Phase-Multiplied Photoelastic and Series Interferometer Arrangement for Full-Field Stress Measurement in Single Crystals

A compact, phase-multiplied, circular polariscope and series interferometer arrangement is developed for high-resolution, full-field stress measurement in single crystals with weak piezo-optical coefficients. We present a general stress-optic law, derived from anisotropic piezo-optical constitutive relations, which provides the theoretical framework for obtaining stress field components from measured optical isoclinic, isochromatic and isopachic phase maps. A new phase image processing technique is also developed, which combines data obtained from different interference configurations for the successful removal of low-modulation zones within isoclinic and isopachic phase maps. The validity and accuracy of the proposed interferometer arrangement and stress measurement methodology are demonstrated through a compression test of a c-cut single crystal sapphire plate loaded by a cylindrical indenter.     

An approximate method of orthotropic photoelastic analysis

An approximate strain-optic law has been derived for photoelastic analysis of orthotropic model materials. Principal-strain difference and the direction of major principal strain can be obtained from only two photoelastic measurements (isochromatic-fringe order and isoclinic angle) by means of this strain-optic law. Limited experiments on models subjected to uniaxial and biaxial stresses indicate good agreement between the experimental results and predictions of the strain-optic law. A parametric study demonstrates that the direction of major principal strain can be predicted to within a few degrees of the exact value and that the principalstrain difference can be predicted within ±20 percent for most practical values of degree of orthotropy and ratio of principal strains. The error levels are quite acceptable considering the significant ease in analysis provided by the new law and the fact that such error levels are not uncommon in experimental investigations.     

On the fiber-reinforced birefringent composite materials

The isochromatic and isoclinic parameters for fiber-reinforced birefringent materials are examined. Experimental results reveal residual birefringence and an initial isoclinic coincident with the axis of material symmetry. These preliminary data also indicate that the isoclinic angle is neither a measure of the principal strain nor the principal-stress directions within the composite.     

复合材料光弹性分析的近似方法

本文提出了一种用于光弹性复合材料的简化应变——光学定律。按照这一简化定律。模型材料的主应变差和主应变方向只要利用光弹性实验测出的等差线与等倾线即可求得。些是一种正交异性光弹性分析的近似方法,这一方法所得结果与实验数据比较,最大误差在10％左右。由于采用简化应变——光学定律使得正交异性光弹性分析工作大为简便,因此它是一种适合于工程应用的近似方法。     

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.     

The interpretation of isoclinics in photo-orthotropic-elasticity

Significant progress has been made in the interpretation of isochromatic fringes in photo-orthotropic-elasticity. However, the isoclinic fringes have not yet been satisfactorily interpreted. While it has been recognized that the isoclinics do not give the principal-stress directions in the composite model, there has been speculation that the isoclinics may give the principal-strain directions. An experimental study of the isoclinic fringes in orthotropic models was undertaken. The model material employed consisted of a transparent, unidirectionally reinforced, E-glass-polyester composite. First, the optical isoclinic parameters were measured in uniaxial stress fields for compression specimens as a function of the fiber-orientation angle. It was observed that, while the optical isoclinic parameter was different from the composite principal-stress angle, it was also different from the composite principal-strain angle. The optical isoclinic parameter was predicted very well by the Mohr circle of birefringence postulated by Sampson. In the second set of experiments, the optical isoclinic parameter was measured in biaxial stress fields by testing a circular disk in diametral compression. The actual state of strain and stress at the center of the disk was measured by means of a rectangular strain-gage rosette. Again it was observed that the optical isoclinic parameter was predicted very well by Sampson's relation. Thus, the isoclinic fringes in orthotropic models can be satisfactorily interpreted and Sampson's scheme can be utilized to obtain the individual principal stresses in orthotropic models.     

功能梯度热释电材料矩形板的三维精确分析

对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析．根据正交各向异性热释电材料基本方程，导出了功能梯度热释电材料的状态方程．假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布，获得了四边简支、接地和等温的矩形板，在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解．通过算例，分析了在机械荷载、电荷载和热荷载分别作用下，材料性质的不同梯度变化对平板结构响应的影响．所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。     

Photoviscoelastic stress analysis of a plate with a central hole

An epoxy resin containing excessive plasticizer was developed and characterized. The material, which deforms viscously at room temperature, has optical properties that depend on stress and strain. A tensile specimen was prepared from the epoxy resin so that the mechanical and optical properties of the epoxy resin could be characterized. The elastic and plastic behavior was determined at 37°C using tensile stresses between 4 and 26 MPa. The birefringence was also recorded as a function of time and stress. From these results, a photoviscoelastic constitutive equation was constructed to describe the dependence of the birefringence on stress and strain. The constitutive equation was then applied to study the deformation of a tensile specimen containing a central circular hole. By using the isochromatic fringes in combination with the isoclinic, the time-dependent variation of the stress field in the specimen was solved.     

