High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization.To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM)is proposed.The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations.The advantage of the proposed method is that the auxiliary lines,grids,and error accumulation which are commonly used in traditional shear difference methods(SDMs)are not required.Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.

Comparative study of various internal fixation methods for treating patellar fractures by three-dimensional photoelasticity

Objective: To compare the biomechanical basis of 3 different internal fixation methods: nitinol patellar concentrator (NT-PC), tension band and wire circle in treating patellar fractures. Methods: The epoxy resin three dimensional photoelasticity patellar models were made by precise moulding, and were fixated by nitinol patellar concentrator (NT-PC), tension band and wire circle respectively. The patellar models with frozen stress stripes were put into the polarized light field and the stress distributions were compared. As for the model fixated by NT-PC, by dividing layer, photographing and tracing, we used the iterative method to calculate the stress value of every internal node of the epoxy resin patellar model, and the character of stress was analyzed. Results: An overall stress field was yielded when the patellar model was fixated by NT-PC, and the stripes were more than that of tension band model and wire circle model, which have only few stress stripes in the fixated layers. Further analysis indicated that there were continuous fixated stresses in the facies articularis and distal pole of patella, and the character of stresses produced by NT-PC were mainly in longitudinal direction, then in transverse direction. The shearing stresses were small. Conclusion: The initiative and continuous memorial stress of NT-PC and its overall stress distribution character are the essence of NT-PC distinguished with tension band and wire circle in treating patellar fractures. The stress character produced by NT-PC is good for the stability of fracture site and prompts fracture healing.

Three-dimensional photoelasticity analysis of Nitinol Patellar Concentrator for treating patellar fractures

Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded with Nitinol Patellar Connector and frozen. After dividing layer, photographing and tracing, iterative method was used to calculate the stress value of every tuteed node. Rasults: Stress values of 1 262 nodes scattered in 12 layers were obtained The stress distribution indicated that an overall stress field was yield when the NT-PC fixated the patellar model, and there existed fixative stress in the facies articularis and distal pole of the patellar model. Conclusion: The NT-PC has evident therapeutic effect for the comminuted patellar fractures. The existing stress is helpful in maintaining anatomical reduction and enhancing fracture healing.

Propagation Properties of Backward Lamb Waves in Plate Investigated by Dynamic Photoelastic Technique

The dynamic photoelastic technique is employed to visualize and quantify the propagation properties of backward Lamb waves in a plate. Higher energy leakage of second-order symmetric backward wave mode S2b in contrast to third-order anti-symmetric backward mode A3b is shown by the dispersion curve of a plate immersed in water, and then verified by experiments. To avoid the considerable high leakage, the plate is placed in air, both group and phase velocities of modes S2b and A3b in the glass plate are experimentally measured. In comparison with the theoretical values, less than 5% errors are found in experiments.

THE VARIATIONAL PRINCIPLES OF COUPLED SYSTEMS IN PHOTOELASTICITY

This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method.

Analysis of the Stress Distribution Pattern of Anatomic and Non-Anatomic Tooth Forms on Maxillary and Mandibular Edentulous Ridges—A Photoelastic Study

Aim: To compare the type of stress distribution pattern occurring with anatomic and non-anatomic tooth forms beneath a complete denture in both maxillary and mandibular arch. Methodology: A photoelastic model of the edentulous maxillary and mandibular ridge was prepared meticulously to simulate the human mandible and maxilla. Two sets of acrylic teeth with anatomic and non-anatomic occlusal forms were used to fabricate upper and lower dentures. A vertical static load of 100 N was applied through the mandibular model to the maxillary model. After load application on the dentures the photoelastic model as well as the upper and lower complete dentures were sectioned in the midline. The sectioned photoelastic model was viewed through a polariscope to observe the fringe pattern indicating varying amounts of stress distribution. In this study, a two-dimensional photoelastic stress analysis technique was utilized. Results: Force per unit area was observed more in anatomic teeth than the non-anatomic counterpart. Hence anatomic tooth forms may increase the possibility of bone resorption rate over a period of time. However, in non-anatomic lower teeth, a decrease in value was observed from posterior to anterior region. Conclusion: Stress of greater magnitude was observed with cuspal teeth whereas non-anatomic (0°) showed slightly less magnitude of stress. Depending upon the clinical situation the clinician needs to choose the type of occlusal tooth forms for edentulous patients.

