Solid State Phenomena Vol. 388

Abstract: A consistent kinematic method was developed to calculate a forming limit curve (FLC) for a material with thickness t^*₀ from a given FLC pertaining to a different thickness t₀ ≠ t^*₀. The developed method is based on the analysis of the bending strains introduced by the Nakajima test method. To calculate the required strains, an explicit and an implicit procedure are presented. In contrast to its implicit equivalent, the explicit method suffers from an intrinsic error which scales with the material’s gauge and can be quantified by considering the neutral case t^*₀ = t₀. Finally, the developed method predicts a linear relationship between and the material thickness, which is in line with practical experience.

Abstract: For high-accuracy finite element (FE) simulation of automobile crashing behavior, a work hardening curve that involves pre-strain from press forming is required. Here, the plastic strains exceeding the uniform deformation region are generally introduced through processes such as bending, but such large pre-strain effect have not been reported. Therefore, in this study, for DP590 steel, the work hardening curve for second-stage tension under pre-strain exceeding the uniform deformation region was identified. This identification was enabled by the diameter measurement tensile test developed by the authors. As a result, in the second-stage tension in the same direction as the first-stage tension, the initial yield stress showed a tendency to overshoot relative to the original work hardening curve, revealing that strain aging occurred. The overshoot portion formed a stress plateau that continued up to an equivalent plastic strain of 0.18. Such a tendency has not been observed in DP590 steel, making this a phenomenon revealed for the first time. When the tensile direction in the second stage was orthogonal to the first stage, the cross-hardening effect (reduction in initial yielding due to the Bauschinger effect and overshoot from the original work hardening curve) was observed. The stress plateau region due to overshoot continued up to an equivalent plastic strain as large as 0.6. These large plateaus concluded that work hardening presents perfect plasticity at large deformed press parts.

Abstract: Magnesium (Mg) alloy sheets are expected to contribute to the lightweighting of structural components, owing to their inherent benefits of low density and high specific strength. However, the limited room-temperature press formability exhibited in Mg alloy sheets remains a barrier to their expanded use. A significant factor contributing to the limited formability is the strong basal texture. To improve the room-temperature press formability, ZX series Mg alloy sheets that weakened the basal texture have recently been developed. In our previous study [Hama et al., Mater. Res. Proc., 28(2003), 711-716], cup drawability of a Mg-1.5mass%Zn-0.1mass%Ca (ZX10Mg) alloy sheet was investigated at room temperature. The obtained cup exhibited that the cup height and thickness strains differed significantly in the circumferential direction of the cup. However, a more detailed discussion on the mechanisms of this anisotropic deformation was hampered by a reliance solely on experimental observations. Therefore, in this study, crystal plasticity finite-element simulations of cup drawing of the ZX10Mg alloy sheet were performed. The simulation results qualitatively reproduced macroscopic and microscopic deformation behaviors during cup drawing. Numerical studies showed that the anisotropic deformation during drawing was primarily induced by the texture of the material, suggesting that anisotropic deformation is inevitable unless the anisotropic c-axes distribution remains in the initial texture.

Abstract: The present study aims to investigate the anisotropic creep behaviour of aluminium alloy 2139 during artificial ageing, through in situ thermomechanical loadings under Electron Backscattered Diffraction (EBSD). EBSD analysis enabled the characterisation of microstructural parameters and the identification of grain misorientations which were further correlated with macroscopic creep strain. In situ analyses were conducted within a Scanning Electron Microscope (SEM) using a micro‑tensile stage that allows simultaneous heating and mechanical loading. Creep tests were performed at 160°C under 50, 100 and 150 MPa along three different orientations in order to investigate the creep behaviour of the alloy. Kernel Average Misorientation (KAM) maps showed a progressive increase of the average KAM values for the different loading conditions, reaching a saturation value after 10 hours. Ex situ tensile tests were conducted on creep‑aged specimens using Digital Image Correlation (DIC). The main mechanical property evolutions (averaged across all orientations) are a 45 % increase in yield stress, a 10 % increase in ultimate tensile stress and a reduction in ductility, characterised by a notable decrease in elongation. Further works will focus on the result repeatability, as well as on the influence of prior deformation on the creep strain.

Abstract: This study investigates the effect of induction-based surface heat treatment on the microstructure and bendability of a commercial hot-rolled martensitic steel with a nominal strength of 1300 MPa. A rapid tempering process was applied at 500 °C and 700 °C using a pilot-scale 60 kW induction heating system, followed by water quenching. Microstructural characterization revealed that the treatment induced minor changes near the subsurface without affecting the centerline. The as-rolled condition exhibited the highest subsurface hardness, whereas surface-treated samples showed progressive softening due to recovery. Three-point bending tests combined with digital image correlation demonstrated a significant improvement in bendability for heat-treated samples. The as-rolled condition fractured at 0.195 strain, while the 700 °C treated specimen did not fracture even at 0.78 strain. These findings highlight that even a modest reduction in subsurface hardness can substantially enhance the formability of ultra-high-strength steels, offering a promising approach for industrial applications requiring high strength and improved bendability.

