Val_004d Billet Upsetting

Problem Description

 

A 3D simulation of billet upsetting is performed. In this test, a cylindrical billet is compressed by 20% strain between two flat, rigid dies that are defined to be perfectly rough. The top and bottom boundaries are constrained in horizontal directions.  Two different plastic material models are simulated:

•Case01 - von-Mises elasto-plastic model

•Case02 - Herschel-Bulkley visco-plastic isothermal (Model 1) and temperature-dependent (Model 2)

 

 

Val_004d_01

Val_004_04

 

 

Problem description

Simulation model

 

 

 

Parameter

Value

W (mm)

10

L (mm)

15

u (mm)

3 (i.e. 20% strain)

Geometry Parameters

 

 

 

Mesh Discretisation

 

Seven element types have been used in this simulation. The followings illustrate some examples of meshed models that have been used in the tests. In general, higher-order elements and elements with mixed formulation are recommended for this problem as sufficient degree of freedom is required to resolve potential volumetric locking problem in the region close to the rigid dies.

 

Val_004d_02

Example of meshed models used in the current test cases

 

 

Data File Descriptions

 

The data files for the different element types are in Val_004\billet. The different cases are in different sub-folders according to the material model (vonMises/Herschel-Bulkley), dimensions (2D/3D), solver (explicit/implicit) and element type used for each specific case.

 

The basic data includes:

1Geometry_data imports geometry file for 3D cases in *.geo format that has been created using Gmsh and made compatible using ParaGeo pre-processing procedures.

2Geometry_set groups multiple geometry entities under convenient geometry set names.

3Group_control_data activates geomechanical field for the current simulation group.

4Group_data sets the group name, element type, material name, porous flow type and the associated volume entity.

5Material_data defines the material properties of the model.

6Support_data constrains the displacement freedom on each surface accordingly.

7Global_loads defines the prescribed displacement loading on the geometry set associated with the compressional loading.

8Damping_global_data defines the damping data used in the explicit analysis data.

9Control_data defines the solution algorithm (e.g. 1 for explicit transient dynamic algorithm, 7 for nonlinear implicit algorithm), termination time, etc.

 

The Global_loads data is shown below.

Global_loads

 

Global_loads defines the prescribed vertical displacement load on the geometry set associated with the billet top surface.

 

Data File

 

 

* Global_loads

! ---------------------------------

 Prescribed_displacement      IDM=3 JDM=1

  /Set 1/                     0  0  -3.0

 Pres_displacement_geom_set         IDM=1

   "top_surf"

 Pres_displacement_geom_ass         IDM=1

   1

 

 

* Time_curve_data

! ---------------------------------

 Time_curve          IDM=2

   0.0        1.0    

 Time_factor         IDM=2

   0.0        1.0    

 Curve_type   1

 

1Vertical displacement -3.0 mm (along z direction) is prescribed on the geometry set "top_surf" via a linear ramp over 1.0 time unit.  Note that this is equivalent to 20% strain.

 

 

 

 

Simulation Cases

 

The two main material models simulated can be found in: ParaGeo Examples\Validation\Val_004\billet.

 

Case 01 von Mises

 

Case 02 Herschel-Bulkley Isothermal (Model 1) and Temperature-Dependent (Model 2)

 

 

References

 

[1] Lippmann,  H. (1979). Metal Forming Plasticity. Springer-Verlag, Berlin.

[2] Cheng., J.H., Kikuchi, N. (1984). An analysis of metal forming processes using large deformation elastic-plastic formulations

[3] https://abaqus-docs.mit.edu/2017/English/SIMACAEEXARefMap/simaexa-c-rezonebillet.htm