Crack velocity measurements through continuous stiffness monitoring of cyclically loaded notched micro-beams of thin graded Pt–Ni-Al bond coats

Abstract

The notched clamped beam geometry has proven to be a useful geometry in evaluating local mechanical properties like fracture and fatigue of thin graded platinum nickel aluminide bond coats. Cyclic fatigue tests performed on different zones of these coatings have shown that the structural stiffness of the beam is a useful parameter in estimating localized damage in front of the notch root, which can arise either due to cyclic softening from micro-crack nucleation and propagation in the crack wake or due to work hardening in the plastic zone surrounding the crack tip. This paper describes the use of finite element method-based analysis to quantify different geometrical factors that affect cyclic stiffness data in the micro-beam bending methodology employed in the present study. Variations in the stiffness values measured at the beginning of each loading cycle can occur due to factors such as the effect of loading line offsets (both lateral and angular) and the notch length to width ratio (a/W). Using this analysis, it was found out that lateral offsets affect the starting stiffness of the beam more profoundly compared to angular offsets. It has also been shown that for beams having lengths of $$\sim $$ $$80-90\,\upmu \mathrm{m}$$ and an a/W ratio of $$\sim $$ 0.3–0.4, the starting stiffness variations can be kept under 10%. The stiffness can also be used to estimate crack velocities (da/dN) in an approximate sense using the finite element method. Detailed finite element analysis has been performed to estimate through thickness crack lengths from cyclic stiffness drops. The applied stress intensity factor for real crack geometries observed during testing have been computed using the extended finite element methodology and da/dN vs $$\Delta $$ K plots have been generated for two cases. This paper highlights the importance of using computational analysis in optimizing and augmenting micro-scale fatigue testing data and thus providing for a richer dataset through such analysis.