PSI - Issue 42

Jürgen Bär et al. / Procedia Structural Integrity 42 (2022) 1061–1068 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1065

5

Fig. 3. Position Time diagram of the ligament. The position of the crack tip at position x=351 on the ligament is indicated with a thin black line. The crack is propagating from the right to the left.

Out of the PT-diagram for different positions on the ligament time-temperature-diagrams and force-temperature loops are extracted. In figure 4 such diagrams for 4 positions far ahead of the crack tip are shown. The temperature time diagram shows a sinusoidal run of the temperature, indicating a predominantly elastic deformation. The temperature amplitude is increasing when the position gets closer to the crack-tip. The cooling under tensile load is significantly greater in amount than the heating under compressive load. This is also clearly visible in the force temperature loops on the right-hand side showing a steeper slope under tension loading compared to compression loading. The loop closest to the crack tip shows an opening, indicating that plastic deformation takes place that causes an additional heating due to dissipated energy.

0.2

0.2

far away from the crack tip

0.1

0.1

0.0

0.0

-0.1

-0.1

Distance to crack tip 2.69 mm 1.40 mm 1.07 mm 0.79 mm

-0.2

-0.2

Temperature change [K]

Temperature change [K]

-0.3

-0.3

-0.4

-0.4

0.00

0.25

0.50

0.75

1.00

-3

-2

-1

0

1

2

3

245

285

325

365

405

445

485

525

Cycle time [1/T]

Force [kN]

Position on the Ligament [px]

(a)

(b)

(c)

Fig. 4. E-Mode image (a) showing the positions of the time-temperature curves (b) and the temperature-force loops (c) far away in front of the crack tip

When the distance to the crack tip is reduced further, the temperature profile becomes increasingly asymmetric. The magnitude of the temperature changes only slightly, but a shift of the zero crossing in the temperature change to shorter cycle times can be observed (Figure 5). The force-temperature hysteresis loops exhibit significant differences in the slopes under tension and compression loading. The hysteresis loops also show an increasing opening as the crack tip is approached, which can be attributed to the increasingly higher portions of dissipated energies.