Issue 48

A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59

0.89

1

 

 14 1  



24





, c t 

t c

t c

1.09 0.09







t c

t c

0.2

0.65

 

M c t 

 

(15)

s

c t   

  c t

  c t

2

4.5





t

0.04

0.09

, c

    t c c t

1.65

  

, c t , c t  

1 1.464 1 1.464 

 

Q c t 

 

(16)

1.65



  1.45, c t 1.1 0.35 , c t c t  

 

 

, s c F c t 

  

(17)

F  

, 1.1 s a

(18)

To guarantee continuity of the K I zone (when a’  2.3  t ), resulting in

(c) expression, Eqs. (10) and (12) should be equivalent at the end of the 2D/1D transition

  t c F c t   , s c

 

 

K c 

M c t 







( ) 1 

K

Q c t

( )

( )

'( )

(19)

I

,1 I D

s

' 2.3 

a

t

Notice that Eq. (19) is a function of c/t only, having a unique solution for c/t  1.23. Therefore, if the ratio c/t is replaced in Eqs. (12-18) by a function r’(c/t, a’/t) that tends to 1.23 as a’ tends to 2.3  t , then continuity of the SIF is guaranteed. So, from Eq. (3), r’ is expressed as       2.3 1.3 , 1.23 1.23 a t r c t a t c t      (20) and the SIF during the transitioning period is then modeled replacing c/t by r’ in Eqs. (12-18). When the imaginary crack depth a’ reaches 2.3  t , Eq. (15) is then used to model the subsequent 1D crack growth. Fig. 4 plots the ratio between the transition and the 1D SIFs calculated using the proposed approach, to show their smooth transition.

Figure 4 : Ratio between the transition and 1D SIF calculated using the proposed approach.

Two main improvements are achieved using this approach. First, the effect of c/t on K I Newman-Raju’s equations than by the expressions used by Johnson. Second, continuity in the K I

(c) is much better modeled by (c) function is guaranteed

616