Free-bending technology represents a novel manufacturing process for forming spatial tubes, enabling the fabrication of complex-axis tubes through continuous adjustment of die positions. As critical geometric parameters for describing tube shapes, curvature and torsion require precise prediction to ensure forming accuracy. This paper presents novel insights into the formation mechanism of free-bending spatial tubes by considering the dual factors of bending plane rotation and additional torque, and establishes a theoretical model for curvature-torsion prediction. To further elaborate the generation mechanisms of additional torque and twist angle—key forming parameters in the theoretical model—during bending die rotation, and their influence on the torsion of the tube axis, a physics-based fully connected neural network (FCNN) prediction model was proposed. By integrating tube material/geometric parameters with equipment process parameters, this model achieves high-accuracy predictions of curvature and torsion while maintaining strong interpretability, overcoming the limitations of intractable theoretical models. Example verification shows that its predicted curvature and torsion exhibit relative errors within 5% and 8%, respectively. Finally, forming experiments of an ellipsoidal-shaped part validated the model's effectiveness in practical manufacturing, demonstrating its capacity to guide spatial tube forming. Additionally, the model provides an alternative approach to determine key forming parameters (e.g., bending moment, torque, twist angle) with significantly higher accuracy and efficiency than traditional theoretical calculations.

This study elucidates the effect of Mn addition (0-1.0 wt%) on the microstructure, mechanical properties and formability of the extruded Mg-1.5Sm-1Zn alloys. All alloys developed a fully recrystallized microstructure after extrusion. Notably, increasing the Mn content resulted in significant grain refinement, reducing the average grain size from 20.32 to 12.05 mu m, and a concurrent weakening texture, with the maximum intensity decreasing from 17.44 to 9.19 m.r.d. These microstructural modifications led to enhanced yield strength (YS) and ultimate tensile strength (UTS). As Mn content increased from 0 to 1.0 wt%, the YS and UTS along the extrusion direction (ED) of Mg-1.5Sm-1Zn-xMn alloy improved from 95.1 to 114.5 MPa and 195.3-218.6 MPa, respectively. However, the elongation to fracture (EL) exhibited a distinct anisotropy, it decreased in the ED but increased in the transverse direction (TD). Most importantly, the Erichsen index (IE), a key indicator of formability, was markedly improved from 2.63 to 4.21 mm with the increase in Mn content from 0 to 1.0 wt%. Mechanistically, this formability enhancement is attributed to the promoted activity of {10-12} tensile twins, the weakening of texture and an increased strain hardening exponent. The synergistic effect of grain refinement, texture weakening and low anisotropic contributed to an optimal combination of strength and formability in the Mg-1.5Sm-1Zn-1Mn alloy.

This paper investigates the deformation behavior of isotropic hardening cylinders under combined tension-torsion loading within the finite deformation elastoplasticity framework. First, the deformation gradient is constructed in polar coordinates. Then, based on the additive decomposition of the deformation rate and the logarithmic objective rate, the governing equations for stress evolution are established, where the deformation characteristics are defined by prescribing the deformation mode. The finite difference method is adopted for stress updating. Combined with boundary conditions and equilibrium equations, the deformation parameters are determined through optimization methods. To validate the proposed analytical model, comprehensive numerical simulations are carried out. The comparison of results demonstrates that the proposed analytical model achieves relatively high accuracy. In general, the coupling effect between tension and torsion promotes axial elongation, and the axial normal stress presents a non-uniform distribution that decreases gradually along the radial direction with slight variation in the elastic region. However, when the deformation becomes sufficiently large, an inhibitory effect arises between the two loadings, and the distribution pattern of axial normal stress changes accordingly. Finally, by neglecting the axial force in the analytical model, the model is directly applied to the analysis of torsional deformation. The results show that axial normal stress still exists even under pure torsional deformation. The axial normal stress decreases along the radial direction and changes from tensile to compressive stress, and the tension-compression transition points under different deformation degrees approximately intersect at one point. The proposed analytical model is capable of effectively capturing the deformation behavior of elastoplastic cylinders.

