A Fatigue Life Model for Predicting Crack Nucleation at Inclusions in Ni-Based Superalloys

Abstract

Engineering alloys such as Ni-based alloys, Al-alloys, and steels often contain non-metallic inclusions in their microstructures. These inclusions, which include oxide particles, carbides, and intermetallic particles, are introduced during component manufacturing processes such as casting, powder-metallurgy, or additive manufacturing methods. The presence of inclusions in the microstructure can promote fatigue crack nucleation by competing against slipband nucleation and reduce fatigue life performance of an engineering component. While it has been reported in many occasions, the competition between fatigue crack nucleation at inclusions and slipbands is still not well understood. In this article, the conditions for the concurrent occurrence of fatigue crack nucleation at inclusions and slipbands are analyzed theoretically. The analysis indicates that there exists a critical inclusion size (diameter) below which there is no fatigue life debit due to crack initiation at inclusions and above which a transition from slip-induced to inclusion-induced crack nucleation occurs. The low-cycle fatigue life model is applied to Ni-based superalloys and the model predictions are compared against experimental data from the literature to assess the dependence of the critical inclusion size on the slip morphology, grain size of the matrix, and the shear modulus of the inclusion.

Appendix

Using Eqs. [2], [5] andnd Eq. [7], it can be readily shown that Eq. [4] can be expressed as

$$ N_{i}^{I} = \left[ {\frac{{\zeta_{S} }}{{\left( {\frac{{2\sigma_{a} }}{{F_{m} }} - 2Mk} \right)}}} \right]^{1/\alpha } \left( {\frac{{\xi_{o} }}{\xi }} \right)^{ - 1/2}, $$

(A1)

which can be rearranged to give

$$ \left( {\frac{{\Delta S_{th}^{I} }}{{F_{m} }} - 2Mk} \right)\left[ {N_{i}^{I} } \right]^{\alpha } = \zeta_{S} \left( {\frac{{\xi_{o} }}{\xi }} \right)^{ - 1/2}, $$

(A2)

where $\Delta S_{th}^{I} = 2\sigma_{a}$ is the fatigue strength of the Ni-based alloy with inclusions. Similarly, Eq. [1] can be rearranged to give

$$ \left( {\frac{{\Delta S_{th}^{S} }}{{F_{m} }} - 2Mk} \right)\left[ {N_{i}^{S} } \right]^{\alpha } = \zeta_{S}, $$

(A3)

where $\Delta S_{th}^{S} = 2\sigma_{a}$is the fatigue strength of the Ni-based superalloy without inclusions. Dividing Eq. [A2] by Eq. [A3] leads one to

$$ \frac{{\Delta S_{th}^{I} - 2F_{m} Mk}}{{\Delta S_{th}^{S} - 2F_{m} Mk}} = \left( {\frac{\xi }{{\xi_{o} }}} \right)^{ - 1/2}, $$

(A4)

which can be simplified to

$$ \Delta S_{th}^{I} = \Delta S_{th}^{S} \left( {\frac{\xi }{{\xi_{o} }}} \right)^{ - 1/2} $$

(A5)

when the 2Mk term is negligible compared to the fatigue strengths. When the 2Mk is not negligible, the threshold stress for inclusion-induced crack nucleation can be obtained from Eq. [A4] to give

$$ \Delta S_{th}^{I} = 2F_{m} Mk + \left( {\Delta S_{th}^{S} - 2F_{m} Mk} \right)\left( {\frac{\xi }{{\xi_{o} }}} \right)^{ - 1/2}, $$

(A6)

which shows the scaling of the threshold stress $\Delta S_{th}^{I}$ with the inclusion size is not exactly a power-law with the − 1/2 exponent when 2Mk is not zero, where k is the critical resolved shear stress for slip to occur.