Development of a Hybrid Method of Reflection Photoelasticity for Crack Problems in Anisotropic Plates

Reflection type photoelastic experiment can be used more effectively than a transmission type photoelastic experiment especially in industrial fields. Moreover, composite materials have been widely used in engineering applications and structures because of their outstanding advantages which individual isotropic components do not have. The development of these materials requires a promising technique such as reflection photoelasticity to analyze their behaviors in service. Unfortunately, there are few experimental studies based on this technique. Therefore, a hybrid method based on this technique was developed in this research to analyze the fracture behavior of opaque anisotropic materials. The application of this method will help to understand the fracture behaviors of anisotropic materials used in engineering components and structures. The validity of this method was verified by comparison of the results obtained from this method with ones obtained from the hybrid methods for isotropic material on the same isotropic specimen. The reflection type photoelastic experiment for orthotropic materials was then applied to orthotropic plates with a central crack of various inclination angles. Using this hybrid method for anisotropic materials, stress intensity factors and separated stress components were obtained at the vicinity of the crack-tip in orthotropic plates from only the isochromatic fringe patterns of the isotropic coating material.     

Stress Wave Field Near a Notched Boundary in Anisotropic Plates under Impulsive Loading

The stress distribution near a rectilinear boundary and a boundary with a notch of different depths in an anisotropic plate is analyzed. The plate boundary is under the action of a surface or embedded impulsive source. The results presented have been obtained using the dynamic photoelastic method for optically sensitive orthotropic plates. The results for orthotropic and isotropic plates with different ratios of notch depth to wavelength are analyzed     

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。     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.     

Photoelastic validation of a theoretical solution for an edge cracked disk

In this paper, the theoretical solution developed by Vaughan and Wu for the stress analysis of a circular disk with a radial edge crack extending to its center is validated by photoelasticity. The photoelastic results include the fullfield isochromatics as well as measurements of the maximum shear stress at a number of test points. Additionally, the experimental stress intensity factor is extracted from the photoelastic data by Irwin's two-parameter method. Good agreement is observed when the theoretical stress field and stress intensity factor are compared with the experimental results. It is concluded that the Vaughan-Wu solution can be confidently applied in fracture mechanics analyses. The application of such a solution to the stress analysis of two-dimensional bodies with complex geometries subjected to complex loading is also noted.     

Photoelastic simulation of the stress wave field around a tunnel in an anisotropic rock mass subject to shock load

The stress wave field around a tunnel in an anisotropic medium subject to shock load is analyzed using the dynamic photoelastic method. The influence of various factors on the distribution and magnitude of boundary stresses around the tunnel are studied by simulating the deformation process. The time dependence of the dynamic stress concentration factor on the tunnel walls is established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 122–125, August 2006.     

MICROMECHANICS ANALYSIS FOR UNSATURATED GRANULAR SOILS

This paper aims at establishing an anisotropic stress expression for unsaturated pendular-state granular soils. Using the second-order fabric tensor, we formulate a micromechanics scheme of soils with statistically averaging method, and reveal that the macroscopic average stress of unsaturated granular soils in pendular-state is not isotropic. Not only is the stress from contact forces anisotropic due to the fabric, but also the capillary stress is directional dependent, which is different from the common point that the capillary stress is isotropic. The capillary stress of unsaturated pendular-state granular soils is determined by the orientation distribution of contact normals, so it is closely related to the initial and induced anisotropy of soils. Finally, DEM numerical simulations of triaxial compression tests of pendular-state soils at different degrees of saturation are used to verify the existence of above anisotropy of stresses.     

Photoelastic analysis of the singular stress field in a bimaterial wedge

This paper presents an experimental investigation of the singular stress field near the vertex of a bimaterial wedge using a digital photoelastic technique. Special attention is given to the casting of bimaterial wedge specimens and analysis technique for extracting stress intensity factors from photoelastic samples. Different bimaterial wedge specimens are made of two different photoelastic materials bonded through a special casting procedure and loaded in simple tension. A new multiple-parameter method is developed to obtain the stress intensity factor reliably from the isochromatic fringe patterns and the series representation of the stress field at the vertex of the wedge. Experimental results are compared with finite element predictions, and good agreement is observed.     

应用新型动光弹系统研究某设备受冲击载荷作用

结构受到冲击时,其应力分布与在静荷载作用下完全不同.本丈应用新型动光弹实验系统研究了某设备在冲击载荷作用下其内部动态应力分布情况.该系统由部分传统的动光弹实验装置、高速摄影系统和数字光弹图像处理系统组成,并且采用激光光源、落锤冲击载荷加载装置.加工制作了该设备模型的光弹性模型,应用到冲击载荷作用下的实验研究中,得到了该...     

多参量断裂力学广义杂交/混合裂纹有限元法

通过研究广为人知的断裂力学单变量八节点位移裂纹QPE元和Akin族奇异单元法，本文运用经典局部裂纹解析解，与非协调假设应力杂交-混合元列式方法相结合，提出用于分层各向异性材料的多变量半解析假设应力奇异广义杂交／混合裂纹有限元法，能克服现有位移裂纹元法的域应力分布精度低和高次单元所需计算容量大的局限性，互为补充，更有利于结构裂纹扩展分析和应用研究。文中设计了一个半解析奇异裂纹平面单元，各向同性材料板算例验证了退化二次八节点协调位移裂纹元及六节点非协调奇异应力裂纹元，说明采用稀疏及加密单元网格，两类裂纹单元分别从上下逼近收敛于实验和理论参考解，可得到吻合程度较好的1／√r奇异应变和应力分量以及应力强度因子值，表明了本文奇异裂纹单元理论的优越性。     

