Rigid-plastic finite element DEFORM–3D® software has been used to investigate the deformation behavior and bending of the lead billet during the multi-hole extrusion process. The solid 3D modeling of die, billet, container and punch were made with same dimensions as used for experiments (explained in Chapter 3, Section 3.2).
The 3D models of the container with die, punch and billet material were modeled in NX 3 Unigraphics®, advanced CAD/CAM/CAE software developed by Siemens PLM Software. The stereolithography (STL) files of the models were transferred to finite element program DEFORM to establish the finite element mesh.
The STL files describe only the surface geometry of a three dimensional object without any representation of color, texture or other common CAD model attributes.
The following assumptions were made for the analysis. The container and dies were considered as rigid bodies. The lead billet was considered as a rigid plastic material.
DEFORM provides different methods of defining the flow stress. For the present simulations, the power law has been used which can be defined as:
K n
σ = ε
, (5.1)where
σ
is the flow stress of the material, K is the material constant,ε
is theeffective plastic strain and n is the strain exponent. The compression test of the lead specimen was carried out in a universal testing machine to find out stress-strain relationship. From the compression test, the following values are obtained and used for the present simulations, material constant, K is 54.59 MPa, strain exponent, n is 0.23. Friction factor m is taken 0.3 at all the interfaces. To determine the friction factor the method followed is explained as follows. Extrusion experiments are carried out with two billets of different lengths. Then the friction factor, m is calculated as [Bakhshi-Jooybari, 2002]
3 o m F
d Lc
πσ
= ∆
∆ , (5.2)
where m is friction factor, σ is the normal flow stress of the billet material, do is internal diameter of the container, ∆F is the difference in punch load and ∆Lcis difference in billet length.
The billet material follows von Mises yield criteria and strain hardening is assumed to be isotropic. Tetrahedral mesh with 19948 elements and 4138 nodes is used to uniformly discretize the billet material. Although the setting of mesh density at the deformation zone can be altered according to the strain and strain rate distribution, in the present work uniform mesh density is considered for simplicity.
A constant incremental punch displacement of 0.3 mm is imposed during the simulation process. Punch speed of 1.5 and 1.8 mm/min are considered for 20 and 30 mm billet length respectively. Stopping criteria is selected as 10 mm of ram traverse.
5.2.1 Comparison of Extrusion Load Obtained from Experiments and Finite Element Simulations for 9-hole die with Different Die Land Length
Finite element simulation of the multi-hole extrusion with nine-hole die was carried out. The maximum extrusion loads obtained from the simulations are compared with the experimental data. The comparative results of extrusion load are shown in Table 5.1 and Table 5.2 for extrusion of 20 mm and 30 mm length billets respectively.
Table 5.1. Comparison of extrusion load obtained from experiments and FE simulations for 20 mm billet length
Extrusion Load (kN) Die Type
Experiment FE Simulation
Die I (10 mm die land) 112.65 125
Die II (10/6.5 mm die land) 109.55 119
Die III(10/3 mm die land) 111.55 113
Die with no die land length − 110
Table 5.2. Comparison of extrusion load obtained from experiments and FE simulations for 30 mm billet length
Extrusion Load (kN) Die Type
Experiment FE Simulation
Die I (10 mm die land) 125.45 131
Die II (10/6.5 mm die land) 118.55 126
Die III (10/3 mm die land) 113.85 121
Die with no die land length − 112
There is a good agreement between the experimental and simulation results for 20 and 30 mm billet extrusion. The minimum extrusion load is observed with the dies having no die land length and maximum extrusion load with the dies having 10 mm die land length (Die I). Extrusion load increases with increase in die land length and billet length for same extrusion ratio. (There is an exception in Table 5.1. Here, the experimental load for Die III is more than that of Die II, although the difference is small and may be attributed to uncontrollable experimental errors.) From simulations, it can be observed that the extrusion load reduces by 15% when the die land length reduces from 10 mm to zero for 30 mm billet length extrusion. The extrusion load reduces by 12% when the die land length reduces from 10 mm to zero for 20 mm billet length extrusion.
5.2.2 Finite Element Simulations on Bending of Extruded Products of 9-hole die Radius of curvature of the extruded product has been studied using finite element simulations. Rigid-plastic finite element DEFORM-3D software has been used to investigate the deformation behavior of the lead billet during the multi-hole extrusion process. Figure 5.1 shows the extruded products with different bend profile during the extrusion process. Maximum bending of the extruded product is observed with the products coming out from the die without die land length. The least bent product is observed with the die of the largest die land length i.e. 10 mm.
The experimental radius of curvature of the extruded products obtained from experiments with Die I, Die II and Die III has been discussed in Sections 4.4 and 4.5 (Chapter 4).
A good qualitative agreement between the experiments and simulations is observed.
Higher extrusion load due to high die land length can be compromised for the better quality of the extruded products.
Figure 5.1. Finite element simulation: extruded products from (a) Die I (b) Die II (c) Die III and (d) 9-hole die without die land.
1
3 2
1
3 2
1
3
2 2
3 1
(a) (b)
(d) 1: Punch, 2: Deformable workpiece and 3: Die (c)