Experimental approach for the determination of the Bridgman’s necking parameters

Abstract

Two ways of determining Bridgman’s parameters are presented to estimate the equivalent Bridgman stress–strain (BSS) curve after the onset of necking in cylindrical specimens. The accurate experimental determination of the minimum necking radius, rN, and the radius of curvature of the necking, RN, are considered to be the main problems in applying Bridgman’s model to obtain the equivalent BSS curve and describe the plastic behaviour of materials. Using the combined technique of 2D digital image correlation and fringe projection, the 3D positions and displacements of the surface elements are determined for each load stage of a tensile test on steel, aluminium (Al) and copper (Cu) bars. The axial displacements are well fitted with an empirical function that allows accurate estimation of the beginning of necking and its location on the specimen. From the 3D positions, both Bridgman’s parameters are estimated by adjusting a torus to the necking zone. The 3D measurements around the necking position have to be well defined to obtain the parameters in a feasible way, because the real necking profile does not fit well with the half-circle proposed by Bridgman. Nonetheless, the estimated rN parameters are noisy, affecting the BSS curve. Therefore, an alternative and simpler way for estimating rN and RN is also proposed, only requiring the measurement of total axial displacements along the loading axis of each surface element. In this way, the BSS curve obtained is smooth, although it somewhat underestimates the same curve obtained using experimentally measured 3D data.

A New Approach for Evaluation True Stress–Strain Curve from Tensile Specimens for DC04 Steel with Vision Measurement in the Post-Necking Phases

“…The practical aspects of measurement motivated additional research to develop new formulae and new gauging techniques. Bridgman’s ACM for stress correction was successfully incorporated into the round bar tension test [ 36 ]. However, modifications continue to be proposed for flat specimens, and new formulae are still being investigated.…”

General Blending Approach of Fundamental Cold Flow Models for an Almost Complete Cold Flow Model in Terms of Tensile Test

“…[5] In recent years, DIC techniques have been used to acquire the flow curves as the direct measurement method. Siegmann et al [23] used a combined technique of 2D-DIC and fringe projection (FP) technique to determine the 3D positions and displacements of surface elements in the tensile test. The 3D information was used to estimate the Bridgman parameters such as the minimum necking radius and the radius of necking curvature.…”

A Forward Identification Method for High-Temperature Stress–Strain Curves of 7075 Aluminum Alloy Sheet Considering the Necking Stage

“…Hence, the finite element inverse analysis method is difficult to perform. Another method is to obtain the local geometric contour parameters or local strain information of the necking region during stretching using image dynamic measurement technology, and directly calculate the stress and strain [ 18 , 19 , 20 ]. Paul et al [ 21 ] carried out a finite element analysis of cylindrical specimen, calculated the equivalent strain and axial true stress according to the local axial strain in the necking region, and converted the axial true stress into equivalent stress by introducing an appropriate correction coefficient.…”