PSI - Issue 42

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

1067

7

0.0 0.1 0.2 0.3 0.4 0.5

0.0 0.1 0.2 0.3 0.4 0.5

far away from the crack tip

near the crack tip

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

PT-Diagram 5 Lock-In Modes 2 Lock-In Modes

Temperature change [K] PT-Diagram

5 Lock-In Modes 2 Lock-In Modes

Temperature change [K]

-3000

-2000

-1000

0

1000

2000

3000

-3000

-2000

-1000

0

1000

2000

3000

0.0 0.1 0.2 0.3 0.4 0.5

0.0 0.1 0.2 0.3 0.4 0.5

crack tip

crack flanks

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1

PT-Diagramm 5 Lock-In Modes 2 Lock-In Modes

Temperature change [K] PT-Diagram 5 Lock-In Modes 2 Lock-In Modes

Temperature change [K]

-3000

-2000

-1000

0

1000

2000

3000

-3000

-2000

-1000

0

1000

2000

3000

Force [N]

Force [N]

Fig. 7. Comparison of the different methods to describe the temperature changes in a loading cycle.

3.4. Temperature changes due to dissipative effects To determine the dissipative temperature changes the thermoelastic effect in the force-temperature-loops must be compensated. This compensation can be performed by the addition of a force-proportional temperature change  T TE,comp according to equation 4. ∆ , = ∙ ∙ ∆ = ∙ ∙ ∙ ∆ (4) One problem with this approach is the different stiffness of the specimen in tension or compression due to the presence of the crack. For this reason, the compensation of the thermoelastic component in the tension and compression phases must be carried out separately, as shown in Fig. 8. The resulting loops (shown in red and blue) give the real temperature changes due to dissipative effects.

Far away from the crack tip

near the crack tip

0.0 0.1 0.2 0.3 0.4

0.0 0.1 0.2 0.3 0.4

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1

without compensation fit tension fit compression

Temperature change [K]

without compensation fit tension fit compression

Temperature change [K]

-3000

-2000

-1000

0

1000

2000

3000

-3000

-2000

-1000

0

1000

2000

3000

Force [N]

Force [N]

Fig.8. Compensation of the thermoelastic effect in the force-temperature hysteresis loops in tension and compression.

In Fig. 9 the resulting dissipative temperature changes at different positions on the ligament as a function of the cycle time are shown. Far in front of the crack tip nearly no temperature changes due to dissipative effects can be observed. Near and direct at the crack tip a distinct temperature increase under tension loading is visible. Under compression only a delayed cooling can be seen, indicating that under compression only small dissipative effects take