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

Journal of Manufacturing and Materials Processing

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

Andreas Hetzel 1,* , Robert Schulte 1, Manfred Vogel 1, Michael Lechner 1, Hans-Bernward Besserer 2 , Hans Jürgen Maier 2 , Christopher Sauer 3 , Benjamin Schleich 3 , Sandro Wartzack 3 and Marion Merklein 1

1 Institute of Manufacturing Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; [email protected] (R.S.); [email protected] (M.V.); [email protected] (M.L.); [email protected] (M.M.) 2 Institut für Werkstoffkunde (Materials Science), Leibniz Universität Hannover, 30823 Garbsen, Germany; [email protected] (H.-B.B.); [email protected] (H.J.M.) 3 Engineering Design, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; [email protected] (C.S.); [email protected] (B.S.); [email protected] (S.W.) * Correspondence: [email protected]; Tel.: +49-9131-8527676

Abstract: Due to rising demands regarding the functionality and load-bearing capacity of functional components such as synchronizer rings in gear systems, conventional forming operations are reaching their limits with respect to formability and efﬁciency. One way to meet these challenges is the application of the innovative process class of sheet-bulk metal forming (SBMF). By applying bulk forming operations to sheet metal, the advantages of both process classes can be combined, thus realizing an optimized part weight and an adapted load-bearing capacity. Different approaches to manufacturing relevant part geometries were presented and evaluated regarding the process Citation: Hetzel, A.; Schulte, R.; properties and applicability. In this contribution, a self-learning engineering workbench was used to Vogel, M.; Lechner, M.; Besserer, provide geometry-based data regarding a novel component geometry with circumferential involute H.-B.; Maier, H.J.; Sauer, C.; Schleich, gearing manufactured in an SBMF process combination of deep drawing and upsetting. Within the B.; Wartzack, S.; Merklein, M. comprehensive investigations, the mechanical and geometrical properties of the part were analyzed. Functional Analysis of Components Moreover, the manufactured components were compared regarding the increased fatigue strength in Manufactured by a Sheet-Bulk Metal Forming Process. J. Manuf. Mater. cyclic load tests. With the gained experimental and numerical data, the workbench was used for the Process. 2021, 5, 49. https://doi.org/ ﬁrst time to generate the desired component as a CAD model, as well as to derive design guidelines 10.3390/jmmp5020049 referring to the investigated properties and fatigue behavior.

Academic Editor: Steven Y. Liang Keywords: sheet-bulk metal forming; mechanical properties; self-learning engineering workbench; functional behavior; fatigue life modeling; Z-integral approach Received: 20 April 2021 Accepted: 11 May 2021 Published: 17 May 2021 1. Introduction Publisher’s Note: MDPI stays neutral Due to increasing economic and ecologic restrictions and a rising demand for global with regard to jurisdictional claims in sustainability, new products and technology approaches are necessary to meet the upcom- published maps and institutional affil- ing challenges [1]. Especially in the manufacturing industry, the development of innovative iations. solutions is essential to meet requirements and emerging challenges. New approaches such as light-weight design and functional integration are applied to reduce weight on the one hand, and to increase the functionality on the other hand [2]. Consequently, conventional manufacturing processes are reaching their limits due to an increased complexity of the Copyright: © 2021 by the authors. components and a lack in production efficiency. The innovative process class of sheet- Licensee MDPI, Basel, Switzerland. bulk metal forming (SBMF) offers the possibility to meet these challenges by an efficient This article is an open access article manufacturing of functional components with a shortened process chain and improved distributed under the terms and mechanical properties [3]. By applying bulk forming operations to sheet metal, the three- conditions of the Creative Commons dimensional stress and strain states can be used to locally adjust the thickness or properties Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ of the component. Within the Transregional Collaborative Research Centre 73 (TCRC 73), 4.0/). this process class is investigated fundamentally, applying different process approaches to

J. Manuf. Mater. Process. 2021, 5, 49. https://doi.org/10.3390/jmmp5020049 https://www.mdpi.com/journal/jmmp J. Manuf. Mater. Process. 2021, 5, 49 2 of 18

manufacture components with varying geometric dimensions and functional elements. An overview of the possible geometries, as well as the corresponding manufacturing processes, are given in [4]. Furthermore, a comparison of the required forming force and the possible material volume by the different operations was presented. During the investigation, the conﬂict between the desired geometry and the process limits could be shown and the neces- sity of pre-calculated values referring to the mechanical properties and the performance in operation for an optimized component design could be demonstrated. Since the functional components are exposed to cyclic load during usage [5], the analysis and evaluation of the fatigue life is mandatory for characterizing the potential of an increased performance. In order to allow a future substitution of conventionally manufactured components with SBMF parts, the comparison between the initial material state and the work-hardened state as a consequence of cold forming appears reasonable. Within this contribution, functional components with circumferential involute gearing manufactured by an SBMF process are investigated regarding their geometrical and mechanical properties. To generate a fundamental data basis and to ensure the manufac- turability of the components, a geometry-based and a data-based approach are combined within the self-learning engineering workbench SLASSY. To support the design of complex components in the context of SBMF, a geometry-based approach, referring to the overview of different manufacturing processes in [4], should be implemented into the self-learning engineering workbench [6]. By fundamentally investigating and evaluating a process combination of deep drawing and upsetting to manufacture functional components with circumferential involute gearing, the mechanical and geometrical properties, as well as the fatigue life of the component, should be analyzed. Besides the use of a conventional blank of the mild deep drawing steel DC04 (1.0338 DIN EN 10130), the potential of process-adapted semi-ﬁnished products applied within the process combination should be evaluated. The applied methodology is exemplarily shown in Figure1. In order to predict different characteristics on the basis of design parameters for possible geometries and to expand the applicability of the engineering workbench SLASSY within the context J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 3 of 19 of SBMF, this contribution is concluded by a data-based analysis of the geometrical and mechanical properties.

FigureFigure 1. 1.Applied Applied methodologymethodology within the the present present contribution. contribution.

2. Geometry-Based Approach within SLASSY Since the process class of SBMF is characterized by a three-dimensional stress and strain state as well as material flow and a complex tool and process setup, the design of such components requires a comprehensive process and component understanding. In this context, the self-learning engineering workbench SLASSY was created. With its application in sheet-bulk metal forming, the synthesis between geometrical parameters and mechanical properties should be enabled [6]. The step of creating design rules with the help of different experimental investigations is thereby replaced by the possibilities of the workbench. SLASSY automatically extracts and presents relevant knowledge during the design process inside the CAD system used. For this purpose, techniques from direct and indirect knowledge acquisition are used. Moreover, machine learning methods are applied to extract implicit knowledge from simulation or experimental data by means of metamodels [7]. These models are a description of the correlation between the input product features, such as the geometry, and output product properties, such as the manufacturing parameters [6]. In the first step, developers design the SBMF part inside their CAD system with the support of the SLASSY workbench. This is the so-called synthesis step, which combines geometrical properties with the related manufacturing process. Sheet- bulk metal formed components can be configured by choosing a basic body element from a given set of primary design elements (PDE) such as flat or curved sheets or cups. Sec- ondary design elements (SDE) such as carriers or gearings can be added to complete the functional component [6]. All presented functional components in [4] are implemented in the database and can be combined to create new parts independently. An overview of the desktop surface with exemplarily depicted elements and the described synthesis step is shown in Figure 2. The combination of the cup as a primary design element and the involute gearing as a secondary design element results in the depicted component on the bottom right side. The generated component is generated in the CAD system used according to the chosen elements and can then be further processed.

