A procedure for measuring biaxial viscoelastic behavior of thermoplastics

In order to accurately simulate the thermoforming or blowmolding manufacturing processes using finite elements or some other suitable computational procedure, it is necessary to know the constitutive behavior of the material being formed. In this study, an apparatus was developed to measure the large deformation behavior of thermoplastic sheet at elevated temperatures. The specifications of the test apparatus, as well as sample data measurements are presented. Biaxial viscoelastic material properities of ABS sheets were determined at forming temperatures. In particular, the nonlinear stress-strain relationship of the material was experimentally measured at various temperatures above the glass transition temperature and the data correlated to a time and strain separable viscoelastic material model. The results of this study show that it is possible to recover the underlying nonlinear elastic response of heated ABS sheet material, at finite strains, from tests exhibiting significant viscoelastic behavior.     

Optical response and yield behavior of a polyester model material

A mixture of flexible and rigid polyester resins is one of the materials that has been used in the past to model elasto-plastic prototype behavior. As a result of recent curtailments in plastic production, one of the constituents of the mixture is no longer available. A different flexible resin of the same family is available, however, and has been shown in this program to be suitable for optical-model studies involving deformations into the plastic range of material response. In this paper, complete mechanical and optical properties for the new model material are presented for both uniaxial tensile and compressive loadings. Results from a series of thin-walled cylinder tests under internal-pressure loadings are also presented which provide some information on the optical and yield characteristics of the polyester model material under a biaxial state of stress. Results of the study indicate that stress-strain curves for the material can be modified significantly by changing the mixture ratio or the test temperature. Optical data from the study indicate that the fringe order in the material is a function of the instantaneous principal-strain difference. Data from the uniaxial tension and compression tests, together with limited data from the cylinder tests, indicate that the polyester material may follow a modified von Mises yield criterion which accommodates differences in tensile and compressive yield strengths of a material.     

Planar Strain Measurements on Wood Specimens

Wood specimens have been tested for compressive loading in the longitudinal direction. Planar deformation was recorded by means of video extensometry on the specimen surfaces. A post processing routine was developed to calculate stress and strain values from the sampled data. The routine made use of mathematical framework used in the finite element method. Material parameters were detected by means of an optimization algorithm, and the determined linear elastic parameters were in general found to be in good agreement with values given in literature. The utilized method offers simultaneous average values for active, passive and shear strains from the measured area. Moduli of elasticity, Poisson’s ratios and shear deformation can thus be evaluated. In addition, the variation of the three strain components over the area is measured. The results can therefore be used for quantification of material inhomogeneity and are further suitable for direct comparison with numerically computed strains comprising non-uniform strain fields. Since video extensometry does not require any physical contact with the specimen, measurements can be undertaken until failure. The present method offers thus an efficient and relatively accurate way to measure and evaluate the material characteristics of anisotropic and inhomogeneous materials like wood.     

Separation of a Gas Mixture by Means of Optical Trapping of the Gas

Contributions of barodiffusion and thermodiffusion to separation of a methane–helium mixture are calculated with the use of a laser-induced interferential lattice with a non-resonant frequency. The process of separation is studied by the direct simulation Monte Carlo method of rarefied gas flows, which can be considered as a numerical method of the stochastic solution of the Boltzmann equation. An analysis of modeling results shows that barodiffusion arising under optical radiation owing to the influence of ponderomotive forces on the species of the gas mixture exerts a significant effect during separation of the gas mixture by means of optical trapping, in addition to the selective action of the lattice. The effect of thermodiffusion caused by heating of the mixture by the optical lattice is found to be significant only in peripheral areas of the lattice.     

An experimental study of thermal stress in porous materials by methods of holography and photoelasticity

In heat-loaded structures of energy equipment at the moment of crisis of heat exchange in working elements, the ultimate state of the material occurs. Thermal stresses were studied experimentally in a bulk porous material with a groove on the surface with a view to finding out the distribution of deformations and thermal stresses due to the location of the heat source. It appeared efficient to apply optical methods. Using holographic interferometry, a pattern of distribution of thermal deformations over the surface of the specimens was obtained. Using the photoelastic method to investigate a grooved porous structure, a physical pattern of the distribution of thermal stresses inside the block and in the groove was obtained. Ways are outlined for designing and reducing the probability of occurrence of destructive cracks. A similarity is observed in the distribution of strains and stresses that indicates the interrelatedness of surface and internal processes. The application of optical methods made it possible to discover a physical pattern of destruction. The results are expected to be used in the future to investigate other porous materials.     