SEPARATION OF PRINCIPAL STRESSES IN DYNAMIC PHOTOELASTICITY

A new and effective method used to separate the transient principal stresses for dynamic photoelasticity is proposed. This is a hybrid method combining the optical method of dynamic caustics and the boundary element numerical method. Firstly, a modified Cranz-Schardin spark camera is used to record simultaneously the isochromatic fringe patterns of photoelasticity and the shadow spot patterns in the dynamic process. By means of the isochromatic fringe patterns, the difference between transient principal stresses in the whole domain and the principal stresses along the free boundary can be solved. In addition, the method of caustics is a very powerful technique for measuring the concentrative load. Then, the sum of the principal stresses is calculated by the boundary integral equation obtained from the Laplace integral transform of the wave equation. So, the transient principal stresses can be determined from the experimental and numerical results. As an example, the transient principal stresses in a polycarbonate disk under an impact load are resolved.

Determination of the full-field stress and displacement using photoelasticity and sampling moirémethod in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials.Various optical measurement techniques such as photoelasticity,moiréand digital image correlation methods have been developed to achieve this goal.However,these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement;however,these elements will disturb the light passing through the tested models using photoelasticity.In this study,by combining photoelasticity and the sampling moirémethod,we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional(3D)-printed photoelastic model with orthogonal grating.Then,the full-field stress was determined by analyzing 10 photoelastic patterns,and the displacement fields were calculated using the sampling moirémethod.The results indicate that the developed method can simultaneously determine the stress and displacement fields.

Design of Three-component Photoelastic Waveguide Accelerometer

In order to realize a high accuracy seismic exploration in the high electro-magnetic field and to improve oil producibility and recovery efficiency,a three-component photoelastic waveguide accelerometer is designed. Based on the photoelastic effect,the Mach-Zehnder integrated optical interferometer is designed to measure the three-orthogonal components of acceleration and the combined three-component simple harmonic vibrator is designed to reduce the cross-talk among the acceleration components. According to the variation of LiNbO3 waveguide phase under the action of the applied acceleration,the cross-axise sensitivity and transverse sensitivity ratio(TSR) were analysed. The results reveal that the accelerometer has wide band and good linearity. It can satisfy the sensor requirements of high accuracy seismic exploration. The main design parameters of the geophone system are:phase sensitivity:1.86×10-4 Rad·m-1·s-2,natural frequency:3 500 Hz,and the transverse sensitivity ratio:0.11%.

COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

In this paper, by applying Lagrange, multiplier method and high order Lagrange multiplier method [1], we systematically derive coupled potential energy principle.coupled complementary energy principle,and generalized coupled potential energy principles and generalized coupled complementary energy principles with two and three kinds of variables in photoelasticity.

FINITE ELEMENT METHOD COMBINED WITH DYNAMIC PHOTOELASTIC ANALYSIS TO DETERMINE DYNAMIC STRESS-INTENSITY FACTORS

The present paper is addressed to the finite element method combined with dynamic photoelastic analysis of propagating cracks, that is, on the basis of [1] by Chien Wei-zang, finite elements which incorporate the propagating crack-tip singularity intrinsic to two-dimensional elasticity are employed. THe relation between crack opening length and time step obtained from dynamic photoelaslie analysis is used as a definite condition for solving the dynamic equations and simulating the crack propagations as well As an example, the impact response of dynamie-bending-test specimen is investigated and the dynamic stress-intensity factor obtained from the mentioned finite element analysis and dynamic photoelasticity is in reasonable agreement with each other.

