PSI - Issue 5

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E-stress

E-stress [

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

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be attributed to motion effects mentioned by Urbanek and Bär (Urbanek 2017) in due to the decreasing stiffness of the specimen with increasing notch depth. 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]

0 1 2 3 4 5 6 7 8 9

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b

20Hz 10Hz 5 Hz

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50 MPa 75 MPa 100 MPa

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E-Mode time shift [ms]

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max stress near notch / norm stress

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distance incl. notch [mm]

frequency [Hz]

Fig. 6. a) time shift curve in ligament of a specimen with a 2 mm notch b) maximum stress at notches at different frequencies

3.4. Comparison of stress profiles of specimen with 3mm notch and 3mm crack

For investigating the differences in the stress fields of a notch and a crack TSA measurements performed on a specimen with a 3 mm notch were compared with a specimen containing a 3 mm crack. In case of the cracked specimen the measurements were undertaken on two specimen with crack lengths of 2.829 mm and 3.119 mm loaded with a nominal stress of 177 MPa. The TSA results of these two experiments were averaged. The notched specimen was loaded with a nominal stress of 150 MPa and the results were scaled up linear to 177 MPa. At a loading level of 177 MPa a crack was initiated immediately without reaching a thermal equilibrium. The stress values for the different modes are computed according to equation (4) by taking the temperature amplitudes of each mode. In case of the notched specimen the D, D1 and D2 mode revealed very small values and were neglected. Figure 7 shows the different amplitude values in front of the crack (symbols) and the notch (red line). The measured elastic stress (E-Mode) at the notch root is higher than the stress at the crack tip. The stress of the notched and the cracked specimen decrease with increasing distance from the crack tip/notch root and meet at the same stress level on at about 8 mm. The stress level there is below the nominal stress, as already described in section 3.3. The virtual stresses of the Modes D, D1 and D2 calculated with the thermo-elastic constant and the temperature amplitudes of the D-Modes decrease from a starting value at the crack tip (at 3 mm) to zero at about 8 mm and are always considerable smaller than the yield strength (R p0,2 = 322 MPa). The stresses calculated from the E-Mode exhibit values above the yield strength up to 5 mm for the cracked and 6.5 mm for the notched specimen, respectively.

100 150 200 250 300 350 400 450 500 550 600

100 150 200 250 300 350 400 450 500 550 600

0.00 0.20 0.39 0.59 0.78 0.98 1.17 1.37 1.57 1.76 1.96 2.15 2.35

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E-Mode D-Mode

D1-Mode D2-Mode 3mm notch

T amp /T m [10 -3 ]

yield strength

stress amplitudes [MPa]

stress amplitudes [MPa]

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Fig. 7. stress curves in front of crack and notch