PSI - Issue 39

O.N. Belova et al. / Procedia Structural Integrity 39 (2022) 761–769 Author name / Structural Integrity Procedia 00 (2021) 000–000

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1. Introduction The photomechanics technique continues to be one of the most advanced and universal interference-optic methods for simulating the stress state in specimens weakened by cracks (Frankovsky et al. (2020), Oiu et al. (2021), Vincitorio (2018), Stepanova (2021), Georges (2020)). The holographic interferometry, which is one of the most useful application of holography, uses polarimeters to measure the relative path difference ∆ between the light waves with vibrations in two directions of 1 σ and 2 σ , while interferometers are used to measure the absolute path differences 1 ∆ and 2 ∆ for each of these light waves with respect to a light wave passing through an unloaded model. The relative path difference is related to the principal stresses by Wertheim’s effect ( ) 1 2 m ct λ σ σ ∆ = = − (1) where , , a b c are opticomechanical constants of the material of the model; t is the thickness of the model; m is the order of the fringe of the isochromes; 1 2 , m m are the orders of the fringe of the absolute divergence (isodromes); λ is the wavelength of the light. The use of holographic interferometry in photomechanics considerably simplifies the measurements since it is possible to determine the principal stresses at any point of the model being investigated in accordance with the expressions (2), without using integration methods (Kitaeva and Trumbachev (1982)). One of the fundamental problems in linear elastic fracture mechanics if determination of the coefficients of the Williams power expansion of the near crack-tip fields in isotropic materials (Ayatollahi, et al. (2011), Dolgikh, and Stepanova (2020), Mirzaeri et al. (2020), Jobin et al. (2020), Stepanova (2021), Yang et al. (2021), Stepanova and Roslyakov (2016)). Nomenclature ∆ the absolute path differences 1 ∆ , 2 ∆ the absolute path differences λ the wavelength of the light 1 2 , m m the orders of the fringe of the absolute divergence (isodromes) ij σ stress tensor components around the crack tip , r θ polar coordinates of the system with its origin at the crack tip m fringe order l k a coefficients of the terms of the Williams series expansion for mode I and mode II of loading , I II K K mode-I and mode II stress intensity factors T T-stresses ( ) , ( ) k l ij f θ known angular functions included in stress distribution related to the geometric configuration, load and mode ( ) , ( ) k l i g θ known angular functions included in displacement distribution related to the geometric configuration, load and mode l index associated to the fracture mode 1 2 , σ σ principal stresses E Young’s modulus ν Poisson’s ration and the absolute path differences by Favre’s law 1 1 1 2 2 2 2 1 , m at ∆ = = + bt λ σ σ m at ∆ = = + bt λ σ σ (2)