Sheet Bending Research Articles

Bending of sheets and profiles on a four-roll machine for rocket bodies, tubular and frame products. Part 8

The theory of bending is developed and the calculation of the parameters of the strain-stress state at the stages of pre-bending, calibration, straightening, bending of the straightened section and bending of the following sections is carried out, taking into account the hardening of the workpiece on a roller machine. Deformations, stresses and forces acting on the workpiece from the side of the rolls are studied by CAD/CAE modeling. The criteria for crack formation, low accuracy and excessive springback of the part after these processing steps are determined. Recommendations are given to eliminate these defects. Keywords: sheet stamping, workpiece, bending, roll machine, pre-bending, calibration, straightening, bending theory, CAD/CAE modeling. dr_zharkov_v_a@mail.ru

Analysis on the Transition Zone of Deformation in Sheet & Plate Bending Processes While Using FEA

Analysis on the Transition Zone of Deformation in Sheet & Plate Bending Processes While Using FEA

Experimental comparison of straight flanging and rotary die bending based on springback

Springback in sheet bending is a well-defined phenomenon; however, variation of springback is difficult to control causing quality problems in especially mass-produced goods such as home appliances. As an alternative to straight flanging, the rotary die bending process offers reduced springback as well as reduced geometric variation; however, there is little knowledge in the literature. The effects of process parameters on the springback behavior of straight flanging and rotary die bending as applied to home appliance side panels are investigated experimentally. For each flange bending method, effects of die radius, punch-die clearance, rolling direction, flange length, and material supplier on springback are tested on EN DC01 carbon and SAE 430 stainless steel sheets. A material-wise factorial experimental design was applied to investigate the factor interactions as well as the main effects using ANOVA. In both methods, die radius was the most dominant factor on springback, clearance being the second, and the inevitable material property variations being the third one. Nevertheless, in rotary die bending, springback values were smaller with significantly less scatter compared to straight flanging. Consequently, rotary die bending is a much more preferable process especially in mass production performed with narrow profit margins.

Investigation of over-bending defect in the cold roll forming of U-channel section using experimental and numerical methods

In spite of product quality increase in the cold roll forming process by previous practical researches for defects prevention, there are some ill-considered defects such as over-bending, which diminished the product quality in the open section products of this process. This defect which happens by superfluous bending of sheet in the forming stand not only lead to defective products, but also trigger other defects such as edge wrinkling. Since in an elaborate process such as cold roll forming, forming parameters play an active role in defect prevention, the effect of some important parameters is investigated on the over-bending defect and product bending angle by doing 68 experimental tests and numerical simulations in the present study. The list of parameters which are investigated includes bend angle increment, flange width, strip thickness, radius of bend, strength of the materials, and inter-distance between successive stands. In addition, the reason behind the effect of each parameter on the accuracy of the bending angle is laid out. Results show that over-bending defect can be compensated or even eliminated by decreasing the bending angle in each stand, a technique called bending angle increment. Increasing the number of forming stands from two to five causes the over-bending to decrease from 6° to 0°. With bending angle increment being the most impactful factor, bending radius, flange width, and strip thickness have a decreasing impact on over-bending. This study also brings forward a reverse relationship between the strength of the material and the intensity of over-bending. The inter-distance between successive stands was found to have the least effect on over-bending. Results highlight the importance of pre-form rolls at the beginning of the roll forming line. Without the usage of pre-form rolls, the folding of strips on a 60° angle, cannot be done in one stand.

Moment at elastic-plastic bending of steel sheet. Part 2. Cubic approximation of steel's hardening zone

The classical approximations by P. Ludwik and A. Nadai of the steel hardening zone do not accurately describe the plastic deformation of steel. That often leads to the significant errors (defects) in the final form of metal products made from a steel sheet during its forming (based on the preliminary analytical and numerical calculations of the given model of metallurgical production) on the presses and dies. For example, the Nadai’s curve does not pass through the ultimate strength’s point of the experimental curve, signifi cantly exceeding the ultimate strength at this point, which is not permissible at calculating stresses and deformations. The Ludwik’s curve does not take into account the elastic deformation zone of the steel (immediately has a stress equal to the yield strength at zero relative deformation) and does not have the maximum (observed on the experimental curve) at the point of the ultimate strength. To eliminate the above-mentioned disadvantages, in the first published part of the paper, the author considered the parabolic approximations of the steel hardening zone in the form of the second-order polynomials, which satisfy three boundary conditions. The constructed parabolic approximations of the steel hardening zone turned out to be an order of magnitude more accurate than the classical approximations by Ludwik and Nadai. In this paper, the author considers even more exact cubic approximations of the steel hardening zone with the same supporting parameters of the experimental curve of the steel hardening zone. In this case, the cubic approximations already satisfy four boundary conditions. The constructed cubic approximations of the steel hardening zone are two orders of magnitude more accurate than the classical approximations by Ludwik and Nadai of the steel hardening zone.

