Extension of flow stress–strain curves of aerospace alloys after necking

Abstract

To define accurately the expansion limits of aerospace materials, determination of the material behavior before and after the onset of necking, as well as the failure threshold are essential requirements. The plastic flow behavior before necking (pre-necking phase) has been fully identified by various mathematical models, such as Hollomon and Swift constitutive equations, but a criterion to satisfy the material behavior after necking (post-necking phase) is lacking. To obtain or calibrate accurately the damage constants in coupled and decoupled damage models, a precise stress-strain behavior after necking is required to reduce significantly the error in predicting fracture in metal forming processes. A tool was developed to determine the true stress-true strain curve for the post-necking regime of different aerospace alloys, such as inconel 718 (IN 718), stainless steel 321 (SS 321), and titanium (Ti6Al4V). Uniaxial tensile tests based on the ASTM E8M-11 standard were performed to determine the true stresstrue strain behavior before necking. Two different methods, a weighted average method and a new hardening function, were utilized to extend the true stress-true strain curve after necking. The two methods resulted in similar post-necking curves for the different materials, with consideration that the new hardening function could be used for more complicated hardening laws. The flow curves were employed in the simulation of the dome height test and then validated through experimentation. The simulation results were compared with the experimental data to verify the accuracy of the proposed methods in this work.

Evaluation on Flexibility of Phenomenological Hardening Law for Automotive Sheet Metals

“…Ludwik [22] pioneered the use of another power law to describe the stress-strain relationship, as expressed in Equation (5a). Furthermore, Swift's [10] power hardening law is widely used to describe the flow curve of steels and irons [20,23,24]. The power laws construct strictly increasing functions of the flow curve.…”

“…Both saturation and power hardening laws are widely used to practically describe the hardening behavior of sheet metals. The limitation of these hardening laws is their inflexibility in capturing the flow curve over wide strain ranges [14,23,25]. The limitation can be deduced mathematically from the formulations of their ODEs, which contain two or three parameters.…”

Inverse determination of the flow curve in large range of strains for cylindrical tensile specimen

“…10 Previous studies based on the direct extrapolations presented poor prediction results of the flow curves. 11,12 Based on the analysis on the distribution of stress and strain in the necking region, Bridgman proposed a stress correction model using the geometrical parameters of the necking section, which has been utilized to experimentally correct the flow stresses after necking for cylindrical specimens. 13 Siebel and Schwaigere 14 and Davidenkov and Spiridonova 15 proposed similar analytical models, respectively.…”

The improvement of stress correction in post-necking tension of cylindrical specimen

“…Moreover, the direct extrapolations merely based on the experimental data from a tensile test generally presented poor prediction results of the post-necking hardening curves. 8–10 Various analytical models have been proposed for determining the post-necking hardening curves. The Bridgman method, 11 which applied an analytical model to stress correction based on two geometrical parameters involving the minimum cross-sectional radius a and curvature radius of neck R , has been widely known to experimentally determine the post-necking hardening curve of cylindrical specimen.…”