The photoelastic method

Khesin, G. L.; Strel'chuk, N. A.

doi:10.1007/bf02400003

Cited by 3 publications

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“…By analogy with (4), (5), the relationship between the optical and mechanical quantities can be expressed in terms of linear differential operators, with Ñ d and Ñ e replaced by the appropriate operators.…”

Section: Cmentioning

confidence: 99%

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Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

2011

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The paper presents a method to calculate the difference of principal stresses and strains in linear viscoelastic optically sensitive polymeric materials from a time-dependent fringe pattern. The governing equations are derived using the direct and inverse Laplace transforms Keywords: photoelasticity, linear viscoelastic optically sensitive polymeric material, direct and inverse Laplace transformsIntroduction. The current level of development of the photoelastic method allows solving engineering problems [3,5] in various fields. The dynamic photoelastic method has recently been developed to be used in the mechanics of anisotropic bodies [8].Optically sensitive polymeric materials used for photoelastic modeling are known [2, 4] to have viscoelastic properties; therefore, it is reasonable to ask the question whether viscoelastic materials can be used for modeling dynamic processes in elasticity [6]. To minimize the error of an experimental method, use is usually made of photoelastic materials with low viscoelastic characteristics, which is quite justified [3,4]. Photoelastic data on the dynamic stresses and fracture of orthotropic plates with cracks can be found in [1,9].The present paper proposes a method to calculate the difference of principal stresses and principal strains in compressible linear viscoelastic optically sensitive materials from a time-dependent fringe pattern. We will establish the relationship between the mechanical and optical characteristics of viscoelastic bodies under dynamic loading.1. Original Equations. The photoelastic modeling of the mechanical behavior of elastic bodies involves the selection of a modeling material with mechanical behavior similar to that of the modeled material, the determination of the stresses and strains in the model, and the transformation to the stresses and strains in the real material.In optical modeling, the stresses are determined from the linear dependence of the fringe order m on the stresses (s 1 , s 2 ) alone with stress optical coefficient Ñ s as a coefficient of proportionality or on the strains (e 1 , e 2 ) alone with strain optical coefficient Ñ e as a coefficient of proportionality:

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Section: Cmentioning

confidence: 99%

“…The current level of development of the photoelastic method allows solving engineering problems [3,5] in various fields. The dynamic photoelastic method has recently been developed to be used in the mechanics of anisotropic bodies [8].…”

mentioning

confidence: 99%

Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

2011

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“…The dynamic calibration test of the ÉD-20 MTGFA material was carried out by simultaneously recording interference fringes m(t) and displacements u(t) [10]. In this test, samples of the material in the form of 4×4×200 mm bars were subjected at one end to a pulse of compression generated by an electric explosion of a conductor [9].…”

Section: Stress State and Failure Of Plates With A Central Curvilineamentioning

confidence: 99%

“…Practically all experimental studies in this area were conducted using the methods of dynamic photoelasticity and dynamic caustics [7][8][9][10][11][12][13][14][15][16].…”

