Quantifying texture evolution during hot rolling of AZ31 Twin Roll Cast strip

Multi-pass rolling experiments with an AZ31 Twin Roll Cast (TRC) alloy were performed on an industrial scaled four-high rolling mill. Within the rolling with an intermediate annealing the evolution of texture was investigated. To quantify the extent of preferred crystallographic orientation experimental X-ray pole figures were measured after different process steps and analyzed using the free and open Matlab® toolbox MTEX for texture analysis. The development of the fiber texture was observed and analyzed in dependence on rolling conditions. In the initial state the specimen exhibits a texture composed of a weak basal texture and a cast texture with {0001}-planes oriented across the rolling direction. During the following rolling process a fiber texture was developed. The expected strength increment of the fiber texture was quantitatively confirmed in terms of volume portions of the orientation density function around the fiber and in terms of the canonical parameters of fitted pseudo Bingham distributions. On the results of this work a model for prediction of the texture evolution during the strip rolling of magnesium in the examined parameter range was developed

Approximation and geometric modeling with simplex B-splines associated with irregular triangles

Bivariate quadratic simplical B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a C1-smooth surface. The generation of triangle vertices is adjusted to the areal distribution of the data in the domain. We emphasize here that the vertices of the triangles initially define the knots of the B-splines and do generally not coincide with the abscissae of the data. Thus, this approach is well suited to process scattered data.\ud \ud With each vertex of a given triangle we associate two additional points which give rise to six configurations of five knots defining six linearly independent bivariate quadratic B-splines supported on the convex hull of the corresponding five knots.\ud \ud If we consider the vertices of the triangulation as threefold knots, the bivariate quadratic B-splines turn into the well known bivariate quadratic Bernstein-Bézier-form polynomials on triangles. Thus we might be led to think of B-splines as of smoothed versions of Bernstein-Bézier polynomials with respect to the entire domain. From the degenerate Bernstein-Bézier situation we deduce rules how to locate the additional points associated with each vertex to establish knot configurations that allow the modeling of discontinuities of the function itself or any of its directional derivatives. We find that four collinear knots out of the set of five defining an individual quadratic B-spline generate a discontinuity in the surface along the line they constitute, and that analogously three collinear knots generate a discontinuity in a first derivative.\ud Finally, the coefficients of the linear combinations of normalized simplicial B-splines are visualized as geometric control points satisfying the convex hull property.\ud Thus, bivariate quadratic B-splines associated with irregular triangles provide a great flexibility to approximate and model fast changing or even functions with any given discontinuities from scattered data.\ud An example for least squares approximation with simplex splines is presented

Medijska pismenost – preduvjet za odgovorne medije: zbornik radova s 5. regionalne znanstvene konferencije Vjerodostojnost medija, ur. Viktorija Car, Lejla Turčilo, Marijana Matović. Sarajevo: Fakultet političkih nauka, 2015., 150 str.

The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.PostprintPeer reviewe