PSI - Issue 28

R.M. Zhabbarov et al. / Procedia Structural Integrity 28 (2020) 1774–1780 Author name / Structural Integrity Procedia 00 (2019) 000–000

1775

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Keywords: digital photoelasticity; stress field near the crack tip; Williams asymptotic solution; higher order terms; coefficients of the higher order terms; finite element analysis.

1. Introduction In the last three deсennary of developments and improvements the technique of digital photoelasticity has been stabilized and the methodology has been successfully applied to a wide range of problems in engineering and science (Ramesh and Sasikumar (2020)). One of the most advanced applications of digital photoelasticity is linear fracture mechanics and experimental determination of coefficients of the multi-parameter Williams series expansion of the near-crack-tip fields (Jobin et al. (2020), Vivekanandan and Ramesh (2019), Dolgikh and Stepanova L.V.(2020), Patil et al. (2017), Tabanyukhova (2020), Stepanova (2020), Ayatollahi et al (2011)). Thus, Patil et al. (2017) used digital photoelasticity technique to estimate the crack tip fracture parameters for different crack configurations. As it is pointed out by Patil et al. (2017) conventionally, only isochromatic data surrounding the crack tip is used for stress intensity factor (SIF) estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The SIF is extracted from those estimated fracture parameters. Nomenclature ij  stress tensor components around the crack tip , r  polar coordinates N fringe order m k a coefficients of the Williams series expansion , I II K K stress intensity factors ( ) , ( ) k m ij f  angular functions related to the geometric configuration, load and mode m index associated to the fracture mode 1 2 ,   principal stresses E Young’s modulus  Poisson’s ration f  the material stress fringe Vivekanandan and Ramesh (2019) studied crack interaction effects at the crack tips of two interacting asymmetric cracks at different interaction angles under different biaxial ratios. The SIF values are evaluated using digital photoelastic technique with the help of digital image processing and a non-linear least squares method. The normalized SIF values are calculated and the amplification and shielding effects are determined. A single crack in a cruciform specimen experiences a shielding effect when biaxial ratio is increased from 0 to 1. Ayatollahi et al (2011) utilized the experimental technique of photoelasticity for calculating bi-material notch stress intensities as well as the coefficients of higher order terms. Employing the equations of multi-parameter stress field allows data collection from a larger zone from the notch tip and makes the data collection from experiments more convenient. The effects of higher order terms in the region near the notch tip are taken into account. For the photoelasticity experiments, a laboratory specimen known as the Brazilian disk with a central notch, consisting of aluminum and polycarbonate, has been utilized. Using this specimen, different mode mixities could be easily produced by changing the loading angle. The bi-material notch stress intensities and the first non-singular stress term (called I-stress) were then calculated for different test configurations. In order to utilize the advantages of whole-field photoelasticity and minimize the experimental errors, a large number of data points were substituted in the multi-parameter stress field equations. Then the resulting system of nonlinear equations was solved by employing an over-deterministic least squares method coupled with the Newton– Raphson algorithm. It has been shown that considering the I-stress term improves, to a large extent, the accuracy of the stress intensities calculated through the photoelasticity technique. The present study is aimed at determination of the higher order coefficients in Williams’ series expansion in the classical specimen for linear fracture mechanics – a plate with central crack using digital photoelasticity method.