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A combined theoretical/experimental approach accurately quantifying post-necking hardening phenomena in ductile sheet materials that initially exhibit diffuse necking in tension is presented. The method is based on the minimization of the discrepancy between the internal and the external work in the necking zone during a quasi-static tensile test. The main focus of this paper is on the experimental validation of the method using an independent material test. For this purpose, the uniaxial tube expansion test is used to obtain uniaxial strain hardening behavior beyond the point of maximum uniform strain in a tensile test. The proposed method is used to identify the post-necking hardening behavior of a cold rolled interstitial-free steel sheet. It is demonstrated that commonly adopted phenomenological hardening laws cannot accurately describe all hardening stages. An alternative phenomenological hardening model is presented which enables to disentangle pre- and post-necking hardening behavior. Additionally, the influence of the yield surface on the identified post-necking hardening behavior is scrutinized. The results of the proposed method are compared with the hydraulic bulge test. Unlike the hydraulic bulge test, the proposed method predicts a decreased hardening rate in the post-necking regime which might be associated with probing stage IV hardening. While inconclusive, the discrepancy with the hydraulic bulge test suggests differential work hardening at large plastic strains.

Uniform tensile ductility (UTD) is crucial for the forming/machining capabilities of structural materials. Normally, planar-slip induced narrow deformation bands localize the plastic strains and hence hamper UTD, particularly in body-centred-cubic (bcc) multi-principal element high-entropy alloys (HEAs), which generally exhibit early necking (UTD < 5%). Here we demonstrate a strategy to tailor the planar-slip bands in a Ti-Zr-V-Nb-Al bcc HEA, achieving a 25% UTD together with nearly 50% elongation-to-failure (approaching a ductile elemental metal), while offering gigapascal yield strength. The HEA composition is designed not only to enhance the B2-like local chemical order (LCO), seeding sites to disperse planar slip, but also to generate excess lattice distortion upon deformation-induced LCO destruction, which promotes elastic strains and dislocation debris to cause dynamic hardening. This encourages second-generation planar-slip bands to branch out from first-generation bands, effectively spreading the plastic flow to permeate the sample volume. Moreover, the profuse bands frequently intersect to sustain adequate work-hardening rate (WHR) to large strains. Our strategy showcases the tuning of plastic flow dynamics that turns an otherwise-undesirable deformation mode to our advantage, enabling an unusual synergy of yield strength and UTD for bcc HEAs.This work shows that by designing appropriate alloying elements in a body-centred-cubic high-entropy alloy, local chemical order and lattice distortion can be tuned, which influences the evolution of planar-slip bands, realizing pure-metal-like tensile ductility at gigapascal yield strength.

The strength–ductility trade-off has long been a Gordian knot in conventional metallic structural materials and it is no exception in multi-principal element alloys. In particular, at ultrahigh yield strengths, plastic instability, that is, necking, happens prematurely, because of which ductility almost entirely disappears. This is due to the growing difficulty in the production and accumulation of dislocations from the very beginning of tensile deformation that renders the conventional dislocation hardening insufficient. Here we propose that premature necking can be harnessed for work hardening in a VCoNi multi-principal element alloy. Lüders banding as an initial tensile response induces the ongoing localized necking at the band front to produce both triaxial stress and strain gradient, which enables the rapid multiplication of dislocations. This leads to forest dislocation hardening, plus extra work hardening due to the interaction of dislocations with the local-chemical-order regions. The dual work hardening combines to restrain and stabilize the premature necking in reverse as well as to facilitate uniform deformation. Consequently, a superior strength-and-ductility synergy is achieved with a ductility of ~20% and yield strength of 2 GPa during room-temperature and cryogenic deformation. These findings offer an instability-control paradigm for synergistic work hardening to conquer the strength–ductility paradox at ultrahigh yield strengths. Harnessing premature necking produces a rapid multiplication of dislocations to interact with local chemical orders for work hardening in VCoNi alloy, achieving ductility of 20% and yield strength of 2 GPa during room-temperature and cryogenic deformation.

The stress–strain behavior of sheet metal is commonly evaluated by tensile test. However, the true stress–strain curve is restricted up to uniform elongation of the material. Usually, after the uniform elongation of the material the true stress–strain is obtained by extrapolation. The present work demonstrates a procedure to find out the true tensile stress–strain curve of the steel sheet after necking using digital image correlation (DIC) technique. Hill’s normal anisotropic yield criteria and local strains measured by DIC technique are used to correct the local stress and strain states at the diffuse necked area. The proposed procedure is shown to successfully determine the true tensile stress–strain curve of ferritic and dual-phase steel sheets after necking/uniform elongation.

Considering the recent and widespread use of half-hard rolled aluminum sheets in various industrial sectors, this study aims to characterize, determine and evaluate the formability of these sheets. The first phase is to experimentally determine the forming limit curve of laminated half-hard aluminum sheet AA1050-H24. The FLC is determined experimentally from the limiting strain values measured at the fracture location of the specimen using the Nakazima test. Different geometries of the laminated sheet were produced to obtain different deformation paths in the plane of the main deformations. However, experimentally determining a forming limit curve is very time intensive and requires dedicated and costly equipment. The second phase is to develop an alternative method to replace the experimental protocol. Indeed, we will propose a hybrid approach between the finite element method and necking criterion for determining the onset of localized necking in order to numerically predict this curve. In order to make a numerical prediction, Abaqus/Explicit was used to perform finite element modeling of the Nakazima test. The necking criterion based on the first component of the limit strain was used the time of appearance of necking and to plot the forming limit curve. A comparison of the experimental and numerical results is carried out to determine the effectiveness of the necking criterion in the numerical evaluation of the formability of aluminum sheet AA1050-H24. The necking criterion can numerically evaluate the formability of the AA1050-H24 sheet.