J. Manuf. Mater. Process. 2021, 5, 49 3 of 18

2. Geometry-Based Approach within SLASSY Since the process class of SBMF is characterized by a three-dimensional stress and strain state as well as material flow and a complex tool and process setup, the design of such components requires a comprehensive process and component understanding. In this context, the self-learning engineering workbench SLASSY was created. With its application in sheet-bulk metal forming, the synthesis between geometrical parameters and mechanical properties should be enabled [6]. The step of creating design rules with the help of different experimental investigations is thereby replaced by the possibilities of the workbench. SLASSY automatically extracts and presents relevant knowledge during the design process inside the CAD system used. For this purpose, techniques from direct and indirect knowledge acquisition are used. Moreover, machine learning methods are applied to extract implicit knowledge from simulation or experimental data by means of metamodels [7]. These models are a description of the correlation between the input product features, such as the geometry, and output product properties, such as the manufacturing parameters [6]. In the first step, developers design the SBMF part inside their CAD system with the support of the SLASSY workbench. This is the so-called synthesis step, which combines geometrical properties with the related manufacturing process. Sheet-bulk metal formed components can be configured by choosing a basic body element from a given set of primary design elements (PDE) such as flat or curved sheets or cups. Secondary design elements (SDE) such as carriers or gearings can be added to complete the functional component [6]. All presented functional components in [4] are implemented in the database and can be combined to create new parts independently. An overview of the desktop surface with exemplarily depicted elements and the described synthesis step is shown in Figure2 . The combination of the cup as a primary design element and the involute gearing as a secondary design element results in the depicted component on J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 4 of 19 the bottom right side. The generated component is generated in the CAD system used according to the chosen elements and can then be further processed.

FigureFigure 2. 2. PartPart design design and and the the synthesis synthesis step withinwithin SLASSY.SLASSY.

TheThe second second step step of of applying applying the the workbench isis thethe analysisanalysis step step of of the the geometry geometry pa- pa- rametersrameters and and mechanical mechanical properties properties considering thethe selected selected experimental experimental results. results. In In the the following,following, the the experim experimentalental investigation of of the the parts parts manufactured manufactured with with the the process process combi- com- binationnation ofof deep deep drawing drawing and and upsetting upsetting is presented.is presented. The The main m aspectsain aspects in this in context this context are the are the geometrical and mechanical properties, as well as the determination of the fatigue life of the sheet-bulk metal formed parts, as compared to conventionally manufactured components.

3. Mechanical Analysis In contrast to the state of the art as described in [8], a combined deep drawing and upsetting process to manufacture functional components with a circumferential involute gearing was investigated in the present contribution, cf. Figure 3. The involute gearing featured a module of 1.0 mm with a tooth width of 2.5 mm, defined by the tip radius of 42.7 mm and the root radius of 40.2 mm. The total number of teeth was 84, which were evenly distributed around the circumference.

Figure 3. Investigated component geometry.

In this chapter, the experimental setup is explained for generating a basic process and component understanding. Furthermore, the forming results, as well as the possibilities for enlarging the forming limits within the described process, are presented.

J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 4 of 19

Figure 2. Part design and the synthesis step within SLASSY.

The second step of applying the workbench is the analysis step of the geometry parameters and mechanical properties considering the selected experimental results. In the following, the experimental investigation of the parts manufactured with the process com- J. Manuf. Mater. Process. 2021, 5, 49 bination of deep drawing and upsetting is presented. The main aspects in this 4context of 18 are the geometrical and mechanical properties, as well as the determination of the fatigue life of the sheet-bulk metal formed parts, as compared to conventionally manufactured components.geometrical and mechanical properties, as well as the determination of the fatigue life of the sheet-bulk metal formed parts, as compared to conventionally manufactured components. 3. Mechanical Analysis 3. Mechanical Analysis In contrast to the state of the art as described in [8], a combined deep drawing and In contrast to the state of the art as described in [8], a combined deep drawing and upsetting process to manufacture functional components with a circumferential involute upsetting process to manufacture functional components with a circumferential involute gearinggearing was was investigated investigated inin the the present present contribution, contribution, cf. Figurecf. Figure3. The 3. involute The involute gearing gearing featuredfeatured a amodule module of 1.01.0 mmmm with with a a tooth tooth width width of 2.5of 2.5 mm, mm deﬁned, defined by the by tip the radius tip radius of of 42.742.7 mm mm and and the the root radiusradius of of 40.2 40.2 mm. mm. The The total total number number of teeth of teeth was 84,was which 84, which were were evenlyevenly distributed distributed around the the circumference. circumference.

FigureFigure 3. 3. Investigated component component geometry. geometry.

InIn this this chapter, chapter, the experimentalexperimental setup setup is explainedis explaine ford generatingfor generat aing basic a basic process process and and J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 5 of 19 componentcomponent understanding. understanding. Furthermore,Furthermore, the the forming forming results, results as well, as well as the as possibilities the possibilities forfor enlarg enlarginging the the forming limits limits within within the the described described process, process are, presented. are presented.

3.1. Forming3.1. Forming Process Process For theFor investigation, the investigation, a mild a de mildep drawing deep drawing steel DC04 steel (1.0338) DC04 (1.0338) was used was with used an with in- an initial sheet thickness of t = 2.0 mm and an initial diameter of d = 100.0 mm. This steel itial sheet thickness of t0 = 2.0 0mm and an initial diameter of d0 = 100.00 mm. This steel is

characterizedis characterized by a high by formability a high formability at medium at mediumstrength and strength is used and in isautomobile used in automobile appli- cationsapplications such as different such as c differenthassis parts chassis or narrow parts orprofiles. narrow The proﬁles. mechanical The mechanical properties propertiesof the materialof the are material presented are presented in Figure in 4. Figure Besides4. Besides the material the material parameters parameters such such as the as yield the yield strength,strength, the flow the ﬂowcurve curve is shown, is shown, which which was wasgenerated generated by layer by layer-compression-compression tests testsand and extrapolated with the Hocket–Sherby approach to enable a realistic material behavior in extrapolated with the Hocket–Sherby approach to enable a realistic material behavior in the context of SBMF processes with three-dimensional compressive stresses. the context of SBMF processes with three-dimensional compressive stresses.

DC04 t = 2.0 mm, d = 100.0 mm 0 0 Value 600 Yield 169 MPa ± σ strength 0.50 MPa MPa Tensile 320 MPa ● Measurement strength ± 0.47 MPa stress 200 ▬ Hocket-Sherby n 0.21

rue 0 HV0.05 124.5 ± 7.4 T 0.00,0 0.20,2 0.40,4 0.60,6 mm- 1,01.0 True plastic strain ε

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

Within the TCRC 73, the process combination of deep drawing and upsetting to manufacture functional components with a demonstrator gearing was fundamentally investigated [8]. This investigation focused on the component with an involute gearing, thus differing in the process and tool setup, as presented in the following paragraph. The setup of the combined, single-stage deep drawing and upsetting process is depicted in Figure 5. The tool consisted of a drawing punch, a drawing die, an upsetting punch, and an upsetting plate. The sheet was placed onto the drawing punch and clamped by the upsetting punch with a clamping force of FC = 400 kN. The deep drawing process began with an axial movement of the drawing die, which was controlled by the drawing force FD 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 FUp 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.

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

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3.1. Forming Process For the investigation, a mild deep drawing steel DC04 (1.0338) was used with an initial sheet thickness of t0 = 2.0 mm and an initial diameter of d0 = 100.0 mm. This steel is characterized by a high formability at medium strength and is used in automobile appli- cations 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.

DC04 t = 2.0 mm, d = 100.0 mm 0 0 Value 600 Yield 169 MPa ± σ strength 0.50 MPa MPa Tensile 320 MPa ● Measurement strength ± 0.47 MPa stress 200 ▬ Hocket-Sherby n 0.21

rue 0 HV0.05 124.5 ± 7.4 T 0.00,0 0.20,2 0.40,4 0.60,6 mm- 1,01.0 True plastic strain ε

Figure 4. Material characterization of DC04 [4]. J. Manuf. Mater. Process. 2021, 5, 49 5 of 18 Within the TCRC 73, the process combination of deep drawing and upsetting to manufacture functional components with a demonstrator gearing was fundamentally investigated [8]Within. This the investigation TCRC 73, the focused process on combination the component of deep with drawing an involute and upsetting gearing, to thus differingmanufacture in the functionalprocess and components tool setup, with as presented a demonstrator in the gearingfollowing was paragraph. fundamentally investigated [8]. This investigation focused on the component with an involute gearing, The setup of the combined, single-stage deep drawing and upsetting process is de- thus differing in the process and tool setup, as presented in the following paragraph. picted inThe Figure setup 5. of theThe combined, tool consisted single-stage of a drawing deep drawing punch, and a upsettingdrawing processdie, an isupsetting de- punchpicted, and in an Figure upsetting5. The toolplate. consisted The sheet of awas drawing placed punch, onto the a drawing drawing die, punch an upsetting and clamped by punch,the upsetting and an upsettingpunch with plate. a Theclamping sheet was force placed of F ontoC = 400 the drawingkN. The punchdeep anddrawing clamped process beganby thewith upsetting an axial punch movement with a clampingof the drawing force of die,FC = which 400 kN. was The controlled deep drawing by the process drawing forcebegan FD to with form an the axial cup movement wall. After of the reaching drawing the die, upsetting which was plate, controlled the upsetting by the drawing process was initiatedforce F withinD to form the the same cup wall.stroke After by reachingthe displacement the upsetting of the plate, drawing the upsetting die as process a consequence was initiated within the same stroke by the displacement of the drawing die as a consequence of an applied upsetting force FUp into the upsetting punch. Subsequently, the cup wall was of an applied upsetting force F into the upsetting punch. Subsequently, the cup wall was reduced in height and a lateralUp material flow into the cavity located on the inner side of reduced in height and a lateral material flow into the cavity located on the inner side of thethe drawing drawing die die was was realized. realized. The The finalfinal heightheight of of the the component component depended depended on the on defined the defined formingforming force. force.