Bending and twisting with a pinch: Shape morphing of creased sheets

In this letter, we introduce a unique behavior seen in creased sheets where localized changes in the folding (i.e., a pinch) result in global bending and twisting deformations. Using isometric deformation theory, we identify the connections between pinching, crease curvature, and crease torsion that begin to explain the shape-morphing behavior. Given the limitations of isometric deformations, we expand our understanding of the behavior using a mechanics-based bar and hinge model of creased sheets, where the sheet is allowed to stretch. With this tool, we found that the increase in crease curvature and torsion due to pinching are proportional to the curvature of the crease before folding and that curved creases facilitate the bending and twisting. Additionally, we explored the bending and twisting of sheets with more than one crease. We found that sheets with an even number of creases generate more intense twisting than those with an odd number of creases and experience twisting even when the creases are straight. The number of creases had little effect on the pinch-induced bending of the origami. The stiffness of the sheets had little effect on the amount of bending and twisting, but greater spacing between the creases resulted in more bending with little effect on the twisting. Based on these results, we created a framework to design crease patterns to have desirable bending and twisting that can be coupled or not, and demonstrated this programmability with simulations and by pinching physical prototypes. Our findings enable shape morphing of creased sheets with a low-complexity input and a versatile output.

Bauschinger Effect, Masing Principle and Hencky Theorem for Bending Moment at Repeated Alternating-Sign Bending of Steel Sheet

In the production of the large-diameter thick-walled steel pipes (with a diameter of 1020-1420 mm and with a wall thickness of up to 32-48 mm from the high-strength steels of the strength class K50-K65) under the SMS Meer technology for the main gas-and-oil pipelines, the steel sheet is bent several times sequentially during the technological transitions from one press to another. At the elastoplastic alternating-sign bends of the sheet, the yield strength of the bending moment of the sheet changes from one bend to another, which causes great difficulties for the metallurgical technologists when they calculate the curvature of the tube’s wall and the final diameter of the pipe. To solve this problem, we propose the new analytical method for calculating the bending moment and curvature of a steel sheet under the low-cycle alternating-sign bending.

Bending properties of sandwich sheets with metallic face sheets and additively manufactured 3D CFRP lattice cores

• Sandwich sheets with representative shell-lattice, truss-lattice and plate-lattice cores are proposed. • Effects of core topologies on mechanical properties and bendability of sandwich sheets are clarified. • Theoretical predictions of failure modes during bending of sandwich sheets with 3D lattice cores. • Bendable sandwich sheets with 3D lattice cores are successfully designed and produced. • Bendable sandwich sheets with multifunctional application potentials. To improve structural performance, bendability and potential functionality of metal-based sandwich sheets, the 3D lattice cores were sandwiched between thin metallic face sheets. The bending properties of sandwich sheets with 3D printed carbon fiber reinforced plastic (CFRP) lattice cores originating from basic topologies of spherical shell, tetrahedral truss and tetrahedral plate were systematically investigated. The effects of core topologies, core relative densities, core heights, face sheet thicknesses on structural properties were clarified. The common failure modes during bending of sandwich sheets, such as face buckling and shear failure of core, were deeply investigated by theoretical models and experimental tests. At a prescribed radius of 60 mm, the sandwich sheets with the bilayered dome, octet truss and plate lattice cores of relative density of 50 %, height of 6 mm and face sheet thickness of 0.5 mm are bendable. This study demonstrates the feasibility of design and production of bendable sandwich sheets with 3D lattice cores based on the theoretical and experimental validations. The designed bendable sandwich sheets can be adopted to replace conventional heavy monolithic metal sheets in various engineering applications, which is anticipated to fulfill the high demand for lightweight functional materials.

Bending Stiffness of Circular Multilayer van der Waals Material Sheets

Abstract We study the bending stiffness of symmetrically bent circular multilayer van der Waals (vdW) material sheets, which correspond to the nonisometric configuration in bulge tests. Frenkel sinusoidal function is employed to describe the periodic interlayer tractions due to the lattice structure nature and the bending stiffness of sheets is theoretically extracted via an energetic consideration. Our quantitative prediction shows good agreement with recent experimental results, where the bending stiffness of different types of sheets with the comparable thickness could follow a trend opposite to their Young’s moduli. On the basis of our model, we propose that this trend may experience a transition as the thickness decreases. Apart from the apparent effects of Young’s modulus and interlayer shear strength, the interlayer distance is also found to have an important impact on the bending stiffness. In addition, according to our analysis on the size effect, the bending stiffness of such symmetrically bent circular sheets can steadily own a relatively large value, in contrast to the cases of isometric deformations.

