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.     

一种基于分子链统计理论的橡胶超弹性混合本构模型

橡胶材料因其独特的超弹性在实际中广泛应用,通过解析应力-应变关系可以为橡胶力学性能的工程应用提供理论指导。为了更准确地描述橡胶材料力学性能,提出一种适用于橡胶材料的超弹性混合本构模型。新模型基于Gaussian模型与八链模型,引入有关拉伸比的权重函数将二者耦合,在拉伸比较小的情况下,新模型退化成Gaussian形式,在拉伸比较大的情况下,新模型可以依靠权重函数改善八链模型在小变形区域的不足。针对取向硬化的应力-应变曲线、无取向硬化的应力-应变曲线、不同拉伸比应力-应变曲线三种力学特征曲线,从单轴拉伸、等双轴拉伸和纯剪切三类实验数据进行预测验证。结果表明,新模型同时保留了Gaussian模型在小变形范围和八链模型在大变形范围内的预测优势,且对拉伸比和应力应变曲线形式没有依赖性,均能给出高精度的预测结果,突破了Gaussian模型和八链模型的使用限制,为橡胶超弹性力学性能的预测提供了新的思路。     

Thermal and mechanical properties of polypropylene in the thermoplastic elastomeric state

One result of the discovery of homogeneous metallocene stereospecific catalysts is the ability to prepare polypropylene in a stereoblock form in which the isotactic stretches give crystallites acting as temporary crosslinks in an elastomeric network structure. The fact that these elastomers are thermoplastic and thus reprocessible increases the importance of establishing their structure-property relationships. In this report, the dependence of their physical properties on isotactic pentad content, molecular weight, and possible strain-induced crystallization are described. Thermal evaluations and mechanical tests of these materials under oscillatory strain, continuous extension and near-equilibrium uniaxial and biaxial elongation showed that they were multiphase, tough elastomeric materials. Their moduli and tensile strengths increased with increase in % isotactic pentad content and with increase in molecular weight. Equilibrium stress-strain measurements showed the occurrence of strain-induced crystallization in uniaxial, but not in biaxial, deformations.     

Mechanical and structural properties of native and alkali-treated bacterial cellulose produced by Gluconacetobacter xylinus strain ATCC 53524

Mechanical properties of hydrated bacterial cellulose have been tested as a function of fermentation time and following the alkali treatment required for sterilisation prior to biomedical applications. Bacterial cellulose behaves as a viscoelastic material, with brittle failure reached at approximately 20% strain and 1.5 MPa stress under uniaxial tension. Treatment with 0.1 M NaOH resulted in minimal effects on the mechanical properties of bacterial cellulose. Fermentation time had a large effect on both bacterial numbers and cellulose yield but only minor effects on mechanical properties, showing that the fermentation system is a robust method for producing cellulose with predictable materials properties. The failure zone in uniaxial tension was shown to be associated with large-scale fibre alignment, consistent with this being the major determinant of mechanical properties. Under uniaxial tension, elastic moduli and failure stresses are an order of magnitude lower than those obtained under biaxial tension, consistent with the fibre alignment mechanism which is not available under biaxial tension.     

On the large strain deformation behavior of silicone-based elastomers for biomedical applications

The results of a comprehensive mechanical analysis of five silicone-based elastomers are presented. Large strain monotonic tests were performed under uniaxial, strip biaxial and equi-biaxial stress states. Based on the multiaxial experimental data, hyperelastic constitutive models were determined for each material. The small strain elastic modulus ranges from 49 kPa to 1.5 MPa, and the materials show different degrees of non-linearity of their stress-strain response. Data on the time and history dependence allow determining the deviation from the behavior predicted using a non-dissipative hyperelastic constitutive model. Next to representing a guideline for a comprehensive characterization of highly deformable materials, the present results provide data which can be used for the selection of an appropriate material, depending on the specific application. The corresponding models can be used to simulate the performance of each elastomer in applications involving large strains and multiaxial loading states.     

