Influencing parameters on measurement accuracy in dynamic mechanical analysis of thermoplastic polymers and their composites

Long-term predictions of material properties such as stiffness and creep resistance are important in many engineering applications and require high reliability and accuracy. This is especially true for polymer materials and their composites as their viscoelastic nature results in time-dependent material behaviour and any measurement uncertainties or errors amplify in long-term predictions. To measure this behaviour at smallest loadings, Dynamic Mechanical Analysis (DMA) is frequently declared as an ideal method. However, the measurement accuracy and repeatability of this method is strongly influenced by (i) the testing fixture and corresponding loading mode, (ii) the sample preparation and (iii) the plotting scale to interpret the test results. In this study, relevant experimental parameters were found for DMA and a proper procedure was designed, which was then applied to measure the viscoelastic behaviour of a highly temperature and creep resistant thermoplastic polymer (polyethersulfone) and of a highly graphite filled polypropylene composite. In combination with finite element simulations and in-situ strain measurements by digital image correlation (DIC), the main influences on measurement accuracy of three-point-bending DMA were identified and subsequently used to determine measurement guidelines. Using these guidelines, DMA measurements allow quantitative determination of the viscoelastic response for rigid polymer and composite materials.     

Viscoelastic modeling of extrusion damage in elastomer seals

ABSTRACT

The viscoelastic behavior of elastomers manifests itself in numerous ways depending on the application. In seals, the viscoelastic response of an elastomer is complex as it depends upon the specific combination of loading pressures, loading rates, chemical environment, temperature and time of loading, and ultimately long-term effects such as creep or stress relaxation can result in seal failure. One specific mechanism encountered in seals under large pressures is extrusion damage. When a seal is pressurized by a fluid, the elastomer is highly constrained; however, there is typically a very small gap between the inner and outer sealing surfaces. Over time viscoelastic creep causes the elastomer to gradually extrude into this gap until the seal ruptures. In this paper the viscoelastic creep behavior of a typical sealing elastomer, NBR, was studied. Compression creep tests were carried out over a range of strains and the measured data were used to develop a strain-dependent viscoelastic material model. The model was then implemented into a finite element analysis (FEA) simulation to study the extrusion creep behavior of an O-Ring seal. Data from the FEA model were then compared against physical test data from equivalent extrusion tests. The FEA model correlated well to the physical test data, with the strain-dependent viscoelastic material model allowing compression creep data to be used to accurately predict extrusion creep.     

Research on viscoelastic behavior of semi-crystalline polymers using instrumented indentation

In this study, the viscoelastic behavior of a polyamide 12 (PA12) polymer was evaluated using instrumented indentation technology based on a rheological model. The creep compliance and retardation spectra were obtained to analyze the viscoelastic response during the holding stage according to the rheological model under different preloading conditions. The results showed that the viscoelastic responses were independent of the indentation depth or load under step loading conditions. However, the creep compliance increases, and the peak intensity of the retardation spectrum decreases with a decrease in the preloading rate owing to the structural relaxation observed during the preloading stage under ramp loading conditions. Furthermore, softening dispersion can be completed during the loading stage under continuous stiffness measurement (CSM) conditions. As the preloading strain rate changes, the peak of the retardation spectrum gradually decreases until it disappears completely. Moreover, studies on indentation creep using the CSM method are challenging because of the complicated viscoelastic response observed during the preloading stage.     

An approximate model for the adhesive contact of rough viscoelastic surfaces

Surface roughness is known to easily suppress the adhesion of elastic surfaces. Here, a simple model for the contact of viscoelastic rough surfaces with significant levels of adhesion is presented. This approach is derived from our previous model (Barthel, E.; Haiat, G. Langmuir 2002, 18, 9362) for the adhesive contact of viscoelastic spheres. For simplicity, a simple loading/unloading history (infinitely fast loading and constant pull-out velocity) is assumed. The model provides approximate analytical expressions for the asperity response and exhibits the full viscoelastic adhesive contact phenomenology such as stress relaxation inside the contact zone and creep at the contact edges. Combining this model with a Greenwood-Williamson statistical modeling of rough surfaces, we propose a quantitative assessment of the adhesion to rough viscoelastic surfaces. We show that moderate viscoelasticity efficiently restores adhesion on rough surfaces over a wide dynamic range.     

