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Crystals with a hexagonal close-packed crystal structure are inherently anisotropic, and have a limited number of independent slip systems, which lead to strong deformation textures and reduced formability in polycrystalline products. In magnesium (Mg), all of the easy slip systems have a Burgers vector in the <a> direction making twinning necessary for arbitrary shape changes. The most common twinning system which allows extension along the c-axis is {10-12}<10-11>. A good predictor of slip is the global Schmid factor, which resolves the externally applied force onto the slip plane and direction of a crystal. The critically resolved shear stress (CRSS) at which a grain twins is not readily measured by experiment and the CRSS for twin initiation often appears larger than for twin propagation. In polycrystals, twin variants with both low and high Schmid factors have been observed indicating that this Schmid factor is inappropriate to predict twinning and more local effects play an important, though still uncertain role. In this work, experiments were devised to dynamically study extension twinning in a polycrystalline Mg alloy AZ31B with a strong basal rolling texture by tensile deformation parallel to the plate normal. Three-dimensional X-ray diffraction using a synchrotron source was used to map the centre-of-mass positions, orientations, and grain-resolved elastic strain tensors of over 1000 grains in-situ up to a true strain of 1.4%. The majority of twins formed in grains with a high local Schmid factor; however, low-ranked twin variants were common. The average grain-resolved stress did not always select the highest twin variant and resulted in some negative Schmid factors. The internal stress state of parent grains and twinned grains did not differ significantly within the large measurement uncertainties. The misorientations between grains ideally oriented for twinning and their nearest neighbours could not explain cases of no twin activity. Results suggest that the controlling factors for twin formation are much more local and not captured within the spatial resolution of the technique. Complimentary measurement of the strain rate sensitivity during twinning, by instantaneous strain rate change tests, suggest that basal slip is a part of this local process. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-03-12 13:40:26.039

This paper briefly describes the theory and methods of x-ray residual stress measurements. Residual stresses can be defined as the stresses which remain in a material in the absence of any external forces. There are many stress determination methods. Some of those methods are destructive and some are nondestructive. X-ray residual stress measurement is considered as a nondestructive method. X-ray diffraction together with the other diffraction techniques of residual stress measurement uses the distance between crystallographic planes as a strain gage. The deformations cause changes in the spacing of the lattice planes from their stress free value to a new value that corresponds to the magnitude of the residual stress. Because of Poisson’s ratio effect, if a tensile stress is applied, the lattice spacing will increase for planes perpendicular to the stress direction, and decrease for planes parallel to the stress direction. This new spacing will be the same in any similarly oriented planes, with respect to the applied stress. Therefore the method can only be applied to crystalline, polycrystalline and semi-crystalline materials. The diffraction angle, 2&#952;, is measured experimentally and then the lattice spacing is calculated from the diffraction angle, and the known x-ray wavelength using Bragg's Law. Once the d-spacing values are known, they can be plotted versus 2 sin &#968;, ( &#968; is the tilt angle). In this paper, stress measurement of the samples that exhibit a linear behavior as in the case of a homogenous isotropic sample in a biaxial stress state is included. The plot of d vs. 2 sin &#968; is a straight line which slope is proportional to stress. On the other hand, the second set of samples showed oscillatory d vs. 2 sin &#968; behavior. The oscillatory behavior indicates the presence of inhomogeneous stress distribution. In this case the xray elastic constants must be used instead of E and &#957; values. These constants can be obtained from the literature for a given material and reflection combination. It is also possible to obtain these values experimentally. Calculation of the residual stresses for these samples is beyond the scope of this paper and will not be discussed here.

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves [74]-85).

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