Anomalous elasticity and damping in covalently cross-linked graphene aerogels

Elasticity in materials is a phenomenon that provides a basis for widespread practical applications in engineering, medicine, and electronics. Most of the conventional materials can withstand only small deformations within the elastic limit, typically below 5% of their original size. Here, we report a graphene aerogel made of covalently cross-linked graphene sheets that exhibits anomalous superelastic behavior up to 92% of compressive and 68% tensile strain. We show that the graphene aerogel has a nonlinear stress-strain characteristic with the compressive and tensile yield strength of 4.5 GPa and 0.6 MPa, respectively. By considering the elastic bending of graphene sheets and buckle folding of pore walls, we develop a quantitative origami model that describes the stress-strain behavior of the aerogel. In addition, we analyze the mechanical oscillations of the graphene aerogel, observing superfast vibration damping within a time scale of 50–250 ns. Our study demonstrates the unusual coexistence of superelasticity and superfast damping within a cellular material with atomically thin pore walls, a phenomenon that does not occur in bulk elastic materials described by Hook’s law.

Finding the pad load to suppress wrinkling in free bending of ultra-high tensile strength steel sheets

The critical pad load to suppress wrinkling in free bending is derived by linking the pad lifting behaviour and the wrinkle disappearing condition that depends on the clearance between the punch and the blank generated by pad lifting at the early stage of bending. The clearance is estimated based on the simulated results that the contacting zone of the blank with the pad at the early stage of bending is confined to the vicinity of the punch shoulder. The usefulness of the critical pad load is confirmed by forming experiments of a T-shaped product from high strength steel sheets.

The Influence of anisotropy on the vibration behaviour of S600Mc sheet metal

Sheet metal anisotropy is the directional dependence of mechanical properties. It is a critical factor that must be considered when using numerical simulation to predict any plastic deformation manufacturing process. Sheet metals prove anisotropic plastic behaves due to crystallographic texture caused by progressive rolling steps, Banabic D. et al. (2000). Cold bending of steel sheets is a widely used manufacturing process in the automotive industry due to its cost efficiency. By avoiding line heating, the oxidative process of steel is thus avoided. The automotive industry's primary application of sheet metal includes doors, fenders, bumpers, roof panels, and seat frames. In this paper, test specimens were laser cut at orientations θ = 0°, 45°, and 90° to the rolling direction. The specimens were subjected to forced vibration on an electromechanical shaker, and the frequency response amplitude was measured using accelerometers. Natural frequency and Q-factors were discussed. Experimental data are used for viscous damping coefficients (alpha and beta) for each direction of the specimen. The measured coefficients are then used to validate each type's finite element, numerical models. The results show the level of dependency between the structural damping and anisotropy of the laminated sheet metal and the influence on the high cycle fatigue performance.

Self-Folding Rigid Origami Based on Auxetic Kirigami

Kirigami is a transformable system obtained by adding cuts on a sheet material and bending or folding the sheet. It is reported that when a tensile force is applied to a thin sheet with a slit pattern, three-dimensional corrugated surfaces are induced by the out-of-plane buckling. We aim to apply buckling-induced kirigami to architectural- scale deployable structures by applying a rigid origami model, i. e., a kinematic model in which rigid bodies are connected by rotating hinges, to such kirigami systems. We propose a parametric family of kirigami structures where two crease lines are added to kirigami connections. We show that the structures form one-DOF mechanisms by showing the kinematic equivalence to a degree-4 single vertex rigid origami. Also, we show that the structure within a specific parameter range can expand in two principal directions, and thus macroscopically forms an auxetic (Poisson's ratio becomes negative) material through an analysis using singular value decomposition. Furthermore, we propose a family of auxetic cellular materials obtained by assembling these structures in multiple layers. Then, we show some results in experiments on self-folding. Finally, we propose a method of using thick panels for this structure.

Structural and vibrational properties of amines adsorbed on graphene

Graphene is a promising material whose properties can be tailored by adsorption of molecules on its surface. Amines, with the -NH2 group, act as an electron donating adsorbate. We have investigated via first principles (density functional theory) the adsorption of three different amines, namely aniline, benzylamine and phenethylamine, on graphene sheets and their subsequent effects on graphene’s structure, vibrational modes position and natural bonding orbitals (NBO) charge. All the amines physically adsorb on graphene, with aniline forming the strongest bond (Adsorption energy = 21.004 kJ mol −1), whereby the bending of the planar graphene sheet is observed due to aniline adsorption. However, after adsorption of benzylamine and phenethylamine, the graphene sheet’s structure does not change. The change in structure is reflected by the change in the position of the vibrational modes as well as on the NBO charge and the highest occupied molecular orbital-lowest unoccupied molecular orbital gap. Aniline’s experimental spectrum shows agreement with the results obtained from the simulation to within 3% error.

