PSI - Issue 39

592 Daniele Amato et al. / Procedia Structural Integrity 39 (2022) 582–598 Author name / Structural Integrity Procedia 00 (2019) 000–000 11 In Figure 8, the -th node is extended from the crack front of the -th step towards the local mission’s deflection angle, , by a quantity dictated by Eq. (8). The orthonormal axes , and represent the normal of the plane locally tangent to the crack, the local front tangent and the local propagation direction, respectively. The plane represented by is tilted by with respect to the local crack plane. 5. Numerical vs. experimental crack path The numerical crack propagation predictions were validated using the tension-torsion experimental tests. For this purpose, the deviation between the numerical crack surfaces and the experimental ones were compared by using the software CT3D_Validator [36], developed in MTU Aero Engines AG. The fracture surfaces of the broken specimens were measured by a GOM ATOS machine using blue light scanning and transformed into a very detailed triangulated model. The deviation between the two crack surfaces was used to find a parameter that indicates the accuracy of FRANC3D in predicting the crack propagation direction. It is intended as a mean distance between the two crack surfaces. By overlapping the numerical crack surface on the fracture surface of the broken specimen digital image, the volume in between the two is calculated and then divided by the predicted crack surface area. The axial deviation, , measured along the specimen’s longitudinal (i.e., tensile) direction, satisfies: = ∑ =1 ∑ =1 = ∑ =1 ∑ =1 (9) For more information on the meaning of all variables involved in calculation, the reader is referred to [36] and [19]. Table 2 summarizes all the load combinations analysed and the relative deviation results. The column label indicates concisely the loading condition, which is fully explained in the next four columns. Proceeding to the right, the axial deviation is shown and the numerical crack propagation length, , measured on the specimen’s free surface; is computed as the Euclidean distance between the first and last break through points. The axial deviation, in fact, depends on the amount of crack propagation considered. Thus, was also calculated as a percentage of the numerical crack propagation obtaining the relative deviation, (%) . The latter can also be converted into an angle deviation, , using the formula: = −1 2∗ (10) With reference to Figure 9, denotes the absolute deflection angle i.e., the angle between the initial notch plane and the experimental propagation direction at the free surface. Eq. (10) can be obtained by applying the sine theorem to the triangle . By overlapping the predicted crack surface on the fractured specimen’s model, the angle deviation quantifies the opening between the two crack surfaces on one lateral face of the specimen. An example of the angle deviation calculation is offered in Figure 9. Due to the symmetry of the applied torsional load i.e., = − 1 , a positive deflection angle is obtained on one free surface of the specimen and a negative one on the diametrically opposite face.

Table 2 Specimens load combinations and deviation results.

(°) ( ) ( ) (%) (°) (°)

0 0 0

− 1 − 1 − 1

0 0 0

1.31 1 0.76

0.2618 0.5713 0.2131

5.26 6.40 6.18

4.9772 8.9266 3.4482

44.5 39.8 31.6

4.10 7.91 3.37

No.

Label

1 2 3

0_1_00_1 0_1_00_2 0_1_00_3