Residual stresses and warp generated by one-sided quench of an epoxy-resin beam

This paper discusses the warp and accompanying residual stress in a rectangular epoxy beam produced by water cooling its lower surface. First, the theoretical values of this warp and residual stress are obtained by the linear-viscoelastic theory. The specimen is then subjected to quenching. The variations in the warp are observed. After quenching, the residual stress is measured by a layer-removal method. The experimental and theoretical results are then compared and discussed.     

Photoviscoelastic behavior and residual thermal birefringence in optical-grade polycarbonates

The stress-optical coefficient functions of two optical-grade polycarbonates (PCs) have been obtained by simultaneous measurements of the relaxation modulus and strain-optical coefficient functions. Nonlinear behavior of the relaxation modulus and strain-optical coefficient was observed at small strains at room temperature. Comparison of these functions in the linear region with those of a commercial grade PC was made. These functions have been incorporated to linear viscoelastic and photoviscoelastic constitutive equations to calculate residual thermal birefringence in freely quenched PC plates. The numerical results have been compared with the measurements indicating a fair agreement between them.     

Modelling viscoelastic materials whose storage modulus is constant with frequency

This paper presents a relaxation function characterising viscoelastic materials whose storage modulus is constant with frequency, and whose loss factor shows the representative peak of damping materials. This behaviour is typical of some composite materials, where the elastic constituents give the constant modulus, and the polymeric components provide the variable loss factor. The new model gives a way to provide comparative data for different materials in a form which can easily be incorporated into simulations. The physical meaning of the model parameters is defined from the analysis of the complex modulus in frequency domain. The presented relaxation function is validated by curve fitting to experimental measurements carried out on polymer concrete specimens, made of epoxy resin matrix with mineral aggregates.     

New model materials for photoelasticity and photoplasticity

Two new materials are proposed as models for photoelasticity and photoplasticity. One is cast resin fully cured epoxy-phenol alloy which is made by the mutual cross linking of pre-condensed resins of epoxy and phenol. While epoxy-phenol alloy resin is available only for photoelasticity, the other, polycarbonate resin, is useful not only for photoelasticity, but also for photoplasticity. Polycarbonate is very tough and has large values of both photoelastic stress sensitivity and modulus of elasticity. The excellent cold workability of polycarbonate is proved by a deep-drawing test. Hence the photoplastic results obtained from a polycarbonate model can be applied by analogy to the plastic stress analysis in other ductile materials. Both resins are very transparent even in the plastic state.     

The influence of epoxy resin on the morphological and rheological properties of PET/PA66 blend

Interfacial reactions have dominant effects on the morphological and rheological properties of compatibilized polymer blends. This work aims to investigate the effect of epoxy resin, as a coupling agent, on the interface properties and subsequent influences on the morphological and rheological properties of polyethylene terephthalate/polyamide66 (PET/PA66) blend. PET/PA66 70/30 blends with different amount of bisphenol A epoxy resin (0, 1, 3, and 5 wt.%) were prepared. SEM micrographs show reduction in droplet size with increasing epoxy resin concentration, confirming the reactive compatibilizing effect of the epoxy resin. Reactions at the interface of the PET-EP-PA66 blend are confirmed by FTIR spectra. Shear viscosity results demonstrates that adding epoxy resin could suppress the interfacial slip at the blend interphase. Obtained results from storage modulus (G′) curves show the presence of one plateau for the blends at low frequency region; nevertheless, relaxation spectra indicate the presence of two more relaxation mechanisms than precursors which are related to the shape relaxation of droplets and the interface relaxation. The presence of the interface relaxation time in the blend without epoxy resin can prove the presence of reactions between two condensation polymers; however, adding the epoxy resin results in reducing both relaxation time and interfacial tension and increasing interfacial shear modulus. These observations indicate that the epoxy resin has been successful to boost the reactions at the interface between two polymers. Fitting the obtained experimental data using Palierne model indicates that the general Palierne model could describe rheological properties of the blends very well.     

Residual-stress analysis of an epoxy plate subjected to rapid cooling on both surfaces

This paper presents theoretical and experimental methods of finding the residual stress in an epoxy plate subjected to rapid cooling on both surfaces. The theoretical residual-stress distributions in a plate are calculated by using the fundamental equations based on the linear viscoelastic theory. The specimens in the experiment are subjected to rapid cooling. The residual stresses are measured by the layer-removal method. The theoretical and experimental results are compared and discussed.     

