Modelling of the viscoelastic behaviour of amorphous thermoplastic/glass beads composites based on the evaluation of the complex Poisson's ratio of the polymer matrix

A series of polystyrene/glass beads composites were studied by using dynamic mechanical spectrometry. From experimental data obtained under isothermal conditions, a simulation method of viscoelastic behaviour of amorphous thermoplastics reinforced by glass beads was devised. Such a theoretical approach confirmed the requirement of considering the Poisson's ratio as a complex component over all the temperature range. This could be related to the difference of many powers of ten between the moduli of the two phases. Thus, we suggest in this paper a method to evaluate the complex Poisson's ratio of the matrix. From these results, the influence of filler content on the magnitude of the mechanical relaxation related to the glass transition is taken into account.     

Micromechanical modelling of bituminous materials’ complex modulus at different length scales

The aim of this work is to establish a multi-scale modelling technique usable in the study of the complex viscoelastic properties of asphalt mixes. This technique is based on a biphasic approach. At each scale, the heterogeneous media is considered as a two-phase material composed of granular inclusions with linear elastic properties and a matrix of bituminous materials exhibiting linear viscoelastic behaviour at small strain values. In this approach, the homogeneous equivalent properties of biphasic composites are transferred from one scale of observation to the next, higher scale of observation. The viscoelastic properties of the matrix and the elastic properties of the aggregates serve as the input parameters for the numerical models. The generalised Maxwell rheological model is used to describe the viscoelastic behaviour of the matrix. Thanks to the rheological properties of bitumen and the elastic properties of the aggregates, the viscoelastic properties of mastic, mortar and hot mix asphalt (HMA) as bituminous composites can be, respectively, estimated using a micromechanical finite element model. Random inclusions of varying sizes and shapes are generated in order to construct the granular skeleton. A cyclic loading was imposed on the top layer of the digital model. The dynamic modulus of the pre-cited bituminous composites, obtained from the presented multi-scale modelling process while passing from the bitumen to the HMA scale, is validated by comparison with experimental measurements when possible. Concerning our results, we have found that at low temperature (?10 °C), the predicted dynamic modulus is satisfactorily comparable to the experimental measurements. On the other hand, an acceptable gap between predicted numerical results and experimental data takes place when the temperature increases.     

Micromechanical modelling of poly(ethylene terephthalate) using a layered two-phase approach

The aim of this study is to assess the interactions between the constituent phases of poly(ethylene terephthalate) and thereby analyse the validity of a hybrid interaction model in a mean-field micromechanical model based on layered two-phase inclusions. Two different modelling approaches are used to simulate the behaviour of semicrystalline polymers. The first approach is the micromechanical model based on interactions of the crystalline lamellae and the adjacent amorphous layers. The second approach is a two-scale finite-element model of the spherulitic microstructure. Isotropic poly(ethylene terephthalate) is selected as the model material. The deformation mechanisms at the microscopic scale are examined. Various crystal geometries are used in the finite-element model to analyse the case when the crystalline regions do not form an interconnected network. It is shown that the predictions of the microscopic deformation measures obtained with the micromechanical and the finite-element models are similar. Experimental evaluation of the elastic moduli has been performed to further estimate the applicability of the micromechanical model to PET.     

Calculation of Thermal Stresses in Glass-Ceramic Composites

Opto-electronics make intensive use of composite materialsbased on amorphous materials, which can be considered as smart materialssince they are capable of high performances in their final state.Particularly, glass-ceramic composites involved in welding operationsfor microelectronics applications are subjected to important thermalstresses during their production, which can deteriorate their propertiesat room temperature, until the failure stage is reached. It is thenessential to be able to predict the evolution of the internal stressesgenerated during the cooling. We have performed finite-elementsimulations in order to quantify the stress evolutions for differentcomposite geometries: a ceramic fiber embedded within a glass matrix, aspherical particle located at the center of a spherical glass matrix,and a dispersion of spherical ceramic particles, this last case beingthe most representative of reality. The thermomechanical modeling of theglassy matrix takes into account its viscoelastic behavior, and theglass transition is described by the decrease during cooling of the freevolume as a function of the temperature history. The combined effect ofthe differential thermal strain during the transition and mechanicalrelaxation of glass on stress evolutions is evidenced. It is shown thatthe consideration of a periodical or random distribution of sphericalceramic particles leads to similar stress profiles.     