Photoelasticity for stress analysis under high hydrostatic pressure

Experimental research relative to pressure effects on the mechanical behavior of materials is frequently handicapped by the difficulties associated with making load and deformation measurements in a hostile environment. The application of photoelasticity in high-pressure experiments provides a means for studying the effect of hydrostatic stress on varying stress fields. The purpose of this paper is to examine the feasibility of using the photoelastic method of stress analysis in a high-pressure environment. The unusual feature of this application is the finite elastic deformations suffered by the photoelastic model under high pressure. As a result, the mechanical and stress-optical properties of the model materials are functions of pressure. Another important feature in this study is the selection of a suitable model material. Since the model must come into contact with the liquid pressure media, chemical and absorption resistance are essential considerations. Although it was found that photoelastic investigations can be carried out at high pressure, limitations are imposed by the presence of the optical vessel and pressurized fluid.     

Applications of the LIF method for the diagnostics of the combustion process of gas-IC-engines

Within the underlying project, the task was to develop methods for optical measurements in a hydrogen-fuelled engine with direct-injection, with the goal of measuring the jet patterns during injection, the stratification of the charge at ignition point and the propagation of the flame during combustion. Therefore, the method of planar laser-induced-fluorescence (PLIF) was chosen. In order to apply this technique for the named tasks, particular methods the visualisation of fuel distribution and the flame front were developed. The measurements were carried out on a single cylinder research engine installed at the Institute for Internal Combustion Engines at Graz University of Technology. This engine features optical access through a quartz-glass liner and a window in the piston while providing a layout equivalent to modern passenger car engines and the possibility to operate in fired mode. As it is hardly feasible to directly excite molecular hydrogen by means of laser light, it is necessary to add a tracer substance to the fuel that provides high fluorescence intensity while not changing the properties of the fuel. Consequently, Triethylamine was chosen as a tracer to be mixed with hydrogen at 200 ppm, which allows it to be used up to a maximum pressure of 200 bar while still providing a strong LIF signal. Due to the excellent linearity of the signal to the local air/fuel-ratio it was possible to develop a method for the calibration of the images in order to compensate for inhomogeneities of the laser beam and staining of the optical access and to ultimately allow a quantification of the fuel distribution. The results are images scaled on air/fuel-ratio which can be used for a direct optimisation of mixture formation processes and the validation of CFD-models. For the analysis of the combustion process the method was adapted with two different approaches. For homogeneous charges a new method was applied by marking the flame front using the tracer within the fuel, so that both are burned together. However, as this method is limited to measurements with a homogeneous distribution of tracer within the measured volume, an alternative technique had to be applied for the measurement of stratified charges. In this case, a direct visualisation of the flame front was achieved by exciting the OH-radicals formed during combustion. As this method has significantly increased demands on measuring equipment and is more time consuming, both methods are used in parallel on specific measuring tasks.     

Uniaxial material damping measurements using a fiber optic lattice: A discussion of its performance envelope

Damping is the internal transfer of kinetic energy to other forms of energy. Today, most methods use either bending or torsional vibration to measure damping. This means that the strain field in the specimen is nonhomogeneous. If the damping of the tested material is linear, strain-independent, the values acquired with these traditional methods will be equal to the intrinsic material damping of the material. If, however, the damping is strain-dependent, nonlinear, the measured value will be an average of the damping of the specimen, and not equal to its intrinsic material damping. To address this problem, a method is required to experimentally determine the damping in uniaxial tension in order to produce the same strain level in all parts of the test specimen and hence obtain a measurement of the intrinsic material damping. Using such a method, it is possible to view the material damping as the phase angle between the stress and the strain in a harmonic oscillation. In this paper, a method is suggested for measuring this phase shift in uniaxial tension to determine the material damping properties. It uses a tensile test machine, an optical fiber Bragg grating technique and a lock-in amplifier. Measurements with the phase shift technique have been suggested previously, but its performance envelope has been overestimated. In this paper, the performance envelope is discussed and restricted. It is shown that the envelope depends on the specimen length, loss factor and test frequency. An optical strain measurement method is also believed to help avoid many electrical measurement problems seen with the originally proposed method.     

Mechanical-optical properties of polycarbonate resin and some relations with material structure

Polycarbonate resin possesses optical and mechanical properties which make it particularly suitable for certain experimental investigations, including two-and three-dimensional photoelastic analysis. The ductility and transparency of this material might be usefully employed in photomechanical investigations of plastic and viscoelastic response. The similarity of the stress-strain law of polycarbonate to that of mild steel could simplify the similitude problem. In addition, its spectral transmittance in visible and infrared makes polycarbonate useful for studies of material properties and structure. The optical creep of polycarbonate is respresented by a normalized creep coefficient. The relationship of this factor to the theory of viscoelasticity is discussed, and the conditions for a valid calibration of birefringent materials are reviewed. The wavelength dependence of relative retardation is represented by the normalized retardation, from which the dispersion of birefringence can be deduced. The stress-birefringence-time-wavelength characteristics of two brands of polycarbonate resin were determined. Because of residual birefringence, it was necessary to heat treat the resin at about 146°C, and properties of both annealed and unannealed resins are presented. Retardation was measured over the visible and near-infrared portions of the electromagnetic spectrum (407 nm to 1900 nm). There exists a definite relationship between dispersion of birefringence, which amounts to 14 percent in visible, and the infrared spectral transmittance, which is indicative of material structure.     

