Error analysis of photoelasticity in fracture mechanics

An error analysis of the use of photoelasticity in the study of fracture problems is attempted. In particular, it was desired to determine the optimum regions of data collection and to ascertain the sensitivity of the extractedK ₁ andK ₂ values to errors in such parameters as crack-tip position and fringe location. Experiments were performed on both Mode 1 and Mixed Mode cases and the results compared with the error analysis     

Use of three-dimensional photoelasticity in fracture mechanics

The philosophy of fracture mechanics is reviewed and utilized to formulate a simplified approach to the determination of the stress-intensity factor photoelastically for three-dimensional problems. The method involves a Taylor Series correction for the maximum in-plane shear stress (TSCM) and does not involve stress separation. The results are illustrated by applying the TSCM to surface flaws in bending fields. Other three-dimensional problems solved by the TSCM are cited.     

General digital picture processing and texture analysis for photoelasticity

In this paper, a general digital picture processing and texture analysis for photoelasticity is developed. Overcoming some defects of references [2] and [3], it presents an effective method to analyse fringe patterns of the photoelasticity. By means of the trigonometric function relationship between the light intensity I and the image fringe order N, the equations of the fringe order N on brightness Z are deduced, and the mechanical parameters are thus obtained. We established a system of sigital picture processing and texture analysis for photoelasticity, which is called OYC-1 system. Finally, this system is checked with an example. It is found that the differences between measured results and the theoretical values are within 2.3 percent.This paper is supported by the science funds of the Academia Sinica.     

Plotting isoclinics for hybrid photoelasticity and finite element analysis

Displacement-based finite element method formulations are coupled with stress-based photoelasticity analysis. As the stress field is discontinuous at the interelement boundaries, the introduced smoothing procedure enables the generation of high-quality digital images acceptable for hybird experimental-numerical techniques. The proposed methods are applicable for the analysis of static and dynamic results of experimental photoelasticity.     

Comparison of the techniques of transmitted caustics and photoelasticity as applied to fracture

A comparison of the optical techniques of photoelasticity and caustics as applied to fracture mechanics is presented. Static as well as dynamic experiments were conducted using the two methods with the same specimen geometry and under the same loading conditions. The results for the crack-tip stress-intensity factor as a function of crack length were obtained from both techniques in three different specimen geometries. A comparison of the results shows good agreement under static conditions but large differences for running cracks.     

Contribution to the analysis of errors in photoelasticity

Photoelasticity data are expressed in terms of the direction and the differences of the principal stresses. To determine the principal stresses, separation is necessary. The author deals with some of the numerical methods of separating principal stresses, permitting evaluation of the stresses along straight sections. In the first part of this paper the author presents methods of separation and in the second part the errors involved.     

Role of photoelasticity in evolving discretization schemes for FE analysis

Experimental Techniques -     

Combining photoelasticity and finite-element methods for stress analysis using least squares

Photoelastic data are combined with the finite-element method for stress solutions over regions partially bounded by free surfaces and axes of symmetry. Least-squares solutions are obtained without presumed values of applied forces at element nodes and without isoclinic data. Varied example problems are used to compare the results to independent photoelastic and finite-element solutions and to theoretical stress values.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

A new method of stress analysis in photoelasticity

A new method of stress analysis in photoelasticity has been developed in this paper. Only the orders of isochromatic fringes and boundary conditions in three sections are adopted to analyse the stress components in these sections. The method requires minimum known data and can quickly analyse stress components. It reduces computational programs.     

Development of electroconvection in liquid dielectrics

The development of electroconvection in liquid dielectrics is analyzed theoretically from the standpoint of the dissociation-injection model of conductivity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 34–42, January–February, 1989.The author wishes to thank the participants in the G. A. Lyubimov seminar for discussing his work and making useful suggestions.     

Model making and slicing for three-dimensional photoelasticity

Problems which can occur during casting of epoxy resin are high exotherm, mottle and residual stress. Some methods for reducing these effects are discussed. Techniques for sawing, holding and machining epoxy models are presented. Particular attention is given to avoidance of chipping or cracking by use of proper tool profiles, cutting speeds and feed rates. Several ways of assembling models are discussed, including inspection of machined models and cemented joints. The effect of cemented joints on stress patterns is demonstrated. Suggestions for laying out, cutting and flattening slices are presented. The effect of scribed lines on a stress pattern is shown. A procedure for surface subslice preparation is given. Two types of edge effect can occur in epoxy frozen-stress models-temporary edge effect due to humidity and permanent edge effect due to oxidation. Methods for avoidance and treatment of edge effect are presented.     

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.     

