A new ‘tailor-made’ methodology for the mechanical behaviour analysis of rubber-like materials: I. Kinematics measurements using a digital speckle extensometry

This paper is the first part of a work devoted to the setting-up of a methodology for the mechanical behaviour characterization of rubber-like materials, using a digital speckle extensometer. We present here the experimental approach, specific to large strain measurements. The proposed method is based on in-plane kinematics measurements using an optical extensometer. The whole two-dimensional field of in-plane displacements is obtained by a digital image processing. We discuss then the correlation calculations and how to achieve the optimal subset matching. Next, we specify how to derive the principal stretch ratios, and the accuracy on these components, issued from a subsequent numerical calibration.Finally, we present experimental data dealing with a carbon black, filled natural rubber, issued from uniaxial traction tests, pure shear tests, and tensile tests performed on double-edge notched tensile specimens.     

Modeling and simulation for the swelling behavior of unvulcanized rubber during the calendering process

A comprehensive understanding of the swelling behavior of unvulcanized rubber during the calendering process is essential for the design of calendered products. In this work, the quasi-static cyclic tensile experiments are carried out to investigate mechanical behaviors of unvulcanized rubber, including elasticity, inelasticity, and softening, as well as their strain-rate dependences. Based on the obtained experimental results, a parallel network model consisting of a rate-independent hyperelastic network and two rate-dependent elastic-viscoplastic networks is developed to characterize the constitutive behaviors of unvulcanized rubber. Then a steady-state finite element method together with the constitutive model is proposed to explore the swelling behavior of unvulcanized rubber in the calendaring process. The divergence of thickness ratio between the simulation and experimental results is only 3.54%, which verifies the validity of the solution strategy. Besides, the effects of the calendar speeds and widths of unvulcanized rubber on swelling ratios are investigated. The numerical results show that the thickness/width swelling ratios increase/decrease rapidly with speeds from 1 m/min to 6 m/min, then tends to be stable at the speed of more than 6 m/min and widths hardly affect the variation laws of the swelling ratios with speeds.     

Material ductility and toughening mechanism of polypropylene blended with bimodal distributed particle size of styrene–ethylene–butadiene–styrene triblock copolymer at high strain rate

The material ductility and toughening mechanisms under high strain rate are characterized in the polypropylene (PP) blended with two different styrene–ethylene–butadiene–styrene triblock copolymer (SEBS) by the tensile tests at the nominal strain rates from 0.3 to 100 s^?1, fracture surface observations, interparticle distances, and the morphological finite element (FE) analyses. It is found that the bimodal‐distributed SEBS particle morphology enhances the impact material ductility by craze bands formation, which is caused by the stress interaction between large rubber particles with the highly elongated small rubber particles inside the fibrils of the craze. It is found that there are three conditions for craze bands formation. The first condition is that the total SEBS content is larger than 15 wt %. Second condition is that the weight ratio of small SEBS particles against total SEBS particles should be larger than 0.06. Third condition is that the interparticle distance of large SEBS particles should be larger than 100 nm. In the numerical aspects, the present constitutive law with the craze nucleation and growth can successfully predict the craze bands in the microstructural FE models, leading to the useful procedure for identifying the ductile brittle transition based on the microstructure. The synergistic effect of these rubber particles gives rise to a strong increase in the ductility of these bimodal rubber particle distributed PP systems. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Numerical analysis of neck propagation in polymeric materials. Part 1 – Neck propagation behaviour of poly (ethylene terephthalate) film

Abstract

Neck formation and propagation in poly (ethylene terephthalate) (PET) films have been investigated using finite element analysis (FEA). First, the criteria for the occurrence of neck propagation are examined and a unique constitutive law for polymers is proposed. Neck propagation is associated with a steep rise of the tangent modulus in the plastic deformation region. The ability of the specimen to form a neck is determined by the ratio of the yield stress to the tangent modulus immediately after the yield point. Next, the characteristic load–displacement behaviour in neck formation and propagation is investigated using FEA. Finally, numerical results are compared with experimental data. The calculated values agree with experimental data on load–displacement behaviour, especially for the decrease in load immediately after yield. An apparent constitutive law representing the load–displacement behaviour of PET film has been successfully obtained. By comparing the experimental results with numerical predictions of the neck localisation and propagation process, it is shown that the decrease in load is related to the recovery of deformation in the region outside the neck.     