FigureFigure 5. Schematic 5. Schematic setup setup of ofthe the combined combined deep drawingdrawing and and upsetting upsetting process process [8]. [8].

3.2. Forming Results

In the first step, a conventional blank with an initial sheet thickness of t0 = 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 tmin = 1.76 mm, whereas the maximum sheet thickness amounted to tmax = 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 FUp = 800 kN. The resulting part contour is presented in Figure6. The cup height after upsetting amounted to h = 8.41 mm. Since the material 3 volume provided by the conventional blank remained constant at Vconv = 6754 mm , the form filling of the tooth area including the cup wall was only dependent on the desired 3 cup height. Referring to a required material volume of Vreq = h × 932.7 mm /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 Figure5. 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. J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 6 of 19

3.2. Forming Results

In the first step, a conventional blank with an initial sheet thickness of t0 = 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 tmin = 1.76 mm, whereas the maximum sheet thickness amounted to tmax = 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 FUp = 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 Vconv = 6754 mm³, 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 Vreq = h × 932.7 mm³/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 J. Manuf. Mater. Process. 2021, 5, 49 6 of 18 to cold hardening in areas of high deformation, thus revealing an increase of 87% up to 233.4 ± 30.1 HV0.05.

Figure 6. Experimental results obtained with a conventional blank. Figure 6. Experimental results obtained with a conventional blank. Regarding the results referring to the use of a conventional blank, the process limits wereRegarding clearly visible. the results To enable referring a near to net-shape the use contourof a conventional of the final blank, part, the the form process filling, limits wereand clearly thus the visible. maximum To enable material a near thickening, net-shape in the contour cup wall of the had final to be part, increased the form by the filling, andapplication thus the maximum of process strategies material in thickening order to control, in the the cup material wall flow. had to be increased by the application of process strategies in order to control the material flow. 3.3. Process Strategies to Enlarge the Form Filling 3.3. ProcessIn order Strategies to avoid to processEnlarge failuresthe Form during Filling the manufacturing of the functional components, a defined control of the material flow was mandatory. Apart from the application ofIn tailored order to surfaces avoid onprocess the tool failures side [ 10during] or thermal the manufacturing grading [11], of the the use functional of rotational components,symmetric a defined tailored control blanks, of the products material with flow process-adapted was mandatory. geometrical Apart from and mechanicalthe application of tailoredproperties, surfaces offers greaton the potential tool side [8]. [10] Additionally, or thermal due grading to the adapted[11], the thickness use of rotational profile of sym- metricthe semi-finishedtailored blanks, products, products the diewith filling process during-adapted the subsequent geometrical forming and process mechanical can be properties,increased. offers Forgreat the potential manufacturing [8]. Additionally, of such tailored due blanks to the with adapted various thickness thickness profile profiles, of the semithe-finished two different products, sheet-bulk-metal the die filling forming during processes the subsequent of orbital forming forming andprocess a circular can be in- flexible rolling process were investigated within the TCRC 73. In order to achieve the creased. For the manufacturing of such tailored blanks with various thickness profiles, the high process forces, which are typical for sheet-bulk-metal forming, both processes have twoincremental different sheet properties.-bulk-metal Thereby, forming the orbital processes forming of processorbital isforming similar and to a conventionala circular flexible rollingupsetting process process, were investigated with the difference within being the TCRC that one 73. toolIn order component to achieve is adjusted the high by process a defined tumbling angle. In Figure7a, the process setup is schematically shown for the initial position, as well as for the tumbling position. This tool concept was used in a TZP400/3 hydraulic deep-drawing press from Lasco with an additional tumbling plate. At the process beginning, the forming force F was applied by the upper punch, which had a defined punch angle, whereby the perpendicular axis was fixed in its position. Subse- quently, the counterpunch, with die cavities as a counterpart of the tailored blank, moved with a defined tumbling motion and angle. The course of the tumbling angle depending on the number of tumbling cycles is shown in Figure7b. It can be divided into three phases, the upcoming phase, where the tumbling angle is increased to the target value. Depending on the process setup, a maximum tumbling angle of 1◦ could be achieved. During the constant phase, the tumbling angle was held constant on the target value with a subsequent decrease to the initial position in the third phase. By using this process setup, tailored blanks with homogenous rotational and cyclic-symmetric thickness profiles [8], as well as discrete functional elements such as involute gearings perpendicular to the sheet plane or both-sided thickenings [12], could be manufactured. Thus, it offers potential for increasing the component quality, as well as for shortening the process chain. J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 7 of 19

forces, which are typical for sheet-bulk-metal forming, both processes have incremental properties. Thereby, the orbital forming process is similar to a conventional upsetting process, with the difference being that one tool component is adjusted by a defined tumbling angle. In Figure 7a, the process setup is schematically shown for the initial position, as well as for the tumbling position. This tool concept was used in a TZP400/3 hydraulic deep-drawing press from Lasco with an additional tumbling plate. At the process beginning, the forming force F was applied by the upper punch, which had a defined punch angle, whereby the perpendicular axis was fixed in its position. Subsequently, the counterpunch, with die cavities as a counterpart of the tailored blank, moved with a defined tumbling motion and angle. The course of the tumbling angle depending on the number of tumbling cycles is shown in Figure 7b. It can be divided into three phases, the upcoming phase, where the tumbling angle is increased to the target value. Depending on the process setup, a maximum tumbling angle of 1° could be achieved. During the constant phase, the tumbling angle was held constant on the target value with a subsequent decrease to the initial position in the third phase. By using this process setup, tailored blanks with homogenous rotational and cyclic-symmetric thickness profiles [8], as well as discrete functional elements such as involute gearings perpendicular to the sheet plane or J. Manuf. Mater. Process. 2021, 5, 49both-sided thickenings [12], could be manufactured. Thus, it offers potential for 7increas of 18 ing the component quality, as well as for shortening the process chain.

FigureFigure 7. ( 7.a) (Processa) Process setup setup and and ( (bb)) characteristics of of orbital orbital forming forming [4]. [4]. In addition to the orbital forming process, a new circular flexible rolling process was investigatedIn addition within to the the orbital TCRC forming 73. The process, fundamental a new principle circular of flexible the rolling rolling process process is was investigatedshown in Figure within8 and the described TCRC 73. in The detail fundamental in [ 8]. At the principle process beginning, of the rolling the initial process is shownblank in was Figure clamped 8 and onto described the rotary in tabledeta byil in a hydraulic[8]. At the blank process holder. beginning, Just as in the the initial orbital blank wasforming clamped process, onto the rotaryrotary table table had by diea hydraulic cavities with blank the geometryholder. Just of theas in counterpart the orbital of form- ingthe process, target tailoredthe rotary blank table geometry. had die Thereby, cavities the with rotary the table geometry could moveof the infinitely counterpart along of the targetthe z-axistailored and bl hadank an geometry. active rotatory Thereby, drive. the On rotary the other table side, could the twomove rolling infinitely tools were along the only pivoted on the x-axis and could move in a linear direction. Due to a defined vertical z-axis and had an active rotatory drive. On the other side, the two rolling tools were only roll displacement ∆t related to the surface of the blank superimposed with the rotational pivotedmovement on the of x the-axis rotary and table could and move the horizontal in a linear movement direction. of theDue rolling to a defined tools, a defined vertical roll displacementmaterial flow ∆t in therelated radial, to axial, the and surface tangential of the directions blank superimposed could be achieved. with By mounting the rotational movementdifferent of rotary the tablesrotary with table varying and the geometries, horizontal the movement same tailored of the blanks rolling as by tools, using a the defined materialorbital flow forming in the process radial, could axial be, manufactured. and tangential Compared direction tos thecould orbital be achieved. forming process, By mount- J. Manuf. Mater. Process. 2021, 5, xing FORthe different PEER advantage REVIEW rotary of the tables flexible with rolling varying machine geometries, was the significant the same reductiontailored blanks of the contact as by using 8 of 19 thearea. orbital Thus, forming the required process forming could forcebe manufactured. was reduced, with Compared the advantage to the oforbital extending forming the pro- process limits for the formability of even higher strength materials. cess, the advantage of the flexible rolling machine was the significant reduction of the contact area. Thus, the required forming force was reduced, with the advantage of extending the process limits for the formability of even higher strength materials.