Viscoelastic properties of epoxy resins derived from creep and relaxation tests at different temperatures

Summary Experimental data have been obtained on the creep compliance and the relaxation modulus of two epoxy resins in their transition regions. These tests were combined with birefringence measurements to follow the changes in bond orientation of the polymers as the strain or stress varies. Experimental data on the stress- and strain-optical coefficients are presented for both creep and relaxation experiments. It was proved that the validity of the time-temperature superposition principle can be extended to these two coefficients characterizing the optical viscoelastic properties of the two epoxy resins.Master curves ofF (t/k) versus log (t/k) were constructed, whereF (t/k) represents in turn one of the quantities studied namely creep compliance, relaxation modulus and stress- or strain-optical coefficients. The creep and relaxation time factorsk, corresponding to the creep and relaxation curves at the various temperatures, are plotted against the inverse of the absolute temperatureT. The approximate equality of the time factors for mechanical and separately for optical creep and relaxation was established from these plots. This equality proves that creepD-functions and relaxationE-functions are the reciprocals of one another at any time and that the variation of birefringence with time follows the same law in the respective creep and relaxation tests.

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Zusammenfassung Es wurden experimentelle Werte der Kriech-Compliance und der Relaxationsmoduln zweier Epoxydharze in ihren Transformationsbereichen festgestellt. Diese Prüfungen wurden mit Doppelbrechungsmessungen kombiniert, um die Änderung der Orientierung in den Polymeren bei Änderung von Spannung und Verformung zu ermitteln. Die experimentellen Ergebnisse für die optischen Koeffizienten sowohl bei verschiedenen Zug- wie Verformungswerten wurden sowohl für das Kriechen wie für die Relaxatíon untersucht. Damit ließ sich prüfen, inwieweit die Zeit-Temperatur-Superposition auf diese beiden Koeffizienten angewendet werden kann, die die optischen visko-elastischen Eigenschaften der zwei Epoxydharze charakterisieren.

     

Investigation of size-dependent quasistatic response of electrically actuated nonlinear viscoelastic microcantilevers and microbridges

This study investigates the size-dependent quasistatic response of a nonlinear viscoelastic microelectromechanical system (MEMS) under an electric actuation. To have this problem in view, the deformable electrode of the MEMS is modelled using cantilever and doubly-clamped viscoelastic microbeams. The modified couple stress theory in conjunction with Bernoulli–Euler beam theory are used for mathematical modeling of the size-dependent instability of microsystems in the framework of linear viscoelastic theory. Simultaneous effect of electrostatic actuation including fringing field, residual stress, mid-plane stretching and Casimir and van der Waals intermolecular forces are considered in the theoretical model. A single element of the standard linear solid element is used to simulate the viscoelastic behavior. Based on the extended Hamilton’s variational principle, the nonlinear governing integro-differential equation and boundary conditions are derived. Thereafter, a new generalized differential-integral quadrature solution for the nonlinear quasistatic response of electrically actuated viscoelastic micro/nanobeams under two different boundary conditions; doubly-clamped microbridge and clamped-free microcantilever. The developed model is verified and a good agreement is obtained. Finally, a comprehensive study is conducted to investigate the effects of various parameters such as material relaxation time, durable modulus, material length scale parameter, Casimir force, van der Waals force, initial gap and beam length on the pull-in response of viscoelastic microbridges and microcantilevers in the framework of viscoelasticity.     

Shearing and mixing effects on synthesis and properties of organoclay/polyester nanocomposites

Mixing of solid nanoparticles in viscous fluids is a key stage in synthesis of nanocomposites and can affect their final properties. A multi-step preparatory mixing is developed to synthesize the nanocomposites of layered silicate in thermosetting polymers. This study aims to investigate the influences of mixing conditions and steps taken to process the thermosetting nanocomposites on the viscoelastic properties of suspensions. We also examine subsequent influences of mixing on the microstructure and dispersion state of cured hybrids of organically modified clays in a polyester resin. The nanocomposites were prepared in a sequential mixing process developed for the model nanocomposites of organoclays and thermoset resin. Depending on the mixing conditions, the final nanocomposites showed mixed intercalated and moderately to highly delaminated structure. TEM images show that the nanoclay galleries are dispersed in the polymer phase after curing reactions. The startup viscosities and linear viscoelastic properties of the nanocomposites are significantly influenced by the extent and the time duration of mixing. These observations indicate that extensive mechanical mixing combined with a stationary step followed by moderate shear mixing can improve the polymer and nanoparticle interactions at the interface. In the last part of this work, we develop a simple but efficient mathematical formulation on the flow of oblate spheroids in viscous media and compare selected model predictions with the measured startup shear viscosities of suspensions.     

