The extrusion process is aimed at compressively forcing or extruding a billet through a cavity or die of a desired cross-section. Special purpose alloys and composite materials require special die designs. Die designs are generally classified into two categories: shear dies which are mainly used for extrusion of aluminum and copper, etc.; and shaped dies for extrusion of "difficult-to-form" and exotic materials. Process design for extrusion using a conical die is presented next.

Conceptual Design

The extrusion process is aimed at achieving the geometry of the material, including the shape, size, tolerance and desired microstructural properties, such as the grain size and volume fraction of the recrystallized grains. The resulting microstructure is a function of the processing history of the materials. The microstructure of the material is dependent on the thermal and the deformation step.

Functional requirements in the deformation process {FRs} :

  • Grain size, do
  • Volume fraction, _
  • Aspect ratio of grains, A
  • desired dimensions/area, Af

Extrusion process parameters, {PVs} include :

  • Extrusion ratio, R
  • Extrusion speed, V
  • Starting billet temp., TB
  • Die temperature, TD

A corresponding set of design parameters {DPs} for deformation processing may include :

  • Starting grain size, do
  • Stress,
  • Strain rate, _
  • Starting aspect ratio of grains, A
  • Temperature, TW
  • Strain, _
  • Critical strain, _c

The functional requirements and design parameters for microstructural development can be related using Suh's principles. The linking of the functional requirements to the process variables and the design parameters is a two step process : the first stage links the process variables {PV} to the functional requirements {FR}, while the second stage relates the process variables {PV} to the design parameters {DP}

Preliminary Design

A round-to-round steel extrusion with an extrusion ratio of 3 through a conical die is employed for the case study presented in this section. The preliminary design of the extrusion through a conical die is accomplished using the slab method. The slab method of analysis is an equilibrium analysis in which the zone of deformation is divided into a number of small segments, or slabs, hence the name. An equilibrium analysis of a representative slab provides the governing differential equation, which when integrated across the deformation zone provides the pressure and hence the force distribution.

Final Design

For a thermomechanical problem it is desired to achieve a required shape with certain microstructure of the material. The microstructure of a material is linked to the mechanical properties of a material and thus plays a pivotal role in hot deformation processes. The finite element methods can once again be employed to test and confirm the extrusion die design. The extrusion process setup with the die, the container, the billet, and the ram are shown in figure 5. ANTARES, a rigid viscoplastic finite element model was employed for the analysis.

Figure 5

The object of this analysis was also to simulate the finite element extrusion to match the actual extrusion conditions. In the actual extrusion process, a small gap is maintained initially between the die container and the billet. The strain plots for the analysis are shown in figure 6.

Figure 6

Since the object of this analysis was to simulate the actual extrusion process, therefore, a plane strain analysis of the complete section was conducted. Figure 6 shows the strain at the end of the billet to be unsymmetric because of the gap between the billet and the container. Initially, the billet tends to buckle to a side and fills the container completely before being extruded.

Figure 7

Figure 7 shows the grain size of the steel extrusion frozen in the middle of the extrusion process. The change of grain size in this case is attributed to the dynamic crystallization of the material. Therefore, the region of interest for the grain size lies under the deformation zone and the extruded portions of the billet. If the grain size of the material was not in the acceptable range the complete design procedure may be tweaked and repeated.


A hierarchical design methodology for metal forming process design has been presented. This methodology is time and cost effective because it provides a systematic means of achieving an optimum process design by limiting the design space in successive, orderly steps. Conceptual design using the axiomatic design principle is used to identify important parameters. Preliminary designs consisting of simplified tools are employed to develop an initial design. As the design space is narrowed more accurate finite element methods are used to analyze the process. The most time consuming and expensive analyses methods are reserved for a very narrow design space.

The design of a rolling and an extrusion process is presented too as an example to the hierarchical design methodology. After conceptual design, various simplified tools are employed which suit a process or operation. The main design iterations were performed in this space, while limiting the final, more time consuming finite element analysis for design confirmation. The two design examples show the working of the methodology and how a proper design can be accomplished which also optimizes the design time. This methodology saves considerable design time and will reduce lead time in a production environment. Furthermore, the design process may be guided by design of experiments ensuring an optimum design at each stage which will be the subject of another publication.

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Peter Habicht, Lead Consultant
Peter specializes in welding and metallurgical engineer with 40 years industry experience in commercial nuclear power plant construction.


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