Shuo Wang

Accurate characterization of the Bauschinger effect is essential for improving springback prediction in simulations of complex sheet-metal components. However, in-plane tension–compression tests are prone to compressive instability and wrinkling during reverse loading, and the selection of clamping force still lacks a theoretical basis. In this study, a critical clamping force prediction model was developed based on energy conservation and the Cao–Boyce instability criterion. The model establishes the relationship between the critical clamping force, material strength coefficient, strain-hardening exponent, specimen geometry, and effective support area. Finite element simulations and experiments were conducted to investigate the contact state, local support effect, and instability-mode transition of Q890 high-strength steel, 2A14 aluminum alloy, and 304 stainless steel under different clamping forces. For Q890 steel, the critical clamping force interval was 900–1000 N, within which the compressive instability strain increased from nearly 0 to 0.085 and the instability mode changed from single-wave to double-wave buckling. After calibrating the boundary correction coefficient using Q890 steel, the predicted critical clamping forces for 2A14 aluminum alloy and 304 stainless steel were 594 N and 278 N, respectively. The optimized clamping forces enabled smooth cyclic tension–compression curves.

Large-scale thick curved components made of high-strength steel are critical to deep-sea pressure hulls and large structural components of engineering machinery. During forming, these components experience reverse loading upon unloading, and the pronounced Bauschinger effect of high-strength steel significantly compromises springback prediction accuracy, leading to costly die iterations. Existing cyclic tension–compression and shear tests are limited to uniaxial stress states and fail to capture the mechanical behavior under in-plane biaxial cyclic loading. Herein, a cyclic four-point bending method is proposed to characterize the Bauschinger effect of Q890 steel under biaxial cyclic loading. By tailoring the width-to-thickness ratio of the specimens, a series of plane stress states with different initial plastic stress ratios were obtained, covering the dominant stress conditions encountered in forming typical large-scale double-curvature thick plates. Full-field strain evolution during cyclic bending was captured in real time via digital image correlation (DIC), enabling systematic acquisition of equivalent stress–strain curves under various biaxial stress ratios over multiple cycles. As the width-to-thickness ratio increases, both forward and reverse yielding progressively degrade: the equivalent yield strength, forward peak flow stress, and reverse yield strength drop from 1098, 1193, and 742 MPa to 934, 1065, and 685 MPa, respectively. Accordingly, the Bauschinger ratio B, Bauschinger hardening parameter BHP, and Bauschinger energy parameter BEP decrease from 0.479, 0.789, and 4.747 to 0.363, 0.655, and 2.900, respectively, revealing a strong stress-ratio dependence of the Bauschinger effect. Notably, the springback ratio also shows clear dependence on the biaxial stress ratio, loading direction, and cyclic history, indicating that in-plane biaxial stress-state effects should be considered when characterizing the Bauschinger effect and springback behavior of Q890 high-strength steel.

Large-scale asymmetric doubly curved thick shells made of high-strength steel are key components in deep-sea and nuclear pressure vessels. Integral pressing is an important manufacturing method for such components, but it still faces two major challenges: excessive clamping force and poor springback predictability. To address these issues, this study conducts a combined experimental and numerical investigation on a 16 mm thick Q890 high-strength steel plate. First, the through-thickness plastic gradient and cyclic stress–strain response of the material were characterized, and a mixed hardening model incorporating through-thickness gradient plasticity was established. To suppress the lateral force induced by the asymmetric geometry, a blank positioning strategy was proposed, reducing the lateral force to below 2 t (Reduced by 65%). More critically, a striking phenomenon is revealed: during the final 1 mm of the clamping stroke, the forming force surges abruptly from approximately 680 t to 5090 t. Detailed analysis identifies the root cause as the synergistic effects of a sharp increase in contact area, a drastic rise in frictional resistance, and the onset of localized upsetting in regions already in contact with the die. To suppress the load surge while maintaining forming accuracy, a normal-direction over-compensation strategy was proposed. By deliberately increasing the normal compensation, the blank retains a bending-dominant deformation mode at the target clamping position, thereby avoiding the critical contact expansion, frictional buildup, and localized upsetting that trigger the force surge. Through iterative simulations, the optimal die surface is determined, achieving a forming force below 1000 t with a simulated shape deviation within 0.96 mm. Experimental validation using a purpose-built die on a 1000 t press successfully produces the shell with a maximum profile deviation of 1.67 mm, meeting high-accuracy requirements. This work establishes a new paradigm for low-load, high-accuracy forming of thick high-strength steel shells by actively managing contact evolution and deformation mode via normal-direction over-compensation, offering a practical pathway to one-shot tryout success for critical pressure hulls.

Experimental flow stress–strain data under different stress states are often used to calibrate the plastic constitutive model of anisotropic metal materials or identify the appropriate model that is able to reproduce their plastic deformation behavior. Since the experimental stress–strain data are discrete, they need to be mathematically returned to a continuous function to be used to describe an equivalent hardening increment. However, the regression results obtained using existing regression models are not always accurate, especially for stress–strain curves under biaxial stress loading conditions. Therefore, a new regression model is proposed in this paper. The highest-order term in the recommended form of the new model is quadratic, so the functional relationships between stress–strain components can be organized into explicit expressions. All the experimental data of the uniform deformation stage can be substituted into the new model to reasonably reproduce the biaxial experimental stress–strain data. The regression results of experimental data show that the regression accuracy of the new model is greatly improved, and the residual square sum SSE of the regression curves of the new model reduced to less than 50% of the existing three models. The regression results of stress–strain curves show significant differences in describing the yield and plastic flow characteristics of anisotropic metal materials, indicating that accurate regression results are crucial for accurately describing the anisotropic yielding and plastic flow behaviors of anisotropic metal materials.