Ductility: Stress and Strain Theory Volume 3 - Issue 3

Paul T E Cusack*

• versatile writer and researcher McGill University, Canada

Received:November 17, 2021   Published: December 21, 2021

Corresponding author: Paul T E Cusack, versatile writer and researcher McGill University, Canada

DOI: 10.32474/ARME.2021.03.000164

Abstract PDF

Van Vlack claims that there is no mathematical relationship between the two measures of ductility viz elongation and reduction of area. In this paper, we prove that there is a relationship between the two measures that involves the golden mean parabola. Even is a subject as old as Mechanics, we can still make discoveries.

Keywords: Ductility; Stress; Strain; Golden Mean parabola; AT Math

Ductility is a measure of a metal’s ability to withstand tensile stress, which is a force pulling the two ends of an object away from each other. Ductility is a measure of a metal’s ability to withstand tensile stress, which is a force pulling the two ends of an object away from each other (Source; Wikipedia). There are two methods to measure ductility. One is elongation (strain); the second is reduction of area . Van Vlack states that there is no mathematical relationship between the two measures of ductility. In this paper, we will unite the two mathematically. Assume a specimen that is circular in cross-section.

So, we provided a mathematical relationship between the two measures of ductility.

1. Van Vlack LH (1989) Elements of Materials Science and engineering. Addison Wessley.