PSI - Issue 32

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

35

4

 

 

 ( ) ( / 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 ( 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                                                 ( ) 1,11 ( ) 1,22 ( ) 1,12 ( ) 2,11 ( ) 2,22 ( ) 2,12      

(2)

(3)

The displacement fields around the crack tip can be described as     2 /2 ( ) , 1 ( , ) / , m k m k k i k m i m k u r a G r g         

where

 

    / 2 ( 1) cos / 2 ( / 2)cos( / 2 2) , / 2 ( 1) sin / 2 ( / 2)sin( / 2 2) , k k k k k k         / 2 ( 1) sin / 2 ( / 2)sin( / 2 2) , / 2 ( 1) cos / 2 ( / 2)cos( / 2 2) . k k k k k k k                

( ) k

( ) ( ) ( ) ( )

g g g g

k k              k     

   

1,1

( ) k

1,2

( ) 2,1 ( ) 2,2 k k

 



 

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

.

The goal of this study is to determine

1

o

m k a in the multi-point series expansion (1) for the double edge notched specimen.

the higher order coefficients

2. Photoelastic experiments: experimental setup and procedure The experimental setup used is shown in fig. 1. All the specimens in this work were made by casting of polycarbonate. Experimental specimens 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 10.41 / f Pa m fringe   . Isochromatic phase maps obtained for the plate with double edge crack notchesunder 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. Fringe tracking and fringe order assignment have become the central topic of current research in digital photoelasticity (Ramesh and Sasikumar (2020)).The skeleton of the fringe is identified first to accurately collect the experimental data from the fringes. The programmeis specially developed for the interpretation and processing of experimental data from the photoelasticity measurement experiments. The algorithm is based on Ramesh’s approach but it uses several new filters, for instance the Frost filter, bilateral filter, and allows us to scan the image in any direction. The developed and approved tool allows us to find points that belong to isochromatic fringes with minimal light intensity. The analysis of the experimental datauses a Java application programmed for the advanced determination of the fracture mechanics characteristics: coefficients of the Williams series expansion (WE) for the stress field in the vicinity of the crack tip.The programming tool allows us to collect experimental points from the photoelasticity tests on the cracked specimens. The skeleton of isochromatic fringes is shown in figs. 3,4. The skeleton is shown by green points. Finally, the chosen points are shown in fig. 5. It should be noted that, as it is revealed in the process of the