Techniques for the determination of absolute retardation in photoelasticity

The purpose of this paper is to give an interpretation to the fringes observed in holographic interferometry when plane-polarized light or circularly polarized light is utilized. It is shown that, when plane-polarized light is utilized and both the loaded and the unloaded states are considered, the obtained patterns are formed by the superposition of three families of fringes: the two families of absolute optical retardation and the family of relative retardation. The intensity distribution is also a function of the orientation of the plane of polarization, and along the points where the plane of polarization is parallel to one of the principal directions, only one of the families of absolute retardation is observed. By utilizing circularly polarized light, the dependence on the orientation of the principal axis is eliminated and patterns consisting of the superposition of the three above-mentioned families are obtained. If only the loaded state is considered, the holographic interferometer behaves as an ordinary polariscope with the reference beam playing the role of the analyzer. The relationships between the observed families are discussed. Examples of application to the disk and ring under diametral compression are also given.     

Dual-beam polariscope and framing camera for dynamic photoelasticity

Dynamic photoelasticity is concerned generally with the determination of transient stresses and strains in machine parts or structures subjected to impact or shock loading. Progress in this field has paralleled the development and application of new advances in high-speed photography. This paper describes the equipment, techniques and methodology used to study dynamic stresses in two-dimensional problems.     

Development of upper bound technique for analysis of fracture in metal forming

Summary An attempt is made to modify the plasticity theory for compressible materials and then to derive the upper bound theorem or the second extremum principle which incorporate normal velocity discontinuity; this discontinuity is considered to be a measure of fracture. The theorem is applied to predict the occurrence of fracture, central bursting in extrusion or drawing. The occurrence of fracture appears to depend on the value of the parameters in the theorem; these parameters may be related to ductility or workability of the material in question. The upper bound technique is then applied to multi-stage extrusion of a carbon steel for which the values of the parameters are given with some assumptions. It is thus shown that the stage at which central bursting occurs agrees with experimental results and that it apparently depends on the extrusion condition.

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Ein obere-schranken-konzept zur bestimmung von bruchvorgängen bei der umformung von metallen

Übersicht Es wird der Versuch unternommen, mit einer modifizierten Plastizitätstheorie für kompressible Werkstoffe den Obere-Schrankensatz bzw. das zweite Extremum-Prinzip herzuleiten, wenn die Normalgeschwindigkeit auf Sprungflächen unstetig ist. Diese Unstetigkeit wird als Indikator von Bruchvorgängen angesehen. Angewandt wird diese Hypothese auf die Vorhersage des Bruchs, d. h. der Materialtrennung im Kern beim Durchdrück- bzw. Durchziehverfahren. Das Auftreten von Brüchen erweist sich als abhängig von den Parametern des Ansatzes. Diese Parameter lassen sich mit der Umformbarkeit des Materials in Zusammenhang bringen. Angewandt wird das Obere-Schranken-Konzept auf das mehrstufige Durchpressen eines Kohlenstoff-Stahls, für den die Parameterwerte mit Hilfe einiger Parameterwerte festgelegt werden. Davon ausgehend wird gezeigt, daß die Preßstufe bei Materialtrennung mit experimentellen Ergebnissen übereinstimmt und offensichtlich von den Durchpreßbedingungen abhängt.

     

Three-dimensional photoelasticity of the rotating body

Report covers the stress distribution of a hydraulically loaded pump impeller obtained with the aid of the stress-freezing method. The similarity of stress distribution of an actual metallic impeller and the photoelastic model is discussed dynamically and hydrodynamically. From the experiments by freezing stresses under centrifugal force and hydraulic forces, the stress distribution of the actual metallic impeller has been estimated on the basis of similarity.     

A fracture damage model for Jointed rock masses and its application to the stability analysis of dam abutments

Based on continuum damage mechanics, for jointed rock masses, a fracture damage model is presented in this paper. First, the damage tensors are defined through the elastic-flexibility of intact rock and the equivalent elastic-damage flexibility for rock mass. Then, by the self-consistent principle of solid mechanics, the equivalent elastic-damage flexibility tensors involving the interaction between multicracks are deduced. The damage evolution law is proposed involving the mechanism of crack propagation process: frictional sliding, crack kinking, growing of branched tension cracks, interlinking of the microcracks near branched crack tips leading to the breakthrough of macro-cracks and finally the failure of rock mass. Thus the evolution of damage variables reasonably unified with the process of crack propagation is given. Finally, a plastic-brittle damage constitutive relation including brittle coupled strain rate, developed and applied to the stability analysis of complicated rock foundation of a dam in China, is described in this paper.