Estimation of the full Nye’s tensor and its gradients by micro-mechanical stereo-inference using EBSD dislocation microscopy

• Published in: International journal of plasticity 2013-11, Vol.50, p.146-157
• Main Authors: Hardin, Thomas J., Adams, Brent L., Fullwood, David T., Wagoner, Robert H., Homer, Eric R.
• Format: Article
• Language: English
• Subjects: Dislocations; Elastic material; Electron back scatter diffraction; Electron microscopy; Equilibrium equations; Error detection; Frames; Mathematical analysis; Microscopy; Numerical algorithms; Tensors
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2013.04.006

•Static stress equilibrium relates Nye’s tensor to elastic distortion fields.•The full Nye’s tensor can be estimated using surface EBSD data and micro-mechanics.•Nye’s tensor gradients into a sample can also be estimated from surface EBSD data. A novel method of micromechanical stereoinference is reported which yields components and gradients of Nye’s GND tensor which are inaccessible by surface EBSD. In particular, it determines the Nye’s tensor gradients going into the sample bulk. The method overcomes limitations imposed by metal’s electron opacity by combining experimentally-accessible Nye’s tensor components and measured infinitesimal elastic distortion tensors with a solution to the underlying stress equilibrium equations. The full Nye’s tensor can be transformed into a crystal coordinate frame and interpreted in the context of slip systems, a more physical sense than in the sample or experimental frame. A demonstration of the method is given for a simulated microstructure. The method is largely robust to random experimental noise but may be sensitive to pattern-center errors.