High Resolution Techniques For Quantifying Lattice Strains In Polycrystalline Solids During Mechanical Loading Using X-Ray Diffraction
Understanding the conditions that drive phenomena like fatigue crack initiation in polycrystalline samples requires knowledge of the stress state at the crystal scale. Even during uniaxial tensile loading, the stress state at the crystal scale is often complicated due to anisotropic single crystal properties and the arrangement of neighboring grains. Instead of manufacturing specimens on the size scale of the microstructure, diffraction of synchrotron x-rays with in situ mechanical loading provides the means to probe the micromechanical response within deforming polycrystals. Measurement of lattice Strain Pole Figures (SPFs) is a robust technique for quantifying the three dimensional micromechanical state within a polycrystalline sample. The focus of this work was to bring the SPF experiment to the level of a measurement capability as opposed to a one-off style experiment. This dissertation is composed of three related studies, each of which is presented as a chapter that can be read independently. Chapter 1 contains a manuscript which was provisionally accepted for publication in Experimental Mechanics . The work investigates the interconnected nature of the SPF coverage and the regions of orientation space probed by each diffraction measurement. The major contribution is a new technique for quantifying how well a set of lattice strain measurements (SPFs) probes each crystal orientation. The orientation space sampling matrix, defined [GAMMA](R), repre- sents the set of lattice strain measurements that interrogate each crystal orientation. The rank of [GAMMA](R) can be used to quantitatively compare different experimental configurations. The net result is a new tool for selecting experimental conditions to produce optimal sets of SPF data. Chapter 2 is a second manuscript that was provisionally accepted for publication in the Journal of Strain Analysis for Engineering Design . The focus of this effort was the development of an expression for the lattice strain uncertainty that delineates the contributing factors into terms that vary independently: (i) the contribution from the instrument and (ii) the contribution from the material under investigation. The instrument portion of the lattice strain uncertainty is explored and modeled using a calibrant powder method (diffraction from an unstrained material with high precision lattice constants). Chapter 3 focuses on quantifying the evolution of lattice strains due to cyclic mechanical loading. To interpret the cycle-by-cycle variation in the lattice strains as experimental fluctuations or material evolution a new methodology was developed that combines x-ray diffraction experiments with in situ mechechanical loading and crystal-based finite element simulations. Merging what can be measured at grain scale with a simulation of the deforming polycrystal provides a robust tool for studying micromechanical behavior. A key finding of the work is that the lattice strain evolution due to cyclic loading occurs rapidly during the earliest portion of the samples fatigue life, and slows as the sample approaches failure.
lattice strains; x-ray diffraction; synchrotron radiation
Miller, Matthew Peter
Brock, Joel Donald; Dawson, Paul Richard
Ph. D., Mechanical Engineering
Doctor of Philosophy
dissertation or thesis