非线性黏弹复合材料有效性质

提出了一个细观力学模型 , 用于预测非线性黏弹聚合物基复合材料的有效性质。该方法利用广义割线模量方法对单积分型热力学本构进行线性化 , 并运用 Laplace变换技术将黏性问题转化为弹性问题。利用热力学本构拟合高密度聚乙烯的实验数据 , 得到基体的材料参数。 利用该模型计算了玻璃微珠填充高密度聚乙烯复合材料(GB/HDPE)在恒应变率下的应力应变关系 , 计算结果与文献实验结果吻合较好。数值计算结果表明 GB/HDPE复合材料表现出明显的非线性力学行为。 该细观力学模型可以很好地预测复合材料非线性黏弹性性质。      

Effective thermal properties of viscoelastic composites having field-dependent constituent properties

This study introduces a micromechanical model for predicting effective thermal properties (linear coefficient of thermal expansion and thermal conductivity) of viscoelastic composites having solid spherical particle reinforcements. A representative volume element (RVE) of the composites is modeled by a single particle embedded in the cubic matrix. Periodic boundary conditions are imposed to the RVE. The micromechanical model consists of four particle and matrix subcells. Micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the subcells. Perfect bonds are assumed along the subcell’s interfaces. Stress and temperature-dependent viscoelastic constitutive models are used for the isotropic constituents in the micromechanical model. Thermal properties of the particle and matrix constituents are temperature dependent. The effective coefficient of thermal expansion is derived by satisfying displacement and traction continuity at the interfaces during thermo-viscoelastic deformations. This formulation leads to an effective time–temperature–stress-dependent coefficient of thermal expansion. The effective thermal conductivity is formulated by imposing heat flux and temperature continuity at the subcells’ interfaces. The effective thermal properties obtained from the micromechanical model are compared with analytical solutions and experimental data available in the literature. Finally, parametric studies are also performed to investigate the effects of nonlinear thermal and mechanical properties of each constituent on the overall thermal properties of the composite.     

Basis for viscoelastic modelling of polyethylene terephthalate (PET) near Tg with parameter identification from multi-axial elongation experiments

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature T_g, the stress vs strain curves present a strain hardening effect vs strain under conditions of large deformations. At a given strain value, the strain rate has also an increasing influence on the stress value. The main goal of this work is to propose a visco-elastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. The visco-elastic model is written in a Leonov like way and the variational formulation is carried out for the numerical simulation using this model. To represent the non–linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained through the comparison with the experimental uniaxial and biaxial tests.     

Micromechanical finite element framework for predicting viscoelastic properties of asphalt mixtures

A micromechanical finite element (FE) framework was developed to predict the viscoelastic properties (complex modulus and creep stiffness) of the asphalt mixtures. The two-dimensional (2D) microstructure of an asphalt mixture was obtained from the scanned image. In the mixture microstructure, irregular aggregates and sand mastic were divided into different subdomains. The FE mesh was generated within each aggregate and mastic subdomain. The aggregate and mastic elements share nodes on the aggregate boundaries for deformation connectivity. Then the viscoelastic mastic with specified properties was incorporated with elastic aggregates to predict the viscoelastic properties of asphalt mixtures. The viscoelastic sand mastic and elastic aggregate properties were inputted into micromechanical FE models. The FE simulation was conducted on a computational sample to predict complex (dynamic) modulus and creep stiffness. The complex modulus predictions have good correlations with laboratory uniaxial compression test under a range of loading frequencies. The creep stiffness prediction over a period of reduced time yields favorable comparison with specimen test data. These comparison results indicate that this micromechanical model is capable of predicting the viscoelastic mixture behavior based on ingredient properties.     