A refined numerical model for determining inflation-burst behavior of composite membrane structures

The airship structures made of multi-layer composite fabrics or membranes can offer the platform for earth observations, wireless communications and space research due to light weight and good mechanical performance. The structural safety and serviceability strongly depend on material properties and working conditions. Available studies are limited within service stress limits or are lack of suitable biaxial tensile constitutive models for understanding structural behavior. This paper thus focuses on a refined numerical model for determining inflation-burst behavior of composite airship structures considering new biaxial constitutive equations, novel failure criteria and manufacture factors.The differences between ideal and real forms of airship structures, e.g. volume difference, demonstrate the necessity for incorporating cutting-pattern effects in the initial numerical model. For structural analysis, stress distributions on real structural forms are different from those on ideal forms because of welding parts that can enhance local stiffness. The ultimate pressures are 56.7 kPa and 59.5 kPa for ideal and real structural forms. Structural breaking initiated at the maximum diameter of ideal structural forms propagates fast while welding parts can prevent breaking propagation for real structural forms. Therefore, the refined numerical model can reveal basic structural behavior and safety performance of airship structures in the inflation-burst processes.     

Finite element simulation for yield stress of hard poly(vinyl chloride)/acrylonitrile-butadiene-styrene blends at different crosshead speeds

Hard poly(vinyl chloride)(PVC)/acrylonitrile-butadiene-sryrene(ABS) blends were prepared using injection-molding and influence of crosshead speed on mechanical properties was examined.Based on morphology parameters obtained from transmission electron microscopy photography and the material parameters from true stress-strain curves of neat PVC and ABS,yield stresses of the blends at different crosshead speeds were simulated employing a two-dimensional nine-particle model based on the finite element analysis(FEA).The FEA results were compared with the experimental yielding stress and the good agreement validated the simulation approach.The FEA approach allowed establishing a yielding criterion related to local yielding of the interstitial matrix between ABS particles.     

Mechanical response of three semi crystalline polymers under different stress states: Experimental investigation and modelling

The mechanical responses of high‐density polyethylene (HDPE), polypropylene (PP) and polyamide 6 (PA 6) were experimentally investigated for a wide range of stress states and strain rates. This was accomplished by testing numerous specimens with different geometries. The uniaxial compression of cylindrical unnotched specimens and the uniaxial tensile behaviour of dumbbell specimens at different strain rates, was determined. A series of biaxial loading tests (combined shear and tension/compression, pure shear, pure tension/compression) using a designed Arcan testing apparatus were also performed. Flat and cylindrical notched specimens with different curvature radii were additionally tested in order to explore a wider range of stress states. The Drucker‐Prager yield criterion was calibrated with a set of experimental data, for which analytical formulae for stresses are available, and then applied to predict the deformation behaviour under different stress states, prior to strain localization. The results of the numerical simulations show that the Drucker‐Prager model can capture the initial elastic range and the post‐elastic response very satisfactorily. For triaxial and biaxial stress states there is a good agreement, however some load‐displacement responses are only satisfactorily described. Deviations observed in the predicted and experimental results are very likely attributed to the third invariant stress tensor, which was not explored in the model calibration. The evolution of stress triaxiality and Lode angle parameters with equivalent plastic strain were extracted and analysed for several specimens. The results show a plastic yielding behaviour sensitive to the stress state, which can be attributed to different combinations of stress triaxialities and Lode angle parameters.     

A new biaxial compression fixture for polymeric foams

This article presents a new biaxial compression test fixture designed for polymeric foam materials. The main advantage of the new fixture is that it is designed for uniaxial testing machines, therefore the biaxial compression measurement does not require a multiaxial test system. The geometries of the fixture and the test specimen, respectively, ensure equibiaxial loading conditions. In order to demonstrate the performance of this new device, equibiaxial measurements of a polymeric foam material are presented. The particular material under consideration is a closed-cell polyethylene foam. In addition, the relation between uniaxial compression tests and equibiaxial compression tests are presented.     

Strain-tunable electronic properties and optical properties of Hf2CO2 MXene

Two-dimensional materials have been extensively applied because of their unusual electronic, mechanical, and optical properties. In this paper, the electronic structure and optical properties of Hf₂CO₂ MXene under biaxial and uniaxial strains are investigated by the Heys-Scuseria-Ernzerhof (HSE06) method. Monolayer Hf₂CO₂ can sustain stress up to 6.453 N/M for biaxial strain and 3.072 N/M for uniaxial strain. Monolayer Hf₂CO₂ undergoes the transition from semiconductor to metal under −12% strain whether it is under biaxial or uniaxial strain. With the increasing biaxial compressive strain, the blue shift of Hf-d, O-p, and C-p orbitals in valence band maximum results in the metallization of monolayer Hf₂CO₂, while the red shift of Hf-d and O-p orbitals in conduction band minimum results in the metallization of monolayer Hf₂CO₂ with increasing uniaxial compressive strain. The analysis of optical properties indicates that uniaxial strain weakens the reflectivity and refractive index of monolayer Hf₂CO₂ in the visible-light range. In addition, the effective mass and the charge distribution under biaxial and uniaxial strains are also explored.     

