A Mechanical Testing Capability for Measuring the Microscale Deformation Behavior of Structural Materials

High energy x-ray diffraction can be used to probe the crystal scale mechanical response of polycrystalline alloys. Recently there have been several efforts to create new high energy x-ray experiments. These include the lattice Strain Pole Figure (SPF) technique. By measuring lattice strains in thousands of directions, the lattice strain tensor associated with each orientation can be determined. The focus of this paper is on transforming the SPF technique from a one-off style experiment to a measurement capability. Such a standardization process is of the utmost importance for the field of mechanics of materials and shifts the discovery associated with these experiments from the measurements themselves, to what they reveal about the material. We define a new technique for quantifying how effectively a set of lattice strain measurements (SPFs) probes each crystal orientation. The polycrystal sampling matrix, defined G^*{boldsymbolGamma^*}, represents the mapping between the most likely strain tensor for each orientation and the lattice strain results. The orientation space sampling matrix, defined G (R){boldsymbolGamma ({bf R})}, represents the set of lattice strain measurements that interrogate each crystal orientation. The rank of G (R){boldsymbolGamma ({bf R})} can be used to quantitatively compare different experimental configurations and systematically investigate G^*{boldsymbolGamma^*}. The net result is a new tool for selecting experimental conditions to produce optimal sets of SPF data. Results are shown for different experiment configurations and an example of the SPF technique is provided for the Low Solvus High Refractory (LSHR) nickel base superalloy. In addition, we show that for the face centered cubic LSHR, with lattice strains measured for the {111}, {200}, {220}, and the {311} crystallographic families, there are at most 25 lattice strain measurements that interrogate a single orientation.