The load-dependent deformation of the cylindrical sandstone specimen SKL4 from Southern Germany (Unterer Buntsandstein formation) was measured by the time-of-flight neutron diffraction method at the EPSILON diffractometer at the pulsed neutron source IBR-2M of the Joint Institute for Nuclear Research, Dubna (RUS), using the ExStress uniaxial load device.
For the strain evaluation of the data mostly the Rietveld refinement method is used, which has the disadvantage to be very complex in use and it often doesn’t treat the mechanical behavior of the specimen in completeness. This work primarily concerns with the approach to theoretically forward model (predict) diffraction data at elevated loads based on load-free measurements. In this approach an elastic-mechanical model for the mechanical behavior of the specimen is set up. The calculations and modelings are performed within the program package SPYDER (Continuum Analytics) by using the programming language Python.
The mechanical model is built of spheres representing the sandstone´s grains. To get the response of the sphere due to the applied load the sphere is cut into quartz single-crystal slices. Each of the slice´s reaction to the load is calculated and used in the modeling. When considering a perfect sphere under load conditions the top and bottom would experience extreme stresses which lead to deformation and flattening of the initial round grain shape. Besides this flattening the model also incorporates the change in pore volume (cementation/compaction) since an increasing flattening causes the spheres getting nearer each other in contrast to the spheres being not flattened.
Because the present examined specimen has to be addressed as a polycrystal the response of the sample due to an applied uniaxial load is calculated according to the models proposed for the elastic behavior by Voigt and Reuss. While the Voigt modeling uses one Young´s modulus and Poisson´s ratio the modeling for fulfilling the Reuss demand incorporates the anisotropic Young´s moduli and Poisson´s ratios of the quartz hkil. In this context a generally applicable formula to convert an arbitrary vector [hkil] referring to a hexagonal system to [uvw] in an orthonormal system has been determined.
In general, the processed forward modelings show a high accordance with the measured data for the Voigt as well as for the Reuss model and for all applied loads. The method is thus able for an accurate prognosis/prediction of the shift of the diffraction patterns´ peaks at elevated uniaxial loads. As a result, the model revealed a better fit to the data by using the Voigt instead of the Reuss model. But the overall difference between these two extreme models is very small. By combining (“mixing”) the Voigt and Reuss model and varying the quantity of flattening the spheres an overall best-fit setting to model the three load stages´ diffraction data can be found. The weighted profile factor Rwp for this best-fit modeling is close to 1 % (without background) and making the quality of the modeled diffraction patterns clear.
Contact: Simon Breuer