ADVANCED MATERIALS & PROCESSES | OCTOBER 2023 41 FEATURE to estimate input parameters for the constitutive model in the FEA simulations[4]. The quasi-static implicit dynamic solver in Abaqus software was used to model wire spinning at 400 Hz to mitigate snap-through instabilities due to wire torsion and contact friction between the faceted wire surface and the round mandrel. Logarithmic strain tensors were calculated over 100 time points between the initial and third rotations, which were then used to calculate alternating and mean strain tensors. The tensors were then used to calculate the globally maximum scalar alternating strains and corresponding scalar mean strains. Contrary to expectations, computational modeling found that the curvature of the wire— and thus the alternating strain—varied along the 90° bend of the mandrel. Terminal portions experienced smaller local curvature while the central portion experienced larger local curvature (smaller bend radii). This localization was more pronounced in smaller mandrels with increasing levels of cyclic phase change (Fig. 2). Most importantly, the authors found that the knee of the ε-N curve marking the transition from low cycle to ultra-high cycle fatigue roughly aligned with εa->m, the tensile strain where martensitic phase transformation was observed to begin during tensile testing. At alternating strains below εa->m, the fatigue life increased from ~105 cycles to ~108 cycles, potentially due to the absence of cyclic phase change. METALLOGRAPHY AND FRACTOGRAPHY The goal of this research is to understand the mechanism of Nitinol ultra-high cycle fractures and to eventually predict when fracture will occur. To this end, the team examined fatigue fracture surfaces and compared the observed inclusions at fracture initiation sites with inclusions in the Nitinol material as measured by standard metallographic analysis. For the fatigue fracture surfaces, inclusions were found at the initiation point of every specimen examined, so the team measured the size of each fracture-inducing inclusion. Figure 3 shows a representative fatigue crack initiation site. For the metallographic analysis of untested material, researchers measured inclusions on both the traditional longitudinal plane and on the transverse plane. Choosing the transverse plane inclusion data as being more relevant to the stress concentration effect on the wire bending stresses, the team measured the distribution of maximum inclusions on the 27 planes examined. Extreme value statistics were used to extrapolate to the larger area of high strain on a tested wire versus the area of a metallographic image. It was found that the metallography accurately predicted the median inclusion size that initiated the fractures but did not reliably model the distribution (Fig. 4). Although Murakami’s equations using the measured distribution of fracture site inclusion sizes match the observed fatigue life through 109 cycles, the model does not predict the individual fatigue life for a given size/shape of inclusion[5]. Fractographic 9 Fig. 2 — From left: Photographs of experimental rotary bend fatigue setup; schematic showing numerical implementation; local maximum alternating strains versus mandrel angle θ; and stress-strain curves at integration points associated with global maximum alternating strains from FEA simulations. The maximum alternating strain versus mandrel angle plot for the smaller mandrel also includes experimental data indicating the angular location of fractures, revealing fracture locations approximately corresponding to the predicted high strain region. Fig. 3 — Corresponding faces of fatigue crack initiation site for a specimen that fractured after approximately 192 million cycles.
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