复合夹层梁瞬态响应的谱有限元法

采用谱有限元法进行复合夹层梁的瞬态响应分析．该方法基于复合夹层梁的六阶运动微分方程,以其波动解作为动力位移形函数,根据标准有限元策略来构建复合夹层梁的动刚度矩阵．在频域内,夹心粘弹性材料的频率相关性采用复模量模型来模拟,进而利用快速傅立叶变换技术(FFT),得到时域内复合夹层梁的瞬态响应分析结果．最后以两端固支夹层梁为例,对其进行了矩形脉冲荷载下的动力响应分析,并与通用有限元程序NASTRAN的计算结果进行了对比,两者吻合良好．     

Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain

Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices. This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain. Firstly, Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam. Secondly, the related analytical solutions are obtained by combining the diffe...     

Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network

Creep tests at constant stress are performed for the carbon-fiber reinforced epoxy composite at various temperatures and initial stresses. A nonlinear viscoelastic constitutive model is developed, and its material parameters are determined by fitting it to creep test data. Model results are found to agree very well with the experimental data at low temperature and low stress conditions. However, the agreement deteriorates at high temperatures, particularly in the vicinity of the glass transition temperature.An alternative model based on an artificial neural network (ANN) is developed to predict the stress relaxation of the polymer matrix composite. The ANN model is trained and validated with 9000 experimental data sets obtained from stress relaxation tests performed at various constant strain (initial stress) and constant temperature conditions. Training of the ANN employs a scaled conjugate gradient method. The optimal brain surgeon algorithm is employed to optimize the topology. The optimal ANN configuration has 88 processing elements (3 in the input layer, 45 in the first hidden layer, 39 in the second hidden layer, and 1 in the output layer) and 410 links. The predictions of the ANN model are found to be more accurate over a wider range of stress and temperature conditions than those of the explicit nonlinear viscoelastic model, in particular near the glass transition temperature.     

Validation of Mechanical Strain Relaxation Methods for Stress Measurement

Most validation studies of mechanical strain relaxation (MSR) methods for residual stress measurement rely on using the saw-tooth residual stress distribution resulting from four point bending and elastic–plastic deformation. Validation studies using simple applied stress profiles in rectangular steel beams are used in this work, together with beams subjected to elastic–plastic bending. Two MSR methods are explored, deep-hole drilling (DHD) and incremental centre hole drilling (ICHD). As well as a series of experiments, finite element analyses are conducted to determine the accuracy in the inversion of measured deformation to reconstruct stress. The validation tests demonstrated that apart from the applied stresses, the initial residual stresses also contribute even when samples are expected to be stress free. The uncertainty in measurement for the two MSR methods is determined, with the uncertainty in near surface measurement found to be significantly larger than uncertainty for interior measurement. In simple loading cases (and simple stress profiles) the uncertainty in measurement and hence the degree of validation is shown to be within about ±50 MPa for steel for “known” stress up to about 140 MPa. However, if the residual stress distribution is more complex there arises increased uncertainty in the predicted residual stress and lack of confidence between measurements methods.     

Molecular investigation on the compatibility of epoxy resin with liquid oxygen

Conventional fiber reinforced plastics(FRPs) have compatibility issues with solid oxygen while used as a fuel tank, which might cause combustion and explosion. To study the compatibility of different epoxy resins with liquid oxygen, molecular dynamics was used to simulate the phase changes of cross-linked epoxy resins under the impact of solid oxygen. Three curing resin systems,which are bisphenol A epoxy resin(DGEBA), bisphenol F epoxy resin(DGEBF), and tetrahydrophthalate diglycidyl ester(epoxy resin 711), are modeled to investigate the rational material system for the application of fuel tanks in launching vehicles. The simulation results show that the order of solid oxygen compatibility of these epoxy resins is DGEBA DGEBF epoxy resin 711 at the same density of crosslinking. The selection of curing agent also has an impact on the compatibility, with the same epoxy, diaminodiphenyl methane(DDM) has more advanced performance comparing to diaminodiphenyl sulfone(DDS).     