Fracture toughness of glass microsphere-filled polypropylene and polypropylene/poly (ethylene terephthalate-co-isophthalate) blend-matrix composites

The fracture behaviour of glass microsphere-filled polypropylene/poly(ethylene terephthalate-co-isophthalate) blend-matrix composites was investigated in comparison with that of the glass microsphere-filled PP composites. Depending on the deformability displayed by the composite, it was carried out through the linear-elastic fracture mechanics or by applying the J-integral concept. The matrix ductility was regulated in the composite through the glass bead surface treatment applied with different silane-coupling agents, as well as with the addition of maleated PP as polymer compatibilizer. Whereas all the composites failed in a brittle manner at moderate impact speed, quasi-brittle fracture behaviour was only observed at low strain rate in composites having high and medium interfacial adhesion level. Results showed that composites containing both aminosilane-treated glass microspheres and maleated PP showed the highest values of fracture toughness. In composites with low adhesion level between matrix and glass beads, the critical J-integral value diminished due to the presence of PET.     

A new method for evaluation of mechanical properties of glass/epoxy composites at low temperatures

The analytical models based on micromechanical properties of composites are applied to predict the behavior of unidirectional (UD) composite under different types of loadings at room temperature and -60°C. In this study, unlike conventional methods which characterize UD composite via experimental tests on UD specimens under tensile, compressive and shear loadings, micromechanical properties of glass fiber and epoxy matrix at room temperature and -60°C are measured. Then by using various analytical models four elastic moduli and strengths at room temperature and -60°C are calculated. To investigate the validity of the results, experimental tests are performed and compared with analytical results. Results show that elasticity model is the best analytical method to predict four elastic moduli at room temperature and -60°C. Good fits are also found between experimental and analytical results for composite mechanical properties at the room temperature and -60°C.     

The effect of physical ageing on the relaxation time spectrum of amorphous polymers: the fractional calculus approach

Empirical models corresponding to a constitutive equation with fractional derivatives are proposed for linear viscoelastic polymers. For these models, the relaxation modulus, the dynamic moduli, the relaxation time spectra, and other material functions can be calculated as a function of a few parameters that characterise the behaviour of a viscoelastic polymer. The fractional calculus approach allows us to calculate the relaxation time spectrum H() via the Stieltjes inversion in the linear viscoelastic zone. Polymethylmethacrylate (PMMA) is chosen as a model amorphous polymer in a temperature range from T_g + 90°C to T_g + 25°C. This polymer is characterised by a non-equilibrium state between at least the and relaxations. The structural recovery of PMMA has been investigated using dynamic mechanical thermal analysis (DMTA) by varying the preparational history. The effect of time and temperature on the model parameters and on the relaxation time spectra are also investigated in the neighbourhood of the glass transition.     

Analysis of flax fibres viscoelastic behaviour at micro and nano scales

In glass or carbon fibres reinforced plastics, creep or stress relaxation, arise from the polymeric nature of the matrix. Plant fibres, used in bio-composites, are also polymers. Therefore, the issue of their service life requires studying the viscoelastic behaviour of both the matrix and the fibres. In this study, we investigate, at different length scales, the response of elementary flax fibres to tensile tests, as well as to nano-indentation tests on their secondary cell walls. The results of these experiments are then analysed via linear viscoelastic rheological models and identification procedures. The values of the identified parameters (relaxation time, viscosity and elastic stiffness) are discussed in relation to the microstructure of the flax fibre (cellulose microfibrils, hemicelluloses and pectins). The nano-indentation technique provides much more deterministic results than tension tests on an entire fibre. The scale of the secondary wall cell is then relevant to assess the viscoelastic behaviour of the fibres.     

