PSI - Issue 42

Florian Garnadt et al. / Procedia Structural Integrity 42 (2022) 1113–1120 F. Garnadt et al. / Structural Integrity Procedia 00 (2019) 000–000

1116

4

(a)

(b)

t h / t h =0/0 min/min � eq,loc =6 %/min R � =-1

Sharp Notch

Mild Notch

Time t

R0.6 60°

R2.7

85

19

85

19

8

Ext. Displacement U

8

t h / t h =3/3 min/min � eq,loc =6 %/min R � =-1

12

12

3 min

Time t

M20

M20

K t,I =1.6 � �

K t,I =2.8 � �

I =0.74 mm -1

I =3.37 mm -1

Ext. Displacement U

3 min

Fig. 2. (a) Geometries of the round bar specimens with circumferential notch characterised by the stress concentration factor and normalized stress gradient, (b) Cycle shapes defined by extensometer displacement over time for the case without dwell times and three minutes dwell times in tension and compression.

the loading axis. A bilinear material model with kinematic hardening is used to describe the elastic-plastic behaviour. This model is set up to represent the cyclic flow curve at midlife cycle approximately. Following the findings of Cochran et al. (2011) the hardening is chosen to be “moderate” to reduce local ratcheting e ff ects near the crack tip and allow for a cycle independent crack closure modelling. The visco-plastic behaviour is modelled by using a creep description based on Garofalo (1965) implemented in a user-subroutine. The simulation procedure is based on a node release scheme to simulate di ff erent crack depths. The structured mesh uses axisymmetric elements of linear geometric order (CAX4). After every second cycle the boundary conditions along the crack path are released for one more node at minimum load and the next simulation is a restart of the previous. Following this procedure, a (visco)plastic wake develops leading to earlier contact or later separation of the crack flanks compared to the cycle reversal points, respectively, which is known as plasticity induced crack closure (PICC), Elber (1971); Newman (1984). The crack tip loading is evaluated in a post-processing step based on the global force displacement curves of the FE simulation procedure of the previous chapter 3.1, shown schematically in Fig. 3 (b). The force and displacement is referenced to the lower point of load reversal for an evaluation of the upper hysteresis branch and vice versa, Lamba (1975); Dowling and Begley (1976). This referencing is necessary to achieve a cyclic value of the J -Integral. The dif ference in energy for crack configuration a and a +∆ a is used to compute the ∆ J by Eq. 2. The same evaluation is done for the dwell times and the creep crack tip loading parameter C t in principle, Saxena (1989). Just the displacements need to be exchanged by the displacement rate due to creep. This is done for the tension dwell time exclusively. Crack opening and closure is considered separately for the upper and lower hysteresis branch, which becomes nec essary for the consideration of the impact of dwell times. In case of the upper branch, the e ff ective ∆ J is automatically achieved at the end of the ramp, because no di ff erence in energy exists as long as the crack is closed. A crack closure criterion is necessary in case of the lower branch, because here the integration of energy di ff erence needs a distinct end point. ∆ J = − d Π d a (2) 3.2. Crack tip loading