Creep relaxation and stress relaxation of PS-HI/SEBS blends

For the selection of the polymer materials and polymer blends for various fields of applications the stability of material under constant deformation and constant load are very important. In this paper, the copolymers high-impact polystyrene, PS-HI, styrene-ethylene/buthylene-styrene block copolymer, SEBS, and their blends PS-HI/SEBS were investigated. The investigations were done by DMA analysis. The secondary viscoelastic functions, creep, creep modulus, stress and flexural relaxation modulus were investigated in creep and stress relaxation experiment at temperatures 25, 35, 45, 55 and 65°C during 1 h. The master curves were created by time-temperature correspondence principle, TTC. The correlation of the secondary viscoelastic functions with time, temperature and content of the hard, PS, phase was discussed.     

A nonlinear uniaxial stress-strain constitutive model for viscoelastic membrane materials

Membrane materials with the excellent thermal, optical, electrical and chemical properties have attracted significant attention in numerous research fields recently. However, while being used to construct the membrane structures, the mechanical behaviors of membrane materials are more foundational than the other properties in evaluating the structure safety. This paper thus proposes a nonlinear stress-strain constitutive model for revealing the viscoelastic behaviors of membrane materials under uniaxial tensile loading. To this end, the constitutive equations for expressing the uniaxial tensile stress-strain relationships of viscoelastic materials are established gradually from the kinematic equations of the generalized Maxwell model that includes several basic Maxwell models and one basic spring element. Meanwhile, the uniaxial tensile tests of two typical viscoelastic membrane materials were carried out in order to examine the proposed constitutive model. The constitutive model parameters of the stress-strain properties of both membrane materials are accurately identified using the least square method. By comparing the true stress-strain curves between experimental results and constitutive models, good agreements with the maximum differences of 4.67% and 3.41% are acquired for the two employed viscoelastic membrane materials, respectively. These observations are able to validate the accuracy and efficiency of this proposed constitutive model in predicting the uniaxial stress-strain behaviors of viscoelastic membrane materials, which are significant in the nonlinear structural analysis of membrane structures.     

Mechanics of contact and adhesion between viscoelastic spheres: An analysis of hysteresis during loading and unloading

Detailed finite element simulations are carried out to study the adhesive contact of viscoelastic spheres. The spheres are brought into contact by a compressive force that increases at a constant rate. Upon reaching a maximum load, the spheres are unloaded until they separate. We studied in detail the effect of loading and unloading rates on hysteresis and on the pull‐off force for a standard viscoelastic solid. The surface interaction is modeled by the Dugdale–Barenblatt model. Numerical results are compared with analytical models for bonding and debonding, including a recent theory proposed by Johnson. There is excellent agreement between analytical and finite element results for the bonding phase. However, for the debonding phase, current analytical models break down unless the loading and unloading rates are slow in comparison with the material relaxation time. Based on the finite element results, a simple approximate analytical model is proposed to quantify adhesive contact in the debonding phase. We also examine the dependence of hysteresis on interfacial parameters such as the cohesive strength and the intrinsic work of adhesion. Our results show that viscoelastic adhesive contact depends on the details of the surface interaction and cannot be determined solely by the work of adhesion. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 772–793, 2002     

Nanoindentation creep of nonlinear viscoelastic polypropylene

Uniaxial tensile creep tests at various applied stresses were carried out to demonstrate that PP is nonlinear viscoelastic. A novel phenomenological model consisting of springs, dashpots, stress-locks and sliders was proposed to describe the nonlinear viscoelasticity. Indentation creep tests at different applied load levels were also performed on nonlinear viscoelastic PP. It was found that the shear creep compliance varies with the applied load level when the applied load is less than 5 mN, which means the indentation creep behavior was nonlinear. To find the real reason for the nonlinearity in indentation creep tests, the elastic modulus at various indentation depths was measured using continuous stiffness measurements (CSM). By analyzing the variation of elastic modulus with indentation depth, the nonlinearity of indentation creep behavior was proved to be caused by the non-uniform properties in the surface of the specimen rather than nonlinear viscoelasticity.     