Photoelastic Fabry－Perot Optical Modulator Based on a Silicon－on－Insulator Structure

A simple photoelastic optical modulator with a Fabry-Perot cavity based on the silicon-on-insulator system was fabricated. A 50 % modulation depth has been obtained at current density of about 1. 5 x 103 A/cm2. The insertion loss was about 15 dB.

Modeling of Orientation-Dependent Photoelastic Constants in Cubic Crystal System

Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotations are utilized in the model relating to crystallographic coordinates with Cartesian coordinates. The symmetry of photoelastic constants is found to have strong dependence with rotation angle. Using the model, one can determine photoelastic constants in any orientation by selecting appropriate rotation angle. The outcome of this study helps to characterize spatial variation of residual strain in crystalline as well as polycrystalline materials having cubic structure using the experimental technique known as scanning infrared polariscope.

Crack-Tip Stress Analysis at a Bi-Material Interface by Photoelastic, Isopachic and FEA

The paper investigates the stress state at the bi-material interface crack-tip by the Photoelastic and Isopachic methods and the Finite Element Analysis (FEA). The principal stresses at the bi-material interface crack-tip are theoretically determined using the combination photoelastic and isopachic fringes. The size and the shape of crack-tip isochro-matic and isopachic fringes, at a bi-material interface under static load, are studied. When the crack-tip, which is perpendicular to interface, is placed at the interface of the bi-material, the isochromatic and the isopachic fringes depend on the properties of the two materials. Thus, the isochromatic and the isopachic fringes are divided into two branches, which present a jump of values at the interface. The size of the two branches mainly depends on the elastic modulus and the Poisson’s ratio of the two materials. From the combination of the isochromatic and the isopachic fringes, the principal stresses σ1 and σ2 can be estimated and the contour curves around the crack-tip can be plotted. For the FEA analysis, the program ANSYS 11.0 was used. The bi-material cracked plates were made from Lexan (BCBA) and Plexiglas (PMMA).

Characterization of Electrical Tree Degradation of Epoxy Resin under Thermal and Temperature Stresses by Photoelastic Effect

Epoxy resin is widely used in the support,insulation,and packaging components of electrical equipment owing to their excellent insulation,thermal,and mechanical properties.However,epoxy-resin insulation often suffers from thermal and mechanical stresses under extreme environmental conditions and a compact design,which can induce electrical tree degradation and insulation failure in electrical equipment.In this study,the photoelastic method is employed to investigate the thermal-mechanical coupling stress dependence of the electrical treeing behavior of epoxy resin.Typical electrical tree growth morphology and stress distribution were observed using the photoelastic method.The correlation between the tree length and overall accumulated damage with an increase in mechanical stress is determined.The results show that compressive stress retards the growth of electrical trees along the electric field,while tensile stress has accelerating effects.This proves that the presence of thermal stress can induce more severe accumulated damage.

SCATTERING OF A GRAZING LONGITUDINAL WAVE PULSE BY A RIBBON-TYPE CRACK—EXPERIMENTAL VERIFICATION BY THE PHOTOELASTIC METHOD

By using the dynamic photoelastic method and our technique of fabricating an internal crack in solid , the scattered waves of incident grazing longitudinal ultrasonic wave pulse by a ribbon-type crack are ob-served and analyzed . In particular, the distribution of the intensity of the scattered head wave is measured quantitatively . The experimental results fairly agree with the theoretical ones given in ref. [ 1 ] .

Application of artificial neural networks for stress state analysis based on the photoelastic method

The present article proposes an evolutionary development of the photoelasticity method for measuring stresses based on annular photoelastic sensors application along with stress pattern recording with the aid of a digital camera and its recognition using artificial neural networks.The analysis of the modern application of the photoelasticity method for various problems within the theory of strength is presented.The principle of operation of photoelastic sensors based on the photoelasticity effect is considered.Optical patterns in an annular photoelastic sensor are presented for various values of the horizontal stress.The calculation of the stress state of the sensor for the following full-scale experiment has been performed,the estimate of the threshold conditions under which the sensor can be applied has been performed.As a result of a laboratory experiment,a dataset of 1500 isochromatic images has been assembled.A subspecies of a neural network,namely a convolutional neural network,has been applied as a machine learning algorithm.Different combination of models and optimizers have been employed.The application of downhole sensors for continuous monitoring of alterations in the rock mass stress state and the integration of this data into a digital field model based on Internet of Things technologies has been proposed.

