Numerical-Experimental Assessment of Stress Intensity Factors in Ultrasonic Very-High-Cycle Fatigue

The continuous enhancement of reliability and durability requirements for many machinery components is significantly pushing the experimental research on the Very-High-Cycle Fatigue (VHCF) response of metallic materials. In order to significantly reduce testing time, ultrasonic testing machines are widely adopted when carrying out VHCF tests. In the VHCF literature, the critical Stress Intensity Factor (SIF) is estimated by applying analytical SIF formulations to the typical semi-circular surface crack geometry revealed by fracture surfaces at final failure. However, when subjected to ultrasonic VHCF tests, analytical SIF formulations valid for static loading conditions could eventually lead to significant estimation errors. The correct computation of the SIF in ultrasonic VHCF loading conditions is a key issue when investigating the crack growth rate curve with pre-cracked specimens or when evaluating critical SIF values from fracture surfaces of failed specimens. Dynamic conditions related to the resonance of the vibrating specimen, contact nonlinearity between crack faces and stress singularity at the crack tip make the SIF computation difficult and cumbersome. Numerical computation through Finite Element Models under non-linear dynamic conditions makes use of direct integration methods (implicit or explicit). However, in the high-frequency regime of ultrasonic VHCF tests, the procedure may lead to unacceptable computational time. The present thesis aims at finding a robust, accurate, and simple method to calculate the critical SIF at final failure fracture of VHCF samples. In order to cope with the inefficiency of the time domain direct integration method, frequency domain analysis, and Multi Harmonic Balance Method were employed in this thesis. Even though the frequency domain analysis significantly reduced the computational time the overall reduction was still considered insufficient. Hence, reduction techniques via Reduce Order Modeling were also applied to decrease the total number of degrees of freedom for the system. The solution obtained with the ABAQUS implicit solver was employed to verify the proposed hybrid technique. Results showed that the present method can accurately predict the displacement field and the SIF together with a drastic decrease of the computational time. The proposed method was then applied to two models based on real sample geometries (Hourglass and Gaussian samples failed under ultrasonic VHCF) in order to evaluate the effect of the geometry on the critical SIF value. Results calculated by classical solutions valid for static conditions were also compared with the results obtained with the proposed hybrid method. The comparison showed that conventional static solutions for SIFs could not be used to compute SIF values in ultrasonic conditions since computational errors are significant. Another important finding was that, for the Gaussian sample, the SIF in both loading conditions (static and dynamic) is smaller than that for the Hourglass sample. The difference in static conditions is considerable and larger than that in dynamic conditions. Besides the efficient and accurate computation of the critical SIF values from samples failed under ultrasonic VHCF tests, the proposed method can also be used: i) to design fatigue crack growth samples for investigating the near-threshold region with ultrasonic testing machines; ii) to accurately evaluate the SIF at the border of the relevant crack growth zones in ultrasonic VHCF (e.g., at the border of the fisheye and of the Fine Granular Area).