Development of novel six-dimensional anisotropic and asymmetric yield approaches applied to the study of dwell fatigue using various x-ray techniques, The

Abstract

In an ever increasingly technological world, it is frequently the case that as industries search for solutions to problems of light-weighting, high-temperature applications, biocompatibility, and cost, they turn towards anisotropic and asymmetric materials such as magnesium (Mg) alloy plate, titanium (Ti) alloy forgings, 3D-printed nickel (Ni) based superalloys, super-elastic Ni-Ti binary alloy extrusions, and a whole host of composites to name but a few. Anisotropy and asymmetry are not only interesting or potentially useful in niche cases, but increasingly vital to understanding and successfully using advanced materials. And yet, the paucity of clear and in-depth understanding and capable mathematical descriptions of the elastic limit for these materials marks a gap in engineering knowledge, a gap worth considering and studying. Galileo once wrote about the importance of comprehending the mathematics of a particular scientific endeavor as a prerequisite to understanding the science itself. Quoting from Sillman Drake’s 1957 translation of Galileo Galilei’s 1623 book Il Saggiatore (page 25 of the original work): [The philosophy of the universe] cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth. This is no less relevant a sentiment in the niche field of solid mechanics or the even more specialized domain of inelastic anisotropy and asymmetry. As such, any endeavor to understand these aspects of material behavior must begin by comprehending the mathematics which underlie and describe them. The geometry of the elastic limit for the most anisotropic of materials requires the actions on each component of stress, or strain, to be considered as independent – unique from other combinations of actions. This demands a six-dimensional perspective to adequately describe anisotropic inelasticity. By describing techniques for visualizing and comprehending such a geometry, new approaches are proposed for mathematically capturing a greater range of behaviors for the elastic limit and for calibrating such theories experimentally. These novel approaches are first tested on the macro-scale inelastic character of a 3D-printed Ni-based superalloy, Inconel 718, to demonstrate their efficacy. The concepts are subsequently studied through applications to the micro-scale phenomena in Ti which give rise to bulk yield behaviors and to dwell-fatigue failures: grain-scale anisotropic elastic limits. Specifically, multiple in-situ X-ray diffraction experiments are proposed and carried out to monitor the states of stress and strain at the grain-scale in order to allow for grain-scale calibrations of anisotropy and asymmetry and for mapping the anisotropic interactions of neighboring grains during dwell-fatigue loading.