Viscoelasticity and viscoplasticity of semicrystalline polymers: Structure–property relations for high-density polyethylene

Observations are reported on two commercial grades of high-density polyethylene (HDPE) in uniaxial tensile tests, relaxation tests, creep tests and cyclic tests with a strain-controlled deformation program. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformation with small strains. A polymer is modeled as a two-phase continuum consisting of a crystalline skeleton and an amorphous phase treated as a transient network of chains. Its viscoelastic response is associated with thermally activated rearrangement of strands in the temporary network. The viscoplastic behavior reflects fine and coarse slip of lamellar stacks and sliding of junctions between chains in the network. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The study focuses on the effect of molecular weight of HDPE on its mechanical properties.     

Constitutive equations for the nonlinear viscoelastic and viscoplastic behavior of thermoplastic elastomers

Observations are reported in uniaxial tensile tests with constant strain rates at moderate finite deformations, as well as in creep and relaxation tests on a thermoplastic elastomer (ethylene–octene copolymer) at room temperature. A constitutive model is developed for the viscoelastic and viscoplastic responses of a polymer at arbitrary three-dimensional deformations with finite strains. A thermoplastic elastomer is treated as an incompressible heterogeneous transient network of strands. Its viscoelastic behavior is associated with separation of active strands from their junctions and merging of dangling strands with the network. The viscoplastic response reflects sliding of junctions between strands with respect to their reference positions. Stress–strain relations are derived by using the laws of thermodynamics. They involve six adjustable parameters that are found by fitting the experimental data. To examine the accuracy of the model predictions, plane-strain compressive tests with constant strain rates and relaxation tests at compression are performed. Good agreement is demonstrated between the observations and the results of numerical simulation.     

Non-linear viscoelasticity and viscoplasticity of isotactic polypropylene

Observations are reported in tensile tests with constant cross-head speeds (ranging from 5 to 200 mm/min), relaxation tests (at strains from 0.02 to 0.08), creep tests (at stresses from 15.0 to 25.0 MPa) and recovery tests (after straining up to the maximal strains ranging from 0.04 to 0.12 and subsequent retraction) on isotactic polypropylene at room temperature. A constitutive model is derived for the time- and rate-dependent responses of a semicrystalline polymer at isothermal deformation with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical cross-links and lamellar blocks). The network is thought of as an ensemble of meso-regions linked with each other. The viscoelastic behavior of the ensemble reflects thermally-induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). To describe the viscoplastic response, the entire plastic deformation is split into the sum of two components: one of them is associated with sliding of junctions in the non-affine network of chains, while the other accounts for coarse slip and fragmentation of lamellar blocks. Stress–strain relations and kinetic equations for the plastic strains are developed by using the laws of thermodynamics. The constitutive equations involve five material constants that are found by fitting the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.     

The effect of temperature on the viscoelastic response of polymer melts

Observations are reported in isothermal torsional oscillation tests on melts of isotactic polypropylene (iPP) and low-density polyethylene (LDPE) in the intervals of temperature between 190 and 250 °C (iPP) and between 120 and 190 °C (LDPE). With reference to the concept of transient networks, constitutive equations are developed for the viscoelastic response of polymer melts at three-dimensional deformations with small strains. A melt is treated as an equivalent network of strands bridged by temporary junctions (entanglements and physical cross-links whose life-times exceed the characteristic time of deformation). The time-dependent behavior of the network is modelled as detachment of active strands from their junctions and merging of dangling strands with the network. The network is assumed to be strongly heterogeneous in the sense that different junctions have different activation energies for separation of strands. The stress–strain relations involve three adjustable parameters (the plateau modulus, the average activation energy for rearrangement of strands and the standard deviation of activation energies) that are determined by matching the dependencies of storage and loss moduli on frequency of oscillations. The difference in the effects of temperature on the material constants of iPP and LDPE is associated with the difference in their molecular architecture.     

The effect of thermal oxidative degradation of polymers on their viscoelastic response

A model is developed for thermal oxidative degradation of polymer melts and its effect on their viscoelastic response. Based on the theory of temporary heterogeneous networks, stress-strain relations are derived for the time-dependent behavior of a polymer melt at arbitrary three-dimensional deformations with small strains. Within the fragmentation-annihilation concept, kinetic equation is proposed for the distribution of strands with various lengths in a network, and its explicit solution is obtained. Material parameters in the constitutive equations are found by fitting experimental data in shear oscillation tests on a polypropylene melt annealed at elevated temperatures for various times. Good agreement is demonstrated between the observations and the results of numerical simulation.     