Simulation of high velocity compaction of powder in a rubber mould with characterization of silicone rubber and titanium powder using a modified split Hopkinson set-up

The paper introduces a method for characterization of silicone rubber and titanium powder in high velocity compaction using the split Hopkinson set-up. The impact test data has been used to estimate parameters in constitutive models for rubber and powder. A finite element study has been performed with different geometrical design of the high velocity compaction of titanium powder against an aluminium mandrel using a rubber mould as pressing medium. One goal of this study is to investigate if and how the manufacturing method can be applied for making dental copings.A conclusion of the experimental work is that it is possible to characterize rubber material and powder material for high velocity compaction of metal powder by the use of a modified split Hopkinson pressure bar set-up. The numerical simulation shows qualitatively good agreement with the experience from practical tests. In conclusion, the work shows the possibility to numerically study the geometric design and to optimize the densification behaviour of a complex high velocity compaction process.     

Damage behaviour of nano-modified epoxy adhesives subject to high stress constraint

This paper presents a combined experimental and numerical study on the damage behaviour of core–shell rubber (CSR)-modified epoxy adhesives subject to high stress constraints. The test method consists of a notched axisymmetric adhesive layer loaded in tension. The stress–displacement curves of the rubber-modified adhesives have been found to exhibit a sudden reduction in stiffness after an initial linear loading region. It has been demonstrated that this corresponds to the cavitation of the rubber particles. The stress of rubber cavitation remained essentially constant at a critical hydrostatic stress of approximately 21 MPa over different rubber contents and different stress constraints. It is important to note that the rubber cavitation stress is also dependent on the size of the rubber particles, and the diameter of the rubber core is approximately 170 nm in current work. The stress constraint had negligible effect on the failure strength of the adhesive joints for the studied systems.     

Characterisation of vulcanised natural rubber behaviour by monotonic and in situ cyclic X-ray scattering tests

Abstract

The effect of curing and loading conditions on the mechanical response of natural rubber are investigated by monotonic and in situ X-ray cyclic tensile tests. Tests are conducted on four samples, which differ by vulcanisation conditions. Samples are subject to two strain rates (2.7?×?10^??3 s^??1 and 16.66?×?10^??3 s^??1), and numerous imposed elongation levels range from 450 to 900%. The coupling between the strain rates and the elongation levels on the stress softening evolution resulting from strain induced crystallisation is investigated. In situ thermomechanical tensile cyclic test is performed in order to withdraw the effect of the strain induced crystallisation on the maximum stress decrease. The experimental results analysis shows that an optimum vulcanisation condition (150°C, 30?min) enhances the hardening process in the monotonic loading due to the strain induced crystallisation. However, under optimum curing conditions, cyclic loading induces a large hysteresis loss, a high stress softening and a high degree of strain induced crystallinity. The material softening sensitivity is controlled by coupled effect of strain ranges and elongation levels. This panoply of experimental measurements present a key information for material parameters identification that are useful to predict the lifetime of engineering components made of natural rubber such as racks, laminated rubber bearings and tires.     

Quantitative modeling of scratch-induced deformation in amorphous polymers

In order to predict scratch performance of polymers, the present study focuses on quantitative assessment of various scratch-induced deformation mechanisms based on a set of model amorphous polymers via numerical modeling. A modification of Ree-Eyring theory is used to account for the rate dependent behavior of the model polymers at high strain rates using the experimental data obtained at low strain rates. By incorporating the rate and pressure dependent constitutive and frictional behaviors in the finite element methods (FEM) model, good agreement has been found between FEM simulation and experimental observations. The results suggest that, by including appropriate constitutive relationship and frictional model in the numerical analysis, the scratch behavior of polymers can be quantitatively predicted with reasonable success. Usefulness of the present numerical modeling for designing scratch resistant polymers is discussed.     