Uncertainty inherently exists in the spatial tube forming process, and uncertainty quantification (UQ) of the critical wrinkling stress is crucial for precise and stable forming as well as structural safety. However, the inherent strong randomness of geometric characteristics and material mechanical properties, together with limited experimental data, increases the difficulty of UQ. Therefore, for the UQ of random wall thickness and material mechanical property deviations, a wall thickness random field, an elastic modulus interval field, and cross-correlated interval fields of plastic mechanical property parameters are constructed, respectively. In addition, geometric deflection imperfections and loads are regarded as one-dimensional random variables. As the first attempt to apply Heterogeneous Graph Neural Network (HGNN) to the spatial tube forming process considering mixed uncertainties of random field, interval fields and random variables, this study adopts a heterogeneous graph data structure to represent finite element node and element information, and constructs a Node-Element Heterogeneous Graph Neural Network (NE-HGNN) surrogate model to predict the critical wrinkling waveform and critical wrinkling stress of spatial tube forming. Mixed uncertainty propagation is realized by replacing large-scale finite element simulations. Through comparative analysis and ablation studies with a MultiHead Convolutional Neural Network, it is proved that the physical coupling behavior between deformation state and stress state can be effectively represented by heterogeneous graph topology. Finally, the proposed NE-HGNN is used to realize the uncertainty quantification of critical wrinkling stress, and the final results are verified by the theoretical analysis. This work effectively integrates the finite element mesh with mixed uncertainty information into the heterogeneous graph structure, providing a general modeling framework for data-driven forming prediction of complex spatial components considering mixed uncertainties.

Wrinkling instability of spatial tubes caused by inappropriate combinations of process parameters during free bending forming (FBF) severely restricts the forming stability. The correlation mechanism between the critical wrinkling loads (CWL) under bending-torsion coupled and the process window remains unclear, which makes it difficult to effectively control wrinkling defects of spatial tubes FBF. This study establishes a critical wrinkling analysis model under bending-torsion coupled (CWAM-CBT) of spatial tubes to calculate CWL. Based on the energy physical meaning of yielding and combined with the quadratic model of bending-torsion buckling (QM-BTB), approximate upper and lower bounds of buckling strength are proposed as the wrinkling criterion. The effects of load ratio, radius-to-thickness ratio, and tube material properties on the CWL and buckling strength are investigated. The validity of the analysis model is verified through a simplified finite element model. By combining the analysis model with finite element simulation of spatial tubes FBF, the critical wrinkling loading path of spatial tubes is constructed according to the relationship between process parameters and load ratios in the stable forming stage. The critical wrinkling loading path divides the process window into three zones, namely the wrinkling zone, the critical wrinkling zone, and the without wrinkling zone. Experiments on spatial tubes FBF have verified that the critical wrinkling loading path can accurately predict the wrinkling behavior under different process parameters, while further validating the effectiveness of the analytical model. This work enhances the in-depth understanding of the bending-torsion coupled wrinkling mechanism during spatial tubes FBF, thereby providing an effective method for the process optimization of complex spatial tube components.

Dynamically coupled multi-parameter systems with stringent physical constraints are ubiquitous in advanced manufacturing processes. Taking the free bending forming of variable curvature/torsion spatial tubes as an example, high-precision prediction of their forming states faces three fundamental challenges: capturing crossparameter coupling effects, modeling complex temporal dependencies, and enforcing physical consistency. To address these issues, this paper proposes a physics-informed adaptive multi-head attention LSTM (PAMA-LSTM) framework for temporal prediction, which establishes a closed-loop architecture integrating coupling capture, feature fusion, physical constraints, and performance optimization. A customized multi-head attention mechanism adaptively captures dynamic coupling patterns. A cross-head fusion layer integrates features and quantifies the contribution of each attention head to reduce redundancy. A physics-informed loss function integrates multihead attention weights with physical constraints as penalty terms to ensure prediction rationality. A Bayesian strategy optimizes hyperparameters to maximize overall performance. Meanwhile, the model leverages LSTM units to capture the dynamic temporal evolution of the forming process, accurately reflecting the influence of historical states on the current state. Experimental results on free bending forming demonstrate that PAMA-LSTM significantly outperforms baseline and ablation models in curvature/torsion prediction and axis reconstruction. PAMA-LSTM offers a systematic approach to integrating process mechanisms with deep learning in complex forming domains, achieving an engineering balance among accuracy, robustness, and physical consistency. It holds significant implications for intelligent manufacturing and real-time process optimization.

