PSI - Issue 32

O.N. Belova et al. / Procedia Structural Integrity 32 (2021) 32–41 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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(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 remain a challenge even today. In this paper for a better understanding of the multi – parameter approximation of the stress field 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 algorithm is presented which utilizes the minimum intensity criterion to identify the fringe skeletons. 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

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

mode-I stress intensity factors

angular functions included in stress distribution related to the geometric configuration,

load and mode

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

f 

the material stress fringe (stress-optical constant)

h

specimen thickness

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 double edge notchesusing digital photoelasticity method. The Williams solution uses the mathematical form of an infinite series to describe the crack tip stresses according to which asymptotic expressions for the stress field in a plane medium with a traction-free crack submitted to mode I and mode II loading are presented as:   2 /2 1 ( ) , 1 ( , ) m k m k k ij k m ij m k r a r f            (1) with index m associated to the fracture mode; coefficients m k a related to the geometric configuration, load and mode,angular functions ( ) , ( ) k m ij f  depending on stress components and mode. Analytical expressions for circumferential eigenfunctions ( ) , ( ) k m ij f  are available (Karihaloo and Xiao (2001)):