Keywords

1 Introduction

Parts produced by cold forging have good mechanical properties and geometrical accuracy [1]. By omitting workpiece heating before forming, energy consumption and CO2 emissions can be reduced. However, the large flow stress of materials formed at room temperature necessitates high forces. Cold forging tools are consequently subjected to high stresses. Preventing tool failure is essential for the economic viability of forging processes, since tooling costs amount to 30% or more for net shape applications [2]. The geometrical complexity of tools is increasing, as there is a demand for more intricate part geometries with functional integration [3]. For complex tool geometries, the main failure mechanism is fatigue [4], which occurs due to high alternating stresses. The high-strength steels or cemented carbides used for forging tools are especially sensitive towards tensile stresses [5], which are present in tangential direction for non-circular symmetrical part geometries [6] or in axial direction when there is a change in cross-section [7]. In increasingly complex tool geometries, local multiaxial tensile stresses in both tangential and axial directions are encountered as well. As fatigue depends on the multiaxial stress state [8], these types of loads are highly relevant, but have as of yet not been analysed in depth. Existing strategies to reduce tensile tool loads by compressive prestressing focus on one stress direction. For example, concepts for local prestressing by reinforcements with adapted interference fits exist both for axial [9] and for tensile stresses [10]. However, the influence on multiaxial tensile stresses is currently unknown. This paper therefore aims to provide a foundation for the analysis of multiaxial tensile tool stresses and methods to influence them. For this purpose, a model process with local multidirectional tensile stresses is designed. As stresses in forging dies cannot be measured experimentally, a numerical model is set up and validated. The model is then used to analyse the stress state and evaluate the influence of conventional prestressing systems on the multidirectional tool stresses.

2 Model Process

In this section, a model process is designed for the analysis of multiaxial tensile tool stresses. The process should be a typical cold forging operation and allow for flexible changes in tool geometry and prestressing system. Therefore, a forward extrusion process for parts with four functional elements is chosen as shown in Fig. 1. Compared to conventional forward extrusion, an additional slope is introduced, so that the functional elements are formed gradually in the tangential direction. This ensures multiaxial stresses with tangential and axial tensile loads at the same position as will be shown in the analysis of the stress state. Furthermore, angles of the extrusion shoulder and slope as well as the geometry and number of functional elements can be varied for future process analysis. Materials typical for cold forging applications are chosen for the process. The workpiece is made out of 16MnCrS5, and the active tool parts punch and die out of the powder metallurgical steel ASP2023. The material of the reinforcement is the hot-working steel 1.2344. The die is inserted into the reinforcement with an interference fit of 3% to induce a tangential prestress. The initial billet has a diameter of 25 mm and a height of 20 mm. In areas where no functional element is present, the diameter is reduced to 20 mm. To achieve this, the punch moves downwards until a fixed distance is reached creating a part height of 25 mm.

Fig. 1
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Model process

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To analyse the stress state, a numerical model is set up using the software Simufact. Forming 15.0. The simulation is carried out in a decoupled approach, in which material flow and die load are calculated separately. The workpiece is modelled with the flow curve shown in Fig. 2, which was determined for the material 16MnCrS5 in previous research [6]. Furthermore, friction is taken into account with a friction factor of 0.04 according to Tresca. This factor was identified for the relevant material pairing of 16MnCrS5 and ASP2023 in a double cup extrusion test using a zinc-phosphate coating on the workpiece in combination with the lubricant soap [6].

Fig. 2
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Flow curve of 16MnCrS5 according to [6]

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Taking into account the cyclic symmetry of the process, a 45° segment is computed. The workpiece is meshed with hexahedral elements with an edge length of 0.5 mm and refinements to 0.25 mm below the extrusion shoulder and 0.125 mm at the extrusion shoulder and the functional elements. In the tool load simulation, die and reinforcement are represented using tetrahedral elements with a maximum geometrical deviation of 0.005 mm. The die’s material ASP2023 is modelled elastically with a Young’s modulus of 230 GPa. To validate the given assumptions, the numerical results are compared to experimental ones in the subsequent section.

3 Validation of the Numerical Model

In order to qualify the numerical model for an evaluation of tool stresses, it needs to be validated by comparison with experimental results. For this purpose, force–displacement curves, part geometries as well as hardness, and true strain distributions are analysed. Figure 3 shows the force–displacement curves obtained in the experiment and simulation. After a slow rise in force, when elastic deformation takes place and transition radii are filled, the force rises steeply during the filling of the extrusion shoulder. Afterwards, the force increases with a less steep slope when the height of the functional elements increases. This type of force curve can be seen both in the simulation and the experiment and is similar to graphs obtained in the forward extrusion of gears [11]. While overall the curves are in good agreement, the increase in force is slightly higher for the simulation resulting in a higher maximum force compared to the experiment. The maximum values deviate by 8% with 334.3 kN in the simulation and 309.4 kN ± 2.2 kN in the experiment. The deviations at the beginning of the process can be explained by elastic tool deformation and varying friction conditions in the experiment, since rigid tools and a constant friction factor were used in the numerical model.

