PSI - Issue 13

M. Hrstka et al. / Procedia Structural Integrity 13 (2018) 1123–1128 Hrstka, M., Zˇ a´k, S., Vojtek, T. / Structural Integrity Procedia 00 (2018) 000–000

1127

5

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.00 0.01 0.02 0.03 0.04 0.05 0.06

F =4675.0 N, K I I =2.04 MPa √ m

F =9706.0 N, K I I =4.24 MPa √ m

y [mm]

− 0.10

− 0.05

0.00

0.05

0.10

0.15

− 0.5

0.0

0.5

1.0

F =10930.0 N, K I I =4.77 MPa √ m

F =11470.0 N, K I I =5.01 MPa √ m

0.0 0.2 0.4 0.6 0.8

y [mm]

− 1

0

1

2

− 2

− 1

0

1

2

3

x [mm]

x [mm]

HRR field

Irwin’s solution

FEM

Fig. 3: Comparison of plastic zones for mode II. Note that there are di ff erent scales on the axes. Axis of the specimen lies at x = 5 . 5 mm, crack surfaces lie on the negative x -axis with a tip in x = 0.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

F =4675.0 N, K I I I =3.08 MPa √ m

F =9706.0 N, K I I I =6.4 MPa √ m

y [mm]

− 0.3

− 0.2

− 0.1

0.0

0.1

0.2

0.3

− 1.5 − 1.0 − 0.5 0.0

0.5

1.0

1.5

2.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

F =10930.0 N, K I I I =7.21 MPa √ m

I I I =7.57 MPa √ m

F =11470.0 N, K

y [mm]

− 2

− 1

0

1

2

3

− 3

− 2

− 1

0

1

2

3

4

x [mm]

x [mm]

HRR field

Irwin’s solution

FEM

Fig. 4: Comparison of plastic zones for mode III. Note that there are di ff erent scales on the axes. Axis of the specimen lies at x = 5 . 5 mm, crack surfaces lie on the negative x -axis with a tip in x = 0.

strain. Plastic zone computed by FEM represents a longitudinal cut (the cuts are defined by areas A and B, see Fig. 2) of plastic strain contour delimited by ε p y 0 . 2 = 0 . 002. Amplitudes of stresses computed by HRR theory are determined by J-integral values. Contrary to K-factors which are defined by empiric relations in Vojtek et al. (2015) for the cylindrical specimen, values J are extracted from finite element simulation by using its intrinsic algorithm. In the small-scale yielding limit, i.e. when the plastic zone is small compared to the crack length and also to relevant geometric dimensions, J can be expressed in terms of the elastic stress intensity factors Rice (1968). Note that the e ff ective thresholds for the ARMCO iron are ∆ K IIe ff , th = 1 . 5 MPa √ m and ∆ K IIIe ff , th = 2 . 6 MPa √ m (Pokluda et al. (2014)). The applied thresholds have usually the values of about 10 MPa √ m or more (Okazaki et al. (2017)).

5. Discussion

For the processes involved in fatigue, the reversed (cyclic) plastic zone is more relevant. At threshold loading the crack propagation rate is approaching one interatomic spacing per cycle and, therefore, the amount of cyclic plastic deformation should also be very small. Determination of the reversed plastic zone of all modes I, II and III is planned. The preliminary results for mode II and mode III indicate that the reversed plastic zone is much smaller than the theoretically estimated size of 1 / 4 of the monotonic zone size (for loading at stress ratio R = 0). This explains why such large plastic zones can be present at threshold loading. It also demonstrates the importance of distinguishing