Bending of sheets and profiles on a four-roll machine for rocket bodies, pipe and frame products. Part 7

The theory and calculation of the parameters of the strain-stress state at the stages of pre-bending, calibration, straightening, bending of a straightened section and bending of the subsequent sections, taking into account the hardening of the billet on a roller machine, is developed. Deformations, stresses and forces acting on the billet from the rolls were investigated by CAD/CAE-modeling. Criteria for the formation of cracks, low accuracy and excessive springback of the part after these stages of processing are determined. Recommendations for the elimination of these defects are given. Keywords: sheet stamping, billet, bending, roller machine, pre-bending, calibration, straightening, CAD/CAE modeling. dr_zharkov_v_a@mail.ru

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.

Layered shock-resistant element parts shape change process selection and modeling

An impact-resistant layered element consisting of two outer layers from highly rigid material and an inner layer from viscoelastic material has been developed. The item reduces the barring effect on the protected object. The design peculiarity is that the outer part has a bend with a deflection arrow within 10… 15 thicknesses, and has a connection of the outer layers from high-stiff material on opposite edges with staples from plastic material, which during plastic deformation flows into the edge holes coaxially in the outer layers, on the inner side of the impact-resistant element is attached a shock-absorbing layer from elastic foamed polymeric material, the back surface of which corresponds to the surface of the protected object. For the parts manufacture it has been developed bending sheet parts method in which the bending the part shelves with a bending element with their subsequent straightening. The aim is to increase the process productivity and the geometric dimensions’ accuracy of the part. Modeling the process of parts spontaneous forming "Impact-resistant element upper sheet" on the reverse and direct schemes is performed by the finite element method in the AnSYS / AutoDYN system. The study purpose is to develop technology and modeling the process of the impact-resistant element sheet parts deformation.

Acoustic Emission during Press-Brake Bending of SS 304L Sheets and its Correlation with Residual Stress Distribution after Bending

Acoustic Emission during Press-Brake Bending of SS 304L Sheets and its Correlation with Residual Stress Distribution after Bending

Experimental and numerical investigations of springback and residual stresses in bending of a three-ply clad sheet

In the present work, springback behaviour of a three-ply clad sheet metal, comprising of layers of SS430 and SS304 sandwiched with a layer of AA1050 is investigated in V-bending by using analytical, experimental and simulation techniques. The developed analytical model is based on theory of bending using Hill’s anisotropic yield criterion. The tensile properties of the clad sheet and individual layers oriented at three different directions w.r.t. the rolling direction are characterized. The tensile properties of the individual layers are used in the material model of analytical and numerical predictions of the springback. It is observed that the samples of the clad sheet which are transverse to the rolling direction, exhibit highest springback values due to higher tensile strength of the sheet when compared with the results acquired for other two orientations w.r.t. the rolling direction. These results are endorsed by the springback results obtained from analytical and simulation methods. The effect of sheet setting on the die during bending is also investigated using different techniques. The resulting longitudinal stresses before and after springback are analysed on inner and outer layers of the tested samples using experimental and numerical simulation procedures. In both the cases of sheet settings, the results of residual stress after springback predicted by simulations agree with the experimental results except a few cases.

Three-layer structure hot bending/diffusion bonding process of reactive sintering Ti-22Al-25Nb alloy and its load response at high temperature

Three-layer structure part as a ideal structure part, that had light weight and enough strength to be widely used, was prepared combining hot bending and diffusion bonding processes in this paper. The Ti-22Al-25Nb sintered alloy that owned better using temperature was applied to manufacture three-layer structure part. The forming processes of manufacturing three-layer structure was divided into hot bending forming of the core sheet and diffusion bonding of three layers sheets. Firstly, the hot bending of core sheet was performed at 1423K for 10MPa in a vacuum furnace. Secondly, the diffusion bonding of three layers sheets was carried out at 1473K for 120min and 10MPa. Furthermore, in order to evaluate the quality and performances of three-layer structure, the microstructure of bonding joint of three layers sheets was analyzed by SEM, and the properties of three-layer structure part were tested at 1073K by compressing test and three-point bending test. Compressing load and compressing strength were 9014N and 10MPa, respectively. Bending strength was up to 54MPa. In addition, the experimental results also indicated that three-layer structure that prepared using the Ti-22Al-25Nb sintered alloy owned good properties.