Fig. 3
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Comparison of force–stroke curves in experiment and simulation

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As second target value, part geometries are compared in Fig. 4. The experimentally formed parts were measured three dimensionally using a 3D sensor type Atos from the company GOM GmbH. A good agreement in part geometry can be seen in the graphs. The cross-section shows that the desired geometry with filled functional elements is reached both in simulation and experiment. Small deviations are present in the sections through the functional element and the extrusion shoulder. Here, the simulation slightly overestimates the material flow along the axis of symmetry. The height of the part in this area deviates by 3% with 24.75 mm for the simulation and 24.02 mm ± 0.04 mm for the experiment with n = 3 measured parts. This may be due to locally deviating friction conditions between the double cup extrusion test and the model process.

Fig. 4
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Comparison of numerical and experimental workpiece geometry

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The small deviation in part height is not expected to have a high influence on the tool load, since the critical die stresses occur at the extrusion shoulder. To verify the correct representation of material flow, hardness, and true strain distributions are compared in Fig. 5. As strain hardening of cold formed material induces a higher hardness, the mappings should be qualitatively similar. To achieve the results, micro hardness measurements were conducted in three different part sections as shown in Fig. 5.

Fig. 5
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Comparison of measured hardness and simulated true strain

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The section through the shoulder and functional elements show increased hardness and true strains near the extrusion shoulder. Both hardness and true strains decrease towards the end of the functional elements and the part centre. The area below the extrusion shoulder shows no true strain and low hardness that corresponds to the initial hardness of the material. In the cross-section, it is evident that the highest strain hardening occurs near the functional elements, where the material is displaced to create the desired geometry. Furthermore, higher strains are present at the part edge than in the part middle, where close to no deformation takes place. Overall, the true strain and hardness distributions are in good agreement. Taking into account the force–displacement curves and part geometries as well, the predictive accuracy of the numerical model is evaluated as good. It is therefore qualified for an analysis of the die stresses in the following section.

4 Analysis of the Stress State

The critical tool stresses occur in the forming die, since it incorporates the negative of the part geometry with the transition to a non-circular symmetrical cross-section. The distribution of tangential, axial, and maximum principal stress is shown in Fig. 6. Axial and tangential stresses are normal stresses in the orientation of a cylindrical coordinate system corresponding to the outer die geometry.

Fig. 6
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Multiaxial stress state in the die

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As is typical for forward extrusion processes, axial stresses are present at the transition of the higher diameter to the extrusion shoulder. In this area, the pressure exhibited by the workpiece on the extrusion shoulder leads to tensile stresses. Furthermore, tangential stresses occur at the back of the functional element, which is in accordance with stresses obtained in dies for parts with functional elements and a constant cross-section [10]. Due to the slope between extrusion shoulder and functional elements, the two stress components overlap creating a multidirectional tensile stress. Consequently, the highest maximum principal stress occurs in this transition area because of the superposition of tangential and axial tensile loads. To illustrate the influence of conventional prestressing systems on this multidirectional tensile stress, axial, tangential, and maximum principal stresses are analysed depending on the interference fit of the reinforcement in Fig. 7. The respective maximum stresses on the inner die wall were evaluated to obtain the graphs.

Fig. 7
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Influence of interference fit on die stresses

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An increase in interference fit induces a higher prestress and therefore decreases all three stress types. However, the influence on the tangential direction is most pronounced with the tangential stress decreasing from 2536 MPa at 1% to 70 MPa at 7%. At the same interference fits, the axial stresses only decrease from 1244 to 683 MPa. From 7% upwards, no relevant tangential stresses are present in the die, because the reinforcement induced sufficient tangential compressive prestress. However, tensile stresses are still present in axial direction. The highest maximum principal stress is therefore equal to the axial stress at 7% and 9%. It is evident that reinforcements mainly influence tangential tensile stresses. For a reduction of axial loads, additional axial prestressing should be used. This is often implemented for horizontally divided dies by applying pressure in a hydraulic press and fixing the tool parts with a nut [1]. The axial prestressing is simulated using a rigid plate applying a force between 200 and 1000 kN on the die in axial direction. The interference fit of the reinforcement is kept constant at 3%. The results of the analysis are shown in Fig. 8.

Fig. 8
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Influence of axial prestressing on die stresses

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While axial loads are influenced strongly by axial prestressing, tangential stresses decrease only slightly. From 0 to 1000 kN prestressing, the axial stress is reduced from 1010 to 62 MPa, while the tangential stress only changes from 1478 to 1291 MPa. When axial loads are neutralised by a sufficient prestressing with 1000 kN, the critical tensile stress represented by the maximum principal stress occurs in tangential direction. While reinforcements are suitable for decreasing tensile loads, axial prestressing should be used for axial stresses. When dealing with multidirectional tensile stresses, a combination of measures is necessary to completely remove critical tensile die loads.

5 Summary and Outlook

Tool failure through fatigue is a major challenge when applying cold forming processes to produce intricate part geometries. As geometries with non-constant and non-circular symmetrical cross-sections create multiaxial tensile stresses, a model process for the research of this stress state was introduced in this paper. The corresponding numerical model was validated, as force–displacement curves, part geometry as well as true strain and hardness distributions are in good agreement between experiment and simulation. The analysis of the stress state showed that prestressing measures like reinforcements and axial prestressing are able to influence one stress direction, but have little influence on the other. A combination of measures is therefore recommended for multidirectional stress states. Further research should focus on the influence of novel local prestressing measures on the stress state. Furthermore, the fatigue behaviour should be analysed experimentally. Lastly, dies made of cemented carbide should be considered in addition to steel materials.