两种各向异性材料界面共线裂纹的反平面问题

本文研究两种各向异性材料界面共线裂纹的反平面剪切问题。利用复变函数方法，提出了一般问题公式和某些实际重要问题的封闭形式解。考察了裂纹尖端附近的应力分布并给出了应力强度因子公式。从本文解签的特殊情形，可以直接导出两种各向同性材料界面裂纹，均匀各向异性材料共线裂纹以及均匀各向同性材料共线裂纹的相应问题公式，其中包括已有的经典结果。     

Acoustoelastic stress analysis of residual stress in a patch-welded disk

The acoustoelastic stress analysis is based on the fact that an initially isotropic material becomes anisotropic under stress. The birefringent effect for polarized ultrasonic shear waves in the stressed material will then be similar to the photoelastic effect in which a light wave and a transparent model specimen are used. In this paper, the velocity differences of acoustical, perpendicularly polarized waves are measured directly by a ‘sing-around’ method using a 5-MHz shear-type transducer. The residual-stress distribution in a mild-steel circular plate with a concentrically patch-welded joint is measured by this method. The acoustoelastic coefficient is obtained separately by uniaxial testing of the base material. The results show that the acoustical stress measurement, carried out nondestructively, agrees well with those obtained by conventional destructive methods as well as with theoretical predictions.     

Photoelastic Stress Analysis by Use of Hybrid Technique and Fringe Phase Shifting Method

0Introduction Photoelasticityisanopticalmeasurementmethodforstressanalysis.Itcanperformwhole field measurementduetotwo dimensionalsignalprocessingoflight.Alsoitcanperformnon contact measurementbecauseoftransmissionorreflectionoflightonaspecimen.Photoelast…     

Stress in transversely isotropic half-space with typical loads acting on its surface

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Photoelectric-computer data processing (PCP) program in experimental photo-stress analysis

A photoelectric-computer data processing(PCP)prog-ram in experimental photo-stress analysis is presented in this paper.The basic equation of photoelastic stress analysis by Chen(1962)is adopted,and a cubic spline function suitable for processing photoelastic data is derived.This program requires minimum data input to the computer.It has been proved that the program is more accurate and more time-saving than any other methods so far as we know.     

含多椭圆孔(核)复合材料加筋层板的应力集中研究

基于各向异性体平面弹性理论中的复势方法,应用杂交变分原理建立了一种与常规有限元相协调的含任意椭圆核各向异性板杂交应力有限元,采用该杂交应力有限元来描述层板的椭圆核区域,采用杆单元来描述加强筋(杆单元的刚度取为层板沿筋条方向的刚度),其余区域采用常规8节点等参单元进行模拟,建立起分析含多椭圆核复合材料加筋壁板问题的力学分析方法,详细讨论了椭圆核大小、位置、筋条尺寸、相对位置、铺层比例等诸参数的影响规律,得到了一些有益的结论。     

The computer-aided holophotoelastic method

The computer-aided holophotoelastic method (CAHPM) is presented and validated. With it complete experimental stress analyses of transparent structures subjected to two-dimensional states of stress can be conducted based solely on experimental data without resort to either a hybrid, iterative, or other numerical procedure. The stress analysis is determined from photoelastic and holographic data, i.e., isochromatic, isoclinic, and absolute retardation results. The experimental setup and procedures are discussed and the algorithms used for the data reduction are also presented. The method is validated using a disk in diametral loading.     

T应力对光弹性条纹影响的理论分析

以裂尖弹性应力场的多参数模型为基础,研究I型、II型以及I/II混合型裂纹参数对光弹性条纹的影响. T应力的存在和符号影响着等色线条纹环的半径大小和旋转方向,对于纯I型或II型裂纹而言,条纹环的旋转角度只与T应力有关;而对于I/II混合型裂纹,条纹环旋转角度与K_{\rm I}, K_{\rm II}和T应力有关. T应力的存在使得I型裂纹在裂尖±π/3方向上出现2个各向同性点(T应力为正时),使得II型裂纹在裂尖后的裂纹面上出现1个各向同性点. 对于I/II混合型裂纹而言,当T应力为正时等倾线出现距裂尖半径不等的3个各向同性点;反之, T应力为负时在裂尖后只存在1个各向同性点,这些各向同性点分别与I型和II型裂纹情况具有相同的规律.      

Stress field tomography based on 3D photoelasticity

A tomographic method for identification of stress fields based on 3D photoelasticity has been developed. A second order tensor field tomographic method based on the general inverse problem of 3D photoelasticity, previously developed by the authors, is found to be highly sensitive to errors in photoelastic observations. In this study a new tomographic method for stress field with fairly high robustness to errors in photoelastic observations has been developed by introducing both equilibrium condition and linear elasticity to the previously developed general tensor field tomographic method. This new stress field tomographic method expands unknown 3D stress distributions as a linear combination of independent set of basis functions and a new inverse problem is posed: identify the amplitudes of basis functions based on photoelastic observations. Just as the inverse problem of 3D photoelasticity, this newly posed inverse problem is also nonlinear and ill posed. Unlike conventional approaches to 3D photoelasticity, both these nonlinearity and ill-posedness are properly treated using a load incremental approach. Load incremental approach chops the nonlinear solution space into segments with unique solutions by conducting photoelastic observations at sufficiently small increments in external load. Validating both numerically and experimentally, it is shown that this new stress field tomographic method has sufficient robustness against errors in photoelastic observations and is applicable to experimental stress measurements.