Finite element analysis of tube hydroforming process in a rectangular die

Presented by Khushboo Shrivastava

Roll No. 123370001

AimUse the Finite Element Method to explore the

plastic flow pattern of a circular tube that is hydraulically expanded or crushed into a rectangular cross-section.

DEFORMThe plastic flow patterns of the forming tube

and the thickness distribution of the formed product are explored while a circular tube is expanded or crushed into a rectangular cross-section, using a commercially available FE code “DEFORM”.

Finite element modelingAn implicit and static FE code “DEFORM”The finite element code is based on the flow

formulation approach using an updated Lagrange procedure. The basic equation for the finite element formulation from the variational approach is

Finite Element Simulations AssumptionsDie is rigid, the tube is rigid-plastic,The plastic deformation of the tube is under a

plane strain state, and the interface between the tube

Die has a constant friction coefficientThe flow stress of the tube material of SUS 304 is

assumed to be expressed by a power law of its equivalent strain, i.e.σ=Ke^n, where K = 1452

MPa is the strength coefficient and n = 0.6 is the strain-hardening exponent.

Modelling ParameterFour-node isoparametric elements are used.The tube is divided into about 1000 elements,

and there are six layers of elements in the thickness direction.

The configurations of the meshes in the tube before crushing and preforming are shown in

Fig.

Iteration MethodsDirect iteration methods Generate a good initial guess for the

Newton Raphson methodNewton-Raphson: Speedy final convergence

Simulation works for expansionThe upper die is always in contact with the bottom

die without movement.The internal pressure input into the tube is

increased gradually. Following the increase of the internal pressure, the tube comes in contact with the short sides of the die and then the corner radius of the free bulged region, R, decreases. When the programmed internal pressure reaches 300 MPa, the simulation is stopped, and the corner radius and the thickness distribution of the formed product are

measured.

Simulation works for crushingThe dimension of the upper die is the same as

that for the expansion process. The step increment is set to be 0:01 s. At the beginning and early stage of the crushing process, no internal pressure is input into the tube to make the tube expanded outwards. On the contrary, two side dies with a radius of 15 mm at the left and right sides of the tube are used to push the tube inwards to prevent the tube from being pinched by the upper and lower dies as the upper die goes downwards.

Simulation works for crushingAfter the side dies move 17 mm inwards, as

shown in Fig. 4(b), the side dies move backwards immediately and then the crushing process starts. As the upper die is ready to touch the lower die, a gradually increased pressure is input into the tube to calibrate the tube and make the tube material 1ow into the corners of the die as much as possible. The crushed and hydroformed

product is shown in Fig. 4(d).

Results from the simulation

ConclusionsFrom the simulation results, some conclusions can

be drawn as below:The maximum forming pressure needed by

crushing processes is only 5% of that by hydraulic expansion processes.

The maximum crushing force needed in the crushing process is only about 7% of the clamping force in the hydraulic expansion process.

The thickness distribution of the formed product obtained by crushing processes is much more uniform than that by hydraulic expansion processes.

ConclusionsThe expansion process is a very simple forming

process that does not need extra equipment, such as the side dies and cylinders, or a procedure control for the internal pressure and movement of the dies. However, it needs a large press machine and a high-pressure hydraulic system.

By introducing the crushing process into the hydroforming processes, the clamping forces and forming pressures

can be greatly reduced. Furthermore, highly uniform thickness distributions of the formed products

can be obtained.

ReferencesF. Dohmann, Ch. Hartl, Tube hydroforming:

research and practical application, J. Mater. Proc. Technol. 71 (1997) 174–186

Finite element analysis of tube hydroforming processes in a rectangular die Yeong-Maw Hwanga; ∗, Taylan Altanb

Thank you