DiffStress is a Python-based diffraction analysis tool that analyzes the tensorial stress state present on a polycrystal sample. The stress analysis utilizes a set of lattice-spacings (interatomic spacings) obtained from a polycrystalline specimen using a diffractometer (either X-ray or neutron)
This python package allows one to analyze both experimental diffraction lattice strains (d-spacing) and model-emulated lattice strains (internal elastic strain), e.g., those data resulting from EVPSC simulations.
For the purpose of experimental d-spacing analysis, it accepts the format of Proto data. Current software can generate various graphics for the purpose of data visualization by using matplotlib and some in-house scripts written for matplotlib, which is also available under current GitHub account (find "mpl-lib").
In order to estimate the experimental/model-predicted stress, current software requires the use of diffraction elastic constants written in the format of 'sff', which is used in the 'PF' software managed by Thomas Gnaeupel-Herold in NCNR, NIST. One may find the template of the 'sff' file from the current software package.
Also, given set of diffraction data (say, from EVPSC code), one can perturb the lattice strains in order to quantify the uncertainty in the obtained stress by conducting Monte Carlo virtual experiments.
- Stress analysis from d-spacings
DiffStress can analyze the d-spacings collected in the form of Proto X-ray system. One can obtain a fitting result in various orientation and nicely illustrate the goodness of fit. Below is an example of an interstitial-free steel, that shows the undulation in d-spacing vs. sin2psi curve. With using experimental DECs obtained at various orientation, one can obtain stress by least-square method. The intensity can be used to 'estimate' the size (or height) of the diffraction peaks.
- Monte Carlo experiments for uncertainty estimation
DiffStress comes with a feature that allows the Monte Carlo experiment to quantify uncertainties present in flow-stress measurement technique using in-situ diffraction experiments. Below image shows the resulting internal elastic strain (that is corresponding to d-spacing vs. sin2psi curve in a real in-situ diffraction experiment) and the fitting result (like the conventional sin2psi method widely used in the community of residual stress measurement).
The stress measurement using the internal elastic strain (d-spacing) should lead to a self-consistent result such that the weighted average of stress (the macro stress) is equivalent to the stress measured by this virtual diffraction experiment. Below figure shows that the two flow stress curves (one with weighted average stress another obtained by this virtual diffraction experiment) are equivalent.
In the real experiments, however, this self-consistency may be challenged by various factors. For example, due to the counting statistical nature and a finite period of exposure time in use when determining the peak position (thus d-spacings), the d-spacing obtained by a diffraction peak may contain a degree of uncertainty. Also, the peak height (the total counts collected at a particular orientation) is influenced by the presence of crystallographic (and its evolution w.r.t p lastic deformation) thus further affecting the uncertainty in the measured d-spacing. In DiffStress, one can mimic various types of uncertainties existing in real experiments and can simulate the propagation of these uncertainties to the final stress estimated using the virtual diffraction experiments. The first procedure is to superimpose these uncertainties to the internal-strain used in the virtual diffraction experiment. The internal-strain is then perturbed by counting statistical error, crystallographic texture, and incomplete measurements of diffraction elastic constants, and the finite number of exposure to X-ray beam. By using the perturbed internal strain, the statistical undertainty in the d-spacing measured by diffraction peak can be mimicked. Finally, the difference between the weighted-average stress and the one obtained by the diffraction technique can quantify the propagated error to the stress measured by the diffraction technique.
The below figure show an ensemble, in which the perturbed internal
strain is scattered and deviated from the 'fitting'.
Based on these perturbed internal strain, the stress obtained by the
virtual experiment deviates from the 'weighted average' stress as below.
One can repeatedly conduct these virtual diffraction experiments to quantify a statistically meaningful uncertainty, which is very difficult to obtain in real experiments.
Youngung Jeong
Now at Changwon National University
yjeong@changwon.ac.kr youngung.jeong@gmail.com
(2014 March - 2016 Feb) Center for Automotive Lightweighting National Institute of Standards and Technology
- Uncertainty in flow stress measurements using X-ray diffraction for sheet metals subjected to large plastic deformations, Y Jeong, T Gnaeupel-Herold, M Iadicola, A Creuziger, Journal of Applied Crystallography 49, (2016)
- Multiaxial constitutive behavior of an interstitial-free steel: measurements through X-ray and digital image correlation, Y. Jeong, T. Gnaeupel-Herold, M. Iadicola, A. Creuziger, Acta Materialia 112, 84-93 (2016)
- Evaluation of biaxial flow stress based on Elasto-Viscoplastic Self-Consistent analysis of X-ray Diffraction Measurements, Y Jeong, T Gnaeupel-Herold, F Barlat, M Iadicola, A Creuziger, M-G Lee (2015) International Journal of Plasticity, 66, 103-118