This paper proposes an analytical model for springback prediction in tube free bending, addressing the challenges of strain path evolution, the Bauschinger effect, and nonlinear unloading-reloading behavior. By integrating a modified Chaboche kinematic hardening law with the Yoshida-Amaishi nonlinear elasticity formulation, the complex loading-unloading phenomena in both stable and transition regions can be described effectively. A major innovation is the first-time identification and quantification of the overshoot/undershoot phenomenon occurring in transition regions. In addition, a novel strain path function is developed to describe the resulting oscillatory behavior. Systematic experimental and numerical validations demonstrate the model's accuracy, outperforming traditional isotropic approaches. The study further quantifies the influence of process parameters (e.g., die offset difference, feeding velocity) and die structural parameters (e.g., chamfer radii, dietube clearance) through multi-factor response surface analysis. This analysis reveals how these parameters affect the overshoot amplitude and the damping characteristics of the strain path. The framework advances the understanding of springback mechanisms under complex strain paths and offers a fresh analytical perspective and practical potential for parameter optimization aimed at reducing defects such as indentation.

Bending and torsion processes are commonly used for the forming of spatial tubes. However, buckling and wrinkling pose a significant challenge to the high-quality and stable forming of spatial tubes. To reveal the interaction mechanism of bending-torsion buckling (BTB) during the forming process, a quadratic model of BTB under plastic buckling instability was proposed. According to the buckling phenomena of simulation and experiment, the BTB state was divided into three zones, namely Zone I (torsion-dominated zone), Zone II (bending-torsion transition zone), and Zone III (bending-dominated zone). The characteristics of bending-torsion response changes, buckling wrinkle features, and critical load variation in the three zones were studied. Considering the complex interaction of bending and torsional buckling, an analytical method for the critical load of tubes under combined bending-torsion action has been provided. This method is based on the energy approach, incorporating pure bending and pure torsion buckling, along with the quadratic model of BTB. The effectiveness of the proposed theoretical model was verified by finite element (FE) simulation, and the influence of tube geometric characteristics, material parameters, and initial imperfection amplitude on the BTB interaction was discussed.

Existing spline partitioning methods exhibit poor applicability to the free-bending process. Addressing this limitation, this paper innovatively proposes a spline partitioning and processing method that explicitly considers the transition section. Our approach accounts for the influence of the transition section length within a pipe fitting on the axis deviation of the formed part. The method uniformly partitions the spline portion of the pipe fitting, using the maximum transition section length as the partitioning unit. Furthermore, we analyze the causes of deviation between the spliced model and the theoretical model within the spline region after partitioning. To address this deviation, we employ a combination of planar arcs, positioning chords, and variable chord angles to reconstruct the spline portion. This ensures the reconstruction error between the spliced model and the theoretical model remains within acceptable limits. Additionally, the relationship between the variation in the tangent vector angle across the spline and the vertical displacement of the bending die is derived, thereby yielding the necessary processing parameters for forming this section. Validation through application to typical parts confirms the effectiveness of this partitioning and processing method in actual pipe fitting forming.

