PSI - Issue 42

Sabrina Vantadori et al. / Procedia Structural Integrity 42 (2022) 133–138 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

135

3

loaded up to the peak load, max P : when such a load is reached, the post-peak stage follows and, when the load is equal to about 95% of max P , the specimen is fully unloaded. Then, the specimen is re-loaded up to failure.

(a)

(b)

Fig. 1. (a) Specimen geometry and loading configuration; (b) crack propagation under Mixed Mode according to the MTPM.

Firstly, by exploiting the value of the initial linear elastic compliance, i C , from the experimental load-CMOD curve, the elastic modulus, E , is computed as follows: ( ) 0 0 2 6 i S a V E C W B  = with ( ) ( ) 2 3 0 0 0 0 2 0 0 66 0 76 2 28 3 87 2 04 1 . V . . . .      = − + − + − (1) being 0 0 / a W  = . Then, the effective crack length ( ) 0 1 2 a a a a cos  = + + (see Fig. 1(b)) is computed from the following equation by using an iterative procedure: ( ) 6 2 4 0 0 1 0 cos 6 cos sin cos cos a a a a S E a V a a V a V         +         = + + + − +    where 1 0 0.3 a a = , the unloading linear elastic compliance u C is obtained from the corresponding load-CMOD curve, and 2 a is the unknown quantity to be determined. Moreover,  is the kinking crack angle, i.e. the angle formed by the kinked crack with respect to the applied load direction (Fig. 1(b)). If the value of 2 a from Eq. (2) is negative, it means that 0 1 a a a cos  = + , being 1 0 0.3 a a  , and then the unknown quantity 1 a is computed from the following equation by using an iterative procedure: ( ) 0 0 1 0 6 2 4 0 0 1 0 2 6 2 2 2 u a a a cos a S E a V cos sin cos a a cos V a V C W B W W W          +          = + + + −                          (3) Finally, the critical stress-intensity factor S ( I II )C K + is computed as follows: ( ) ( ) ( ) 0 1 2 max ( ) 0 1 2 2 cos 3 cos 2 S I II C a a a P K a a a f W W B      + + + =  + +  =   when 1 0 0.3 a a = (4) or   ( ) max 0 1 ( ) 0 1 2 3 cos cos 2 S I II C P a a K a a f W W B      + + = + = when 1 0 0.3 a a  (5) being: ( ) ( ) 0 0 1 0 2 3 2 0 1 2 0 1 0 1 2 0 1 2 2 2 cos cos cos cos sin cos cos cos cos u W   W W     C W B a a + a a a + a a + a V a a V W W                               +                + + + − +    (2)

2

1 1 99 1 . (

2 15 3 93 2 70 . . − +

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− −

 

 

(6)

f ( ) 

=

3 2 /

( )( 1 2 1

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

+ −

 