FigureFigure 8. 8.Process Process setup setup of ﬂexible of flexible rolling [rolling8]. [8].

Depending on the process control strategy, similar thickening heights could be achieved Depending on the process control strategy, similar thickening heights could be with orbital forming [8], as well as with the ﬂexible rolling processes [13]. In Figure9, the averageachieved sheet with thickness orbital is shownforming for a[8] rotational, as well and as awith cyclic-symmetric the flexible tailored rolling blank processes [13]. In geometry.Figure 9, Thethe respectiveaverage sheet target geometrythickness is is shown shown on thefor righta rotational side. While and an a average cyclic-symmetric tai- sheetlored thickness blank ge ofometry.tavg = 2.51 The± 0.51respective mm was target achieved geometry by the tumbling is shown of a on rotational the right side. While symmetric tailored blank, a thickening of tavg = 2.46 ± 0.47 mm could be achieved by the an average sheet thickness of tavg = 2.51 ± 0.51 mm was achieved by the tumbling of a ﬂexible rolling process. Especially when manufacturing a cyclic-symmetric tailored blank rotational symmetric tailored blank, a thickening of tavg = 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. The application of tool sided tailored surfaces can also be used for the targeted control of the material flow for the manufacturing of tailored blanks. Investigations in [14] have shown that an increase in the die filling can be achieved by applying high-feed milled surfaces. Depending on the orientation of the modified surface, the material flow can be improved or inhibited.

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

Comparing the overall results, the tailored blanks manufactured by orbital forming showed the highest average material thickness in the desired area. Therefore, the tailored blank was further processed in the combined deep drawing and upsetting process, aiming at improved part properties. After the deep drawing operation, the cup height amounted to h = 13.41 mm. Thus, the cup drawn from the tailored blank was more than 1.3 mm lower than the cup drawn from the conventional semi-finished product due to the cold hardening of the material and the reduced thinning at the drawing punch radius. In the subsequent upsetting operation, the cup height was reduced by applying a maximum upsetting

J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 8 of 19

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

Depending on the process control strategy, similar thickening heights could be achieved with orbital forming [8], as well as with the flexible rolling processes [13]. In Figure 9, the average sheet thickness is shown for a rotational and a cyclic-symmetric tailored blank geometry. The respective target geometry is shown on the right side. While an average sheet thickness of tavg = 2.51 ± 0.51 mm was achieved by the tumbling of a rotational symmetric tailored blank, a thickening of tavg = 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 J. Manuf. Mater. Process. 2021, 5, 49by the material flow during the orbital forming process. 8 of 18 The application of tool sided tailored surfaces can also be used for the targeted control of the material flow for the manufacturing of tailored blanks. Investigations in [14] havegeometry, shown that it can an be increase seen that in a the more die homogenous filling can be sheet achieved thickness by applying can be achieved high-feed in the milled surfaces.thinned Depending area for the ﬂexibleon the rollingorientation process, of sincethe modified the center surface, thinning effectthe material is caused flow by the can be improvedmaterial or ﬂow inhibited. during the orbital forming process.

J. Manuf. Mater.Figure Process. 9. Average 2021, 5, x sheet FOR thicknessesPEER REVIEW for the orbital forming and flexible rolling processes for different geometries. 9 of 19 Figure 9. Average sheet thicknesses for the orbital forming and flexible rolling processes for different geometries. The application of tool sided tailored surfaces can also be used for the targeted control ofComparing the material the flow overall for the manufacturingresults, the tailored of tailored blanks blanks. manufactured Investigations by inorbital [14] have forming showforceshowned o thef thatFmax highest = an 800 increase kNaverage to inthe the materialdrawn die fillingcup. thickness According can be in achieved theto the desired process by applying area. description Therefore, high-feed in S the milledection tailored blank3.1,surfaces. wasthe material furt Dependingher inprocessed the on cup the wallin orientation the was combined forced of the to deep modifiedflow drawinginto surface, the gear and the cavity.upsetting material The flowprocess,additional can beaiming at improvedmaterialimproved allocated orpart inhibited. properties. within the After manufacturing the deep drawingof the tailored operation, blank theenabled cup heightan improve- amounted ment of the die filling and the reduction of the deviation to the target geometry, as pre- to h = 13.41Comparing mm. Thus, the overallthe cup results, drawn the from tailored the tailored blanks manufactured blank was more by orbital than 1.3 forming mm lower sentedshowed in theFigure highest 10. average material thickness in the desired area. Therefore, the tailored than the cup drawn from the conventional semi-finished product due to the cold harden- blankBy was applying further the processed orbital formed in the combined tailored blank deep drawingin the investigated and upsetting process process, chain, aiming the ing of the material and the reduced thinning at the drawing punch radius. In the subse- providedat improved volume part in properties. the outer Aftersegment the reached deep drawing VTB = 8152.5 operation, mm³. theReferring cup height to the amounted formula quenttoto calculateh upsetting= 13.41 the mm. operation, required Thus, the material the cup cup drawn volumeheight from wasVreq the reduced= h tailored × 932.7 by blank mm³/mmapplying was and morea maximum an than actual 1.3 upsetting cupmm heightlower of than h = the8.98 cup mm, drawn the form from filling the conventional could be increased semi-finished to 98%. product due to the cold hardeningThe functional of the material component and theshowed reduced only thinning minor areas at the of drawing insufficient punch die radius. filling. In This the underlinessubsequent the upsetting potential operation, of the application the cup heightof tailored was blanks reduced in SBMF by applying processes. a maximum The mi- crostructureupsetting force depicted of Fmax in= Figure 800 kN 10 to confirms the drawn this cup. potential, According as both to the process process failures description were reducedin Section by 3.1applying, the material a tailored in theblank. cup Furthermore, wall was forced the homogeneity to flow into the of the gear hardness cavity. Thein- creasedadditional due material to an improved allocated material within flow the manufacturing control. The average of the tailoredhardness blank value enabled of 220.3 an ± 22.9improvement HV0.05 represented of the die fillinga decrease and theof 6% reduction compared of the to the deviation hardness to theof the target conventionally geometry, as manufacturedpresented in Figure component. 10.

Figure 10. Experimental results obtained with the investigated tailored blank layout. Figure 10. Experimental results obtained with the investigated tailored blank layout.

Within this paragraph, the properties of the components, as well as the possibility of optimizing the target values, were presented. This geometrical and mechanical properties can be used as basic metadata for the engineering workbench. To comprehensively evaluate the industrial applicability of the components, investigations on the fatigue behavior were carried out.

4. Fatigue Life Testing and Modeling In order to predict the fatigue life of the sheet-bulk metal formed components, a fatigue model was elaborated and parameterized. Subsequently, cyclic fatigue experiments were carried out on the components’ external toothing for validation. The fatigue model could then be used to calculate a fatigue life prediction for the work-hardened material state and also for the initial state of the DC04 mild steel. This is assumed to be a good indicator for comparing the benefits of the forming technology in contrast to manufacturing by machining. By implementing the fatigue model into the SLASSY workbench, the influence of alternative geometries to the components’ fatigue strength could be determined.

