PSI - Issue 57

Magnus Andersson et al. / Procedia Structural Integrity 57 (2024) 307–315 M. Andersson et al. / Structural Integrity Procedia 00 (2023) 000–000

311

5

Equivalent stress intensity factor range, ∆ K I , eq ( a , v ), for N eq [cycles / hour] are calculated using Rainflow Cycle Counting (RFCC) ASTM E 1049-85 where { ∆ K I ( a , v ) } and { N } are length N class vectors with ranges and number of cycles. N class is the chosen number of classes in the RFCC algorithm:

RFCC [ K I ( t , a , v )] →{ ∆ K I ( a , v ) } , { N }

∆ K I , eq ( a , v ) =

m

1 / m

1 N eq

N class i = 1 N i ·

∆ K I , i ( a , v )

3.7. Updating crack depth a and angle v

There exists several models for predicting the crack angle propagation. In ABAQUS three di ff erent criteria may be used. They all give similar results regarding the crack angle propagation. In this method the maximum tangential stress criterion (MTS) has been implemented, in which the change of crack angle is given by:

II + K K 2

1

3 K 2

4 I + 8 K

2 I K

2 II

dv = cos −

2 II

I + 9 K

The thickness of the weld, L , is dependent on the crack angle, v . If a / L ( v ) < 0 . 5 then update to next increment n + 1: a n + 1 = a n + da and v n + 1 = v n + dv and go to 3.4 otherwise stop and go to 3.8.

3.8. Fatigue crack growth

Paris law, see Anderson (1995), is integrated from initial crack size a i to final crack size, a f = a / L ( v ) = 0 . 5:

da dN

m eq ( a )

= C · ∆ K

Paris law parameters, C and m are defined for steel welds in Hobbacher (2007). The number of cycles from the Paris law integration is divided by N eq to achieve the fatigue life in hours for the given load input.

4. Sensitivity analyses for input parameters

4.1. Influence of initial crack angle on the predicted fatigue life

In the example a single sided fillet weld (i2a5) is used. The ratio of membrane to bending stress is set to σ m / σ b = 0.2. In the first case the initial crack angle is set to v = 0 ◦ and in the second case to v = 30 ◦ , see Fig. 7. It can be seen that the crack angles in the the two cases rapidly merge into one crack angle path at approximately a = 0.5mm. The di ff erence in fatigue life for the two cases is 0.3 %. In Fig. 7(b) the surface represents β I , UCb ( a , v ) from the database.