PSI - Issue 7

Hans-Jakob Schindler / Procedia Structural Integrity 7 (2017) 383–390 H.-J. Schindler / Structural Integrity Procedia 00 (2017) 000–000

385

3

2. Experimental observations and empirical aspects Most published experimental data indicate that da/dN in the Paris-regime are R-dependent. There is no doubt about it for R < 0, since in the load phase where K I < 0 the crack faces are in contact with each other and enable compressive stresses to be are transmitted across the cracked by contact pressure, which shields the crack-tip from singular stresses. The situation is less clear for R > 0. Among the guidelines mentioned in the introduction, only ASME (2010) provides the Paris-constant C P as a function of R, namely

( )

0 C C R P p

25.72

(3)

( )

S R

=

=

(

) 3.07

2.88

R

−

for structural steel. The corresponding Paris exponent is given as n = 3.07, so the exponent in (3) seems to be equal to n. Unfortunately, no reference for (3) is given in ASME (2010). However, the ASME-code is known to be carefully evaluated by its standardization committee, so (3) can be expected to be well founded by experimental data. Several authors consider the phenomenon of plasticity-induced crack closure discovered by Elber (1971) to be the main cause for R-dependence of C P . In fact, in case of crack closure, S(R) as defined in (2) is readily found to be

n

f R 1 ( ) −

  

  

(4)

( )

S R

=

(

)

1

f R ⋅ − = (1 (

0))

R

−

where f(R) = K op /K max . However, as pointed out by Vasudevan (1994), Kujawski (2001), Huang and Moan (2007) and others, comparison with experimental data reveals that (4) often leads to an overestimation of the effect of R on C p . Referring to empirical findings of Walker (1970), Kujawski (2001) suggests the parameter K*= K max α · ∆ K 1- α to be used instead of ∆ K in (2), with α being a material-dependent constant that has to be determined by curve fitting from da/dN-data measured at different R-ratios. Replacing ∆ K by K* in (2) results in

1

(5)

( )

S R

=

(

) n R ⋅ α

1

−

Fig. 1: Comparison of S(R) as defined in (4) according to eqs. (3), (4) and (5), for n=3.07, α = 0.35; K op /K max = 0.3. S(R) according to (3), (4) und (5) are compared with each other in Fig. 1. For the sake of simplicity and as a first approximation, f(R) in (4) is assumed to be constant, f(R)= 0.3. S(R) according to (5), obviously, strongly depends on the open parameter α . For the purpose of comparison in Fig. 1, α was chosen such that the slope of the curve S(R) at R=0 was the same as for S(R) according to (3), which is the case for about α = 0.35. It is interesting to note that this value is reported by Kujawski (2001) to hold for structural steel. Considering (3) as a reference, the comparison in Fig.