Torsion testing – plastic deformation to high strains and strain rates

Abstract

A new method of calculating stress-strain curves from torsion measurements is .described. Contrary to the usual calculation of stress and strain at the surface of the specimen -where the material properties are distorted by microcracks, notch effects, etc. -stress and strain are determined at a 'critical radius' inside the specimen. For this purpose an initial approximation for the flow curve of the type (Jf""" ¢o¢m is improved by calculating a 'correction function' from the test results. This calculation is based on a Taylor series expansion which converges more strongly if tubular specimens are used instead of solid ones. Tubular specimens are therefore used if the flow curve appears to deviate strongly from the exponential law. The new method of test evaluation makes use of the fact that contrary to tensile and upsetting tests, in torsion tests the measured curve gives an almost undistorted linear projection of the flow curve. In fact the test evaluation consists only of 'calibrating' the measured torque and angle of twist in terms of yield stress or equivalent strain, respectively. MST/94 . cP. equivalent strain ¢ time derivative of ¢ a radius of solid or tubular specimen at inner radius of tubular specimen B constant defined by equation (30) C constant in equation (8) Dij deformation rate tensor f mean value of fey, y) defined by equation (20) fey, y) 'correction function' for shape of flow curve f2(yp, Yp) second approximation of fey, y), for r = rp F force h height of upsetting test specimen jk(a, at) parameter defined by equation (19) 10 length of cylindrical section of specimen m strain rate sensitivity index M torque Mo calculated torque assuming zero approximation for flow curve n strain hardening exponent p abbreviation (p = n +m) P normalized torque r distance from axis of specimen distance) r p critical radius R notch radius x relative variation of dimension z axial coordinate (distance from median plan of specimen) f3 constant defined by equation (10) y shear strain (finite Lagrangian strain tensor component) y shear strain rate Ya shear strain at radial distance r = a (surface) Ya time derivative of Ya Yat shear strain at inner radius r = at of tubular specimen Yat time derivative of Yat Yp shear strain at critical radius rp Y P time derivative of Yp Yr shear strain at radial distance r Yr time derivative of Yr e angle of twist e time derivative of e (J f yield stress O"t constant in equation (1) O"rt constant in equation (2) TO zero approximation for shear stress T 2 second approximation for shear stress

A radial compression test for plastic flow studies

“…In these experiments, each specimen was gradually compressed and deformed until its contour deviated visibly from its original annular shape or its inner diameter diminished beyond our measuring resolution. The pressure difference and the average inner and outer radii were measured during deformation and used to compute the ratio Ke = Po -Pi (8) 21n( Ro / Ri ) needed to estimate K from the closed-form solution. 9 Each test was repeated for a few identical specimens.…”

Ultra‐low cycle torsion fatigue of annealed copper

“…Measured data of twisting moment M and angle of twist θ were converted into true, von Mises equivalent stress σ and true, von Mises equivalent strain ε according to . Those correlations can be described in a simplified manner as follows: σ ~ M / r 3 and ε ~ θ · r / L .…”

Achieving High Strains in Sheet Metal Characterization Using the In-Plane Torsion Test

“…The in-plane torsion test was firstly presented by Marciniak [9]. Further developments were realized by Pöhlandt and Tekkaya [10] and Bauer [11]. A round sheet specimen is clamped concentrically on the outer rim and in the center (Fig.…”