balance) that has a second order time derivative term in the form of micro-inertia. It is revealed that this term, whose physical origin is traced to dynamically evolving dislocations, has a profound effect on the macro-continuum plastic response. Based on energy equivalence between the micro-part of the kinetic energy and that associated with the fictive dislocation mass in the continuous dislocation distribution (CDD) theory, an explicit expression for the micro-inertial length scale is derived. The micro-force balance together with the classical momentum balance equations thus describes the viscoplastic response of the isotropic polycrystalline material. Using rational thermodynamics, we arrive at constitutive equations relating the thermodynamic forces (stresses) and fluxes. A consistent derivation of temperature evolution is also provided, thus replacing the empirical route. The micro-force balance, supplemented with the constitutive relations for the stresses, yields a locally hyperbolic flow rule owing to the micro-inertia term. The implication of micro-inertia on the continuum response is explicitly demonstrated by reproducing experimentally observed stress–strain responses under high strain-rate loadings and varying temperatures. An interesting finding is the identification of micro-inertia as the source of oscillations in the stress–strain response under high strain rates.     

A comparison of the dynamic response of the ACS and SLS models for linear viscoelasticity

Using asymptotic analysis and numerical computation, we compare the behaviour of the three-parameter viscoelastic model proposed by Achenbach and Chao (ACS) with that of the Standard Linear Solid (SLS) in one-dimensional wave propagation. Our study shows that the models behave very similarly in both the near and far fields and that the much simpler form of the fundamental solution for the Achenbach-Chao model may take it preferable in many applications.     

A simplified over-stress analytical model of the dynamic buckling of a perfectly plastic column under axial impact

I.Introduction-Tllet1niaxiaIyieldingstrengthofastrain-raterelativemateriaIvariesobviuoslyunderdynamicloadstll.Sotheslrain-rateeffectshou1dbeincludedintheanalysisofplasticdynamicbucklingofacolumnl:J.ThispaperappliesMalvern'sover-stressmodell3jtoperfectplasticn'aterialsinthepIasticdynamicbucklinganalysisofacolumn.ThedifferentialequationofdynaI11icsaboutthenexuraIdeflectionofthecolumnisdeduced.Thedominantbucklingmode.thecriticalloadandthebucklingtimeissolvedviatheamplifyingfunctionmethodl4l.F…     

金属材料的率-温耦合响应与动态本构关系综述

金属材料在冲击、爆炸等高应变率加载下的塑性流动行为具有不同于静载下的率-温耦合性和微观机制。航空航天、航海、能源开采、核工业、公共安全、灾害防治等方面的金属结构设计与性能评估需要进行大量的动载实验和数值模拟,建立准确的材料动态本构模型是结构数值模拟可靠性的基础和关键。本文中,总结了金属材料的率-温耦合变形行为及内在机理,回顾了金属动态本构关系研究的起源与发展脉络,分别针对唯象模型、具有物理基础的模型和人工神经网络模型进行了详细介绍和横向比较。唯象模型和人工神经网络模型分别因易应用和高预测精度而受到青睐,基于物理概念的宏观连续介质模型可以描述体现内部演化的真实物理量,从而涵盖更大的应变范围,更好地反映应变率、温度和应变的影响机制。

     

A Pulse-Heated Kolsky Bar Technique for Measuring the Flow Stress of Metals at High Loading and Heating Rates

The National Institute of Standards and Technology (NIST) has developed an electrical pulse-heated Kolsky Bar technique for measuring the constitutive response of metals at heating rates of up to 6,000 K/s and strain rates up to 10⁴ s⁻¹. Under these conditions, which are approaching those found in high speed machining, thermally activated microstructural processes such as grain growth, solid state phase transformation and dislocation annealing can be bypassed, leading to unique non-equilibrium superheated microstructural states. Flow stresses can thus differ significantly from equilibrium high temperature conditions. This paper describes the NIST pulse-heated Kolsky bar technique in detail, including a thorough assessment of uncertainties in temperature and flow stress measurement.

A predictive model for impact response of viscoelastic polymers in drop tests

We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum.     

PVDF压电薄膜用于Hopkinson压杆测量泡沫金属的动态性能

首先对PVDF(polyvinylidene fluoride)压电薄膜在不同温度不同压力作用下的响应进行了系统的试验研究。然后在Hopkinson压杆系统的透射杆之间夹上PVDF压电薄膜,对其动态响应进行了检验。最后应用这个镶嵌PVDF压电薄膜的Hopkinson压杆系统,测试了泡沫铜材料在不同应变率下的应力应变关系。结果表明:(1)PVDF压电薄膜的压电常数D33是随温度和压力而变,实际应用时应对其进行标定;(2)PVDF压电薄膜可有效的用于Hopkinson压杆系统来测试低强度泡沫材料或低阻抗材料的动态响应;(3)当应变率小于0.1/s时,泡沫铜的塑性流动应力对应变率不敏感,在约400/s到5000/s应变率范围,应变小于40%下泡沫铜对应变率也不敏感。但当应变大于约20%,应变率高于400/s时,与低应变率下的值比较,塑性流动应力的应变率敏感性增加。     

