An Efficient Iterative Approach for Determining the Post-Necking True Stress-Strain Response of Aerospace Metals

To numerically simulate and predict the plastic deformation of aerospace metal alloys during extreme impact events (e.g., turbine engine blade-out and rotor-burst events, bird strikes, and foreign object damage), accurate experimental knowledge of the metal’s hardening behavior at large strains is requisite.  Tensile tests on round cylindrical specimens are frequently used for this purpose, with the metal’s large-strain plasticity ultimately captured by an equivalent true stress vs. equivalent true plastic strain curve.  It is now well known that if axial strain is measured using an extensometer (either a physical clip-on extensometer or a digital image correlation virtual extensometer), the equivalent true stress-strain curve calculated from this measurement is valid only up to the onset of diffuse necking.  That is, once the strain field heterogeneously localizes in the specimen gage (onset of necking), extensometers, which average the strain field over the length of the gage section, are unable to capture the local strain at the site of fracture initiation.  Thus, a number of approaches have been proposed and employed to correct the post-necking hardening response.  Perhaps the most widely used technique is an iterative approach commonly referred to as finite-element model updating.  This approach involves inputting a suite of candidate post-necking equivalent true stress-strain curves into finite-element software.  For each candidate curve, a finite-element simulation matching the exact conditions of the physical test is run.  The true stress-strain curve that produces the best agreement between simulation and experiment (using comparisons of force-displacement and surface principal strain data) is ultimately adopted.  In this talk, a novel variation of this iterative approach is presented, aimed at decreasing computational expense and iterative effort with a better first guess and a bounded fan of prospective true stress-strain curves.  In particular, we use local surface true (Hencky) strain data, obtained from a digital image correlation virtual strain gage, to generate an upper bound on the true stress-strain response for the iterative simulation process.  This upper bound also serves as the initial guess in the iterative simulation process.  To assess its performance and robustness, the proposed approach is benchmarked using experimental data for a menu of aerospace relevant metal alloys (In-625, In-718, Al-6061, 17-4 PH stainless steel, and Ti-6Al-4V) that span various crystallographic structures and exhibit different plastic (hardening) behaviors.  For each of these metals, our approach substantially decreases the number of candidate curves and meaningfully reduces iterative effort, a trend that holds across a broad range of crystal structures and corresponding hardening behaviors.