PSI - Issue 5

Jürgen Bär et al. / Procedia Structural Integrity 5 (2017) 793–800 Jürgen Bär et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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4. Short crack growth at notches

As shown above, the cyclic lifetime of 7475-T761 is determined by the propagation of short fatigue cracks. In case of the investigated specimens cracks are predominantly initiated at the corners of the notch root and they propagate in form of quarter elliptical cracks into the material. The long semi axis c of the quarter ellipse propagates along the notch root and the short axis a on the specimen surface (figure 4a). Despite the good resolution, the potential drop method is not suitable for investigating propagation behavior of short cracks. In figure 4b the crack length a of cracks with different crack front shapes is shown as a function of the potential drop. All values in this graph have been determined by FEM calculations using ANSYS.

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a + a k [mm]

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a k

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two quarter ellipse (a:c = 1:2) two quarter ellipse (a:c = 1:3) through the thickness crack front Johnson's formula

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1.05 U/U 0

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Fig. 4. (a) Definition of the crack lengths for edge cracks at notches; (b) crack length for different crack geometries obtained from FEM calculations.

Firstly, it is clearly visible that the crack length a obtained from the calculated potential drop depends on the crack geometry. Secondly, Johnson’s formula underestimates the real crack lengths at this early stage of crack propagation, even if compared to a through-the-thickness crack front . Accordingly, Johnson’s formula is suitable for long cracks only. An approach developed by Knott (Knott 1980) improved the accuracy of the crack length measurement of short cracks, but the consideration of different crack geometries was not included. The development of the crack front shape can be investigated using overloads to mark the crack front on the crack surfaces (Bär 2014), but overloads influence the crack propagation and possibly the crack initiation sites so that this method is also not suitable. For the investigation of the propagation of short cracks at notches an optical investigation seems to be the only way to study the propagation of short cracks at notches. For the purpose of obtaining reliable short crack propagation data, fatigue crack experiments with constant stress amplitudes have been conducted. The cyclic loading of the investigated specimens was interrupted in defined intervals to measure the crack lengths a and c on the surface and in the notch root using a SEM. The results of this examination are shown in figure 5 for two specimens with a notch depth of 1 mm loaded with a stress amplitude of 80 MPa (left hand side) and specimens with a notch depth of 2 and 3 mm loaded with 60 and 50 MPa, respectively (right hand side). FEM calculations showed that in all four experiments nearly the same maximum stress at the notch root of about 310 MPa was reached due to the specific combination of notch depth/notch factor and load amplitude. The figures show an intersection of the specimen perpendicular to the loading axis; the lower margin of the drawings is located in the notch root and the crack propagates bottom up. In all cases, two cracks at the corner of the notch root are initiated within the first 20,000 cycles. The specimen investigated with shorter intervals (upper left in figure5) shows a crack initiation within 5,000 cycles; up to 20,000