Biodegradable polyhydroxybutyrate as a polyol for elastomeric polyurethanes

In the proposed work, new elastomeric bio-polyol based polyurethanes (bio-PUs) with specific mechanical properties were prepared by a one-shot process without the presence of a solvent. Commercial non-degradable polyether polyol derived from petrochemical feed stock was partly (in the amount of 1 mass %, 5 mass %, and 10 mass %) substituted by the biodegradable polyhydroxybutyrate (PHB). Morphology of elastomeric PU composites was evaluated by scanning electron microscopy and mechanical properties of the prepared samples were obtained by both tensile measurements and prediction via the Mooney-Rivlin equation. Electron microscopy proved that the prepared materials have the character of a particle filled composite material, where PHB particles are regular with their size of about 1?C2 ??m in diameter. Tensile measurements demonstrated that the Young??s modulus, tensile stress at break, and tensile strain at break of each sample increase with the increase of the volume fraction of the filler. From the measured stress-strain data, the first and the second term of the Mooney-Rivlin equation were calculated. The obtained constants were applied to recalculate the stress-strain curves. It was found that the Mooney-Rivlin equation corresponds well with the stress-strain behavior of the prepared specimens.     

Mechanical properties of diboron-porphyrin sheet under strain: A density functional theory study

The mechanical properties of a new two-dimensional semiconductor material named diboron-porphyrin (DP) are studied based on density functional theory. The behavior of DP monolayer under uniaxial and biaxial loadings as well as shear stress is investigated. The in-plane stiffness, Poisson's ratio, bulk and shear moduli of the DP monolayer are found to be close to those of a graphene sheet. It can be concluded that the DP monolayer has stiffness close to the graphene sheet. The difference in magnitude of in-plane stiffness and Poisson's ratio along x- and y-directions shows slightly anisotropic mechanical properties of DP monolayer. It is also observed that DP monolayers can bear high tensile strains before failure. The high stability and hardly deformable structure of DP monolayer are due to its high planar packing density which is comparable with graphene sheet. The fantastic mechanical properties of DP show these materials are desirable for application in nanomechanical devices.     

碳纤维三向织物/环氧树脂复合材料的制备与力学性能

选择不同纱线间距[即二经(纬)纱之间的中心距]尺寸的碳纤维三向织物, 采用热压成型技术制备了碳纤维三向织物/环氧树脂复合材料. 研究了纱线间距及样品裁剪角度等对力学性能的影响, 并与碳纤维二向织物/环氧树脂复合材料的力学性能进行对比. 结果表明, 随着纱线间距尺寸从2 mm增加到6 mm, 0°方向断裂强度从221.7 MPa下降到148.1 MPa, 撕裂强力从1000 N下降到600 N; 90°方向断裂强度从50.0 MPa下降到22.1 MPa, 撕裂强力从330 N下降到100 N; 顶破强力从424 N下降到216 N. 这些力学性能的逐渐降低是单位面积的碳纤维增强体含量减少和织物的孔洞增大共同作用的结果. 纱线间距为2 mm的碳纤维三向织物复合材料在0°(以纬纱为基准), 30°, 45°, 60°和90°方向的断裂强度分别为221.7, 48.5, 44.3, 227.7和50.0 MPa, 即断裂强度在0°和60°方向大于在30°, 45°及90°方向. 由三向织物的编织原理可知, 0°与60°方向完全相同, 因此其断裂强度相似, 且样品中有一组纱线与外加载荷平行, 对形变破坏具有一定的约束作用, 而30°, 45°和90°方向样品中三组纱线所在的方向均和外加载荷存在一定的夹角, 有效分散外加载荷的能力减弱. 对比碳纤维三向织物/环氧树脂复合材料与碳纤维二向织物/环氧树脂复合材料的断裂强度、 撕裂强力和顶破强力发现, 前者的综合性能明显优于后者, 碳纤维三向织物/环氧树脂复合材料的断裂强度、 撕裂强力、 顶破强力分别为221.7 MPa, 1000 N和424 N, 三向织物的优势得到凸显, 为后续制备多种类型的碳纤维三向织物复合材料及应用奠定了基础.     