Dynamic mechanical analysis of heat,microwave and visible light cure denture base resins

The clinical durability and performance of a denture are limited by the properties of the denture base resins used in the fabrication of the prosthesis. Among the properties considered important for denture base resins are viscoelastic properties such as storage modulus, damping and glass transition. In this study, dynamic mechanical analysis using a flexural mode of deformation in the temperature range 25–180°C has been used to characterize the viscoelastic properties of three denture base resins with different curing modes including conventional thermal cure, microwave cure and visible light cure. The resins studied were popular commercial systems. The results indicate that the microwave cure and conventional thermal cure resins are significantly different in their viscoelastic properties from the current visible light cure resin system. The latter resin is characterized by higher flexural modulus and loss modulus across the entire range of temperatures investigated and in addition shows higher glass transition temperature relative to the other resins studied. The results indicate that filler loading and crosslinking effects may be responsible for this behaviour of the visible light cure resin and may indicate a potential brittle behaviour not desirable in a permanent denture.     

Time-dependent response of active composites with thermal, electrical, and mechanical coupling effect

The mechanical and physical properties of materials change with time. This change can be due to the dissipative characteristic of materials like in viscoelastic bodies and/or due to hostile environmental conditions and electromagnetic fields. We study time-dependent response of active fiber reinforced polymer composites, where the polymer constituent undergoes different viscoelastic deformations at different temperatures, and the electro-mechanical and piezoelectric properties of the active fiber vary with temperatures. A micromechanical model is formulated for predicting effective time-dependent response in active fiber composites with thermal, electrical, and mechanical coupling effects. In this micromechanical model limited information on the local field variables in the fiber and matrix constituents can be incorporated in predicting overall performance of active composites. We compare the time-dependent response of active composites determined from the micromechanical model with those obtained by analyzing the composites with microstructural details. Finite element (FE) is used to analyze the composite with microstructural details which allows quantifying variations of field variables in the constituents of the active composites.     

Simplified determination of long-term viscoelastic behavior of amorphous resin

The time-temperature superposition principle has been applied to predict accurately the long-term viscoelastic behavior of amorphous resin at a temperature below the glass transition temperature from measuring the short-term viscoelastic behavior at elevated temperatures. A simplified method for the determination of the long-term viscoelastic behavior of amorphous resin using dynamic mechanical analysis is proposed. The automatic horizontal and vertical shifting method is used to construct the smooth storage modulus master curve, and then the accurate time-temperature shift factors can be obtained. The validity of our simplified determination method is confirmed experimentally.     

阳离子染料可染共聚酯的结构及性能

采用动态力学分析法(DMA)、热重法(TGA)及X射线衍射法对常规PET、CDP及醚型ECDP的结构及性能进行了研究。结果表明,CDP的Tg高于PET,但其Tα′及Tm均低于PET。ECDP的Tg、Tα′及Tm均低于PET和CDP,并且随PEG含量及分子量的增加而降低;热解活化能(ΔEd)随着SIPE与PEG含量的增加而降低,即热稳定性降低;另外,与常规PET相比,CDP及ECDP的衍射峰位置基本没有改变,改性共聚酯的组分并未砌入晶格,而是存在于无定型区。     

Characterisation and micromechanical modelling of the elasto-viscoplastic behavior of thermoplastic elastomers

The first objective of this study is to characterise the physico-chemical and mechanical properties of thermoplastic elastomers (TPE) and their constituents. In parallel with the experimental study, a model describing the mechanical behaviour of such materials at room temperature and without damage is proposed. The composite materials studied in the present work are processed by blending particles of vulcanized rubber ethylene-propylene-diene (EPDM) into an isotactic polypropylene (PP) matrix. These particles, obtained from a recycling process, have an average diameter of 70 $\mathrm{\mu }$m. The constitutive equation for TPE composites is developed within the framework of a self-consistent micromechanical approach which considers the mechanical behaviour of each phase. A preliminary analysis of various TPE in linear elasticity justifies the choice of a morphological pattern for the model, which views elastomer particles as embedded in the thermoplastic matrix. In the non-linear domain, the PP matrix is modelled by means of an elastoviscoplastic model whose parameters are fitted using tensile and instrumented spherical micro-indentation tests. The elastomer exhibits viscoelastic behaviour. Having determined the material parameters by inverse analysis, the proposed micromechanical model is compared with tensile and bending tests performed before damage initiation and for various elastomers contents.     