J. Manuf. Mater. Process. 2021, 5, 49 9 of 18

By applying the orbital formed tailored blank in the investigated process chain, the 3 provided volume in the outer segment reached VTB = 8152.5 mm . Referring to the formula 3 to calculate the required material volume Vreq = h × 932.7 mm /mm and an actual cup height of h = 8.98 mm, the form filling could be increased to 98%. The functional component showed only minor areas of insufficient die filling. This underlines the potential of the application of tailored blanks in SBMF processes. The microstructure depicted in Figure 10 confirms this potential, as both process failures were reduced by applying a tailored blank. Furthermore, the homogeneity of the hardness increased due to an improved material flow control. The average hardness value of 220.3 ± 22.9 HV0.05 represented a decrease of 6% compared to the hardness of the conventionally manufactured component. Within this paragraph, the properties of the components, as well as the possibility of optimizing the target values, were presented. This geometrical and mechanical properties can be used as basic metadata for the engineering workbench. To comprehensively evaluate the industrial applicability of the components, investigations on the fatigue behavior were carried out.

4. Fatigue Life Testing and Modeling In order to predict the fatigue life of the sheet-bulk metal formed components, a fatigue model was elaborated and parameterized. Subsequently, cyclic fatigue experiments were carried out on the components’ external toothing for validation. The fatigue model could then be used to calculate a fatigue life prediction for the work-hardened material state and also for the initial state of the DC04 mild steel. This is assumed to be a good indicator for comparing the beneﬁts of the forming technology in contrast to manufacturing by machining. By implementing the fatigue model into the SLASSY workbench, the inﬂuence of alternative geometries to the components’ fatigue strength could be determined.

4.1. Fatigue Life Modeling A fracture mechanical approach was used for predicting the fatigue life of the sheet- bulk metal formed components. To consider the elastic–plastic material behavior, the cyclic ∆J-integral approach [15], also referred to as the Z-integral approach [16], was employed. Thereby, the crack propagation per cycle da/dN was calculated depending on the elastic Wel,eff and plastic Wpl energy densities converted during one cycle (Equations (1) and (2)). This approach was established for unalloyed and low-alloy steels [17].

da = C ·(Z)mJ (1) dN J Z = a· 2.9·Wel, eff + 2.5·Wpl (2)

The parameters CJ and mJ 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 Wel,eff and Wpl can be determined. Wpl is provided by the area below the ascending hysteresis-branch [18]. The effective elastic energy density Wel, eff can be obtained from the effective stress amplitude ∆σeff, for which the fatigue crack is opened and capable of growth, and from the Young’s modulus E as ∆σ 2 W = eff (3) el, eff 2E

The number of cycles to failure Nf can then be calculated by integrating the crack propagation from an initial crack length a0 to a given crack length af, which is used as the failure criterion: (1−m ) (1−m ) a J − a J N = f 0 f mJ (4) CJ·(1 − mJ)·(2.9·Wel, eff + 2.5·Wpl) J. Manuf. Mater. Process. 2021, 5, 49 10 of 18

4.2. Data Acquisition on Different Material States Since the secondary form elements were too ﬁligree to extract fatigue specimens and also possessed strongly graded properties (cf. hardness mapping in Figure 10), a material state had to be produced that featured mechanical properties similar to the components, as presented in more detail in [5]. For this purpose, sheet metal strips from DC04 were rolled from their initial sheet thickness of 3 mm to 1 mm using a two-roll rolling mill. In hardness measurements, this material state showed an average hardness of 193 HV10 (determined at 5 measuring points, standard deviation <3%) and agreed well with the hardness in the tooth root area of the component (cf. Figure 10). From these sheet metal strips, the specimens for strain-controlled fatigue experiments were extracted in the rolling direction, as schematically depicted in Figure 11a. Stress–strain hysteresis on those specimens were recorded during the fatigue tests at different strain amplitudes (∆ε/2 = 0.2% to 0.8%). The energy densities per cycle were calculated as described, and a cyclic stress–strain curve was determined that described the cyclic stress–strain J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 11 of 19 behavior for the cyclically stabilized (here, cyclically softened) material state. In addition, such tests were carried out on the DC04 initial state to record the corresponding data.

FigureFigure 11. (a) 11. Specimen(a) Specimen geometry geometry and and orientation, orientation, (b ()b test) test setup setup of of the strain-controlledstrain-controlled fatigue fatigue experiments. experiments.

For Forthe thefatigue fatigue experiments, experiments, a servo a servo-hydraulic-hydraulic testing testing machine machine (M (MTS,TS, Landmark Landmark 100 100 kN) and appropriate buckling supports were used to avoid the buckling of the speci- kN) and appropriate buckling supports were used to avoid the buckling of the specimens mens (cf. Figure 11b). Thereby, graphite spray was used to minimize the friction between (cf. Figurethe buckling 11b). supportThereby and, graphite the specimen. spray Thewas tests used were to minimize performed the with friction a mean between strain of the bucklingεm = 0 support(strain ratio andRε the= − 1) specimen. and a test frequencyThe tests of were 3 Hz. performed The hysteresis with loops a clearly mean show strain of εm =the 0 (strain increased ratio strength Rε = −1) of and the rolleda test andfrequency work-hardened of 3 Hz. The material hysteresis condition loops compared clearly toshow the increasedthe initial state, strength see Figure of the 12 rolled. and work-hardened material condition compared to the initial state, see Figure 12.

(a) DC04 Initial state (b) DC04 Rolled material 600 600

MPa400 MPa400

200 200 σ σ 0 0 Stress Stress −200-200 −200-200

−400-400 −400-400

−600-600 −600-600 −-11 −-0,50.5 0 0,5% 1 −-11 -0,5−0.5 0 0,5% 1 Strain ε Strain ε

Figure 12. Hysteresis loops for the (a) initial state and (b) the rolled material state.

Based on the upper reversal points of these hysteresis loops, cyclic stress–strain curves were determined as shown in Figure 13. These were employed as material data for the simulation of the resulting equivalent stress distribution at the form elements of the component under an assumed service load.

J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 11 of 19

Figure 11. (a) Specimen geometry and orientation, (b) test setup of the strain-controlled fatigue experiments.

For the fatigue experiments, a servo-hydraulic testing machine (MTS, Landmark 100 kN) and appropriate buckling supports were used to avoid the buckling of the specimens (cf. Figure 11b). Thereby, graphite spray was used to minimize the friction between the buckling support and the specimen. The tests were performed with a mean strain of εm = 0 (strain ratio Rε = −1) and a test frequency of 3 Hz. The hysteresis loops clearly show J. Manuf. Mater. Process. 2021, 5, 49 11 of 18 the increased strength of the rolled and work-hardened material condition compared to the initial state, see Figure 12.

(a) DC04 Initial state (b) DC04 Rolled material 600 600

MPa400 MPa400

200 200 σ σ 0 0 Stress Stress −200-200 −200-200

−400-400 −400-400

−600-600 −600-600 −-11 −-0,50.5 0 0,5% 1 −-11 -0,5−0.5 0 0,5% 1 Strain ε Strain ε

FigureFigure 12. 12.Hysteresis Hysteresis loops loops for for the the (a ()a initial) initial state state and and (b ()b the) the rolled rolled material material state. state.

BasedBased on on the the upper upper reversal reversal points points of of these these hysteresis hysteresis loops, loops, cyclic cyclic stress–strain stress–strain curves were determined as shown in Figure 13. These were employed as material data for J. Manuf. Mater. Process. 2021, 5, x FOR PEERcurves REVIEW were determined as shown in Figure 13. These were employed as material12 dataof 19 for the simulation of the resulting equivalent stress distribution at the form elements of the the simulation of the resulting equivalent stress distribution at the form elements of the component under an assumed service load. component under an assumed service load.

