PSI - Issue 13

Katharina Dibblee et al. / Procedia Structural Integrity 13 (2018) 322–327 Katharina Dibblee et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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As soon as the crack front reaches the material grading the kinking angle changes and the crack grows along the material grading. However, if the crack growth in the material area begins with the more favourable fracture mechanical material properties, in both cases the crack path does not kink even when the material grading is reached. In these cases, the crack continues to grow under stress control. The crack propagation behaviour in a CTMM specimen with a grading angle of φ M = 30° is different. Here nothing changes in the crack propagation path, independent of the existing material areas. From these results it can be concluded that, in addition to the stresses present at the crack front, both the local material properties and above all the locally existing grading angles have a decisive influence on the crack propagation behaviour.

3.2. Crack propagation prediction and lifetime influence using the example of an induction hardened cog wheel

In industrial production, more and more functionally graded structures such as induction hardened cog wheels are used, Brill and Schibisch (2014). Due to the local hardening of the tooth flanks, these show an increased wear resistance, which should result in a longer lifetime for these cogs. At the same time, the fracture mechanical material properties in the hardened area are reduced, resulting in fracture mechanical material grading.

Fig.4. Influence of mechanical material grading on the crack path of cog wheels: (a) Crack growing in an induction hardened cog wheel (b) Crack growing in a homogeneous isotropic cog wheel

When crack growth simulations are performed on such hardened cogs, considerable differences can be seen both in the crack paths and in the expected lifetime. Fig. 4 (a) shows the crack path of a hardened cog. Therefore, two material areas were generated in the FE model of the cog wheel. In the hardened area, the threshold relevant for fatigue crack propagation is  K I,th (M1) equals 10% of the  K I,th (M2) for the second material area, which represents the base material of the cog wheel. The crack initially grows under load until the crack front has reached the grading limit. From this point on, the crack continues to grow along the grading limit, influenced by the local change in material properties. Already after a few simulation steps an unstable crack propagation occurs, which will lead to an early failure of the cog wheel. In comparison, the crack growth simulation using a homogeneous material shows a crack propagation path that grows almost straight through the structure over a very long period of time until an unstable crack propagation occurs. Figure (5) illustrates the influence of fracture mechanical material grading in relation to the achievable number of load cycles, assuming that a technical crack has already occurred in the cog. It can be seen that with a hardened cog with a technical crack, the lifetime is significantly shorter than with a non-hardened cog. Since the crack growth already starts in the material area that is less favourable from a fracture mechanical point of view, the possible number of load cycles is reduced from the outset. Due to the mixed-mode situation at the crack front when the material grading limit is reached, the propagation rate increases undiminished and contributes to premature failure of the component , since the crack toughness values of the fracture-mechanically less favourable material area are decisive.