PSI - Issue 40

O.N. Belova et al. / Procedia Structural Integrity 40 (2022) 46–60 O.N. Belova, L.V. Stepanova / Structural Integrity Procedia 00 (2022) 000 – 000

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photoelasticity is the extraction of isochromatic and isoclinic data from the fringe pattern seen on the model under stress (Ganesan and Mullick (2008)). In general, the interference fringes appear as broad bands rather than as thin lines. To identify the actual fringe from the broad band and to extract data for further processing, various algorithms have been proposed invoking techniques from the area of digital image processing (DIP) (Ganesan and Mullick (2008)). In DIP, the image is identified as an assembly of picture elements (pixels). The intensity of light transmitted or reflected by each pixel is assigned a number, between 0 and 255, and the image is transferred into a matrix of numbers. Subsequent manipulations of the matrix using a digital computer can be effectively employed to extract various features of the image. These algorithms are, in general, time consuming and complex (Yang et al. (2021)). Further, these algorithms fail in zones of high stress concentration. In the fringe band, the minimum intensity positions actually form the fringe contour. Thus, the digital image processing in the photoelasticity method is clearly still subject to ongoing studies. The second area of development of the digital photoelasticity method is diverse and multiple applications of the photoelasticity technique (Ramesh and Sasikumar (2020), Ganesan and Mullick (2008)), such that hydraulic fracture propagation in rock materials (Ham and Kwon (2020)), dentistry and other applications in biomechanics (Pirmoradian et al (2020)) and integrated use of experimental, manufacturing and numerical methods, for instance, rapid 3D prototyping and photoelasticity (Liu et al. (2020)). Thus, in (Ramesh and Sasikumar (2020)) the succinct and contemporary review proposes to readers to extrapolate the photoelasticity technique to tackle newer problems in the uncharted territory and domains. Finally, the third area of research in the wide field of photoelasticity is aimed at building the multi-parameter Williams series expansion for the stress field in the vicinity of the crack tip in a linear elastic isotropic material (Stepanova (2020), Dolgikh and Stepanova (2020), Stepanova and Roslyakov (2016)). The higher order terms of stress field influence significantly the stress distribution in the vicinity of the notch tip and crack tip and consequently can play an important role in brittle fracture. Therefore, in the brittle fracture assessment of interface notches, it is important that to take into account not only the singular stresses but also the higher order terms. However, it is imperative to develop and improve algorithms of accurate photoelastic data extraction from interference fringe patterns obtained in experiments. Some questions and problems remain a challenge even today. In this paper for a better understanding of the multi – parameter approximation of the stress and displacement fields in the vicinity of the tip of cracks and notches the experimental technique of photoelasticity has been utilized for calculating the coefficients of higher order terms of the multi-parameter stress field. In the present study a new type of the cracked specimen is presented. This type of the cracked specimen is useful for study of the mixed mode loading. Then, the experimental photoelasticity results were compared with the corresponding values obtained from finite element analysis and a good correlation was observed.

Nomenclature ij 

stress tensor components around the crack tip

, r 

polar coordinates of the system with its origin at the crack tip

N k a

fringe order

m

coefficients of the terms of the Williams series expansion for mode I and mode II of loading

, I II K K , ( ) k m ij f  ( ) ( ) , ( ) k m i g 

mode-I and mode II stress intensity factors

known angular functions included in stress distribution related to the geometric configuration, load and mode known angular functions included in displacement distribution related to the geometric configuration, load and mode

m

index associated to the fracture mode

1 2 ,  

principal stresses Young’s modulus Poisson’s ration shear modulus

E



G