Investigation of Grain Anisotropy on Surface Area between Carbon Steel Wire and Die at Drawing

Drawing is characterized by non-uniform character of plastic deformation, which is transferred from the die to the processed wire. Such impact causes specific change of wire microstructure. In the surface area the thin layer with highly deformed grains is observed. It is important to measure the thickness of this thin layer. For this purpose it is proposed in this paper to use the value of coefficient of anisotropy, which is calculated as the ratio of mean quantity of phase particles, crossed by secant line perpendicular to deformation axis on the unit of secant line length to the mean quantity of phase particles, crossed by secant line parallel to deformation axis on the unit of secant line length. Distribution of coefficient of anisotropy, both for low and high carbon steel wire after drawing, was obtained by Thixomet PRO software. It made it possible to calculate the thickness of highly deformed area automatically taking into consideration the difference of steels microstructure.

A “Close” Look at Linear Approximations

Approximation is a concept that underpins many big ideas in calculus. Students approximate the slope of a tangent line using secant-line slopes and eventually evaluate limits of those approximations. Linear approximation has uses in differential calculus. To help my students understand linear approximation, I adapted an activity from the Instructor's Guide for Stewart's Calculus (Shaw 2015). Students construct multiple representations of four functions and analyze each function's behavior near the origin using Desmos® (Desmos Graphing Calculator 2016) or similar technology, for better visualization.