Characterising the behaviour of composite single lap bonded joints using digital image correlation

Three-dimensional and two-dimensional Digital Image Correlation (DIC) have been used to evaluate the evolution of deformation and strain in composite single lap bonded joints prior to failure. In general, composite components are increasingly being joined using structural adhesives for aerospace and other safety critical applications. Reliable design requires that the mechanical behaviour of composite bonded joints is well understood. In this respect, experimental tests are crucial to (a) characterise the deformation and strains induced under load and (b) develop and validate realistic numerical models. Although modern numerical models contain many degrees of freedom, only a few degrees of freedom are typically measured using conventional instrumentation such as strain gauges and extensometers. However, 3D DIC provides an opportunity to measure full-field deformations and surface strains. In the current study, 3D DIC was successfully used to measure full-field in-plane surface strains and out-of-plane surface deformations for composite single lap bonded joints (adherends manufactured from both fibre preimpregnated resin (pre-preg) and resin infused non-crimp-fabric (NCF)). Moreover, strategically located strain gauges were used to validate the strains measured by 3D DIC. Finally, 3D DIC measurements may be useful in detecting subcritical damage as shown in the case of the pre-preg joint. The specific location and magnitude of the maximum principal strain in the adhesive fillet region were determined using high magnification 2D DIC.     

Constitutive modeling of the behaviour of cermet compacts during reaction sintering

This study deals with the identification of a constitutive equation describing the mechanical behaviour of a nickel ferrite based cermet during sintering. This constitutive equation considers the material as a continuum and may enable one to predict the densification behaviour of a powder under different thermal treatments and the impact of compact geometry, external loading on strain and stress generation. A classical viscous equation of the Newtonian type that includes a term describing free sintering densification has been chosen. The method used for the identification of the parameters of this equation is the one proposed Gillia et al., which is based on dilatometry measurement. It includes a stairway thermal cycle for the determination of the free sintering term and intermittent loading for estimating the viscosity. This approach has been successfully applied to nickel ferrite cermet. The model has been found to be adequate to model the densification behaviour up to 1250 °C, but experimental and theoretical efforts must be accomplished to describe the behaviour above this temperature, when the material exhibits swelling.     

Mechanical behaviour at large strain of polycarbonate nanocomposites during uniaxial tensile test

The present study focuses on the mechanical behaviour of polycarbonate nanocomposites reinforced by alumina or silica nanoparticles at low levels of incorporation. More particularly, we present an experimental approach, specific to large strain measurements by using a Digital Image Correlation (DIC) technique. The mechanical mechanisms involved during uniaxial tensile test of polycarbonate nanocomposites were studied at two-dimensional scales. First, elastic properties of the nanocomposites were determined at macro-homogeneous scale and compared to values obtained by continuum-based elastic micromechanical models. Then the in-plane kinematics measurements at the central part of a double-edge notched sample is analysed locally. The evolution during the test of the volumetric strain and axial strain profiles were studied before and after the yield stress: this analysis revealed the existence of several damage processes during the test up to rupture and put in relief the influence of fillers. Finally, the necking phenomenon was statistically studied and the shape of the neck in terms of strain intensity and localisation was analysed.     

油浸式电抗器用阻尼橡胶材料压缩阻尼特性与本构模型

通过对油浸式电抗器器身-油箱间阻尼橡胶材料进行轴向压缩滞回性能试验,研究了其阻尼特性;依据实验数据并结合ABAQUS数值模拟结果,校正了适用于油浸式电抗器器身-油箱间阻尼橡胶材料的Mooney-Rivlin和Yeoh本构模型参数。结果表明,相比普通抗振橡胶试件,丁腈橡胶试件的轴向压缩刚度更大,滞回曲线更饱满,耗能能力更强;Mooney-Rivlin模型和Yeoh模型均适用于NBR试件的小变形和大变形行为,其中Mooney-Rivlin模型参数和Yeoh模型参数计算结果最大误差分别为-11.31%和-12.21%。     

Mooney-Rivlin模型在硅橡胶应力锥受力分析中的应用

采用Mooney-Rivlin模型作为应力锥硅橡胶的本构模型,计算电缆终端应力锥的变形。MooneyRivlin模型的参数C01和C10通过拟合硅橡胶单轴拉伸试验的数据得到。通过Abaqus软件对应力锥进行数值模拟,得到应力锥的受力变形,同时通过实验对应力锥的变形进行测量,发现数值模拟结果和实验结果相吻合,证实了Mooney-Rivlin模型能在电缆终端应力锥硅橡胶材料数值分析中的准确性。     