The role of poly(ethylene terephthalate-co-isophthalate) as interfacial agent in polypropylene–matrix composites

The effect of modifying the particle/matrix interfacial region on the morphology and tensile behaviour of glass bead-filled polypropylene (PP) composites was studied. The interface modification was promoted by blending PP with a small concentration (5% by weight) of poly(ethylene terephthalate-co-isophthalate) (co-PET). Ten different PP/co-PET/glass beads ternary composites were prepared, characterized and compared with the homologous PP/glass beads binary ones. Maleic anhydride-grafted PP was added as a compatibilizing agent for PP and co-PET in some of the studied formulations, and its effect studied. Furthermore, four different silane-treated glass beads were used to prepare the composites (50 wt.%). Results showed that three different interfaces, corresponding to three different levels (low, middle and high) of particle/matrix adhesion, could be obtained in these composites by varying the matrix composition and the silane coupling agent on the glass bead surface, which resulted in a wide range of tensile properties, from ductile composites with low tensile strength and high elongation to brittle ones with high tensile strength. It was found that co-PET embeds glass bead surface independently of the silane coupling agent employed. Finally, the adhesion degree differences between the different composite phases seemed to be the main cause to explain the differences found in the sensitivity of the composite tensile characteristics to the strain rate.     

低温保护剂溶液固化性质的DSC研究

利用差示扫描量热仪,研究了乙二醇、丙三醇、1,3丙二醇、1,3丁二醇和2,3丁二醇水溶液的水合性质、玻璃化转变温度和反玻璃化转变温度,得出了这些性质与溶液浓度的关系.研究发现未冻水含量在低浓度时没有明显的规律性,而在中高浓度则随着溶液浓度的增大而增大.对于玻璃化转变,中低浓度区溶液形成的是部分晶体的玻璃态,紧接着在高浓度区溶液形成完全的玻璃态.部分玻璃化的温度不随浓度变化,而玻璃化的温度随浓度增大而升高.形成反玻璃化的浓度范围比较小,反玻璃化的温度随浓度增大而升高.保护剂在玻璃化转变温度和反玻璃化转变温度的明显差异,则反映它们在玻璃化能力方面的强与弱.     

Micro-mechanical modelling of Young’s modulus of semi-crystalline polyamide 6 (PA 6) and elastomer particle-modified-PA 6

In this study semi-crystalline polyamide 6 (PA 6) and its composites consisting of a semi-crystalline PA 6 matrix filled with up to 32.9 vol.% submicron elastomeric copolymer particles are investigated. The aim of this paper is to show how micro-mechanical modelling can predict the elastic behaviour of these composites from the experimentally observed morphology and determined parameters.Semi-crystalline PA 6 possesses a spherulitic morphology, consisting of a radial assembly of amorphous layers and nano-sized crystalline lamellae. In the continuum mechanical representation of semi-crystalline PA 6, nano-sized crystallite lamellae are considered as a phase which is additionally embedded into the amorphous matrix. The 2D self-consistent embedded cell model was chosen to predict the Young’s modulus of the semi-crystalline PA 6 material. In this model a rectangular lamella is surrounded by an amorphous matrix, which is again embedded in the semi-crystalline PA 6 material with the mechanical behaviour to be determined iteratively in a self-consistent manner. The Young’s modulus of PA 6 has been calculated by an appropriate integration of results of all orientations of the crystalline lamellae. The Young’s modulus of PA 6/elastomer composite is also predicted by a 3D self-consistent embedded cell model. In this model a circular inclusion is surrounded by the PA 6 polymer matrix, which is again embedded in the PA 6/elastomer composite. Good agreement is obtained between experiments and the prediction with the self-consistent embedded cell models.