Abstract: Forming limit curve (FLC) is the most common used manifestation of the failure criterion today in the sheet metal forming industry. All commercial simulation software uses this concept to evaluate the failure strains and to detect the most dangerous section(s) of the workpiece. The laboratory determination of the FLC is standardized. However, because experimental measurement is cumbersome, theoretical calculations of FLCs using mechanical properties from well-defined test conditions are still interesting. Such calculation concepts are already developed by different authors. This paper presents calculated FLCs using the models of Abspoel et al., Stören and Rice and Swift. All the equations include tensile tests data that have been measured physically at room temperature, with quasi-static strain rates. Calculated results of DC04 cold rolled steel sheet with relatively high plastic anisotropy coefficient was compared to a nearly isotropic DP800 high strength steel. Based on the results it is observed that r-value influences the shape of the left-hand side of the FLC as well as the plane strain point significantly, for the DC04 sheet. These effects are less pronounced for the DP800 material, which has lower r-value. At the same time, n-value and total elongation raise or lower the curves, generally. These observations are briefly explained by function analyses using fictitious r-values in the calculations.

Abstract: The prediction of sheet failure remains a highly relevant topic in metal forming research, particularly in relation to the experimental and theoretical determination of forming limit curves (FLCs). While the experimental construction of FLCs is a well-established but time-consuming process, theoretical and numerical approaches provide a more efficient alternative. However, their accuracy must be critically assessed, all the time. In this work, the formability of steel sheet with tensile strengths of 1500 MPa is investigated by combining experimental Nakajima tests with theoretical predictions of FLCs. Previous studies, such as models by Abspoel, Swift, Hill etc. have not addressed such high strength levels, where the diffuse and local neck points are quite close, leaving open the question of whether existing approaches remain valid for these materials. To provide a reference baseline, additional tests and calculations were also performed on lower-strength steel sheet (DP800). Our results show that the FLC points can be well estimated by two different theories in the positive quadrant, but there are noticeable differences between the measured and calculated values close to the plane strain point.

Abstract: Forming limit curves are sensitive to the strain-path. Numerous methods were proposed in the literature since the 1970’s to the last decades for taking into account this sensitivity. The aim of this work is to consistently compare these methods with practical application in mind. First, a literature review revealed that many available methods are different in form but all rely on the empirical assumption of iso-equivalent failure strain for all strain paths sharing the same final strain mode, independently of the strain path leading to it. The models relying on this hypothesis are summarized. A significantly different approach, called here “interpolation method”, relies on different hypotheses – also empirical. The two approaches are further compared in order to identify the similarities and differences between the two. It appears that most stress-based approaches for the correction of FLC strain-path dependence rely on the same hypothesis as the iso-equivalent-strain method and they reduce to it under the assumption of isotropic hardening. The iso-strain method and the “interpolation” approach provide similar predictions in a series of configurations, while they significantly differ for other configurations. No theoretical or experimental proof is available to further discriminate the most accurate approach for strain-path correction of FLCs; the research opens new directions for the investigation of the topic.

Abstract: Efficient characterization of formability of tubal sections is essential for designing lightweight aluminum extrusion components, particularly since the presence of weld seams and extrusion-induced inhomogeneities influence deformation behavior. This study evaluates the formability of Al–Mg–Si alloy tubes after being subjected to four different heat-treatment conditions, using a non-conventional rubber-assisted bulge test. A solid polyurethane (PU) plug was employed as pressure medium to enable full-scale deformation. Digital image correlation (DIC) was used to quantify circumferential and longitudinal strain evolutions, while post-fracture thickness measurements provided complementary insight into through-thickness strain.The measured circumferential strain at fracture ranged from 0.15 to 0.24 across the investigated tempers. The W-tempered condition exhibited the highest surface strain while maintaining moderate thickness reduction, whereas the soft-annealed tubes showed the largest thinning. The as-received and naturally aged conditions displayed similar deformation responses. These results demonstrate that tube formability, as evaluated by the present testing approach, is characterized by the combined evolution of surface strain and thickness reduction, both of which are influenced by heat treatment. Overall, the study shows that PU-assisted rubber bulge testing provides a practical and robust experimental framework for the comparative assessment of formability in extruded aluminum tubes.