PSI - Issue 80

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L. Gritti et al. / Procedia Structural Integrity 80 (2026) 392–402 Luca Gritti et al. / Structural Integrity Procedia 00 (2019) 000 – 000

397

= √

3 2 ⋅ (

The plane-strain fracture toughness K (i) was estimate at force P (i) as follows

)

) 1 2 [1.99 − ( ) (1 − ) (2.15 − 3.93 ( ) + 2.7 ( ) 2 )] 2 (1+2 ) (1 − ) 3 2

( )= 3(

(2)

It was calculated J (i) for each cycle as sum of elastic and plastic contribution (equation (3))

( ) = ( ) + ( ) ( ) = ( ) 2 ⋅ (1− 2 )

(3)

Defining the elastic component as follows And plastic component as follows ( ) =[ ( −1) +( ( −1) −1 ) ⋅ ( ) − ( −1) ] ⋅ [1− −1 ⋅ ( ⋅ −1 −1 )] Where ( ) was defined in equation (4) as the increment of plastic area under the chosen force versus plastic displacement record between lines of constant plastic displacement between two cycles.

( ) = ( −1) + [ + −1 ] ⋅ [ ( ) − ( −1) ] 2 −1 = [ − −1 ] =2+0.522 −1 −1 = 1.0 + 0.76 ⋅ −1

(4)

Thus, it was possible estimate the ( ) − ( ) curve at first attempt. The standard suggests fitting the data to correct the value of first estimation on initial crack length a 0 solving the system in equation (5). Thus, it was estimated the new K (i) and new J (i) as shown in the equations (2) (3).

∑ − ∑ 2 ∑ 2 − ∑ 3 2 ∑ 3 − ∑ 4 2 }

∑ 2 ∑ 3 ∑ 2 ∑ 4 ∑ 5 ∑ 3 ∑ 5 ∑ 6 ]

⋅ { 0 }

=

(5)

[

{

3.2. Estimation J Q values and validation of data To estimate the critical initiation J Q , a construction line was defined to establish the fitting area for validating the results, as outlined in the ASTM 1820 standard. The J Q was then estimated by the intersection between the J-curve and