Disk-shaped compact tension test for asphalt concrete fracture

A disk-shaped compact tension (DC(T)) test has been developed as a practical method for obtaining the fracture energy of asphalt concrete. The main purpose of the development of this specimen geometry is the ability to test cylindrical cores obtained from in-place asphalt concrete pavements or gyratory-compacted specimens fabricated during the mixture design process. A suitable specimen geometry was developed using the ASTM E399 standard for compact tension testing of metals as a starting point. After finalizing the specimen geometry, a typical asphalt concrete surface mixture was tested at various temperatures and loading rates to evaluate the proposed DC(T) configuration. The variability of the fracture energy obtained from the DC(T) geometry was found to be comparable with the variability associated with other fracture tests for asphalt concrete. The ability of the test to detect changes in the fracture energy with the various testing conditions (temperature and loading rate) was the benchmark for determining the potential of using the DC(T) geometry. The test has the capability to capture the transition of asphalt concrete from a brittle material at low temperatures to a more ductile material at higher temperatures. Because testing was conducted on ungrooved specimens, special care was taken to quantify deviations of the crack path from the pure mode I crack path. An analysis of variance of test data revealed that the prototype DC(T) can detect statistical differences in fracture energy resulting for tests conducted across a useful range of test temperatures and loading rates. This specific analysis also indicated that fracture energy is not correlated to crack deviation angle. This paper also provides an overview of ongoing work integrating experimental results and observations with numerical analysis by means of a cohesive zone model tailored for asphalt concrete fracture behavior.     

An efficient method for the identification of the modified Cockroft–Latham fracture criterion at elevated temperature

The paper presents the theoretical part of a method for the identification of the modified Cockroft–Latham ductile fracture criterion at elevated temperature. Quite a general viscoplastic model is adopted to describe material behavior. The original criterion is path-dependent and involves stresses. Therefore, the identification of constitutive parameters of this criterion, as well as many other ductile fracture criteria, is rather a difficult task that usually includes experimental research and numerical simulation. The latter is impossible without a precisely specified material model and boundary conditions. It is shown in the present paper that for a wide class of material models usually used to describe the behavior of materials at elevated temperatures, the criterion is significantly simplified when the site of fracture initiation is located on traction-free surfaces. In particular, this reduced criterion solely depends on two in-surface logarithmic strains. Since there are well-established experimental procedures to measure surface strains, the result obtained can be considered as a theoretical basis for the efficient method for the identification of the modified Cockroft–Latham ductile fracture criterion at elevated temperature.     

Differential schemes for the elastic characterisation of dispersions of randomly oriented ellipsoids

The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids: we start from the theory of strongly diluted mixtures and successively we generalise it with a differential scheme. The micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent elastic moduli of the overall composite materials. This micromechanical technique has been explicitely developed for describing embeddings of randomly oriented not spherical objects. In particular, this study has been applied to characterise media with different shapes of the inclusions (spheres, cylinders and planar inhomogeneities) and for special media involved in the mixture definition (voids or rigid particles): an accurate analysis of all these cases has been studied yielding a set of relations describing several composite materials of great technological interest. The differential effective medium scheme (developed for generally shaped ellipsoids) extends such results to higher values of the volume fraction of the inhomogeneities embedded in the mixture. For instance, the analytical study of the differential scheme for porous materials (with ellipsoidal zero stiffness voids) reveals a universal behaviour of the effective Poisson ratio for high values of the porosity. This means that Poisson ratio at high porosity assumes characteristic values depending only on the shape of the inclusions and not on the elastic response of the matrix.     

On the use of electrical-resistance foil strain gages for plastic-wave studies in solids

The use of electrical-resistance foil strain gages for the measurement of plastic-wave profiles is investigated. It is shown that the wave speeds and maximum strains are obtained to about the same accuracy as optical techniques. It should be noted that the plastic wave speed and the maximum strain are the two most important parameters which are used to infer dynamic response of a material.     

Photovisco-elastoplastic behavior of polycarbonate material under creep and tension tests

Polymers are widely used as photomechanical models of a prototype material (often a metal). Photoplasticity is one of the methods used in order to show the behavior of plastic materials stressed beyond the linear elastic limit. To illustrate this process we have analyzed the photovisco-elastoplastic behavior of polycarbonate as a photoplastic material. In this paper a technique for local and simultaneous measurement of birefringence and principal strains is presented. The mechanical and optical properties, at room temperature, have been evaluated by means of uniaxial tension tests. A series of creep tests has been carried out in order to study the photovisco-elastoplastic behavior of polycarbonate. In two different experiments we analyzed nonlinear birefringence and the amplitude of the corresponding strains. We could thus evaluate the distribution of strains and the distribution of uniaxial stress for each birefringence state and vice versa.     

