Sheet-bulk forming of three-dimensional features in metal and polymer blanks

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1 Original article Sheet-bulk forming of three-dimensional features in metal and polymer blanks Proc IMechE Part L: J Materials: Design and Applications 0(0) 1 9! IMechE 2018 Article reuse guidelines: sagepub.com/journals-permissions DOI: / journals.sagepub.com/home/pil JP Magrinho, MB Silva and PAF Martins Abstract The main objective of this paper is to investigate material flow and force requirement in sheet-bulk forming processes where loading is applied perpendicular to sheet thickness. The presentation draws from material characterization to experimental and numerical analysis of process parameters related to the material and geometry of the blanks, and to the shape of the forming punches. The work is performed in aluminum AA-5754-H111 and polycarbonate and is a step towards exploring the potential of using sheet-bulk forming to produce polymer parts at room temperature. Incremental sheet-bulk forming of polymer rack gears demonstrate the potential of the process to fabricate small batches of complicate parts widely used in machines and mechanisms. Keywords Sheet-bulk forming, metals, polymers, gears, experimentation, finite element method Date received: 7 July 2018; accepted: 5 August 2018 Introduction Lightweight design and construction of machines and mechanisms has been stimulating the development of new fabrication processes that allow minimizing the number of parts, reduce weight, and cut assembly and maintenance costs by combining two or more functional features together in a single sheet metal part. The combination of different functional features with tight geometric tolerances and the specification of variable thicknesses to reduce weight often incurs in sheet metal parts with increasing geometric complexity, ineffective material utilization, and substantial manufacturing costs. 1 In addition, the technical specifications of these parts may also not fall within the scope of applicability of conventional manufacturing processes. These challenges encouraged the development of a new group of advanced metal forming processes designated as sheet-bulk forming by Merklein et al. 2 and plate forging by Mori and Nakano, 3 which combines plane-stress conditions of sheet forming and three-dimensional stress settings of bulk forming. The goal in sheet-bulk forming is to produce sheet parts with massive local shape changes and smaller surface-to-volume ratios than the original blanks. The changes in surface-to-volume ratios result from making geometric details outside the plane of the blanks from which they are produced. In case of sheet metal parts with gear features, several sheet-bulk forming processes have been proposed in which compression is combined with drawing and ironing, 4 compression is combined with flanging, 5 and forging is combined with fine blanking, 6 among others that are comprehensively described in the state-of-theart review by Merklein et al. 7 In contrast to the above sheet-bulk forming processes that aim to produce sheet metal parts in a single or a limited number of press strokes, there are situations in which small batches and customized production requirements demand the use of incremental sheet-bulk metal forming processes that circumvent the utilization of complex and expensive tool systems installed in large capacity presses. The first step in this direction was given by Sieczkarek et al., 8 who proposed the fabrication of functional features in sheet metal parts by incremental compression in the direction perpendicular to thickness. The deformation mechanics of this process and its application to the fabrication of disk gears made from DC04 steel were subsequently investigated by Sieczkarek et al. 9,10 This paper revisits the incremental sheet-bulk forming of metals by investigating material flow and force requirements in the indentation of rectangular and circular aluminum blanks by flat, curved, and IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal Corresponding author: PAF Martins, IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Av. Rovisco Pais, Tecnologia Mecanica, Lisbon , Portugal. pmartins@tecnico.ulisboa.pt