一个描述脆性材料非线性行为的损伤力学模型

提出了一个分析和描述脆性材料各向异性损伤的宏观力学模型。在小变型的情况下，利用损伤面和损伤势的概念以及材料性能和材料受损后的弹性响应取决于损伤变量而与加载路径无关的假设，文中导出材料弹性损伤的一般本构关系及联系材料系数与损伤面和损伤势的表达式。当损伤面和损伤势的构造确定后，建立了损伤变量的演变方程和材料性能的变化规律。文中以两种具体材料为例说明该理论模型的应用．     

复合材料光弹性分析的工程方法

本文在推导均衡光弹性复合材料应力(应变)—光定律的基础上,导出了均衡光弹性复合材料的近似应变—光定律。然后加以推广,提出适用于一般光弹性复合材料的近似应变—光定律.精度分析及实验验证表明:作为工程计算,在采用本文推荐的参数时,光弹性复合材料可视作各向同性材料进行光弹性分析。     

Experimental caustics analysis in fracture mechanics of anisotropic materials

The originally developed reflection method of caustics is presented for application to cracks in mechanically anisotropic materials such as fiber-reinforced composites. The derived solutions for the combination of crack-opening modes I and II show that the size of the dark spot depends on the load intensity, whereas its shape depends strongly on the mechanical properties of the material, the orientation of the crack tip and the mixed-mode mixture. The evaluation of optical effects is possible using the diameter-measuring method or the advanced multipoint overdeterministic data reduction method. To find the exact position of caustics, the experimental images are analyzed by the simple boundary value method and a more sophisticated differential method, which is accomplished by shifting the real image onto the gradient image. The standard experimental testing procedure is performed for cracks oriented 0 deg, 45 deg and 90 deg to the material axes in carbon-fiber-reinforced polymer composites.     

Polarized Image Correlation for Large Deformation Fiber Kinematics

The underlying fiber architecture of soft tissues, like bat wing skin, plays an important role in the material’s overall mechanical behavior. The mesoscopic birefringent fiber architecture of the bat wing skin can be visualized directly under polarized light. This inherent property is the key to the new experimental technique developed in this work: polarized image correlation (PIC). PIC is a technique for determining full field material strains and fiber kinematics of mesoscopically resolved fibrous tissues during biaxial mechanical testing. Not only is the material birefringence used to determine fiber kinematics under finite deformations, but it is also used for image correlation and strain field computation. Pure translation tests performed with PIC verify the accuracy of the technique. A segmental image processing method was developed to solve an experimental issue of changing birefringent properties to construct accurate continuous deformation profiles. By integrating PIC with traditional digital image correlation, both surface and subsurface data give additional insight into through thickness tissue behavior. The PIC technique is applicable to semi-transparent tissues with birefringent mesosopic structures; incorporation of microscopy would resolve smaller fiber structures. Future work includes extending the techniques to three dimensions to analyze curved surfaces.     

The birefringent response of a potential photoelastic material with variable elastic properties

In photoelastic stress analysis, a need sometimes exists for a birefringent material in which the experimenter has the ability to vary its mechanical or elastic properties. It was the intent of this investigation to produce a homogeneous, isotropic solid with variable mechanical properties and which was suitable for photoelastic use. This goal is accomplished through the fabrication of a discontinuous composite where the birefringent constitutents have matched indices of refraction in the unstressed state. The constituents of this composite are solid-glass microspheres embedded in a polyester matrix. Three theories are formulated to define the stress-induced birefringent phenomena found in composites of this nature. Conventional photoelastic techniques were employed to produce data appropriate for comparison to the predictions of these theories.     