A novel three-component hybrid-integrated optical accelerometer based on a Mach-Zehnder interferometer with a LiNbO_3 photoelastic waveguide

An investigation of the properties ofa LiNbO3 photoelastic waveguide via the acceleration-induced effect is presented. A novel three-component hybrid-integrated optical accelerometer based on a Mach-Zehnder interferometer with a LiNbO3 photoelastic waveguide has been designed, which is capable of detecting seismic acceleration in high-accuracy seismic exploration. The Mach-Zehnder interferometer was successfully fabricated and a lighting test used to check its quality. The frequency response characteristic of the accelerometer was measured2 The accelerometer with a resonant frequency of 3549 Hz was demonstrated to show good linear frequency responding characteristics in the range of 100-3000 Hz. The accelerometer also shows good stability and consistency. Experimental results indicate that the outputs of the on- and cross-axis are 147 and 21.3 mV, respectively.

Improvement of the physical properties of poly(methyl methacrylate) by copolymerization with N-pentafluorophenyl maleimide; zero-orientational and photoelastic birefringence polymers with high glass transition temperatures

Copolymers of N-pentafluorophenyl maleimide (PFPMI) with methyl methacrylate (MMA) were synthesized by a free radical initiator, such as AIBN. The refractive indexes of the copolymers remained nearly constant (1.4970 at 532 nm) regardless of the polymer composition. These copolymers also showed high thermal stability. The orientational and photoelastic birefringence of the copolymers obtained were measured. Since both of the orientational and photoelastic birefringences of PMMA are negative whereas poly(PFPMI) exhibits positive, thus we have obtained nearly zero orientational and photoelastic birefringence polymers when the ratios of MMA/PFPMI were 91.8/8.2 and 97.0/3.0 mol%, respectively. Based on the experimental data, the ratios of MMA/PFPMI for zero birefringence were determined to be 88.9/11.1 and 93.8/6.2 mol% for orientational and photoelastic birefringence, respectively. The Tgs of corresponding copolymers were estimated to be 128 and 122 ℃.

Automatic extraction method of force chain information and its application in the flow photoelastic experiment of granular matter

The force chain is the core of the multi-scale analysis of granular matter.Accurately extracting the force chain information among particles is of great significance to the study of particle mechanics and geological hazards caused by particle flow.However,in the photoelastic experiment,the precise identification of the branching points of force chains has not been effectively realized.Therefore,this study proposes an automatic extraction method of force chain key information.First,based on the Hough transform and the Euclidean distance,a particle geometric information identification model is established and geometric information such as particle circle center coordinates,radius,contact point location,and contact angle is extracted.Then,a particle contact force information identification model is established following the color gradient mean square method.The model realizes the rapid calibration and extraction of a large number of particle media contact force information.Next,combined with the force chain composition criterion and its quasilinear feature,an automatic extraction method of force chain information is established,which solves the problem of the accurate identification of the force chain branch points.Finally,in the photoelastic experiment of ore drawing from a single drawpoint,the automatic extraction method of force chain information is verified.The results show that the macroscopic distribution of force chains during ore drawing from a single drawpoint is left–right symmetrical.Strong force chains are mostly located on the two sides of the model but in small numbers and they mainly develop vertically.Additionally,the ends are mostly in a combination of Y and inverted Y shapes,while the middle is mostly quasilinear.Weak force chains are abundant and mostly distributed in the middle of the model,and develop in different directions.The proposed extraction method accurately extracts the force chain network from the photoelastic experiment images and dynamically characterizes the force chains of granular matter,which has significant advantages in particle geometry information extraction,force chain branch point discrimination,force chain retrieval,and force chain distribution and its azimuthal characterization.The results provide a scientific basis for studying the macroscopic and microscopic mechanical parameters of granular matter.