# Functional Analysis of Components Manufactured by a Sheet-Bulk Metal Forming Process

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## Abstract

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## 1. Introduction

## 2. Geometry-Based Approach within SLASSY

## 3. Mechanical Analysis

#### 3.1. Forming Process

_{0}= 2.0 mm and an initial diameter of d

_{0}= 100.0 mm. This steel is characterized by a high formability at medium strength and is used in automobile applications such as different chassis parts or narrow profiles. The mechanical properties of the material are presented in Figure 4. Besides the material parameters such as the yield strength, the flow curve is shown, which was generated by layer-compression tests and extrapolated with the Hocket–Sherby approach to enable a realistic material behavior in the context of SBMF processes with three-dimensional compressive stresses.

_{C}= 400 kN. The deep drawing process began with an axial movement of the drawing die, which was controlled by the drawing force F

_{D}to form the cup wall. After reaching the upsetting plate, the upsetting process was initiated within the same stroke by the displacement of the drawing die as a consequence of an applied upsetting force F

_{Up}into the upsetting punch. Subsequently, the cup wall was reduced in height and a lateral material flow into the cavity located on the inner side of the drawing die was realized. The final height of the component depended on the defined forming force.

#### 3.2. Forming Results

_{0}= 2 mm was applied as a semi-finished product for the reference geometry. As presented in the previous chapter, the deep drawing operation was used to realize the basic cup shape of the component. After deep drawing, the cup height amounted to h = 14.78 mm. Due to the occurring stress and strain states, a material thinning at the drawing punch radius occured, analogous to [8]. The minimum sheet thickness amounted to t

_{min}= 1.76 mm, whereas the maximum sheet thickness amounted to t

_{max}= 2.02 mm due to tangential compression stresses in the lower area of the cup wall. Subsequently, the drawn cup was upset with a maximum upsetting force of F

_{Up}= 800 kN. The resulting part contour is presented in Figure 6. The cup height after upsetting amounted to h = 8.41 mm. Since the material volume provided by the conventional blank remained constant at V

_{conv}= 6754 mm

^{3}, the form filling of the tooth area including the cup wall was only dependent on the desired cup height. Referring to a required material volume of V

_{req}= h × 932.7 mm

^{3}/mm, derived from the CAD-Model, the form filling with a height of h = 8.41 mm reached up to 86%. The contour of the experimentally manufactured part, however, showed large deviations to the target geometry. The buckling of the cup wall was identified as a major process failure for insufficient material volume in previous investigations [9], and required the application of process-adapted semi-finished products [8]. The other characteristic failure for the application of conventional semi-finished products was the folding of the material at the drawing punch radius, as shown in the depicted microstructure in Figure 5. The results of the micro hardness distribution demonstrated the increase of the hardness due to cold hardening in areas of high deformation, thus revealing an increase of 87% up to 233.4 ± 30.1 HV0.05.

#### 3.3. Process Strategies to Enlarge the Form Filling

_{avg}= 2.51 ± 0.51 mm was achieved by the tumbling of a rotational symmetric tailored blank, a thickening of t

_{avg}= 2.46 ± 0.47 mm could be achieved by the flexible rolling process. Especially when manufacturing a cyclic-symmetric tailored blank geometry, it can be seen that a more homogenous sheet thickness can be achieved in the thinned area for the flexible rolling process, since the center thinning effect is caused by the material flow during the orbital forming process.

_{max}= 800 kN to the drawn cup. According to the process description in Section 3.1, the material in the cup wall was forced to flow into the gear cavity. The additional material allocated within the manufacturing of the tailored blank enabled an improvement of the die filling and the reduction of the deviation to the target geometry, as presented in Figure 10.

_{TB}= 8152.5 mm

^{3}. Referring to the formula to calculate the required material volume V

_{req}= h × 932.7 mm

^{3}/mm and an actual cup height of h = 8.98 mm, the form filling could be increased to 98%.

## 4. Fatigue Life Testing and Modeling

#### 4.1. Fatigue Life Modeling

_{el,eff}and plastic W

_{pl}energy densities converted during one cycle (Equations (1) and (2)). This approach was established for unalloyed and low-alloy steels [17].

_{J}and m

_{J}are material-dependent and can be determined from long crack growth experiments. By analyzing the stress–strain hysteresis in strain-controlled fatigue experiments, the elastic and plastic energy densities W

_{el,eff}and W

_{pl}can be determined. W

_{pl}is provided by the area below the ascending hysteresis-branch [18]. The effective elastic energy density W

_{el, eff}can be obtained from the effective stress amplitude Δσ

_{eff}, for which the fatigue crack is opened and capable of growth, and from the Young’s modulus E as

_{f}can then be calculated by integrating the crack propagation from an initial crack length a

_{0}to a given crack length a

_{f}, which is used as the failure criterion:

#### 4.2. Data Acquisition on Different Material States

_{m}= 0 (strain ratio R

_{ε}= −1) and a test frequency of 3 Hz. The hysteresis loops clearly show the increased strength of the rolled and work-hardened material condition compared to the initial state, see Figure 12.