550 DC04 Initial state Rolled material MPa450 σ 350 Stress 250

150 0,00 0.20,2 0.40,4 0.60,6 0,8% 1,01.0 Strain ε

Figure 13. Cyclic stress–strain curves determined for the initial and rolled material state, compiled Figurefrom 13. [5]. Cyclic stress–strain curves determined for the initial and rolled material state, compiled from [5]. 4.3. Fatigue Testing of the SBMF-Components 4.3. FatigueIn the Testing fatigue of experiments,the SBMF-Components single teeth of the toothing were subjected to alternating loads.In the A fatigue test ﬁxture experiments, was constructed single teeth that of engaged the toothing one tooth were andsubjected could to be alternating clamped in loads.a universal A test fixture testing was machine, constructed as shown that in engaged Figure 14one. These tooth experimentsand could be were clamped performed in a universalemploying testing force machine control, as at shown a frequency in Figure of 5 14. Hz. These The experime tested componentsnts were performed had a toothing em- ployingheight force of 8.8 control mm (corresponds at a frequency to of the 5 Hz. overall The z-heighttested components as shown inhad Figure a toothing 10) and height were oftested 8.8 mm with (corresponds load amplitudes to the betweenoverall z- 900height N andas shown 1800 N. in In Figure order 10) to beand able were to plottested the withresults load in amplitudes an SN-diagram, between the 900 resulting N and maximum1800 N. In order tooth rootto be stresses able to plot were the calculated results in for anthese SN-diagram, loads by the a quasi-static resulting maximum simulation tooth using root the stresses software were Ansys, calculated as exemplarily for these shown loads in byFigure a quasi 14-statica. To simulation estimate the using equivalent the software stresses Ansys, for the as component,exemplarily theshown cyclic in Figure stress–strain 14a. Tocurves estimate of thethe rolled equivalent material stresses state shownfor the incomponent, Figure 13 were the cyclic used asstress the– materialstrain curves data. of The thesimulation rolled material yielded state the shown largest in Figure equivalent 13 were stress used in as the the area material of the data. tooth The root simulation where the yieldedcomponents the largest in the equivalent tests also stress showed in the the area occurrence of the tooth of fatigue root where cracks, the see components Figure 14b. in the tests also showed the occurrence of fatigue cracks, see Figure 14b.

Figure 14. (a) Calculated von Mises stress for a service load of 1800 N and (b) the test setup for the fatigue tests.

4.4. Fatigue Life Prediction and Experimental Results To calculate the fatigue life, the hysteresis loops recorded from the rolled material condition were evaluated and the corresponding values were used in Equation (4). For the crack propagation parameters, CJ = 6.4 ×∙10−9 mm/cycle and mJ = 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].

J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 12 of 19

550 DC04 Initial state Rolled material MPa450 σ 350 Stress 250

150 0,00 0.20,2 0.40,4 0.60,6 0,8% 1,01.0 Strain ε

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

4.3. Fatigue Testing of the SBMF-Components In the fatigue experiments, single teeth of the toothing were subjected to alternating loads. A test fixture was constructed that engaged one tooth and could be clamped in a universal testing machine, as shown in Figure 14. These experiments were performed employing force control at a frequency of 5 Hz. The tested components had a toothing height of 8.8 mm (corresponds to the overall z-height as shown in Figure 10) and were tested with load amplitudes between 900 N and 1800 N. In order to be able to plot the results in an SN-diagram, the resulting maximum tooth root stresses were calculated for these loads by a quasi-static simulation using the software Ansys, as exemplarily shown in Figure 14a. To estimate the equivalent stresses for the component, the cyclic stress–strain curves of the rolled material state shown in Figure 13 were used as the material data. The simulation J. Manuf. Mater. Process. 2021, 5, 49 12 of 18 yielded the largest equivalent stress in the area of the tooth root where the components in the tests also showed the occurrence of fatigue cracks, see Figure 14b.

FigureFigure 14. 14. ((aa)) Calculated Calculated von von Mises Mises stress stress for for a a service service load load of of 1800 1800 N N and and ( (bb)) the the test test setup setup for for the the fatigue fatigue tests. tests.

4.4. Fatigue Life Prediction and Experimental Results 4.4. Fatigue Life Prediction and Experimental Results To calculate the fatigue life, the hysteresis loops recorded from the rolled material To calculate the fatigue life, the hysteresis loops recorded from the rolled material condition were evaluated and the corresponding values were used in Equation (4). For condition were evaluated and the corresponding values were used in Equation (4). For the crack propagation parameters, CJ = 6.4 ×∙10−9 9mm/cycle and mJ = 1.48 were assumed. the crack propagation parameters, CJ = 6.4 × 10 mm/cycle and mJ = 1.48 were assumed. TheseThese values were were determined determined in in long-crack long-crack growth growth experiments experiments on work-hardened on work-hardened DC04 DC04and converted and converted accordingly accordingly for the Z-integral for the Z-integral approach approach [5]. These [5] results. These corresponded results corre- to spondthe expectationsed to the expectations for low-alloy for steels low-alloy as reported steels as in reported the literature in the [19 li].terature [19]. The crack length at failure was set to af = 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 a0 = 5 µm was chosen for the fatigue life calculation. Employing these parameters, the calculated fatigue life corresponded well with the results of the fatigue experiments on individual teeth, as shown in Figure 15. For an optimal adaptation to the experimental results, a virtual initial crack length of about 2.5 µm could be determined by an inverse calculation. Thus, the crack length was in the range of microstructural defects, as they were caused by ductile damage. Here, performing further adaptions to the fatigue model was renounced, as the data available for an optimization were quite small. In general, the data points of the fatigue experiments (gray dots in Figure 15) showed a certain scattering, as was to be expected from the tests on the components. In this case, slight deviations of the mold filling or notches on the surface of the form elements had an influence on the fatigue life. J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 13 of 19

The crack length at failure was set to af = 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 a0 = 5 µm was chosen for the fatigue life calculation. Employing these parameters, the calculated fatigue life corresponded well with the results of the fatigue experiments on individual teeth, as shown in Figure 15. For an optimal adaptation to the experimental results, a virtual initial crack length of about 2.5 µm could be determined by an inverse calculation. Thus, the crack length was in the range of microstructural defects, as they were caused by ductile damage. Here, performing further adaptions to the fatigue model was renounced, as the data available for an optimization were quite small. In general, the data points of the fatigue experiments (gray dots in Figure

J. Manuf. Mater. Process. 2021, 5, 49 15) showed a certain scattering, as was to be expected from the tests on the components.13 of 18 In this case, slight deviations of the mold filling or notches on the surface of the form elements had an influence on the fatigue life.

Experimental Data (Fatigue tests on SBMF parts) 500 calculated (Work hardened material state) calculated (Initial state)

MPa400 /2 σ ∆ 300

200 amplitude

100 Stress

0 1.0001000 10.00010,000 100.000100,000 1.000.0001,000,000

Cycles to failure Nf

Figure 15. S-N-curves determined for the different material states. Figure 15. S-N-curves determined for the different material states. In order to evaluate the influence of work hardening due to the cold forming on the In order to evaluate the influence of work hardening due to the cold forming on the fatigue life, Figure 15 also shows a predicted SN-curve that resulted from the material data fatigue life, Figure 15 also shows a predicted SN-curve that resulted from the material set for the DC04 in its initial state. Comparing the two material states, it can be seen that data set for the DC04 in its initial state. Comparing the two material states, it can be seen the bearable stresses could be approximately doubled. This shows that the work hardening thatdue the to thebearable cold formingstresses ledcould to be a significant approximately increase doubled. in service This life. shows Thus, that it the can work be deduced hard- eningthat thedue performance to the cold forming in operation led to can a significant be considerably increase increased in service by life. the formingThus, it processcan be deducedcompared that to the manufacturing performance by, in e.g.,operation machining. can be considerably increased by the forming process compared to manufacturing by, e.g., machining. 5. Data-Based Approach within SLASSY 5. DataIn-Based this section, Approach the potentialwithin SLASSY application of the findings from the previous chapters insideIn thethis engineeringsection, the workbenchpotential application SLASSY are of shown. the findings In the from first paragraph, the previous the chapters function- insideality ofthe the engineering training of theworkbench metamodels SLASSY based are on shown. the validated In the simulation first paragraph, data is the described. func- The investigative part of this contribution is closed with a prediction of the analyzed component parameters and an optimization on the basis of the generated metamodels in order to generate a manufacturable part.

