Issue 68

Z. Moqadaszadeh et alii, Frattura ed Integrità Strutturale, 68 (2024) 186-196; DOI: 10.3221/IGF-ESIS.68.12

Depending on the GSED criterion, crack expansion happens in the angle of direction ( 0  ) while the value of S at the c r from the crack tip is minimum and brittle fracture happens when S attains its critical value ( S cr ) at a critical radius from the crack tip. Critical value of S and c r are constant material properties. Angle of crack growth and beginning of fracture is obtained from Eqn. (6) and Eqn. (7) respectively.

0 bK bK bKK bT rK bT rK                2 0 ( 2 ) ( 2 ) S

(6)

2 II

0

I

I II

c

I

c

II

1

2

3

4

5

1

2

2 II

2 (2 ) ] 



1 2 a K a K a K K a    I II I 2 3

( 2 ) 

r K T a 

( 2 ) 

r K T a r T 

S

[

cr

I

II

4

5

6



G

16

(7)

1

2 Ic



1) k K 

S

(

cr



G

8

where ( 1:6) i b i  coefficients are as follows:



0  sin (2cos

0 

k  

b b b

1)

1



0  sin (6cos

0 

k  

1)

2



0 1)cos ) sin (5(cos(2 ) cos ) ( 2 cos (5(cos(2 ) cos ) ( k             0 0 0 0 0 (2cos(2 ) (

3



k  

b

1))

(8)

4



k  

b

3))

5

0

0

2



b

0

6

More details about the GSED criterion are provided in [5]. The SED criterion is obtained by vanishing the terms including the T in Eqn. (6) and Eqn. (7), that these equations are simplified to:

 

S

2

2 II

   



b K b K b K K

0

0

(9)

 

0  

I

I II

1

2

3

1

2

2 II



2 a K a K a K K  

S

[

]

(10)

cr

I

I II

1

2

3

G 

16

HCSP S PECIMEN

ig. (2) demonstrates loading setup and the geometric characteristics of the HCSP laboratory sample. HCSP refers to a square plate with specific dimensions: it has an edge length denoted as W, a thickness indicated as B, a circular hole in the middle with a diameter of D, and two cracks with a length of 2a, located around the inner hole, radially. Fracture tests are conducted by applying tensile loads ( P ) which do not need sophisticated loading apparatus put to use in the conventional tensile testing equipment due to the simple geometry of HCSP specimen. HCSP experiences pure mode I loading when the angle of crack orientation in relation to Exerted load ( P ) is 90 o . Each proportion of in-plane mixed-mode will be produced at every angle relative to the applied load. Also, pure mode II loading will be attained at a significant angle which relies on the two other parameters as 2 / a W and / D W . F

189