Thermo-viscoelastic response of nanocomposite melts

Observations are reported in shear oscillatory tests with small strains (the frequency-sweep mode) on a hybrid nanocomposite melt [thermoplastic elastomer (ethylene-octene copolymer) reinforced with various concentrations of montmorillonite nanoclay] at temperatures ranging from 150 to 210 °C. A constitutive model is developed for the viscoelastic behavior of a nanocomposite melt at arbitrary three-dimensional deformations with small strains. The melt is treated as an inhomogeneous, permanent polymer network with sliding junctions (entanglements and physical cross-links at the surfaces of nanofiller). It is assumed that macro-deformation induces sliding (plastic flow) of junctions between strands with respect to their reference positions, and the strain energy of the network depends on strain tensors for elastic and plastic deformations. Stress-strain relations are derived by using the laws of thermodynamics. These equations involve four adjustable parameters that are found by fitting the observations. It is demonstrated that (i) the governing equations correctly reproduce the experimental data and (ii) the material parameters change consistently with temperature and concentration of filler.     

Creep rupture and viscoelastoplasticity of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformations with small strains. The stress-strain relations involve eight material constants that are found by fitting the experimental data. The model is applied to the numerical analysis of creep failure of polypropylene under various deformation modes (uniaxial tension, equi-biaxial tension, shear, multiple-step creep tests).     

The effect of temperature on the viscoelastic response of rubbery polymers at finite strains

Summary Constitutive equations are derived for the viscoelastic response of rubbery polymers at finite strains. A polymer is thought of as a network of long chains connected to temporary junctions. At random times, chains detach from the junctions, which is treated as transition from their active state to the dangling state. A dangling chain captures a new junction in the vicinity of its free end at a random instant and returns to its active state. Breakage and reformation of long chains are modeled as thermo-mechanically activated processes. Stress-strain relations for a rubbery polymer are developed using the laws of thermodynamics. Adjustable parameters in the model are found by fitting observations in uniaxial tensile tests for a carbon black filled rubber at various temperatures. Fair agreement is demonstrated between experimental data and results of numerical simulation.     

Viscoelasticity of polyethylene/montmorillonite nanocomposite melts

Observations are reported on low-density polyethylene melts reinforced with montmorillonite nanoclay at concentrations of filler ranging from 0 to 10 wt.% in small-amplitude shear oscillatory tests, start-up tests with a constant strain rate, and relaxation tests. Constitutive equations are derived for the time-dependent response of a nanocomposite melt at three-dimensional deformations with finite strains. The model accounts for (i) inhomogeneity in the distribution of nanoparticles, (ii) non-affinity of an equivalent polymer network with sliding junctions, and (iii) evolution of energies of inter-chain interaction driven by orientation of clay platelets. It is demonstrated that the stress–strain relations correctly describe the experimental data and adjustable parameters change consistently with nanoclay content.     

A constitutive model for the viscoplastic behavior of rubbery polymers at finite strains

Summary. A constitutive model is derived for the viscoplastic behavior of rubbery polymers at finite strains. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The elastic response of the network is attributed to the elongation of strands, whereas its plastic behavior is associated with the sliding of nodes with respect to their initial positions. Unlike conventional stress–strain relations in finite viscoplasticity, the rate-of-strain tensor for the sliding of junctions is expressed in terms of the rate-of-strain tensor for macro-deformation. Constitutive equations are developed by using the laws of thermodynamics. These relations are simplified for simple shear of an incompressible medium with finite strains. The governing equations are determined by 3 material constants. To verify the model, a series of shear tests is performed on polycarbonate melts reinforced with short glass fibers. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is shown that the material constants change with the filler content in a physically plausible way.Department of Chemical Engineering, Kuwait University, Safat 13060, Kuwait     

Creep failure of polypropylene: experiments and constitutive modeling

Observations are reported on isotactic polypropylene in uniaxial tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at ambient temperature. Constitutive equations are derived for the viscoelastic–viscoplastic responses and damage of a semicrystalline polymer at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The model is applied to predict creep-failure diagrams in the entire interval of stresses. A phenomenological approach is proposed to determine a knee stress, at which transition occurs from ductile to brittle rupture. Accuracy of this method is evaluated by numerical simulation.     

Thermo-visco-plastic behaviour of fibre-reinforced polymer composites

The effect of temperature and strain rate on the tensile behaviour on a series of polymeric matrix-unidirectional glass–fibre composites was studied. Dynamic mechanical analysis (DMA) experiments, as well as tensile tests at three different strain rates and three different temperatures below T_g were performed on off-axis specimens of three different orientations. The strong temperature and strain rate dependence, exhibited by the materials examined, was further described theoretically by applying a formulation of finite elastoplasticity. Constitutive laws based on the material anisotropy, were applied, in combination with constitutive equations of hypoelasticity, written in their objective form. Moreover, empirical equations for the hardening coefficients, arising from the thermal activation theory, were proposed to formulate the temperature and strain rate effect.     