A simplified optical method for measuring residual stress by rapid cooling in thermosetting resin strip

This paper presents a simplified optical method for measuring the residual stresses by rapid cooling in thermosetting resin strips. First, the fundamental equations for calculating the residual stress from the residual birefringence were obtained by the linear photoviscoelastic theory. The specimens were then subjected to rapid cooling. After rapid cooling, the residual stress was measured by two methods, the simplified optical method mentioned above and the well-known layer-removal method. The effectiveness of the simplified optical method was discussed by comparing results of the two methods.     

Quasi-static properties of a photoviscoelastic material

This paper describes the results of mechanical and optical measurements in plasticized polyvinyl chloride under conditions of creep and relaxation at room temperature. It covers one task of a broader investigation aimed at developing experimental methods for viscoelastic stress analysis. The moiré method of strain analysis was found well suited for continuous recording of axial and transversal deformation in creep tests. The material exhibits linear viscoelastic behavior, both mechanical and optical. Strain, stress and birefringence measured from creep and relaxation tests gave straightline plots on log-log scale and, thus simple empirical formulas were possible to derive. The theoretical prediction that birefringence in a linear viscoelastic material not exhibiting flow can be expressed as a linear relationship of stress and strain was satisfactorily substantiated.     

固化温度对碳纤维/环氧基体界面行为影响的分析

对界面粘结性能及热残余应力影响下的单纤维复合材料的界面行为进行了分析。采用界面的弹性-软化内聚力模型,用解析法对单纤维复合材料由固化引起的热残余应力、以及单纤维碎断过程纤维的轴向应力分布进行了模拟,得到了碳纤维/环氧树脂在常温和高温固化两种情况的界面粘结性能。结果表明：与常温固化相比,高温固化后,界面的剪切强度增幅不大,界面的断裂韧性显著增加;高温固化后形成的界面,使界面的软化提前、界面的脱粘延迟;高温固化产生的纤维轴向和界面径向热残余应力对界面的软化均有延迟作用;界面径向热残余应力还对界面的脱粘有延迟作用。     

A MICROMECHANICAL FRAMEWORK WITH AGGREGATE-MASTIC INTERFACE EFFECT FOR PREDICTING UNIAXIAL COMPRESSION CREEP OF ASPHALT MIXTURE

According to the elastic-viscoelastic correspondence principle, an elastic microme- chanical framework taking the inclusion-matrix interface effect into account is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded in a viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different temperature and stress conditions in order to determine the matrix constitutive parameters, the framework presented is validated by comparison with the experiment, and then some predictions of uniaxial compression creep behavior of asphalt mixture in different temperature and stress conditions are given.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

海水环境中环氧值对环氧树脂涂层摩擦学性能的影响研究

环氧树脂是一类具有优异的粘接、耐腐蚀和电气绝缘等性能的高强度热固性高分子材料,在黏结剂、防腐涂料和复合材料方面展现出广阔的应用前景,其摩擦学行为与环氧值密切相关.本研究中采用线棒涂布器在铸铁表面分别制备了3种具有不同环氧值的环氧树脂涂层.借助傅里叶红外光谱仪(FT-IR)、X射线光电子能谱仪(XPS)、扫描电镜(SEM)、纳米压痕仪、热重/差热综合热分析仪(TG/DTA)、UMT-3摩擦磨损试验机和表面轮廓仪研究了涂层的结构、硬度、耐热性及摩擦学性能.研究结果表明:涂层在干燥条件和海水环境中的摩擦系数和磨损率均随环氧值的增大而升高;海水环境中涂层的摩擦系数和磨损率均较干燥条件下低.涂层的磨损机理在干燥条件下包括了疲劳磨损、黏着磨损和磨粒磨损,而在海水中仅为疲劳磨损.本研究成果为高性能防腐耐磨涂层的设计与应用提供理论指导.