Failure analysis of plain woven glass/epoxy laminates: Comparison of off-axis and biaxial tension loadings

An experimental study was focused on investigation of the failure properties of plain woven glass/epoxy composites under off-axis and biaxial tension loading conditions. Four fibre orientations (0°, 15°, 30° and 45° with respect to the load direction) were considered for off-axis tests and two biaxial load ratios for biaxial tests to study failure characteristics and mechanism. Four classical polynomial failure criteria - Tsai-Hill, Hoffman, Tsai-Wu and Yeh-Stratton - were analysed comparatively to predict off-axis and biaxial failure strength of the composites. For failure prediction of the plain woven composites under multiaxial tension loads, the Tsai-Wu criterion was modified by introducing an interaction coefficient F₁₂ obtained from 45° off-axis or biaxial tension tests and the Yeh-Stratton criterion was modified with the interaction coefficient B₁₂ = 0 or obtained from the biaxial tension test. The former criterion was found to have higher accuracy. Finally, according to macroscopic and microscopic studies, the failed specimens showed mostly distinct failure with a specific fracture orientation, mainly exhibiting fibre or fabric tensile fracture mode and a combination of matrix cracking and delamination, both in off-axis and cruciform samples.     

Orientation of the α- and γ-modification of elastic polypropylene at uniaxial stretching

New metallocene catalysts applied to propylene polymerization expand the range of properties of polypropylene (PP), resulting in semi-crystalline materials having crystallinities below 60% up to X-ray amorphous highly elastic ones. To date the origin of the unique elastic mechanical behavior of such low crystalline PP is not completely understood. Therefore, the microscopic orientation of those PPs due to uniaxial stretching was investigated using wide-(WAXS) and small-angle X-ray scattering (SAXS). The aim of this study was to correlate these orientations or changes in the developed fiber textures with the macroscopic stress-strain behavior. This includes efforts to come closer to the main question of the nature of the physical cross-links in these not chemical cross-linked homopolymers, which is the reason for the high elastic behavior. Therefore, high molecular weight metallocene PPs showing different crystallinities (0-36%) were stretched to several elongations and the structural changes during the deformation were recorded by X-ray scattering. Stress-strain measurements show the great potential of these PPs as a thermoplastic rubber material. For quantitative analysis and discussion of the polymer chain orientations, the orientation functions were calculated. Correlations between the orientation functions and the stress-strain curves allow an interpretation of the macroscopic behavior on a microscopic scale. A higher cross-linking density in elongated samples indicates that the network, which is responsible for the elasticity, mainly built up by strain-induced morphology changes and chain orientations.     

Dynamic uniaxial extension of elastomers at constant true strain rate

Elastomers are widely used for damping components in various industrial contexts because of their remarkable dissipative properties: they can bear severe mechanical loading conditions, i.e., high strain rates and large strains. Depending on the strain rate, the mechanical response of these materials can vary from purely rubber-like to glassy. In the intermediate strain rate range (1-100/s), uniaxial extension experiments are classically conducted at constant nominal strain rate. We present here a new experimental methodology to investigate the mechanical response of soft materials at constant true strain rate in the intermediate strain rate range. For this purpose, the displacement imposed on the specimen by the tensile machine is an exponential function of time. A high speed servo-hydraulic machine is used to perform experiments at strain rates ranging from 0.01 to 100/s. A specific specimen is designed in order to achieve a uniform strain field (and thus a uniform stress field). Furthermore, an instrumented aluminium bar is used to measure the applied force; which overcomes the difficulties due to dynamic effects. Simultaneously, a high speed camera enables the measurement of strain in the sample using a point tracking technique. Finally, the method is applied to determine the stress-strain curve of an elastomer for both loading and unloading responses up to a stretch ratio λ = 2.5; the influence of the true strain rate on both stiffness and dissipation of the material is then discussed.     

