Search

In conventional bulging process, it is usually assumed that sheet metal deforms under normal pressure regardless of the frictional force between the sheet and the pressure-carrying medium. However, there is a phenomenon that sheet metal is bulged under the combined action of normal pressure and beneficial frictional force, which is resulted from the special characteristics of the pressure-carrying medium. Effects of constant tangential stress (beneficial frictional force) caused by rubber or urethane have been studied analytically and experimentally in previous works. Yet, the tangential adhesive stress imposed on sheet metal by viscous medium is correlated with its flow velocity due to its rate-dependent property, which can be controlled and measured by loading equipment. This kind of rate-dependent tangential adhesive stress has been taken into account to establish an analytical model to analyze its effects on the viscous pressure bulging (VPB) process. Then a numerical approach is presented to solve the problem, which utilizes incremental strain to start an iteration loop by considering different magnitudes of adhesive stress. Results have shown that rate-dependent beneficial frictional force in VPB process can promote longitudinal deformation of the bulged part to help make the strain distribution more uniform. The location of maximum thickness strain point deviates from the pole the outer radius, which means that when polar strains remain at the same level, higher bulging height can be obtained for larger magnitude of rate-dependent tangential stress; this characteristic mainly accounts for the postponement of fracture instability of sheet metal in VPB. The theoretical predictions of strain components and geometric parameters are analyzed and compared with experimental results. The comparisons have shown good agreement to validate the analytical model. [ABSTRACT FROM AUTHOR]

For a rigid-plastic solid obeying Tresca's yield criterion which deforms by the mechanism of extended slip, it conforms to the principle of rotation-rate continuity if the yield shear stress remains constant. It has been proved on this basis that the divergence of the strain-rate tensor is zero and the velocity vector field obeys the Laplace equation in the deformation region. This property can lead to two general solutions, one is derived into three-dimensional slip-line field theory; the other is applied to solve the problem of transverse deflection of a clamped plate deflected by a flat-ended rigid punch. For concentric loading conditions explicit analytical solutions can be obtained directly, while for eccentric loading conditions the method of fundamental solutions (MFS) is applied in the deformation region which is seen as a doubly-connected domain obeying the harmonic equation. The punching force needed for the deflection and strain components are then calculated. It has been obtained that the contour lines and the lines of steepest descent are two principle lines of any point in the deformation region, so the method of steepest descent is used to depict the trajectories of the principle lines. Numerical calculations have been made using commercial finite element software ANSYS-LSDYNA. It turns out that the results obtained from numerical calculations fit quite well with the analytical results based on the principle of rotation-rate continuity and MFS. Finally, NURBS curves and Coons surface are used to construct the configurations of slip-planes in this problem, where the normal of slip-planes and the planes on which the two families of slip-lines located are both curved. [ABSTRACT FROM AUTHOR]

• A general form of kinematically admissible velocity field has been proposed for three-dimensional upset forging of elliptical disks and rings. • Three control functions with free parameters have been introduced to take consideration into sidewise spread, lateral bulging and movement of neutral surface in the upset forging of elliptical rings. • By changing the proposed three control functions, different forms of the assumed general kinematically admissible velocity fields can be derived for the upset forging of various shapes of disks and rings. • The forging load and deformed profiles of the billet can be calculated by minimizing the total plastic dissipation power using the upper-bound method and simplex algorithm. An analysis is carried out for three-dimensional upset forging of elliptical disks and rings based on the upper-bound method. A general form of kinematically admissible velocity field has been proposed by introducing three control functions, each of which contains a free parameter, thus the sidewise spread, lateral bulging along thickness direction as well as movement of neutral surface which occurs in the upset forging of elliptical rings can all be taken into consideration. It is shown that the kinematically admissible velocity fields proposed in previous references by other researchers can be obtained by choosing different control functions in the proposed general form. By optimizing the free parameters using the simplex algorithm in the upper-bound method, the forging load and deformed profiles of the billet can be calculated at certain stages of deformation. Calculation for different billet shapes and friction conditions have been conducted, the obtained theoretical results are in good agreement with the experimental results in previous studies and results obtained from finite element analysis carried out in this paper. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Generalized solution behavior of transverse deflection of a clamped plate subjected to eccentric and multiple punches loading has been found. • The method of fundamental solutions (MFS) has been introduced to find the solution of the Laplace equation in a multi-connected domain. • The ratio of punch section area to plate section area and the deviation distance of the punch center from the plate center will both influence the punching force. For most of the studies concerning about the transverse deflection of plates subjected to the loading of a rigid punch, the sections of the punch and the plate are usually circular and concentric. However, eccentric loading conditions in which the punch and the plate may not be circular and concentric have seldom been discussed. This paper firstly studied the solution behavior for a rigid-plastic clamped plate under quasi-static eccentric loading conditions based on the theory of rotation-rate continuity and the method of fundamental solutions (MFS). For eccentric loading, four types of loading conditions have been applied: circular punch vs circular plate (C C), circular punch vs elliptical plate (C-E), elliptical punch vs circular plate (E-C) and elliptical punch vs elliptical plate (E-E). The load position of the punch is also arbitrary with respect to the plate. Contour lines of transverse deflection, principal stress and strain and punching force-punch displacement curves have been obtained for different loading conditions. It has been proved that the circuit integral of the product of transverse deflection gradient and contour line's outer normal is constant for any contour line, leading to a linear relationship between the punching force and deflection of the punch. It turns out that the ratio of punch section area to plate section area and the deviation distance of the punch center from the plate center will both influence the value of the circuit integral term, which is correlated with the punching force, as they increase the punching force will also increase if the punch displacement is fixed, and vice versa. Finally, accounting for the merits of MFS in solving the Laplace equation, the solution procedure can be extended to multiple punches loading conditions. Results have revealed that rotation-rate continuity still prevails in rigid-plastic solids in this case. Finite element analysis has been conducted to show that its results agree with the analytical results at a satisfactory level. Image, graphical abstract [ABSTRACT FROM AUTHOR]

