PSI - Issue 5

Ralf Urbanek et al. / Procedia Structural Integrity 5 (2017) 785–792 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

790

6

small deviation in the phase values. Experiments undertaken with different frame rates showed, that this delay is increasing with decreasing frame rate. This delay has to be considered in the evaluation to get correct phase information.

0.013

170

a

b

160

150

0.012

140

130

120

0.011

110

phase of thermoelastic stress [°] X5 - 50 MPa

100

Cu - 50 MPa Cu - 75 MPa

7075 - 50 MPa 7075 - 100 MPa 7075 - 150 MPa

shift between load and stress [s]

X5 - 50 MPa X5 - 100 MPa X5 - 150 MPa

Cu - 50 MPa Cu - 100 MPa

7075 - 50 MPa 7075 - 100 MPa 7075 - 150 MPa

X5 - 100 MPa X5 - 150 MPa

90

0.010

5

10

15

20

5

10

15

20

loading frequency [Hz]

loading frequency [Hz]

Fig. 4. a) phase shift of thermo-elastic effect b) time shift between load and stress.

3.3. Influence of the frequency on stress measurements at notched specimen

Figure 5 shows the stress in the ligament of steel specimens (X5) with a notch depth of 1mm (Fig 5a) and 3 mm (Fig 5b) loaded with nominal stresses of 50, 75, 100 MPa. In all cases, the stress concentration at the notch is clearly visible. In case of the specimen with a notch depth of 1 mm the stress decreases to the level of the applied stress. For the specimen with a notch depth of 3 mm notch the stress falls below the level of the applied stress. This effect may be caused by a multiaxial stress state due to notch opening effects. It should be mentioned at that point that with TSA only the sum of main stresses is displayed. The curve form is nearly the same for all loading levels. Far away from the notch is no frequency influence visible. Close to the notch, higher loading frequencies lead to higher stress values. This may be caused by heat flow near the notch that causes local violation of adiabatic constraints.

250

100 125 150 175 200 225 250 275 300 325 350 375 400

a

b

20Hz 10Hz 5Hz

20Hz 10Hz 5Hz

225

50 MPa 75 MPa 100 MPa

50 MPa 75 MPa 100 MPa

200

175

150

125

100

E-stress [MPa]

E-stress [MPa]

75

50

25 50 75

25

0 1 2 3 4 5 6 7 8 9 10 11 12 0

0 1 2 3 4 5 6 7 8 9 10 11 12 0

distance incl. notch [mm]

distance incl. notch [mm]

Fig. 5. a) stress curve in ligament of a specimen with a 1 mm notch b) stress curve in ligament of a specimen with a 3 mm notch

0 1 2 3 4 5 6 7 8 9

a

b

20Hz 10Hz 5 Hz

4.5

50 MPa 75 MPa 100 MPa

The time shift is computed out of the phase shift between the loading and the E-Mode as described in Section 3.2. Figure 6a shows the different time shifts supporting this assumption of violation. The time shift is only changed by the frequency changes and lower frequencies lead to higher shifts. Figure 6b shows the stress concentration at the notch normed by the applied stress as a function of the loading frequency for the different notch depths. For all notch depths the stress increase seem to reach a boundary value at higher frequencies. In due to the testing rig experiments with higher frequencies could not be performed. The value for the different load level seem to be constant. The increasing spreading of the values with the high notch depth can 2.0 2.5 3.0 3.5 4.0 E-Mode time shift [ms]

50 MPa 75 MPa 100 MPa notch epth 1 mm 2 mm 3 mm

1.5

0 1 2 3 4 5 6 7 8 9 10 11 12 -2 -1

max stress near notch / norm stress

1.0

5

10

15

20

25

distance incl. notch [mm]

frequency [Hz]