PSI - Issue 28

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

1776

3

However, this type of experimental specimen allows us to elucidate the influence of the higher order terms of the Williams series expansion on the stress field description. Asymptotic expression for the stress field in a plane medium with a traction-free crack submitted to mode I and mode II load have been derived:   2 /2 1 ( ) , 1 ( , ) m k m k k ij k m ij m k r a r f            (1) with index associated to the fracture mode; coefficients related to the geometric configuration, load and mode. Angular functions depending on stress components and mode. Analytical expressions for circumferential eigenfunctions are available (Karihaloo and Xiao (2001)):       ( ) 1,11 ( ) 1,22 ( ) 1,12 ( ) ( / 2) 2 / 2 ( 1) cos( / 2 1) ( / 2 1)cos( / 2 3) , ( ) ( / 2) 2 / 2 ( 1) cos( / 2 1) ( / 2 1)cos( / 2 3) , ( ) ( / 2) / 2 ( 1) sin( / 2 1) ( / 2 1)sin( / 2 3) , k k k k k k f k k k k k f k k k k k f k k k k k                                              (2)





  ( ) ( / 2) 2 / 2 ( 1) sin( / 2 1) ( / 2 1)sin( / 2 3) , ( ) ( / 2) 2 / 2 ( 1) sin( / 2 1) ( / 2 1)sin( / 2 3) , ( ) ( / 2) / 2 ( 1) cos( / 2 1) ( / 2 1)cos( / 2 3) . k k k k k k f k k k k k f k k k k k f k k k k k                                                  ( ) 2,11 ( ) 2,22 ( ) 2,12

(3)

m k a are the unknown mode I parameters. The SIFs can be computed from the coefficients as

The coefficients

1 1 2

2 1 2

I K a 

II K a  





1 2 a is related to T-stress as

1 2 4 . a

  

and

.

1

o

2. Photoelastic experiments The experimental setup used is shown in fig. 1. All the specimens in this work were made by casting of polycarbonate. Circular and semi-circular shapes were machined from the sheet to get the test specimens. Material properties of the photoelastic material are Young’s modulus 3 E GPa  , Poisson’s ration 0.3   and the material fringe constant is found to be 18.38 / f Pa m fringe   . Isochromatic phase maps obtained for the plate with central crack under different loads are shown in fig. 2. One can see from fig. 2 that it is not possible to provide an accurate description of the stress field in the vicinity of the crack tip using the one-term asymptotic series expansion.

Fig. 1. Photograph of the experimental apparatus used to visualize and capturing the fringe patterns.