Non-linear mechanical behaviour of carbon black reinforced elastomers: experiments and multiscale modelling

Abstract

Antivibrating parts in automotives are often made of natural rubber reinforced by carbon black. This reinforcement, which comes from the filler–filler and filler–rubber interactions, leads to an increase in the elastic modulus, the tensile strength and the hysteresis. The aim of this work is to develop a micromechanical model within a generalised self-consistent scheme for filled rubber in the moderate elongation range (|?|≤0·5). A complex morphological pattern, representative of the microstructure of the material, and which takes into account the occluded rubber, the bound rubber and a percolating network, is proposed and the effective elastic properties are compared with experimental results obtained in both uniaxial and oedometric compression. The influence of the specific surface of the filler is investigated, using N330 and N650 carbon blacks. The model is extended to the non-linear accommodation of the stress heterogeneities between the phases. Model predictions are compared with experimental values in compression and simple shear.     

A visco‐hyperelastic constitutive model to characterize both tensile and compressive behavior of rubber

The strain rate–dependent finite deformation behavior of three types of rubber under tension and compression are experimentally characterized using a Hopkinson bar. Based on the measured data, a frame‐independent incompressible visco‐hyperelastic constitutive equation is proposed to describe the tensile and compressive responses of rubber under high strain rates. The equation comprises two parts: a three‐parameter component based on an elastic strain energy potential, to characterize static hyperelastic behavior, and another with four parameters, developed from the BKZ model, to define rate sensitivity and strain history dependence. Established static and dynamic experimental techniques are employed to determine the seven parameters in the constitutive relationship. Comparison of predictions based on the proposed model with experiments shows that it is able to describe the visco‐hyperelastic behavior of rubber‐like materials under high strain rates. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 523–531, 2004     

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

In this article, visco‐hyperelastic constitutive model is developed to describe the rate‐dependent behavior of transversely isotropic functionally graded rubber‐like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate‐dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo‐Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history‐integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye‐BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber‐like materials in different deformation and wide ranges of strain rate. POLYM. ENG. SCI., 56:342–347, 2016. © 2016 Society of Plastics Engineers     

Cure kinetics of a polymer‐based composite friction material

In the present article, cure kinetics of a commercially available composite friction material used in railroad vehicles is investigated using the rheometer measurements. Effect of ingredients of friction material compound, including rubber matrix, phenolic resin, and fillers, on overall cure kinetics of friction compound is also investigated by comparing the cure kinetics of friction material and rubber matrix compound. A phenomenological model and an Arrhenius‐type equation is developed for cure kinetics and induction time of both friction material and rubber matrix. The parameters of the models are extracted from experimental data, using the rheometer at different temperatures and utilizing appropriate optimization method. The good agreement between experimental measurement and models prediction indicates the good performance of the models developed in this study. The results demonstrate that phenolic resin and fillers have dominant effects on the overall cure behavior of the friction material compound. A comparison between the present results and other published data based on the differential scanning calorimetry (DSC) shows a reasonable agreement as well. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 100: 9–17, 2006     

Effect of viscoelasticity in the film‐blowing process

Numerical simulations have been undertaken for the film‐blowing process of viscoelastic fluids under different operating conditions. Viscoelasticity is described by an integral constitutive equation of the K‐BKZ type with a spectrum of relaxation times, which can fit the experimental data well for the shear and extensional viscosities and the normal stresses measured in shear flow. Nonisothermal conditions are considered by applying the Morland–Lee hypothesis, which incorporates the appropriate shift factor and pseudotime into the constitutive equation. The momentum and energy equations are expressed in the machine direction only by using a quasi‐one‐dimensional approach introduced earlier by Pearson and Petrie. The resulting system of differential equations is solved using the finite element method and the Newton‐Raphson iterative scheme. The method of solution was first checked against the Newtonian and Maxwell results for various film characteristics given earlier. The simulations are compared with available experimental data and previous simulations in terms of film shape, velocity, stresses, and temperature. The present results show that the existing modeling of force balances is inadequate for quantitative agreement with the experimental studies. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007