7.1 Introduction 7.1.1 Background Advanced structural alloys often possess complex microstructures and low symmetry crystal structures that exhibit twinning, phase transformation and variations in strength between families of slip systems. These attributes may give rise to asymmetric mechanical behaviors, while processing (e.g., rolling, drawing, extruding, etc.) may further impart anisotropy. As such, their three-dimensional mechanical behaviors often cannot be fully understood through uniaxial characterizations. Historically, planar biaxial experiments have been developed to address the need for multiaxial characterizations during tension–tension loading of sheet metals—the primary mode of loading they experience during forming processes [1–11]. A standard cruciform geometry capable of tension–tension planar biaxial loading has been established [1]. A few planar biaxial experiments have been extended to tension–compression or compression–compression loading by clamping support plates on the specimen to prevent buckling [12, 13]. These approaches have been limited in their ability to drive localized deformation into the gage of the sample without influence from stress concentrations at the gage edges or the intersections of the arms of cruciform loading structures. Thus, the first challenge we aimed to address in designing a new experiment was to design planar biaxial specimen geometries capable of arbitrary compression–compression, tension–compression, and tension–tension gage deformations uninfluenced by the sample loading structure. We reported on the major features of such a sample at the 2015 Society of Experimental Mechanics meeting [14]. Here, we report on the final sample designs, including some modifications from last year’s paper, and we also include a validation study. We also document the design of the custom planar biaxial load frame has been built that is capable of in situ multiaxial loading of these sample geometries during X-ray diffraction experimentation. The instrument and sample are capable of any arbitrary plane-stress deformation, in addition to load path change events. Thus, the micromechanics of full plane stress yield and transformation loci may be quantified in addition to path-dependent behaviors. The 3D X-ray diffraction technique “far-field High Energy Diffraction Microscopy (HEDM)” allows for non-destructive micromechanics measurements via serial reconstruction of 2D diffraction patterns taken at small intervals (often 0.1 to 0.25 ) as samples are rotated (typically 360 ) [15–17]. Using Continuum Mechanics and crystallography, the (x, y, z) position of the center of mass of each grain within a polycrystalline sample, as well as the volume, phase, orientation tensor, and small strain tensor of each grain can be measured. From these data, multiscale micromechanical analyses can be performed to identify slip [18], twinning [19], and phase transformation mechanisms. The primary limitation of this technique is spatial resolution of X-ray diffraction measurements, which is on the order of 1 μm, meaning grain sizes must be larger than 5 μm for application of this technique to be feasible. Still, for large grain materials, it is possible to measure subgrain phenomena. Modern detector technologies and X-ray energies restrict the number of grains that can be observed at once to the order of 10,000, with 1000 or less grains being desirable. This latter limitation, however, is not a limiting factor in most experiments, as it is fairly easily overcome with X-ray focusing and collimation. In the past, computational analysis of the data were more limiting than any of these other challenges—analyzing the first data sets collected by a new research group took on the order of several years. However, years of focused and growing efforts has resulted in an ability to analyze some datasets as they are collected, and most data sets within several weeks. Users of the technique also have a variety of software choices including Fable [20], HEXRD [21], and MIDAS [22–25]—the best choice depends on the phenomena to be studied. Data analysis for far-field HEDM was carried out at the Advanced Photon Source (APS) of Argonne National Lab on their Orthros computing cluster using the MIDAS software package. 7.2 Methods 7.2.1 Experimental Setup In situ diffraction experiments were carried out at Sector 1 in the 1-ID-E hutch of the Advanced Photon Source (APS) at Argonne National Lab. Key components of the experimental setup include incoming monochromatic X-ray beam that can be tuned to energies ranging from less than 30 to more than 120 keV (an energy of 71.676 keV was used in the experiments reported here), the planar biaxial load frame with mounted specimen, area X-ray detector in a far-field, transmission position, and stereo digital image correlation (DIC) assembly, all shown in Fig. 7.1a, b. Each of the four independent servohydrualic actuators built into the load frame has a 25 kN load capability and 50 mm of stroke. Each axis can be 62 G.M. Hommer et al.
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