#### 4.3. Fatigue Testing of the SBMF-Components

#### 4.4. Fatigue Life Prediction and Experimental Results

_{J}= 6.4 × 10

^{−9}mm/cycle and m

_{J}= 1.48 were assumed. These values were determined in long-crack growth experiments on work-hardened DC04 and converted accordingly for the Z-integral approach [5]. These results corresponded to the expectations for low-alloy steels as reported in the literature [19].

_{f}= 1 mm. To apply the fracture mechanics approach, crack growth starting from an initial crack length was assumed to occur in the first cycle. This initial crack length was considered to be in the order of the magnitude of microstructural defects such as ductile damage in the form of voids in the microstructure [20]. These voids are formed during the cold forming process and grow and coalesce to crack-like defects [21]. Several experiments on differently pre-loaded material states of DC04 steel have shown that these defects can have a size between a few nanometers up to more than 10 µm [22]. Furthermore, it could be shown that crack growth can indeed start from these defects [23]. In the present study, a mean initial crack length of a

_{0}= 5 µm was chosen for the fatigue life calculation.

## 5. Data-Based Approach within SLASSY

#### 5.1. Metamodel Training

#### 5.2. Application inside SLASSY

## 6. Discussion

## 7. Conclusions

- A process combination of deep drawing and upsetting within sheet-bulk metal forming can be used to manufacture cup-like components with circumferential involute gearing. However, process failures in the form of folding and buckling were identified during the evaluation of the geometrical and mechanical properties. Since the required material volume in the area of the gearing was not sufficient, possibilities to enlarge the form filling are required.
- By applying orbital formed semi-finished parts in the investigated process combination of deep drawing and upsetting, the maximum form filling can be increased significantly by up to 98%. Furthermore, the process failures can be prevented, and the homogeneity of the hardness distribution outlines the improved forming results.
- The fatigue life of the components can be described well by employing the Z-integral approach. The mechanical properties of the sheet-bulk metal formed material state can be approximated by analyzing a similarly work-hardened state produced by rolling.
- With an assumed initial crack length of 5 µm, the fatigue life is predicted well. By an inverse calculation, the virtual initial crack length was determined to be about 2.5 µm for an optimal fit to the experimental results. With these values, the initial crack length is in the range of the size of microstructural defects such voids that occur due to ductile damage.
- The comparison of the predicted SN-curves for the initial state and the work-hardened material state shows that the fatigue life of the SBMF-components is significantly increased due to work hardening. This shows an advantage of the forming process compared to other manufacturing processes.
- The findings regarding fatigue life could be modeled with the aid of exponential function based metamodels to allow for the prediction of arbitrarily selected part design parameters. The prediction quality is within an acceptable range, as it has shown a coefficient of prognosis of around 95%.
- Moreover, the degree of form filling could be modeled, allowing for the prediction of different selected part design parameters. This data-driven approach allows for further investigations with different part designs or form elements.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Material characterization of DC04 [4].

**Figure 5.**Schematic setup of the combined deep drawing and upsetting process [8].

**Figure 8.**Process setup of flexible rolling [8].

**Figure 9.**Average sheet thicknesses for the orbital forming and flexible rolling processes for different geometries.

**Figure 11.**(

**a**) Specimen geometry and orientation, (

**b**) test setup of the strain-controlled fatigue experiments.

**Figure 13.**Cyclic stress–strain curves determined for the initial and rolled material state, compiled from [5].

**Figure 14.**(

**a**) Calculated von Mises stress for a service load of 1800 N and (

**b**) the test setup for the fatigue tests.

**Figure 16.**(

**a**) Resulting curves for different tooth heights predicted by the trained metamodel, and (

**b**) the predicted degree of form filling for a conventional and a tailored blank.

**Figure 17.**(

**a**) Prediction of tooth height for given cycles to failure and load amplitude and (

**b**) the respective degree of form filling for conventional and tailored blanks, evaluated by the trained metamodels.

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**MDPI and ACS Style**

Hetzel, A.; Schulte, R.; Vogel, M.; Lechner, M.; Besserer, H.-B.; Maier, H.J.; Sauer, C.; Schleich, B.; Wartzack, S.; Merklein, M.
Functional Analysis of Components Manufactured by a Sheet-Bulk Metal Forming Process. *J. Manuf. Mater. Process.* **2021**, *5*, 49.
https://doi.org/10.3390/jmmp5020049

**AMA Style**

Hetzel A, Schulte R, Vogel M, Lechner M, Besserer H-B, Maier HJ, Sauer C, Schleich B, Wartzack S, Merklein M.
Functional Analysis of Components Manufactured by a Sheet-Bulk Metal Forming Process. *Journal of Manufacturing and Materials Processing*. 2021; 5(2):49.
https://doi.org/10.3390/jmmp5020049

**Chicago/Turabian Style**

Hetzel, Andreas, Robert Schulte, Manfred Vogel, Michael Lechner, Hans-Bernward Besserer, Hans Jürgen Maier, Christopher Sauer, Benjamin Schleich, Sandro Wartzack, and Marion Merklein.
2021. "Functional Analysis of Components Manufactured by a Sheet-Bulk Metal Forming Process" *Journal of Manufacturing and Materials Processing* 5, no. 2: 49.
https://doi.org/10.3390/jmmp5020049