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confidence: 99%

Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

Malezhik

Zirka

et al. 2005

Int Appl Mech

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The method of dynamic photoelasticity is used to study the dynamic failure of structural members in the form of plates with a curvilinear (circular or elliptic) hole and an isolated crack under impulsive loading. The time-dependences of the stress intensity factors and the crack tip velocity are investigated for two types of models Introduction. Considerable advances have been made in the development of the theory and methods of solving static and dynamic problems for isotropic and anisotropic structural members weakened by stress concentrators of various types and shapes (holes, cutouts, cracks) [1-3, 11, 14, etc.]. The publications [2-6] provide the most complete account of the results obtained in using analytic and numerical methods to determine stress intensity factors (SIFs) for bodies with stress concentrators (cracks) under static and dynamic loading.Also of interest is to use the recent achievements in the field of classical and computational mathematics to solve dynamic problems for bodies of various configurations with holes and cracks. Note that experimental methods applied to analyze the dynamics of crack propagation [11] allow us to model their mechanical behavior in one way or another. An analysis of studies on the subject indicates that the mathematical description of the final stage (fast crack propagation) involves severe difficulties. All the available theoretical solutions are idealized ones and have been obtained, except in [2], by using the linear approach. The theoretical solutions cannot unambiguously explain the spasmodic crack propagation, the finiteness of the crack growth rate, microdamages ahead of the crack front, their influence on crack development, etc.The difficulties faced in measuring the parameters of fast-growing cracks restrict the number of experimental investigations in this field compared with the total number of strength studies. Practically all experimental studies in this area were conducted using the methods of dynamic photoelasticity and dynamic caustics [7][8][9][10][11][12][13][14][15][16].Of chief interest are studies of the diffraction of waves by stress concentrators (holes, cracks). In many cases, waves cause high local stress concentration at the hole periphery or crack tip. This phenomenon may lead, for example, to fast crack growth and even to real failure. However, the available experimental data are not yet sufficient to understand the mechanism of interaction of stress waves and stress concentrators, since the majority of studies address compressional waves. It is well known that other types of waves such as tensile waves can equally be generated in complex structures.The present paper studies the failure of plates with stress concentrators (holes and cracks) under single pulses of tension. Use is made of the dynamic photoelasticity method and high-speed photographic recording [9, 10].1. Choice of Model. When the crack growth rate is high, inelastic strains develop only within a small area near the crack tip; therefore, the only criterion for deciding on a...

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“…Among them are photoplasticity [8], photoviscoelasticity [13], integral photoelasticity [1], dynamic photoelasticity [6,8], and radiowave and infrared photoelasticity [9].…”

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confidence: 99%

Development and application of radiowave photoelasticity for the fracture analysis of dielectrics

2011

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The radiowave photoelasticity method is developed and is justified for use in the fracture mechanics of dielectrics. The damage tensors of a material with microcracks are considered. The basic equations of the method are given. The time-dependence of microcrack density is analyzed. Numerical results are presented and analyzed Keywords: radiowave photoelasticity method, dielectrics, damage, microcrack density Introduction. The development of theoretical (analytic, numerical) and experimental methods for stress analysis of modern structures and their elements (plates, shells) made of homogeneous and inhomogeneous anisotropic materials is of importance for various branches of engineering. There is an increasingly urgent need for experimental methods for studying the time-dependent mechanical behavior of isotropic and anisotropic bodies, especially if they have crack-like stress concentrators.The most complete results on the development of the photoelastic method are presented in [8]. Among them are photoplasticity [8], photoviscoelasticity [13], integral photoelasticity [1], dynamic photoelasticity [6,8], and radiowave and infrared photoelasticity [9].The fracture of bodies (materials) involves the nucleation and propagation of cracks that create free surfaces under loading. This process is considered in static, kinematic, and dynamic aspects. The fracture of a material is known to be a complex process, even in the ideal case (isotropic homogeneous material). The process is even more complicated if the material is anisotropic or has plastic strains, residual strains, defects, or inhomogeneities. Fracture theory devotes particular attention to fatigue failure due to gradual crack growth under cyclic or long-term loading. In these cases, fatigue failure results from the accumulation of irreversible damage in the material. Cracks (changes in the material) start developing in bodies long before their failure (either plastic or brittle).Dynamic photoelasticity [6] in the macrofracture mechanics of anisotropic materials was addressed in the papers [14-18] which analyzed the stress-strain state (SSS) of isotropic and anisotropic plates with cracks subject to creep or dynamic loading.The present paper develops the radiowave photoelasticity method for the stress analysis of solid bodies. It is based on the distribution of electromagnetic waves in anisotropic and isotropic bodies (dielectrics and semiconductors including ceramics, plastics, ferrite, etc.) opaque to visible light. This method is advantageous over photoelasticity by making it possible to analyze the SSS of dielectrics using the invisible (ultrahigh frequency) spectrum of electromagnetic waves.Our goal is to justify the use of polarized radio-waves for examining (detecting and analyzing) microcracks in dielectrics.1. Macroscopic Damage Tensor. The nucleation and propagation of submicrocracks in dielectrics can be described based on the dislocation model [3] because cracks are generated by some type of incompatibility in a continuum. A crack is represented by a s...

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The photoelastic method

Cited by 3 publications

References 0 publications

Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

Development and application of radiowave photoelasticity for the fracture analysis of dielectrics

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