Modeling instrumented indentation testing to evaluate the behavior of PA11 and CaCO3 composites for offshore applications

PA/PCC micro-composites were prepared with different PCC contents. Compatibility tests were conducted with crude oil at aging times up to 28 days. The experimental phases of the instrumented indentation test (loading, creep and unloading) were modeled. Moreover, the heuristic method of differential evolution was used to fit the parameters. Loading curves showed higher scattering than the subsequent unloading, regardless of the aging time. The two unloading parameters exhibited quasi-linear dependency, but their dispersion was quite different. The mechanical and viscoelastic properties revealed that the PCC filler acted as a reinforcing agent. However, a higher PCC content did not lead to an increase in modulus, probably due to the poor interaction between particles and polymer. The hardness results showed that this property is not so sensitive to the material's morphology as are modulus data. All systems still had predominantly plastic behavior even after aging.     

A new high frequency dynamic mechanical analysis system: An approach to direct high frequency testing of tire tread rubber

Dynamic Mechanical Analysis (DMA) systems are measurement devices for obtaining master curves and complex modules of viscoelastic materials, such as rubbers. The conventional DMAs measurement systems in market have several limitations, which restrict their ability for operating at high frequencies. Thus, Williams, Landel and Ferry (WLF) relation is used to produce master curves and predict the material properties at high frequencies. In conventional DMAs, experiments are done in a range of temperatures, and then a master curve is made for a chosen reference temperature by shifting the measurements data to high frequencies. Therefore, the obtained results, which are not based on direct measurements, can be inaccurate. In order to overcome this problem a new simple shear high-frequency DMA (HFDMA) system is designed and built to directly measure the dynamic mechanical properties of viscoelastic material at high frequencies and the strain levels sufficient for tire manufacturers. The new HFDMA can be used to test any viscoelastic materials which have glass transmission temperature (Tg) lower than room temperature (about 23 °C) such as the Styrene-butadiene rubber (SBR). The SBR is the base material for tire tread. The designing process of this new HFDMA is presented in this paper. The rubber specimen shape is chosen by taking into account the shear elastic wave effect, bending, buckling effect and heat generation in the specimen. The repeatability test is accomplished to ensure that the results obtained from the new HFDMA are repeatable and the repeatability uncertainty is about 0.04%. The new HFDMA is validated by comparing to the direct test results of conventional DMA at 100 Hz. The direct high frequency (5 kHz) complex shear modulus and damping factor are compared with the master curve of the conventional DMA developed by the use of WLF relation for SBR. This comparison revealed that the complex shear modulus and damping factor of the SBR obtained from the HFDMA at 5 kHz and 0.05% strain amplitude are about 7% and 6.5% higher than those obtained from the conventional DMA, respectively.     

Determination of the Poisson’s ratio of viscoelastic materials based on the linear rheological model using instrumented indentation

Based on the linear rheological constitutive model that is used to describe viscoelastic-plastic behavior of viscoelastic materials, a formula of the Poisson’s ratio was deduced according to the relationship between the shear creep compliance and tensile compliance. Instrumented indentation under various loading conditions and universal creep tests were performed on polyamide 12 samples to obtain the relevant rheological parameters. Results show that the Poisson’s ratio for a step load indentation can obtain a constant but overrated value. However, the Poisson’s ratio approaches an asymptotic value and an accurate value can be gained at a certain loading rate.     

A statistical approach to characterize the viscoelastic creep compliances of a vinyl ester polymer

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer with variations in its experimentally obtained material properties under combined isothermal and mechanical loading. Short-term tensile creep experiments were conducted at three temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. The measured creep strain versus time responses were used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of a VE polymer was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using a two-parameter Weibull distribution. Both Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and, subsequently, the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for constant CDF values and compared with the experimental data. The predicted creep compliances of the selected VE polymer in the design space are in good agreement with the experimental data for all three test temperatures.     

Creep loading response and complete loading–unloading investigation of industrial anti-vibration systems

This article presents engineering approaches to evaluate creep loading response and a complete loading–unloading procedure for rubber components used as anti-vibration applications. A damage function for creep loading and a rebound resilience function for mechanical unloading are introduced into hyperelastic models independently. Hence, a hyperelastic model can be extended for both creep and unloading evaluations. A typical rubber product and a dumbbell specimen were selected to validate the proposed approaches. It has been demonstrated that the predictions offered by the new models are consistent with the experimental data. In addition, a loading procedure using the same final value, with and without involving unloading, prior to a creep test can produce different results. The proposed approach can capture this phenomenon which was observed in the literature. The proposed approach can also be easily incorporated into commercial finite element software (e.g., Abaqus). It is demonstrated that the proposed method may be used for anti-vibration products at an appropriate design stage.     

