Geometrically Necessary Dislocation Density Evolution in Interstitial Free Steel at Small Plastic Strains
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TRODUCTION
THE so-called geometrically necessary dislocation (GND) density tensor was first described by Nye in 1953.[1] Concepts of GND density and the dislocation density tensor were developed further by Bilby,[2] Ashby,[3] and Kro¨ner.[4] Total estimation of the GND density tensor involves measurement of the lattice curvature in three dimensions. With knowledge of all possible dislocation types (slip planes and Burgers vectors), a measure of the required dislocation density that would result in the observed curvatures is obtained. This is not a unique solution, but is a lower bound estimate as minimization procedures are used to obtain the lowest possible dislocation density that would result in the observed curvatures. Many researchers have adopted this approach over the past decade as reliable measurements of lattice curvature are reasonably obtained using various adaptations of electron backscatter diffraction (EBSD)[5–13] or other micro-diffraction techniques used to measure local crystallite lattice orientations.[12] Components of Nye’s dislocation
AMRITA KUNDU is with the Metallurgical and Material Engineering Department, Jadavpur University, Kolkata 700032, India. Contact e-mail: [email protected] DAVID P. FIELD is with the School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920. Manuscript submitted October 7, 2017.
METALLURGICAL AND MATERIALS TRANSACTIONS A
density tensor can be determined by using lattice curvature data from EBSD. This eventually will lead to an estimate of the GND density.[1] The cross-correlation EBSD technique that gives relatively high angular resolution measurements of crystallite lattice misorientations is generally referred to as high-resolution EBSD (HR-EBSD).[8,10–19] This technique is distinct from conventional EBSD in both the measurement technique as well as the information obtained, but both techniques can yield estimates of GND density. A significant literature has evolved on the intricacies of each of the techniques including the care that must be taken to obtain reasonable results.[5,8,10–21] HR-EBSD offers better resolution in measuring misorientation than conventional EBSD. Accuracy in measurement of GND density is also slightly better in HR-EBSD. HR-EBSD is effective in measuring elastic deviatoric strain. It is possible to estimate five components of Nye’s tensor using HR-EBSD[16]. All the partial derivatives of the infinitesimal elastic distortion tensor can yield all components of Nye’s tensor. However, conventional EBSD cannot estimate derivatives normal to the sample surface. Therefore, all components of Nye’s tensor cannot be measured using conventional EBSD. While both techniques have their advantages and challenges, reasonable estimates of GND density can be obtained from either technique. Conventional EBSD techniques are used in the present study. The results could potentially differ with the use of HR-EBSD, but it
is likely that the results would follow the same trends as those obtained herein. Justification for this i
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