含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系．最后,对影响材料损伤的细观结构参数进行了分析．     

Orthotropic elastic–plastic material model for paper materials

Paper and paperboard generally exhibit anisotropic and non-linear mechanical material behaviour. In this work, the development of an orthotropic elastic–plastic constitutive model, suitable for modelling of the material behaviour of paper is presented. The anisotropic material behaviour is introduced into the model by orthotropic elasticity and an isotropic plasticity equivalent transformation tensor. A parabolic stress–strain relation is adopted to describe the hardening of the material. The experimental and numerical procedures for evaluation of the required material parameters for the model are described. Uniaxial tensile testing in three different inplane material directions provides the calibration of the material parameters under plane stress conditions. The numerical implementation of the material model is presented and the model is shown to perform well in agreement with experimentally observed mechanical behaviour of paper.     

A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: Modelling

A constitutive model for anisotropic elastoplasticity at finite strains is developed together with its numerical implementation. An anisotropic elastic constitutive law is described in an invariant setting by use of structural tensors and the elastic strain measure C_e. The elastic strain tensor as well as the structural tensors are assumed to be invariant in relation to superimposed rigid body rotations. An anisotropic Hill-type yield criterion, described by a non-symmetric Eshelby-like stress tensor and further structural tensors, is developed, where use is made of representation theorems for functions with non-symmetric arguments. The model also considers non-linear isotropic hardening. Explicit results for the specific case of orthotropic anisotropy are given. The associative flow rule is employed and the features of the inelastic flow rule are discussed in full. It is shown that the classical definition of the plastic material spin is meaningless in conjunction with the present formulation. Instead, the study motivates an alternative definition, which is based on the demand that such a quantity must be dissipation-free, as the plastic material spin is in the case of isotropy. Equivalent spatial formulations are presented too. The full numerical treatment is considered in Part II.     

A review of the rheo-optical properties of linear high polymers

Some principles ans laws, expressing the mechanical and optical behavior of linear viscoelastic materials, are reviewed. The mechanical properties of the polymers in the transition region may be represented by a condensed general method containing Ferry's modulus or compliance-reduction scheme, the time-temperature superposition principle and the Gauss error integral representation. The optical behavior of high polymers is expressed by the stress- and strain-optical coefficients in creep or relaxation, which relate birefringence to stresses or strains. It was recently shown experimentally that, instead of a pair of independent linear differential operator relations, which characterize the mechanical properties of the viscoelastic materials, only one operator relation is needed and the initial value of another at the glassy or rubbery state. Then, a single test is sufficient for the complete determination of the mechanical and optical viscoelastic behavior, provided the value of another elastic constant at the glassy or rubbery state is also determined and the variation of birefringence with time is simultaneously measured with the mechanical-characteristic quantities of the material.     

Anisotropic Elastic-Viscoplastic Properties at Finite Strains of Injection-Moulded Low-Density Polyethylene

Injection-moulding is one of the most common manufacturing processes used for polymers. In many applications, the mechanical properties of the product is of great importance. Injection-moulding of thin-walled polymer products tends to leave the polymer structure in a state where the mechanical properties are anisotropic, due to alignment of polymer chains along the melt flow direction. The anisotropic elastic-viscoplastic properties of low-density polyethylene, that has undergone an injection-moulding process, are therefore examined in the present work. Test specimens were punched out from injection-moulded plates and tested in uniaxial tension. Three in-plane material directions were investigated. Because of the small thickness of the plates, only the in-plane properties could be determined. Tensile tests with both monotonic and cyclic loading were performed, and the local strains on the surface of the test specimens were measured using image analysis. True stress vs. true strain diagrams were constructed, and the material response was evaluated using an elastic-viscoplasticity law. The components of the anisotropic compliance matrix were determined together with the direction-specific plastic hardening parameters.     

Time-dependent optical characterization in the photoviscoelastic study of stress-wave propagation

Dynamic photoviscoelastic analysis requires the time and temperature dependency of the material to be taken into account. Mechanical relaxation processes have generally been incorporated in dynamic analysis, but there has been no widespread application of optical relaxation or creep functions over the complete time spectrum in photomechanics of birefringent polymers. Using material characterizations previously developed, this study compares a theoretical viscoelastic solution and its predicted fringe patterns for stress-wave propagation in a thin rod of polyurethane material (Solithane 113) with the photoviscoelastic data from a similar experimental arrangement. The agreement demonstrates both the validity and general necessity of such an approach for the time-domain characteristic of wave-propagation phenomena in low-modulus polymers.