Lattice structures have drawn significant interest owing to their exceptional mechanical properties, e.g. lightweight, strong, and tough performance. Here, inspired by the biostructure of the beetle elytra, a new tube-plate hybrid lattice structure (TPHL) is proposed. The TPHL lattice specimens are fabricated by the selective laser melting (SLM) technique, and the compression mechanical properties are analysed. The compression responses of the TPHL are compared with conventional Octet (OCT), simple cubic (SC), and simple tube (TUBE) lattice structures. An optimisation model is developed to further improve the energy absorption characteristics. The TPHL lattice structure exhibits maximum 50.30% (relative density is 0.10) higher specific energy absorption (SEA) than SC pure plate lattice, and maximum 42.25% $\lpar \bar{\rho } = 0.18\rpar$(rho=0.18) higher specific energy absorption than OCT pure plate lattice. The novel lattice structure shows the transition of the deformation modes and dual energy-absorbing plateaus. The enhanced energy absorption is mainly ascribed to the interaction of the cross-assembled tubes and plates in the second plateau. Besides, the configuration of the TPHL lattice structure after optimisation demonstrates significantly enhanced energy absorption characteristics. The bioinspired design strategy and potential mechanical mechanism provide useful guidance for designing lattice structures with exceptional energy absorption properties.

In this paper, the equilibrium problem of incompressible hyperelastic circular tubes under combined bending and torsional deformation is studied. By using polar coordinates on the axis, a three-dimensional kinematic model of the longitudinal bending of a circular tube with wall thickness variation is established. Due to the adoption of the semi-inverse method, the displacement field specified in the model contains three unknown functions. Lagrangian and Eulerian analyses are performed on the model to determine the (first) Piola-Kirchhoff stress and Cauchy stress, clarify the equilibrium equations and boundary conditions, and thus solve for the unknown parameters in the kinematic model. In addition, the established model is validated by comparing it with the finite element (FE) results. The results show that the established model is effective and exhibits high accuracy. It describes the combined deformation of bending and torsion quite well and obtains the axial normal stress and torsional shear stress with relatively high precision. It can characterize the distribution of the wall thickness and the strain-neutral layer (SNL) after deformation with quite high precision. According to the deformation angle, the corresponding bending moment and torque are obtained, and the relative errors are all at a low level. Finally, the axial elongation rates of tubes with different specifications are analyzed, and it is found that they increase with the increase of the outer diameter or the inner diameter.

Tubular components subjected to combined bending-torsion loading exhibit complex elastoplastic deformation mechanisms, particularly the phenomenon of neutral layer shifting (NLS), which critically affects forming quality and springback prediction. This study proposes a novel and comprehensive analytical-numerical framework for elastoplastic NLS under combined bending-torsion loading, addressing key limitations in existing models by explicitly incorporating axial thrust and the torsional influence on bending deformation. For the first time, the NL concave reconstruction behavior under significant torsion is identified and a newly defined slope parameter is introduced to quantitatively characterize it. As torsional deformation intensifies, the NL is shown to transition from a parallel shift to a concave profile, markedly influencing strain and stress distributions. Additionally, the model compensates for the omission of NLS in prior elastoplastic moment calculations for bending and torsion. The results reveal that the degree of NL concavity is directly correlated with the torsional angle and curvature radius. Finite element (FE) simulations and free-bending experiments validate the model, demonstrating its enhanced accuracy in predicting NL displacement, springback, and wall thickness variations.

As a foundational configuration of spatial tubes, the spiral metal tube has been widely used in the industrial tube line system. Unfortunately, its precise forming remains a challenge up till now. In this paper, an improved analytical model is presented to reveal the forming mechanism of the spiral tube taking various processing parameters into account and verified by the FE simulations and four-axis free-bending (FFB) bending experiments. The method of springback prediction for the spatial configuration is given, and the transformation between four-axis and six-axis free bending process is provided. The conclusions can be drawn that the curvature radius primarily decreases with the increment of the offset, and the pitch mainly diminishes with the growth of the ratio defined as pushing velocity versus angular velocity of the panel. When the ratio is constant, the forming result remains unchanged, which is consistent with the theoretical model. Meanwhile, the evolution mechanism of forming quality is explored to provide a certain reference for the actual forming process. For the same tube configuration, reduction/thickening of wall thickness and cross-section distortion can be improved with the synchronous increase of the ratio of pushing velocity and angular velocity. It was innovatively found that the nonuniform distribution of shear stress under lower loading velocities is the dominant reason for the lower forming quality. This research effectively reveals the spiral tube forming mechanism and the evolution mechanism of forming quality, which establishes the foundation for analyzing the forming issues of complex spatial tubes in this field.