5.1. Metamodel Training After the fatigue model was validated in the previous chapter and the findings regarding the degree of form filling were shown in Section3, the tooth height could be identified as a relevant design parameter for the fatigue curve. To evaluate the influence of different parameter combinations, a simulation study was carried out as described in Section 4.3. Therefore, the tooth height was varied in five steps between 7 mm and 10 mm, also including the experimental result at 8.8 mm. These points could be used to train metamodels for the application inside SLASSY. Based on the five simulations carried out, the resulting load amplitude over cycles to failure was plotted and the resulting data points were extracted. These data were then stored inside a tabular dataset and used to train a metamodel. When a dataset was added for the first time for the training, the input (in this case, the tooth height) and targets (the load curve and the degree of form filling) had to be selected manually. Each time SLASSY was reopened, the initial dataset was checked for changes, and when new data were available, the model was trained with the updated dataset automatically. An exponential function showed the best potential to predict curves for arbitrarily selected tooth heights. After training, the metamodel was able to predict the resulting curve with an average coefficient of prognosis (CoP) [24] of 95.88% and a root J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 14 of 19

tionality of the training of the metamodels based on the validated simulation data is described. The investigative part of this contribution is closed with a prediction of the analyzed component parameters and an optimization on the basis of the generated metamodels in order to generate a manufacturable part.

5.1. Metamodel Training After the fatigue model was validated in the previous chapter and the findings regarding the degree of form filling were shown in Section 3, the tooth height could be identified as a relevant design parameter for the fatigue curve. To evaluate the influence of different parameter combinations, a simulation study was carried out as described in Sec- tion 4.3. Therefore, the tooth height was varied in five steps between 7 mm and 10 mm, also including the experimental result at 8.8 mm. These points could be used to train metamodels for the application inside SLASSY. Based on the five simulations carried out, the resulting load amplitude over cycles to failure was plotted and the resulting data points were extracted. These data were then stored inside a tabular dataset and used to train a metamodel. When a dataset was added for the first time for the training, the input (in this case, the tooth height) and targets (the load curve and the degree of form filling) had to be selected manually. Each time SLASSY was reopened, the initial dataset was checked for changes, and when new data were available, the model was trained with the updated J. Manuf. Mater. Process. 2021, 5, 49 dataset automatically. An exponential function showed the best potential to predict14 of 18 curves for arbitrarily selected tooth heights. After training, the metamodel was able to predict the resulting curve with an average coefficient of prognosis (CoP) [24] of 95.88% andmean a root squared mean error squared (RMSE) error of (RMSE)±85.7 N. of A ±85.7 possible N. A prediction possible prediction of the trained of the metamodel trained metamodelfor the resulting for the fatigue resulting curve fatigue for a selectedcurve for tooth a selected height tooth of 9.0 height mm and of two9.0 mm curves and for two the curvesneighboring for the neighboring tooth heights tooth with heights±0.5 mm with are ±0.5 shown mm in are Figure shown 16 a.in ToFigure predict 16a. the To degree predict of theform deg filling,ree of aform dataset filling, of tooth a dataset heights of rangingtooth heights between ranging 8 mm between and 10 mm 8 mm and and the resulting10 mm anddegree the resulting of form filling degree for of a conventionalform filling for blank, a conventional as well as for blank a tailored, as well blank, as for was a used.tailored The blankresults, was of chapterused. The 3 were results collected of chapter and 3 stored were insidecollected SLASSY’s and stored database. inside For SLASSY’s the prediction database.of the For degree the prediction of form filling, of the a decisiondegree of tree form regressor filling, [25a decision] was used tree within regressor the metamodel, [25] was usedwhich within basically the metamodel, consisted of anwhich ensemble basically of linear consisted models of andan ensemble was able toof predictlinear models the data andpoints was withable ato coefficient predict the of data prognosis points with of 97.85% a coefficient and a root of prognosis mean squared of 97.85% error and of ± a 2.05%root meanfor the squared degree error of form of ±2.05% filling. for Both the degree prediction of form qualities filling. wereBoth estimatedprediction usingqualities an were 80/20 estimatedtrain-test-split using a [26n 80],/ which20 train indicated-test-split an [26] 80%, which use indicated of the datapoints an 80% use for of training the datapoints and 20% forfor training the testing and and20% evaluation for the testing of CoP and and evaluation RMSE. Figureof CoP 16 andb shows RMSE. the Figure prediction 16b shows of the thedegree prediction of form of filling the degree for the of conventional form filling andfor the tailoredconventional blank. and Lastly, the thetailored data andblank. the Lastly,metamodels the data were and stored the metamodels in tabular form were inside stored SLASSY’s in tabular own form SQL-based inside SLASSY’s database. Thisown is SQLmandatory-based database. for subsequent This is retrievalmandatory and for application. subsequent retrieval and application.

(a) (b) Tailored Blank 8.5 mm 2000 100 Conventional 9.0 mm N % 1600 9.5 mm 90 85 1400 80 1200 75 1000 70 800 65 0 0 Load amplitude 0 250,000250000 550000000,000 - 1,000,0000 00.00.00 8,508.50 9,009.00 mmmm 10,0010.00 Degree of form filling Cycles to failure NFNf Tooth height

FigureFigure 16. 16. (a()a Resulting) Resulting curves curves for for different different tooth tooth heights heights predicted predicted by by the the trained trained metamodel metamodel,, and and (b ()b the) the predicted predicted degree degree ofof form form filling ﬁlling for for a aconventional conventional and and a atailored tailored blank. blank.

5.2. Application inside SLASSY In order to use the generated data for the evaluation of the geometrical parts, as shown exemplarily in Figure2, a ﬁnal analysis step inside SLASSY was required. With

this step, the prediction of resulting product properties, for example, the load curve or the degree of form filling from known or given product characteristics (tooth height) was now possible [27]. For this step, the described metamodels were implemented into the database and the properties were displayed in the analysis table. As shown in Figure2, the current geometric parameters such as the tooth height were transmitted into SLASSY directly from the CAD system; in the presented case, Dassault Systèmes CATIA V5-6R2013x. Afterwards, the database was then able to predict the resulting curve and degree of form filling in the analysis step. This was set up via a bidirectional interface described in [6]. The resulting curves and the degree of form filling could then be presented to the product developers via datasheets or plots, as in Figure 16. With the presented data-driven approach, it was possible to use the generated data inside SLASSY to optimize the current part design, regarding an ideal degree of form filling or fatigue life requirements with implemented optimization algorithms, as shown in [28]. By selecting a desired value of the investigated parameter, the data-driven approach enabled the determination of the respective geometrical parameters, as exemplarily shown in Figure 17a. For example, 1000 N was selected for a desired maximum load amplitude, and the minimum number of cycles to failure had to be 500,000. Thus, the tooth height was predicted at a value of 9.7 mm by the trained metamodels. As shown in Figure 17b, the degree of form filling only reached 74.7% using a conventional blank. In this case, for the J. Manuf. Mater. Process. 2021, 5, x FOR PEER REVIEW 15 of 19

5.2. Application inside SLASSY In order to use the generated data for the evaluation of the geometrical parts, as shown exemplarily in Figure 2, a final analysis step inside SLASSY was required. With this step, the prediction of resulting product properties, for example, the load curve or the degree of form filling from known or given product characteristics (tooth height) was now possible [27]. For this step, the described metamodels were implemented into the database and the properties were displayed in the analysis table. As shown in Figure 2, the current geometric parameters such as the tooth height were transmitted into SLASSY directly from the CAD system; in the presented case, Dassault Systèmes CATIA V5-6R2013x. Af- terwards, the database was then able to predict the resulting curve and degree of form filling in the analysis step. This was set up via a bidirectional interface described in [6]. The resulting curves and the degree of form filling could then be presented to the product developers via datasheets or plots, as in Figure 16. With the presented data-driven approach, it was possible to use the generated data inside SLASSY to optimize the current part design, regarding an ideal degree of form filling or fatigue life requirements with implemented optimization algorithms, as shown in [28]. By selecting a desired value of the investigated parameter, the data-driven approach enabled the determination of the respective geometrical parameters, as exemplarily shown in Figure 17a. For example, 1000 N was selected for a desired maximum load am- J. Manuf. Mater. Process. 2021, 5, 49 15 of 18 plitude, and the minimum number of cycles to failure had to be 500,000. Thus, the tooth height was predicted at a value of 9.7 mm by the trained metamodels. As shown in Figure 17b, the degree of form filling only reached 74.7% using a conventional blank. In this case, forpreviously the previously described described parameter parameter combination, combination, SLASSY SLASSY could predictcould predict that a conventional that a con- ventionalblank was blank not feasiblewas not forfeasible realizing for realizing an acceptable an acceptable degree ofdegree form of ﬁlling. form However,filling. How- the ever,system the suggestedsystem suggested the application the application of a tailored of a blank tailored in theblank investigated in the investigated process in process order to inreach order an to acceptable reach an acceptable degree of formdegree ﬁlling of form of 90.1%. filling of 90.1%.