单向纤维加强复合材料的总体弹粘塑性响应

应用GMC方法计算了单向纤维加强复合材料在承受不同载荷之后的总体松驰响应。Bodner和Partom的弹－粘塑性统一模型用于描述非弹性相的本构关系，该模型不假设存在屈服条件，也就不必指定加载和卸载条件，可以在加载和卸载的任何时刻使用相同的公式，计算表明，与有限元方法相比，利用GMC方法和统一模型计算单向纤维加强复合材料的总体非弹性响应简单快捷。     

功能梯度材料结构分析的半解析数值方法研究

一种典型的半解析数值方法——线法被引入功能梯度材料的结构分析。首先推导了功能梯度材料位移形式的平衡方程和边界条件,然后阐述了线法功能梯度材料结构分析的基本步骤和数值原理。该方法的基本思想是通过有限差分将问题的控制方程半离散为定义在沿梯度方向离散节线上的常微分方程组,然后应用B样条函数Gauss配点法求解该常微分方程组得到问题的解答。为演示线法在功能梯度材料结构分析中的应用,给出了线性梯度和指数梯度功能梯度材料板分别受恒定位移、均匀拉伸载荷和弯曲载荷作用的数值算例。与相应问题解析解和其他数值方法的比较表明,线法的计算结果具有很高的精度,而且不需要任何特殊的考虑就能够有效模拟材料内部物性参数的连续变化,也无需事先选取满足特定条件的待定场函数,是一种非常适合功能梯度材料结构形式和材料特点的半解析数值方法。     

Large deformation plasticity and the Poynting effect

The aims of this paper are fourfold: (1) To develop a set of constitutive equations that are applicable to isotropic inelastic materials with large elastic and plastic strains using the multiconfigurational framework (Rajagopal, K.R., Srinivasa, A.R. Int. J. Plasticity 14 (1998) 945; Rajagopal, K.R., Srinivasa, A.R. Int. J. Plasticity 14 (1998), 948), in such a way as to generalize the central ideas (such as isotropy, constant elastic modulii, quadratic yield surfaces and non-hardening behavior) of the Prandtl–Reuss theory to finite deformations, (2) to examine the consequences of using a physically plausible criterion of maximum rate of mechanical dissipation, (3) to examine the relationship of the resulting models to the classical Prandtl–Reuss theory as well as other possible formulations (specifically those that rely on the use of a maximum plastic work postulate), and (4) to consider the effect of finite elastic strains on the response of the material subject to some simple homogenous deformations. By considering the response under simple shear, it is shown that the elastic-plastic counterpart of the well known Poynting effect in finite elasticity has a profound influence on the post-yield behavior of such materials. In particular, it is shown that this gives rise to a strain softening effect even though the overall response is that of a non-hardening material.     

Compressive failure strengths and modes of woven S2-glass reinforced polyester due to quasi-static and dynamic loading

The failure strengths and modes of the woven S2-glass reinforced polyester thick laminate are characterized through a comprehensive set of experiments. Compression strength tests in different directions were performed, and optical and scanning electron microscopy studies of the fractured specimen surfaces were conducted. The failure modes are complex involving a combination of failure mechanisms. The failure stresses and strains in the ply lay-up direction were higher than those in the plane of the lamina. The material's dynamic response was determined using both the split Hopkinson pressure bar and the direct disk impact techniques. The material was found to be significantly strain rate sensitive.     

Investigation of shrinkage-induced stresses in stereolithography photo-curable resins

An experimental study has been undertaken to investigate the shrinkage characteristics of acrylic-based and epoxy-based stereolithography (SL) photopolymer resin systems after they have been laser cured and post-cured under ultraviolet (UV), and thermal exposure. The induced residual stresses and strains were determined by the shadow moiré and the hole-drilling strain-gage methods. Out-of-plane displacements (warpage) of acrylic-based post-cured resin plates were recorded by means of the shadow moiré method and correlated to the shrinkage strains by theoretical analysis. The induced residual stresses in the epoxy-based cylindrical resin specimens were determined from strains of three-element strain-gage rosettes of the blind-hole drilling method. Results are presented for the shrinkage stresses and strains for both material systems as a function of the post-curing process (UV, thermal). It was found that the shrinkage strains in the acrylic-based photopolymer resin were of considerable magnitude, while thermal post-curing resulted in higher shrinkage stresses for both material systems. The values of the shrinkage stresses compare well with those of the existing literature.