Evidences of non-linear short-term stress relaxation in polymers

Back in 1986, investigating the Space Shuttle Challenger disaster, famous physicist Richard Feynman clearly showed how viscoelastic behavior of a polymeric material is of paramount importance in practical engineering. At present day a definitive universal rheological law is not yet available for polymers, as a consequence both theoretical models and experimental investigations of viscoelastic behavior must be necessarily focused independently on each single polymer or, at least, on well-defined classes of polymers. Accurate experimental evidences are needed in order to properly evaluate the mechanical properties of a polymeric material, as a function of its particular applications. In this paper measurements of the stress relaxation behavior of six polymeric materials under uniaxial tension and uniaxial unconfined compression tests, are performed and experimental results are modelled using a stretched exponential function, known as Kohlraush-Williams-Watts time-decay function. In particular the short-term stress relaxation is investigated, as a function of typical environmental temperature range, in order to assess viscoelastic behavior of tested polymeric materials for peculiar industrial and biomedical applications.     

Orientability of the Minor Director of Homeotropically Aligned Smectic‐A Elastomers in External Mechanical Fields

We present studies on bulk smectic‐A copolymer networks with end‐on attached homeotropically oriented mesogens that show spontaneous optical biaxiality at room temperature. Orthoscopic and conoscopic investigations under uniaxial extension in the layer planes give first evidence of the orientability of the minor director in mechanical fields yielding biaxial monodomains with 3‐d orientational long‐range order of all three principle axes. This is an important step towards the synthesis of permanently oriented biaxial monodomain elastomers for which highly interesting mechanical and optical properties are expected.     

Mechanical properties of fluorinated ethylene propylene (FEP) foils in use for neutrino detector project

The use of fluorinated ethylene propylene (FEP) foils as engineering materials for aerospace, solar thermal collector and neutrino detector applications has attracted considerable attention in recent decades. Mechanical properties are indispensable for analyzing corresponding structural behavior to meet the demands of safety and serviceability. In this paper, uniaxial tensile tests taking into account loading speeds, uniaxial tensile cyclic tests in terms of stress amplitude and loading cycles and creep tests considering loading stress and time were carried out to characterize mechanical properties. For uniaxial tensile properties, elastic modulus, yield stress, breaking strength and elongation were analyzed in detail. It is found that these mechanical properties except breaking elongation increased with loading speeds and that mechanical properties obtained in transverse direction were more sensitive than those obtained in machine direction. For cyclic properties, elastic modulus and ratcheting strain tended to be stable after certain cycles, demonstrating that cyclic elastic moduli were more suitable for analyzing structural behavior than those obtained in uniaxial tensile experiments. For creep properties, apparent strain at 6 MPa suggested that special attention was necessary for analyzing structural behavior if maximum stress was larger than 6 MPa. In general, this study could provide useful observations and values for understanding mechanical properties of FEP foils.     

DISPERSION AND TENSILE BEHAVIOR OF POLYPROPYLENE/MONTMORILLONITE NANOCOMPOSITES PRODUCED VIA MELT INTERCALATION

Most of the anicles on polymer nanocomposites focus on the importance of chemistry used to modify the surfaceof the clay, usually montmorillonite (MMT), and characterization of the nano-scale structure obtained. The role andimportance of processing were also discussed recently. However, few papers concerning the correlation between morphologyof MMT and mechanical properties were published. In order to understand the tensile behavior of PP/Montmorillonite(MMT) nanocomposites better, and to further improve the reinforcement efficiency, we first prepared the PP nanocompositesvia direct melt intercalation using conventional twin-screw extrusion. The dispersion and tensile property of the compositeswere then investigated by SEM, XRD, TEM and a video-controlled tensile set-up. The macroscopic and microscopicdispersion of MMT in PP matrix was verified by XRD and TEM, combined with SEM. The tensile properties were obtainedby video-controlled tensile set-up, which gives true stress-strain curve. It was found that a partly intercalated and partlyexfoliated structure (also called incomplete exfoliation) existed in the system. Though the tensile strength of PPnanocomposites is not much improved in engineering stress-strain curves, more than 20% increase of true stress was found ina true stress-strain experiment at high true strain, which indicates that only oriented silicate layers can have a big effect ontensile properties. Not only orientation of silicate platelets but also the degree of exfoliation is a key factor to determine thereinforcement efficiency. The reinforcement efficiency of MMT has been discussed based on the "continuum" Halpin-Tsaiequations. A good agreement was found between experimental data and theoretical prediction by changing N value (number of platelets per stack) which corresponding to different state of the dispersion of MMT in PP matrix.