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.