PSI - Issue 7

Stanislav Žák et al. / Procedia Structural Integrity 7 (2017) 254 – 261

259

6

Stanislav Žák et al. / Structural Integrity Procedia 00 (201 7 ) 000 – 000

Mode II SIF which is investigated in this paper can then be expressed as a function of angles α and β :

  

3               sin 2 2 α α ⋅

α    

( ) , α β

( ) cos 2 cos ⋅

( ) α β

/ k K

1 sin

cos

= −

⋅

⋅

+

II

II

2                3 sin 2 2 α α +

(7)

( ) ( ) ( ) β

2

1 cos +

(

)

( ) sin 2 1 sin α ν ⋅ −

( ) β

2

sin sin 2 cos α α ⋅ ⋅

.

+

⋅

⋅

4

Equation (7) can be easily used to assess the local mode II SIF component of a rough precrack provided the value of R L of its front is determined and the characteristic dimensions d m and Δ a are defined (usually comparable to the grain size). Averaged value along the crack front can be evaluated by following formula:

α

m

1

( ) ,

⋅ ∫

d α β α .

(8)

/ k K

/ k K

=

II

II

II

II

2

α

m

−

α

m

This approach to obtain local stress intensity factors at kinked and twisted crack front was compared with that proposed by Zhang and Wang (1997) who assumed an asymmetric kink combined with crack twist just to improve basic equations for the kinked crack (Cotterell and Rice (1980)). However, this simple approach does not give as accurate results as the above-mentioned method (equations (3) - (6)) when compared to the numerical results. Therefore, only the results obtained using the tensor transformation method are mentioned hereafter. 3. Results and discussion The calculations were performed for two types of statistical distribution of crack front asperities (see chapter 2.1). Each set of crack-front asperities was specified by an average value of the linear roughness R L : the first set of 1.078 and the second one of 1.261. These values of the crack front roughness were used to evaluate angles β and α m (equations (1) and (2) respectively). The averaged local SIF k II for one-facet model, obtained from equation (8) and normalized to the remote SIF K II for an equally loaded smooth crack o f the projected length a p = a + Δ a calculated using normalized stress tensor components in equations (3), were compared with those numerically computed for the corresponding real-like crack front. The values d m = 20µm and Δ a = 80µm were employed in the one-facet models. The numerical results along the crack front were normalized to the function K II (z) ( z is the position along the crack front) obtained from the same model (Fig. 1) but containing a smooth crack front. To ensure the correctness of the numerical approach the simulations were compared with the original equation for calculation of K II for the CTS specimen (Plank and Kuhn (1999); Richard (1981)):

1 2

      

      

p a w a −

0.23 1.4

− +

F

(

)

1

−

p

K

a

π

=

⋅

⋅

⋅

,

(9)

w a −

p

II

p

2

t

   

   

a

a

p

p

1 0.67 −

2.08 + ⋅

w a −

w a −

p

p

where w is the width of the specimen, t is its thickness and F is the loading force (see Fig. 1).