On the mechanics of large inelastic deformations: kinematics and constitutive modeling

Summary In this paper we examine the complexities associated with the kinematics of finite elastoplastic deformations and other issues related to the development of constitutive equations. The decomposition of the total strain and strain rate tensors into elastic and plastic constituents is investigated by considering both a multiplicative decomposition of the deformation gradient and an additive decomposition of the deformation vector field. Physically based definitions for the elastic and plastic strain rate tensors are given and compared with other values found in the literature. Constitutive equations for the plastic flow are derived by considering both a phenomenological-energy approach and a physically motivatedmesomechanical approach based on the double-slip idealization. It is shown that by resorting to the mechanics of the double slip, specific relations for the plastic stretching and plastic spin can be rigorously derived, taking into account the effect of noncoaxiality and material rotation. Finally, the implication of such effects to large deformations is examined in connection with the localization phenomenon.     

A structural experimental technique to characterize the viscoelastic behavior of concrete under restrained deformations

An innovative variable restraint frame is proposed to characterize the viscoelastic behavior of concrete under tensile stresses induced by restraints to shrinkage deformations (mainly due to drying). Two concrete specimens with the same cross section are used, subjected to equal thermal and moisture conditions: one is made of plain concrete, to assess the “free” deformations due to shrinkage and temperature; the other is reinforced with two steel threaded rods, which induce a manually controlled axial restraint to shrinkage. The restrained specimen is installed on a reaction frame, being stretched in force control mode. The concrete and the rods are instrumented with strain gauges and temperature sensors, which allow separation of the different components of concrete strains with the aid of equations based on equilibrium and compatibility conditions. This permits identifying the elastic and tensile creep concrete strains, as well as the concrete tensile stresses induced by the restrained shrinkage. The device also allows assessing the concrete modulus of elasticity during the test and remains operational even upon concrete cracking, features of great interest for the intended material characterization.     

An unusual elastoplastic response of thermoplastic elastomers at cyclic deformation

Observations are reported on a thermoplastic elastomer (ethylene–octene copolymer) in uniaxial tensile tests. The experimental data reveal a rather unusual mechanical response: unlike particle-reinforced rubbers, for which preconditioning causes a monotonic decrease in tensile stress compared with that in a virgin specimen, cyclic preloading of the thermoplastic elastomer induces a reduction in stress at small strains and its noticeable growth at relatively large elongation ratios.A constitutive model is derived for the elastoplastic behavior of a polymer network with constrained chains at three-dimensional deformations with finite strains. The stress–strain relations involve five adjustable parameters that are found by fitting the experimental data. Good agreement is demonstrated between the observations and the results of numerical simulation. It is shown that the material parameters are affected by intensity of preloading in a physically plausible way.     

CuZn37黄铜板料微塑性成形中的尺寸效应研究

为研究金属微塑性成形特点,对厚度不同及粗细两种晶粒尺寸的黄铜箔试样进行了单向拉伸和微弯曲实验,并采用经典塑性理论和应变梯度理论对弯曲回弹角进行了预测.粗晶粒板料试样单向拉伸实验表明,CuZn37黄铜的硬化曲线存在一种明显的尺寸效应,即板料厚度越小,屈服强度越高.弯曲回弹实验结果也存在另一种明显的尺寸效应现象,即板料厚度...     

Effect of temperature on the viscoelastic and viscoplastic behavior of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various cross-head speeds and relaxation tests in a wide interval of temperatures ranging from room temperature to 120°C. A constitutive model is derived for the viscoelastic and viscoplastic responses of a semicrystalline polymer at arbitrary deformations with small strains. The stress–strain relations involve 6 adjustable parameters that are found by fitting the experimental data. The presence of a critical temperature is demonstrated at which some parameters of the model reach their maxima. This temperature is associated with the α-relaxation temperature of polypropylene.     

Simultaneous determination of in-plane shear and transverse moduli of unidirectional composite laminae at different strain rates and temperatures

A semi-empirical method is proposed for the extraction, simultaneously, of the transverse tensile and in-plane shear moduli of unidirectional laminae, at various strain rates and temperatures, from tests on symmetric and balanced ±65 ° angle-ply composite laminates. The extraction method is applied to data obtained from tests on Kevlar-49/epoxy and carbon/ epoxy filament-wound tubes which were subjected to internal pressure loading at three key temperatures of −45, 20 and 70 °C at different strain rates of up to 80/s. The combined effect of strain rate and temperature on these extracted properties is studied by applying strain rate temperature equivalence principles. It is found that the variation of the mechanical properties of the two materials with strain rate and temperature can be adequately described by semi-empirical equations similar to the Arrhenius and Williams-Landel-Ferry relationships, usually used for homogeneous solids.     

Dynamic mechanical analysis of some randomly-oriented viscoelastic short-fiber composites

The mechanical properties of two series of composites consisting of tanned leather fibers in an ethylene-vinyl acetate copolymer matrix were studied by means of tensile and dynamic mechanical tests. The effect of fiber content on Young's modulus and the viscoelastic properties was studied by using five distinct fiber concentrations. Dynamic measurements were carried out at a frequency of 11 Hz and temperatures from - 70 to 80°C. The applicability of the Hashin correspondence principle was tested in order to provide a better understanding of the fiber content effect on the viscoelastic properties of these composites.