Nanoscale small-volume metallic materials typically exhibit high strengths but often suffer from a lack of tensile ductility due to undesirable premature failure. Here, we report unusual room-temperature uniform elongation up to ~110% at a high flow stress of 0.6–1.0 GPa in single-crystalline -oriented CoCrFeNi high-entropy alloy nanopillars with well-defined geometries. By combining high-resolution microscopy and large-scale atomistic simulations, we reveal that this ultrahigh uniform tensile ductility is attributed to spatial and synergistic coordination of deformation twinning and dislocation slip, which effectively promote deformation delocalization and delay necking failure. These joint and/or sequential activations of the underlying displacive deformation mechanisms originate from chemical compositional heterogeneities at the atomic level and resulting wide variations in generalized stacking fault energy and associated dislocation activities. Our work provides mechanistic insights into superplastic deformations of multiple-principal element alloys at the nanoscale and opens routes for designing nanodevices with high mechanical reliability. Small-scale metallic materials often suffer from a lack of tensile ductility. Here, the authors report an unusual room-temperature super-elongation in CoCrFeNi nanopillars from spatial and synergistic coordination of deformation twinning and dislocation slips due to chemical heterogeneities.

Sheet metals subjected to biaxial plane stress loading typically fail due to localized necking in the thickness direction. Classical plasticity models using a smooth yield surface and the normality flow rule cannot predict localized necking at realistic strain levels when both the in-plane principal strains are tensile. In this paper, a recently developed multi-surface model for porous metal plasticity is used to show that the development of vertices on the yield surface at finite strains due to microscopic void growth, and the resulting deviations from plastic flow normality, can result in realistic predictions for the limit strains under biaxial tensile loadings. The shapes of the forming limit curves predicted using an instability analysis are in qualitative agreement with experiments. The effect of constitutive features such as strain hardening and void nucleation on the predicted ductility are discussed.

Uniaxial tensile creep tests were conducted under different loads at 210 °C. Using the overall creep test data as the optimization objective, a genetic algorithm was employed to obtain the creep material parameters for the modified Kachanov-Rabotnov(K-R) creep damage method of duralumin alloy 2A12. The optimized Kachanov-Rabotnov(K-R) creep damage method was defined via a user subroutine, and the finite element method was used to estimate the creep damage of duralumin alloy 2A12. The optimized numerical results, experimental measurements, and finite element simulations were consistent. The finite element results indicated that creep damage developed more rapidly near the center, leading to noticeable necking. Additionally, the optimization method can be well used to process experimental results and to calculate the creep damage performance parameters of materials corresponding to certain aviation metal structures.

Mechanical shearing introduces a material limit lower than the onset of local necking. This new limit is critical for understanding and predicting material performance in industrial forming applications. The sheared edge condition, influenced by strain hardening and microstructural damage, reduces ductility in the shear-affected zone, posing challenges for reliable characterization and numerical prediction. This study presents an approach that integrates finite element modelling (FEM) with geometric shape matching to establish a practical, simulation-compatible material limit for sheared-edge formability. Instead of relying on localized strain measurements, the methodology determines the punch displacement in FEM simulations that best replicates the experimentally observed deformed geometry of Hole Expansion Capacity (HEC) test specimens, along with the corresponding maximum deformation of elements at the stretched edges. The method proves effective for industrial forming processes, enhancing FEM-based edge failure prediction and providing a valuable tool for process optimization and defect troubleshooting in sheet metal forming.

L360QS pipeline steel, due to its high toughness, high strength, resistance to sulfide stress cracking, and resistance to hydrogen-induced cracking, is increasingly being used in pipeline network construction. Its fracture behavior is a critical factor for safe operation in mountainous steep-slope environments, but it has not yet been widely studied. Therefore, this paper conducts extensive experiments on the ductile fracture of L360QS pipeline steel. The tests employed standard tensile, notched tensile, shear, and compression specimens, covering a stress triaxiality range from approximately -0.33 to 0.92. The study combined Ling's iterative method to establish an elastoplastic constitutive model considering post-necking behavior, and incorporated it into finite element models to extract the average stress triaxiality and equivalent plastic strain at the moment of fracture initiation for each type of specimen. Based on the extracted data, a piecewise ductile fracture model was established: a simplified Johnson-Cook criterion is used in the high triaxiality range, while an empirical function is used to describe fracture behavior in the medium, low, and negative triaxiality ranges. The model was validated using a train-test split approach, predicting fracture displacements for an independent test set of specimens. The results showed all prediction errors were within 5%, demonstrating the model's high accuracy. Furthermore, a Spearman correlation analysis quantified the influence of geometric factors, revealing that notch curvature has the strongest monotonic relationship in controlling average stress triaxiality and fracture strain. The fracture model established in this paper can accurately predict the fracture behavior of L360QS pipeline steel and provides a reliable basis for failure prediction and safety assessment under complex service conditions (such as mountainous steep slopes).