This paper proposes an innovative multi-scale method for determining gas pressure parameters of superplastic forming, which is based on the quantitative relationship between the grain growth mechanism and fracture mechanism of Ti-6Al-4V alloy. The high-temperature tensile tests were conducted on the material at temperatures ranging from 700, 800, 840, 890, 920, and 950°C, strain rates were selected as 10-2∼10-4/s. The grain size measurements were observed using electron back-scatter diffraction (EBSD). Particularly, the relation between grain size changes and fracture behaviour is specifically discovered using a physically-based dynamic material model (DMM), and the grain size thresholds for each forming limit are proposed. The physical fracture mechanism is named the "Grain growth based fracture (GGBF)" mechanism. Furthermore, an innovative method based on the GGBF mechanism is proposed to design the superplastic forming loading, and practical four-layer hollow structures experiments are applied to validate the fracture mechanism in superplastic forming. In total, A superplastic forming GGBF mechanism has been verified, and it is expected to be helpful for shape and property control in the forming process of complex structures.

Spatial tubes, known for their attributes of lightweight, large section modulus, and high strength, find extensive applications across various industries. Nevertheless, in the course of forming spatial tubes, springback poses a significant challenge in enhancing the forming quality. In this paper, the bound approximations for the combined bending and twisting of circular tubes employing the power-hardening material model are deduced innovatively. Drawing upon the boundary approximation theory, the interactive mechanism of bending and twisting is meticulously examined. The forming principles of the four-axis free-bending (FFB) are expounded. Concurrently, an innovative method for predicting springback, based on the established bound approximations within the framework of total plasticity theory, is introduced, which holds significant importance for addressing combined bending and torsion issues in engineering applications. Noteworthy findings reveal that the interaction between bending and twisting exhibits a predominant sensitivity to the hardening exponent and the higher the material has, the less pronounced the interaction will be. The augmentation of torsion contributes to mitigating the springback resulting from bending, and conversely, a similar effect is observed with the influence of bending on torsion. These findings contribute significantly to the understanding of combined bending and twisting problems. The proportionality coefficients of bending and twisting, denoted as and , are defined and investigated via comprehensive finite element (FE) simulations. Furthermore, this method of springback prediction is corroborated by FE simulations as well as the FFB experiments.

With the improvement of application requirements, the combination of precise shape and high performance of tube components has become a burning issue. This work investigates the free-bending process of 6063 aluminum alloy tubes using cross-scale numerical modeling. The cross-scale framework integrates macroscopic finite element model (FEM) and crystal plasticity finite element model (CPFEM) through strain history. CPFEM exhibits excellent agreement with the macroscopic FEM and experimental results for both the Mises stress and texture evolution. Predictions indicate that as bending deformation increases, the volume fractions of the initial Cube texture decrease, while the Goss texture component increases. The overall texture strength continuously decreases. Meanwhile, slip mode plays a critical role in texture evolution, causing similar trends in the inner and outer bend regions. Additionally, the findings from the cross-scale simulation accurately predict the detailed texture evolution of the 6063 aluminum alloy tube under various feeding speeds. The development of Goss texture in various forming regions and the formation of substructures within Goss-oriented grains are primary factors contributing to reduced tube formability, which could illustrate the primary mechanisms for variation in tube bendability effectively. The proposed cross-scale method lays the foundation for research on complex spatial tube components as well. Moreover, cross-scale simulation facilitates the prediction of macroscopic deformation and microstructural evolution in critical regions of tube components, allowing for the optimization of bending processes based on cross-scale simulation results.

