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

Abstract

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...