A model for the viscoelastic behavior of polymers at finite strains

Summary A constitutive model is derived for the isothermal nonlinear viscoelastic response in polymers, which do not possess the separability property. The model is based on the concept of transient networks, and treats a polymer as a system of nonlinear elastic springs (adaptive links), which break and emerge due to micro-Brownian motion of chains. The breakage and reformation rates for adaptive links are assumed to depend on some strain energy density. The viscoelastic behavior is described by an integral constitutive equation, where the relaxation functions satisfy partial differential equations with coefficients depending on the strain history. Adjustable parameters of the model are found by fitting experimental data for a number of polymers in tension at strains up to 400 per cent. To validate the constitutive relations, we consider loading with different strain rates, determine adjustable parameters at one rate of strains, and compare prediction of the model with observations at another rate of strains. Fair agreement between experimental data and results of numerical simulation is demonstrated when the rates of strains differ by more than a decade. Received 1 July 1997; accepted for publication 7 October 1997     

Limitations of the Phan-Thien non-linear network viscoelastic model

The failure of the Phan-Thien non-linear network viscoelastic model to predict realistic stress-strain relationships under certain conditions is illustrated in two examples. Care in the application of the model when applied in situations where high shear rates are expected is indicated.     

大药片落锤撞击感度研究

设计建立了一种炸药大药片撞击感度试验方法,落锤质量为20 kg、落高度为0~15 m,对规格20 mm5 mm、重约2.8 g的大药片进行撞击感度测试。试验测试了两种典型炸药Tetryl和JOB-9003炸药的落锤撞击感度,落锤撞击Tetryl炸药和JOB-9003炸药的爆炸阈值落高分别约3.5 m和6.5 m。对落锤撞击JOB-9003炸药样品的过程进行了数值计算,计算结果与试验值相符。试验结果表明,该试验方法可以测量炸药的落锤撞击感度。     

A model of traps for yield in amorphous glassy polymers

Summary  Constitutive equations are derived for the viscoelastic and viscoplastic behavior of amorphous glassy polymers at isothermal loading with small strains. The model is based on the trapping concept: a disordered medium is treated as an ensemble of plastic flow units (with the characteristic size of micrometers), which, in turn, consist of a number of cooperative rearranging regions (with the characteristic length of nanometers). The viscoelastic response is described by rearrangement of relaxing regions, whereas the viscoplastic behavior is modeled as irreversible deformation of plastic units. Adjustable parameters are found by fitting observations for aromatic polyesters, nylon-66, polycarbonate block copolymers and an epoxy glass. Fair agreement is demonstrated between experimental data and results of numerical simulation. Received 17 November 1999; accepted for publication 23 March 2000     

A molecular network model to describe the nonlinear viscoelastic behavior of polymers

A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed. The project supported by the National Natural Science Foundation of China and Doctorial Fund     

储液容器跌落冲击动力学神经网络建模

运用LS-DYNA程序中的ALE算法模拟储液容器在不同的跌落角度、跌落高度、壳体厚度下的跌落冲击过程,获取神经网络预测模型的训练样本集;利用BP神经网络建立储液容器结构参数、跌落冲击参数与接触点最大应力之间的映射关系预测模型,并将各种参数下的接触点最大应力网络预测值与仿真值比较,两者差异较小,表明该方法是有效的,可以为实际生产过程中参数选择提供理论依据.     

Constitutive equations for fiber suspensions in viscoelastic media

The kinetic theory of elastic dumbells with a friction factor that depends on the fiber orientation is used to obtain constitutive equations for fiber suspensions in a polymer matrix. We followed the approach of Fan (X.J. Fan, in P. Moldenaers and R. Keunings (Eds.), Theoretical and Applied Rheology, Proceedings XIth International Congress on Rheology, Brussels, Elsevier, Amsterdam, 1992, pp. 850–852), and derived equations for polymer solutions based on the FENE-P, FENE-CR, and Giesekus models. Start-up and steady-state free shear flows are studied to explore the effects of the fiber-polymer coupling as well as the fiber volume fraction. Predictions based on different types of closure approximations for the fourth-order fiber orientation tensor are also discussed.     

A non-linear viscoelastic model for ceramics at high temperatures

High-temperature mechanical behavior of ceramics is characterized by non-linear rate dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to rupture. Moreover, rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the non-linear, asymmetric time-dependent behavior, a new non-linear viscoelastic model is proposed. Non-linearity and asymmetry are introduced in the volumetric component. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Non-linear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of rupture lives. Numerical simulation results compare well with results of four-point bending experiments.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

On the analytic expression of the free energy in linear viscoelasticity

Two definitions of free energy for a linear viscoelastic material, due to Graffi and to Coleman and Owen, are considered, and the compatibility of these definitions with some expressions of the free energy proposed in the literature is examined. For the expressions of Staverman and Schwarzl and of Breuer and Onat, the two definitions are proved to be equivalent, and the set of all relaxation functions for which the two expressions are indeed free energies is determined. Two more expressions, proposed by Volterra and Graffi and by Morro and Vianello, are taken into consideration. For them, only the classes of relaxation functions for which they are free energies according to the first definition, is completely characterized. All results are established under regularity assumptions weaker than those usually made in the literature.     