Lattice structures have shown tremendous prospects in engineering fields, because of the ultralight, strong and toughness properties. In this paper, a novel configuration of lattice structure (GSIBCC) inspired by the hierarchical skeleton system of glass sponges is proposed. The new configuration of the unit cell is based on modifying the inner cross struts of the body-centered cubic (BCC) lattice, by considering the double diagonal reinforcements and hybridization of unit cells. The compression properties and deformation mechanism of the GSIBCC lattice structure are compared with BCC, OCT (Octet) and other glass sponge inspired lattices. A multi-objective optimization method is established, for maximizing the specific energy absorption (SEA) and simultaneously reducing the compression strength. The novel GSIBCC lattice exhibits superior specific energy absorption than BCC, OCT, and other glass sponge inspired lattices. For example, GSIBCC shows maximum 145.06% improvement (rho=0.124) of SEA with respect to BCC, and maximum 117.4% improvement (rho=0.124) of SEA with respect to OCT. The novel lattice exhibits the whole deformation type and obvious second stress reinforcement effect. Besides, the mechanical properties of GSIBCC are further improved using the multi-objective optimization. The reported biomimicry design strategy, deformation and failure mechanism, and multi-objective optimization method will be beneficial for enriching the lattice system and promoting the multifunctional applications of lattice structures in engineering fields.

The finned special-shaped tube (FSST) has better heat dissipation, compression resistance, and deformation resistance than round and square tubes, making them more suitable for meeting the application needs of new structural-functional integrated heat dissipation pipelines in high-end equipment such as aerospace engines and gas turbines. Nevertheless, the intricate cross-sectional structure of FSST makes it difficult to form, making its spatial spiral forming unachievable. In this work, firstly, the FSST spatial spiral-forming method based on three-axis free bending technology was established and its forming principle was analyzed. Secondly, Based on the Frenet framework, a workable method for characterizing the parameters of FSST spiral forming after springback was presented. Thirdly, an analytical model for solving the bending moment and torque on the FSST cross-section in fully plastic state was established during the bending-torsional coupling forming. Then, the reliability of the forming method and the accuracy of the analytical model were verified through the FE method and actual experiments. The FE model also showed good agreement with the actual experiments. Finally, the cross-sectional deformation of FSST throughout the spiral-forming process was analyzed using the FE model. In short, the present study fills a gap in the research of bending-torsional coupling forming of complex section tubes.

Free bending technology is an important bending process for forming spatial tubes with variable curvature. By continuously adjusting the position of the die, tube axis with complex shapes can be formed, so accurately obtaining process parameters is crucial for precisely forming complex tubes. According to the geometric characteristics of tubes formed by free bending technology, the tubes are divided into stable segments with constant curvature and transitional segments with variable curvature, and the process parameters and geometric parameters of the formed tubes are described by the parameter sets. In this paper, based on the knowledge base, a new acquisition strategy was proposed to obtain the process parameters of spatial tubes with variable curvature. Aim at forming transitional tubes, in order to establish an effective correlation between process and geometric parameters, a surrogate model based on SVD-RBF has been proposed to quickly predict the axis shape of the transitional tube. In addition, applying this strategy to the forming experiment of the typical tube, it was found that the shape deviation Emax/L is 0.7806

Spatial tubes, which possess the characteristics of lightweight, large section modulus, and high strength, are widely used in various industries. However, during the forming process of spatial tubes, springback poses a significant challenge in enhancing the forming quality. In this paper, the forming mechanism of circular tube components, formed through the four-axis free-bending (FFB) equipment is our main concern. The bound approximations for the combined bending and twisting of circular tubes employing the power-hardening material model are deduced. Based on the boundary approximation theory, the interactive influence between bending and twisting is discussed. Meanwhile, a new strategy for the springback prediction depending on the bound approximations in the frame of total plasticity theory is provided. Some interesting results show that the interaction between bending and twisting is merely sensitive to the hardening exponent n kind of material parameters and the higher the material has, the less obvious the interaction will be. The increasing torsion could resist the springback of bending and in contrast, so does the effect of bending on torsion. The bending and twisting proportionality coefficients λM and λT are defined and explored through FE simulations. Further, this method of springback prediction is validated by FE simulations and FFB experiments.