Experimental verification of yield strength of polymeric line contact structures

Polymeric line contact structures are increasingly being used in engineering applications, so that the determination of the yield strength of the structures is of great importance. However, experimental investigation has shown that the current prediction of the yield strength in engineering provides conservative results relative to the actual yield behaviour of the structures. In the present study, a more accurate assessment for the yield strength of a line contact structure is proposed and, more importantly, this assessment was verified by a series of specially designed line contact tests based on optical full-field measurements. Specifically, the validity of this proposed assessment was examined by loading and unloading a polymeric line contact structure at different loading levels, and its accuracy was validated by singly loading line contact structures made from different polymeric materials until the occurrence of significant global plastic deformation. The experimental results confirmed that this proposed yield strength assessment enables accurate determination of the yield behaviour of line contact structures.     

Deformation behavior of oriented UHMW-PE fibers

The mechanical behavior of gel-spun, ultra-drawn, UHMW-PE fibers was investigated as a function of temperature, stress, and time under static and dynamic loading conditions. From a phenomenological point of view, two separate contributions to the deformation behavior could be distinguished, i.e., a reversible (viscoelastic) contribution and an irreversible plastic flow component. It was investigated whether or not this distinction can be rationalized on a molecular basis. The fibers were studied using static (creep) and dynamic mechanical analysis (DMA), dilatometry, and wide-angle x-ray scattering (WAXS). The results of the combined experimental observations are discussed in an attempt to relate the deformation behavior of highly oriented PE fibers to events occurring on a molecular scale.     

Using developed creep constitutive model for optimum design of HDPE pipes

Unlike metal pipes, high density polyethylene (HDPE) pipes are not susceptible to erosion and corrosion. However, the most important mechanical feature of the HDPE pipes is that this material creeps even at room temperature. Therefore, it is essential to study the creep behavior of this material in order to develop a model. In this paper, creep behavior of HDPE at different temperature and stress levels has been experimentally studied to obtain the creep constitutive parameters of the material. These parameters are used to predict the creep behavior of different structures such as HDPE pipes. For this purpose, a number of specimens have been machined from industrial manufactured pipe walls. Uniaxial creep tests have been carried out and creep strain curves with time for each test were recorded. Then, a constitutive model is proposed for HDPE based on the experimental data and optimization methods. The results of this model have been compared with the test data and good agreement is observed. The developed constitutive model and reference stress method (RSM) were used to produce graphs which provide optimum creep lifetime and design conditions for HDPE pipes that are subjected to combined internal pressure and rotation. These graphs can facilitate the design process of HDPE pipes.     

单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale.To date,the Hertzian theory was used for analyzing force- distance curves as the simplest model among several contact mechanics between elastic bodies.However,the preexisting methods based on this theory do not consider the adhesive interaction in principle,which cannot be neglected in the ambient condition.A new analytical method was introdu...     

橡胶在动态载荷下的能量损耗分析

以交联密度不同的同类轮胎胎面胶A1和A2为研究对象,通过动态拉伸实验得到储能模量及损耗模量随频率变化的曲线.建立了黏弹性广义Maxwell模型来定量分析不同温度的橡胶在不同频率的动态载荷下的能量损耗.采用非线性规划的方法分别在低频(10~25 Hz)及高频(25~60 Hz)下拟合模量-频率曲线,得到黏弹性广义Maxwell模型的参数值.采用有限元软件Abaqus模拟胎面胶动态拉伸过程并计算胎面胶的损耗角正切,得到不同温度下胎面胶的损耗角正切随激振频率的变化规律,通过和实验结果的比较证明文中所述黏弹性广义Maxwell模型及其参数获取方法可准确应用于胎面胶的动态拉伸性能分析.预测了在不同温度及频率下每一循环载荷周期中胎面胶的应力-应变迟滞回线以及单位体积胶料的能量损耗,阐释了不同温度下的胎面胶的能量损耗随频率的变化规律,同时结合2种胎面胶的交联密度测试数据分析了胶料的构效关系.