Nonlinear dynamic buckling of a viscoelastic model under impact loading

A simple nonlinear buckling analysis is applied to a one-degree-of-freedom arch under impact loading in which viscous damping may also be included. Such a loading consists of a falling body striking centrally the joint mass of the arch in such a way that a completely plastic impact can be postulated. When there is no damping the exact dynamic buckling load for such a kind of loading-associated with an unbounded motion can be established by using a static criterion (approach). More specifically, it was shown that the dynamic buckling load corresponds to that unstable equilibrium state where the total potential energy of the system is zero. Furthermore, it was proved that the second variation of the total potential energy at the foregoing unstable equilibrium state is negative definite. This implies that the curve loading versus displacement resulting by the vanishing of the total potential energy has always a maximum on the afore mentioned unstable state. It was also found that the system may become sensitive to initial conditions. If damping is included the foregoing static criterion yields lower bound buckling estimates. These findings were verified by employing a highly efficient approximate technique as well as the numerical scheme of Runge-Kutta for solving any nonlinear initial-value problem.     

Numerical simulation of Taylor impact tests

The present paper discusses some aspects in the numerical simulation of Taylor impact tests. A phenomenological internal variable theory is presented and restricted by the second law of thermodynamics. The constitutive model consists of a thermo-hyperelastic equation for the stresses and an evolution equation for the plastic internal variable. Specific thermo-plastic constitutive functions are proposed and corresponding material parameters are identified. Taylor impact tests are numerically simulated using the explicit finite element program LS-DYNA augmented by an user-defined material subroutine and the effect of variation of selected model parameters is discussed. Numerical results allow new interpretations of experimental observations and test data and gives advice on identification of material parameters in rate-dependent inelastic constitutive models.     

聚乙烯泡沫单填充纸瓦楞管的轴向跌落冲击缓冲吸能特性

利用聚乙烯闭孔泡沫单填充纸瓦楞管开展轴向跌落冲击试验,对比分析了结构参数和冲击参数对其缓冲吸能特性参数（比吸能、行程利用率、压缩力效率、比总体效率）的影响。结果表明,X向单填充管的动态缓冲吸能特性优于Y向单填充管,而静态缓冲吸能特性差于Y向单填充管。正四边形单填充管的动态缓冲吸能特性优于正五、六边形单填充管,X向正四边形单填充管的比吸能相较于正五、六边形管分别提高了114.4%和182.3%。对于跌落冲击压缩,单填充管的比吸能、行程利用率、比总体效率随着管长比的增大而减小,管长比为1.4的X向单填充管的比吸能相较于管长比为2.2和3.0的单填充管分别增加了45.8%和117.9%,而压缩力效率随着管长比的增大而增大。随着跌落冲击质量或冲击能量的增加,比吸能、行程利用率、压缩力效率和比总体效率皆呈增大趋势,冲击质量对X向单填充管的影响较大,而冲击速度则对Y向单填充管的影响较大。

     

A procedure for measuring biaxial viscoelastic behavior of thermoplastics

In order to accurately simulate the thermoforming or blowmolding manufacturing processes using finite elements or some other suitable computational procedure, it is necessary to know the constitutive behavior of the material being formed. In this study, an apparatus was developed to measure the large deformation behavior of thermoplastic sheet at elevated temperatures. The specifications of the test apparatus, as well as sample data measurements are presented. Biaxial viscoelastic material properities of ABS sheets were determined at forming temperatures. In particular, the nonlinear stress-strain relationship of the material was experimentally measured at various temperatures above the glass transition temperature and the data correlated to a time and strain separable viscoelastic material model. The results of this study show that it is possible to recover the underlying nonlinear elastic response of heated ABS sheet material, at finite strains, from tests exhibiting significant viscoelastic behavior.     

A nonlinear atomization model for computation of drop size distributions and spray simulations

A model has been developed to provide a comprehensive simulation of a spray formed by a high‐speed liquid jet. The primary atomization process is simulated in a completely nonlinear fashion using the boundary element method under the assumption of axisymmetric, inviscid flow. The presence of the orifice boundary layer is simulated with a ring vortex whose strength and location are uniquely determined from boundary layer properties at the orifice exit plane. Droplet and axisymmetric ligament tracking models have been developed to provide more comprehensive spray simulations. The breakup of the axisymmetric ligaments shed from the parent surface is assessed both in a nonlinear fashion as well as using the linear stability analysis of Ponstein. Using this latter approach, drop size distributions have been generated from first principles and compared with the popular Rosin–Rammler model. Copyright © 2005 John Wiley & Sons, Ltd.     

A rationally-based correlation of mean fragment size for drop secondary breakup

A correlation was derived for the Sauter mean diameter of fragments produced in the bag and multimode drop breakup regimes for drops having Ohnesorge numbers less than 0.1. Development of the correlation focused on the growth of capillary instabilities on the toroidal rim seen during the final stages of bag breakup. The model linked the time scale for drop breakup and the time scale associated with growth of the unstable waves. The instability scale was approximated from the results of linear stability theory for capillary waves on liquid cylinders. The drop breakup scale was based on correlations available in the literature for drops subjected to a rapid (relative to drop deformation time scales) rise in relative velocity. Though development focused on bag breakup, the resultant expression was also shown to correlate the multimode regime data reasonably well.     

A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation

The present work focuses on the development of a physically-based model for large deformation stress-strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic-viscoplastic model of [Boyce et al., 1988] and [Boyce et al., 2000]. The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic-viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core-hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress-strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.