Issue 37

S. Vantadori et alii, Frattura ed Integrità Strutturale, 37 (2016) 215-220; DOI: 10.3221/IGF-ESIS.37.28

The initial compliance, i C , is used to determine the elastic modulus, E [15]:   BWC VaS E i 2 0 0 6  

(1)

where S, W and B are the loading span, depth and thickness of the specimen, respectively, 0 a is the notch length, and i C is the linear elastic compliance. Further, the parameter V can be expressed as follows [15]:   W a V 0 0 2 0 3 0 2 0 0 0 with 1 66.0 04.2 87.3 28.2 76.0              (2) Therefore, if the crack propagates under pure Mode I, the effective critical crack length, a , is determined from the following equation by employing an iterative procedure:   BWC VaS E u 2 6   (3) where u C is the unloading compliance, and    V is obtained from Eq. 2 by replacing 0 a with a . Finally, the Mode I critical stress-intensity factor, S IC K , is computed by employing the measured value of the peak load, max P [15]:

) ( BW S P K   fa

3

S IC 

2 max

(4)

2

where:

   2

 99.11 ) (

  

W a

) 70.2 93.3 15.2() 1(

f

with

(5)



    2/3

1 21

M ODIFIED TWO - PARAMETER MODEL

A

modified procedure is hereafter proposed when crack propagates under Mixed Mode loading (Mode I and Mode II). Specimens geometry and experimental test procedure are equal to those presented in the previous Section (see

Fig. 2(b)). The elastic modulus is determined through Eq. 1. Under Mixed Mode loading, the effective critical crack length,

2 1 0 a a aa   , is obtained from the following equation by

employing an iterative procedure:

S E

6

{

) ( 

0 

0 Va BWC

2

u

cos 1 0 W a aV a a    0 0 ) Va

( [ [

[(]

)

] ) ( 

(

6

2

4

cos

sin

cos

cos 1 0

2

2

2

(6)

cos W a a aV a    cos 1 0 2 )

][(

)

(

3

2

cos sin 

)]} 1 0 cos a a

cos

cos

2

cos 1 0 W a aV a a 

()

 

cos 1 0

217

Made with FlippingBook Annual report