A dislocation-mechanics-based constitutive model for dynamic strain aging

Dynamic strain aging (DSA) is an important phenomenon in solute hardened metals and seriously affects the mechanical properties of metals. DSA is generally induced by the interaction between the moving dislocations and the mobile solute atoms. In this paper, only the interaction between moving dislocations and mobile solute atoms in a dislocation core area (core atmosphere) will be taken into account. To establish the constitutive model which can describe the DSA phenomenon, we improved the Zerilli-Armstrong dislocation-mechanics-based thermal viscoplastic constitutive relation, and added the effect of the interaction between the moving dislocations and core atmosphere. Because the constitutive relation established is based on the Zerilli-Armstrong relation, it can describe not only the DSA phenomenon, but also the mechanical behavior of metals over a broad range of temperatures (77K∼1000K) and strain rate (10⁻⁴∼10⁴ s⁻¹). The model prediction for tantalum fits well with the experimental data. Projected supported by the Chinese Academy of Sciences and the High Technical Project.     

Temperature effects on the dynamic response of viscoelastic dielectric elastomer

Viscoelasticity and temperature can significantly affect the performance of a dielectric elastomer. In the current study, we use a thermodynamic model to describe the effect of temperature and viscoelasticity on the electromechanical response undergoing a cyclic electric load by taking into account of the temperature dependent dielectric constant. Because of the significant viscoelasticity in the dielectric elastomer, the deformation and the nominal electric displacement can not keep in phase with the electric field at low frequencies. The results show that the magnitude of the cyclic electromechanical actuation strain increases with the decrease of the temperature and decreases with the increasing frequency, and viscoelasticity can result in significant hysteresis for dielectric elastomers under a relative low temperature and a low frequency.     

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion for high strain and ballistic applications is presented. A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson–Cook failure criterion. The weakening in the elastic law and in the Johnson–Cook-like constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. Additionally, the mesh size dependency on the prediction of the fracture patterns was studied, showing that was crucial to predict such patterns.     

点火能对丙烷-空气预混气体爆炸过程及管壁动态响应的影响

在长12 m的无缝不锈钢直管中,通过改变初始点火能量,探究了点火能对封闭管道内丙烷-空气混合气体爆炸传播特性和激波对管壁动态加载的影响。结果表明,初始点火能对预混气体爆炸火焰传播规律以及管壁的动态响应有显著影响：点火能越大,爆炸越剧烈,爆炸压力峰值压力和管壁最大应变就越大,且压力波和管壁应变的发展一致。火焰在传播过程中受到管道末端反射波的作用会发生短暂熄灭和复燃;管壁承受冲击波加载,应变信号主要分布在0~781.25 Hz,管壁最大应变率大于10^-3 s^-1,实验工况下管壁应变属动态响应。

     

A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites

The dynamics of polymer melts and concentrated solutions reinforced with nanoscale rigid spherical particles is analyzed. Nanocomposites with low filler volume fraction and strong polymer-filler interactions are considered. Entanglement effects are represented by requiring the diffusion in the chain contour direction to be more pronounced than in the direction transverse to the chain primitive path. Filler particles are treated as material points. They reduce the polymer mobility in both longitudinal and transverse tube directions due to short-range energetic filler-polymer interactions. Hence, the contribution to chain dynamics and stress production of both filler-polymer and polymer-polymer interactions is considered to be purely frictional in nature. In the model, the strain rate sensitivity is associated with the thermal motion of chains, with the convective relaxation of entanglement constrains and with the polymer-filler attachment/detachment process. The effect of model parameters is discussed and the predictions are compared with experimental data.     

一种基于电磁霍普金森杆的材料动态包辛格效应测试装置及方法

金属材料在复杂载荷条件下的动态力学行为研究一直备受关注,但受限于实验设备,金属材料的动态包辛格效应响应一直都难以获得。为了探究金属材料的包辛格效应与应变率效应之间的关系,本文中提出一种基于电磁霍普金森杆(electromagnetic split Hopkinson bar,ESHB) 的非同步加载实验技术,为测试金属材料在高应变率加载下的包辛格效应提供了一种有效的实验方法。本文中,首先介绍了非同步加载装置的主要特点,即可以用两列由脉冲发生器产生的应力波对受载试样进行连续的一次动态拉-压循环加载,且加载过程保证了应力波的一致性。分析了应力波对试样加载过程中的波传播历程,确保了加载过程的连续性。随后介绍了动态加载过程,数据处理方法和波形分离手段,并对动态加载过程进行应力平衡性分析,论证了实验装置的可靠性。最后采用该方法测试了5%预应变下6061铝合金动态压缩-动态拉伸的包辛格效应,并与准静态下的实验结果进行对比。实验结果表明,该材料单轴压缩没有明显的应变率效应,但其包辛格效应具有应变率依赖性,高应变率下材料的包辛格应力影响因子由0.07增大至0.17,具有显著的提升,这对传统意义上铝合金材料应变率不敏感的结论提出了挑战。

     

A fundamental relationship between the relaxation spectra and the tangent distribution function in the theory of linear viscoelasticity

The tangent distribution function (TDF) is analyzed within the theory of linear viscoelasticity on mechanical properties. A proof is given that both the relaxation and retardation spectra can be derived from the TDF, through a Fredholm integral equation. Furthermore, the relaxation strength can be calculated as a consequence of this relationship. Finally, as an example, the relationship is applied to discrete spectra.