PSI - Issue 2_B

Pavel Pokorný et al. / Procedia Structural Integrity 2 (2016) 3585–3592 Author name / Structural Integrity Procedia 00 (2016) 000–000

3589

5

Fig. 3. (a) Measured v - K data ( R ratios were considered: -1; -0.5; -1); (b) The dependence of threshold value  K th on stress ratio R ; (c) The dependence of threshold value K th,max on stress ratio R .

2.2. Fatigue crack propagation rate description Very common approach NASGRO [NASGRO manual (2002)] was chosen for the interpolation of experimental data:

p

K



  

  

th

1



n

  

  

1 1

dN da

N a

R f



 

K



  

  

,

(6)

C

K





q   



   1

K

max



K

c

where C , n are material constants and p , q empirical constants describing the curvatures that occur near the threshold and near the instability region of the crack growth curve, respectively and f is crack opening function. The residual fatigue lifetime is dominantly given by propagation rate of relatively small crack in the studied case, see Fig. 2b, therefore the denominator (1-K max /K c ) q (corresponding to rapid propagation of longer cracks) can be neglected. Then the NASGRO can be expressed in the form: p th n K K K R f C N a dN da                       1 1 1 . (7)     

Note that Eq. (7) was used for fit of material data in Fig. 3a. The stress intensity factor range is function of the crack length a, therefore: ( ) ( ) 2 ( ) ( ) , ,min ,max K a K a K a kK a I B I I     .

(8)

The effective stress intensity factor range considers different crack closure under different R ratios: K R f K eff      1 1 .

  

 

(9)

The opening function f is defined by Newman empirical description: f A A R 0 1   ,

-2  R<0

(10)

2

3

, max(

)

f

3 2 0 1 R A A R A R A R   



,

R  0

(11)