(a) (b) ‒ 9 mm FF Tailored Blank 2000 100 ‒ Determind tooth height 9.7 mm FF Conventional N ‒ 10 mm % 1600 90 1400 85 80 1200 75 10001000 70

Load amplitude 800 65 9.7 mm 0 0

0 250,000250000 500,000500000 - 1,000,0001000000 Degree of form filling 0.000.00 8,508.50 9,009.00 mmmm 10,0010.00 Cycles to failure Tooth height

FigureFigure 17. 17. ((aa)) Prediction Prediction of tooth heightheight forfor givengiven cycles cycles to to failure failure and and load load amplitude amplitude and and (b) ( theb) the respective respective degree degree of form of formﬁlling filling for conventional for convention andal tailoredand tailored blanks, blank evaluateds, evaluated by the by trained the trained metamodels. metamodels.

6.6. Discussion Discussion WithinWithin this this contribution, a a fundamental fundamental process process understanding understanding of the of combinedthe combined deep deepdrawing drawing and and upsetting upsetting process process for manufacturingfor manufactur thin-walleding thin-walled functional functional components compo- nentswith with circumferential circumferen gearingtial gearing could could be generated. be generated. In particular, In particular, the the influence influence of theof the use useof differentof different semi-finished semi-finished products products on on the the forming forming results results werewere investigated.investigated. Using Using a a conventionalconventional blank blank made made out out of of the the mild mild deep deep drawing drawing steel steel DC04, DC04, the the material material volume volume providedprovided in in the the area area ofof the the later later cup cup wall wall was was not notsufficient sufficient to allow to allow a proper a proper filling filling of the of cavity,the cavity, hence hence only onlyreaching reaching a maximum a maximum of 86%. of 86%. Consequen Consequently,tly, process process failures failures such such as bucklingas buckling and andfolding folding could could be detected, be detected, thus contributing thus contributing to the results to the resultsin [9] for in a [ 9differ-] for a entdifferent geometry. geometry. An increasing An increasing material material strength strengthdue to cold due hardening to cold hardening during the during forming the operationforming operationrepresented represented another limiting another factor limiting for realizing factor for the realizing desired the geometry, desired geometry,reaching reaching an average of 233.4 ± 30.1 HV0.05, thus showing an increase of 87% compared to the initial hardness and revealing an inhomogeneous distribution across the cup wall, referring to the high standard deviation. In this context, the control of the material flow could be identified as a major challenge [4]. In order to increase the degree of form filling by adjusting the material flow into the cavity and to prevent the process failures, a new process strategy was applied. By using process-adapted semi-finished parts with a local material pre-distribution, the material could be provided in the required areas. Due to further available material volume, the form filling of the component could be increased up to 98%. The evaluation of the hardness distribution revealed a decreased average hardness value of 220.3 ± 22.9 HV0.05, thus supporting the material flow due to a reduced strength compared to the conventional blank. Furthermore, the homogeneity of the formed tooth in form of the standard deviation could be increased significantly, and the process failures could be prevented, thus confirming the results in [8]. The components manufactured out of a tailored blank offered the highest values for the degree of form filling, thus being identified as the most applicable for the subsequent investigation of the fatigue life. To consider the performance of the components already in the design phase, the data of a fatigue model were provided for the SLASSY workbench. Therefore, the fatigue properties of the component could be simulated by means of a work-hardened material state that featured almost the same hardness as the components’ toothing. Assuming an initial crack length of 5 µm, a good agreement of the calculated fatigue life with the results of fatigue experiments could be achieved. Furthermore, the improvement of the fatigue properties due to the cold forming was shown here in comparison with a further J. Manuf. Mater. Process. 2021, 5, 49 16 of 18

data set for the material condition of the DC04 steel as received. By extending these data by further degrees of deformation as presented in [5], the fatigue model could be used to calculate a fatigue life prognosis for any work-hardened material state after forming. Implemented in the SLASSY workbench, this enabled the calculation of a fatigue life prognosis for any part geometry, considering the hardness of the respective form element after the forming process. In order to implement the generated data into the workbench, a data-driven approach was applied. In this context, an exponential function for the prediction of the resulting curves for a given tooth height could be identified as the most promising approach regarding the prediction quality. For predicting the degree of form filling of either conventional or tailored blank designs, a decision tree regressor could be classified as sufficient, regarding the root mean squared error and the coefficient of prognosis. The presented metamodels were mathematical constructs to inter- or extrapolate between the data points, created in the simulation and experimental studies described previously. For this representation, it was possible to predict the resulting values for a selected input value, in this case, the tooth height. Moreover, both models showed acceptable prediction qualities for general usage, as their values of the coefficient of prognosis were well above 90%, and the root mean squared error was orders of magnitude lower than the total value. The presented methods offer the potential for application to various processes and different geometries within sheet-bulk metal forming, as previously presented in [6]. Based on the simulations and experimental studies, the presented metamodels can be used to optimize a given part design regarding its manufacturing properties inside SLASSY. For example, the values for optimization can be the degree of form filling or the desired load amplitude and cycles to failure. These metamodels can also be used in the context of rapid prototyping to generate different design alternatives for product developers. The presented methods can be applied to all different tooth and part designs within the context of sheet-bulk metal forming. To create metamodels for other geometries, the desired process or geometry parameter must be investigated for the respective geometry. Furthermore, the fatigue-life-model needs to be updated regarding the part design.

7. Conclusions In this contribution, a fundamental analysis of the mechanical properties of components manufactured by sheet-bulk metal forming processes was carried out. To determine the fatigue life, a fatigue model was presented and validated by cyclic experiments on the functional form elements of the components. To allow the synthesis between the geometrical and mechanical properties of the parts, the self-learning engineering workbench SLASSY was trained with the help of metamodels to calculate the maximum achievable form filling, as well as the fatigue life, on the example of different component heights. The main conclusions of this research can be summarized as follows: • 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 J. Manuf. Mater. Process. 2021, 5, 49 17 of 18

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. In order to evaluate the transferability of the fatigue model used in combination with the data-driven approach of the workbench, further research should focus on the investigation of different geometries in the context of sheet-bulk metal forming. Furthermore, the database could be expanded by the application and evaluation of different material classes and strength levels within the presented setup.

Author Contributions: Conceptualization, A.H., R.S., M.V., M.L., H.-B.B., H.J.M., C.S., B.S., S.W. and M.M.; methodology, A.H., M.L., H.-B.B. and C.S.; software, A.H., H.-B.B. and C.S.; validation, A.H., H.-B.B. and C.S.; formal analysis, M.L., H.J.M., B.S., S.W. and M.M.; investigation, A.H., R.S., M.V. and H.-B.B.; resources, H.J.M., S.W. and M.M.; data curation, A.H., H.-B.B. and C.S.; writing—original draft preparation, A.H., R.S., M.V., H.-B.B. and C.S.; writing—review and editing, M.L., H.J.M., B.S., S.W. and M.M.; visualization, A.H., R.S., M.V., H.-B.B. and C.S.; supervision, M.L., H.J.M., B.S., S.W. and M.M.; project administration, M.L. and M.M.; funding acquisition, M.M. All authors have read and agreed to the published version of the manuscript. Funding: This work is funded within the scope of the Transregional Collaborative Research Centre TCRC73 by the German Research Foundation under Grant number TRR73-68237143. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The related data generated and analyzed for the contribution is available from the corresponding author on request. The related code for the metamodels, used within the workbench, is available from C. Sauer on request. Acknowledgments: This study was supported by the German Research Foundation (DFG) within the scope of the Transregional Collaborative Research Centre on Sheet-Bulk metal forming (TCRC 73). It has been realized in particular with the help of the subprojects A1, B1, C6, and T02. Furthermore, special thanks go to the research group “Component Properties and Function” which is also active in the context of the TCRC 73 research compound. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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