To investigate drag reduction by a surfactant in a zero‐pressure gradient flat‐plate turbulent boundary layer flow, the velocities were measured by a two‐component laser Doppler velocimeter, and the buildup as well as relaxation of micelle shear‐induced structures in a simple shear flow was then analyzed by a strain‐controlled rheometer through applying and releasing a given constant shear strain rate. The surfactant was cetyltrimethyl ammonium bromide mixed with sodium salicylate as a counterion in a molar ratio of 1:2 at 60 and 100 ppm by weight. It has been found that the drag reduction rate first increases and then decreases with decreasing wall shear stress in the streamwise direction for the two concentrations of solutions, which is totally different with that in a pipe flow. In addition, the drag reduction in a lower concentration solution boundary layer flow reaches the maximum earlier. Moreover, a shorter buildup time for the micelle shear‐induced structures makes the maximal drag reduction reach earlier in surfactant solution boundary layer flows. [ABSTRACT FROM AUTHOR]

In flexible die forming processes employing semi-solid or elastic materials as pressure-carrying medium, there exist tangential adhesive stress or friction at medium/blank interface, which may improve sheet formability and has been experimentally verified. However, the mechanism behind this phenomenon has not been clarified yet. In order to fill this gap, analytical investigations were implemented in this paper based on previous studies involving through-thickness shear stress. Concretely, the analytical model of axisymmetric shell bulging process considering tangential adhesive stress and the extended M-K model under non-planar stress state were established at first. Accordingly, the relationship between tangential adhesive stress and through-thickness shear strain was deduced together with the relationship between through-thickness shear stress (strain) and sheet forming limit. On the basis of that, the viscous pressure forming (VPF) process was taken as an example to exhibit the characteristic that forming limit changes with tangential viscous adhesive stress and through-thickness shear stress (strain). It is shown that the tangential viscous adhesive stress has positive correlation with through-thickness shear strain which results in increased sheet formability. Tube bulging tests employing viscous medium with different molecular weight as pressure-carrying medium were conducted to give an experimental evidence of the proposed analytical results. [ABSTRACT FROM AUTHOR]

To provide intelligent control options during sheet metal forming process, magnetorheological (MR) fluid has been applied as a property-adjustable flexible-die. However, the mechanism of the magnetic field effect on the sheet deformation behavior is not clear yet. In this paper, to clarify the deformation mechanism, the bulging behavior of thin-walled Al1060-O sheet was systematically investigated through experiment and numerical simulation. Special attention was paid to the effect of magnetic field on loading curve, bulge dome height, and thickness strain distribution. Results showed that the maximum bulging force increased obviously with the increase of magnetic flux density. The bulge dome height and thickness strain were influenced by magnetic field condition and magnetic particle content synthetically. Appropriate magnetic field condition and magnetic particle content can improve formability. However, excessive magnetic flux intensity and magnetic particle volume fraction, for example, B = 0.20 T and φ = 46%, would lead to premature rupture. Finite element analysis was adopted to assist in explaining the bulging behavior. Detailed analysis indicated that the flow stress variations caused by magnetic field affect the stress states, velocity distribution of MR fluid, and sheet/MR fluid contact condition, further leading to different stress and strain distribution of sheet metal. Finally it causes the great difference in specimen geometry and wall thickness distribution. [ABSTRACT FROM AUTHOR]