2 2 Proc IMechE Part L: J Materials: Design and Applications 0(0) gear tooth punches, and gives the first step towards the extension of sheet-bulk forming to polymers. The potential of producing polymer gears by incremental sheet-bulk forming is investigated and comparisons are made with gears fabricated in aluminum. Results show that incremental sheet-bulk forming of polymers can be successfully applied to low-volume production, at room temperature, of gears that are widely used in machines and mechanisms. Experimentation Materials and mechanical characterization The work was carried out in aluminum AA5754-H111 and polycarbonate (PC) sheets with 5 mm of thickness. The mechanical characterization of the aluminum alloy was performed by means of stack compression tests 11 in specimens that were assembled by pilling up three circular discs with 15 mm diameter and 5 mm thickness machined out of the supplied sheets. No tensile tests were performed because the stack compression test is able to provide the mechanical characterization of the aluminum alloy for larger strains than the onset of necking in tension. The mechanical characterization of PC was performed by means of tensile and stack compression tests, because the material is pressure sensitive and provides different stress response in tension and compression. The tensile specimens were machined out of the supplied sheets in accordance to the ASTM D standard, 12 whereas the stack compression specimens were prepared in a similar manner to that of aluminum. The tensile and stack compression tests were carried out at room temperature in a hydraulic testing machine (Instron SATEC 1200 kn) with a cross-head speed of 5 mm/min. The resulting stress strain curves are shown in Figure 1 and the local drop in stress that is observed in the PC stress strain curves is attributed to the transition between viscoelastic and plastic material flow regimes. Work plan, methods, and procedures The tool utilized in the experiments is schematically shown in Figure 2(a) and was installed in the hydraulic testing machine where material characterization tests were performed. Its design is an evolution of a concept originally proposed by Silva et al. 13 to allow forming both rectangular and circular blanks with different punch shapes (Figure 2(b) and (c)). The main components of the tool are: (a) the punch holder, (b) the blank holders, (c) the die shoe, and (d) the guide rails. The punch holder moves vertically with the press ram and securely fastens the sheetbulk forming punches. The forming punches have three different shapes (Figure 2(b)) and are made from a tool steel C265, which was tempered to ensure a surface hardness of approximately 64 HRC. The blank holders are made from PM400 steel plates and include screws to clamp the blanks firmly in position during the indentations. The die shoe is also made from PM400 steel and holds and ensures the alignment of the blank holders for thicknesses up to 10 mm. The guide rails allow the die shoe to slide horizontally in order to move the blanks with the required pitch length to fabricate rack gears made of a series of straight teeth. In case of disk gears, the blanks are rotated by means of a small rod inserted through a hole in the blank holder. All the blanks were positioned with 20 mm above the surface of the blank holders in order to ensure free thickening of the plastically deforming region during the entire sheet-bulk indentation depths (forming depths). The experimental work plan consisted of two different sets of tests. The first set of tests involved the indentation of rectangular and circular blanks in the direction perpendicular to thickness by flat, circular, and gear tooth punches. The geometry of the gear tooth punch was defined in accordance to the DIN 867 profile, module 1.5. The main objective of these tests was the characterization of plastic flow in sheet-bulk indentation and the overall work is an extension to polymers of a previous investigation in aluminum EN AW-1050A. 9 The tests performed in AA5754-H111 were utilized for reference purposes. The second set of tests involved multiple indentations to produce rack and disk gears. For this purpose, the blanks were moved horizontally by a distance corresponding to the pitch p (in case of rack gears, Figure 3(a)) or, were rotated by an angle (in case of disk gears, Figure 3(b)) after each indentation. The angle of the circular pitch was determined from ¼ p R p ð1þ where R p is the radius of the pitch circle (Figure 3(b)). Finite element modeling The sheet-bulk indentation of rectangular and circular blanks was numerically simulated with the in-house finite element computer program i-form. The program is based on the irreducible finite element flow formulation and accounts for the contact with friction between rigid and deformable objects Z Z ¼ _ " dv þ 1 2 K _" 2 v dv T i u i ds V V ZS T Z Z jur j þ f du r ds ð2þ S f 0

3 Magrinho et al. 3 Figure 1. Stress strain curves of the aluminum AA5754-H111 and polycarbonate sheets. Figure 2. Sheet-bulk indentation of rectangular and circular blanks: (a) schematic representation of the experimental setup with a circular blank; (b) flat, curved, and gear tooth punches; and (c) rectangular and circular blanks. Figure 3. Schematic representation and notation in multiple sheet-bulk indentation by a gear tooth punch: (a) fabrication of a rack gear in a rectangular blank; and (b) fabrication of a disk gear in a circular blank.

4 4 Proc IMechE Part L: J Materials: Design and Applications 0(0) Figure 4. Initial mesh utilized in the finite element simulation of the sheet-bulk indentation of a rectangular blank by a gear tooth punch in the direction perpendicular to thickness. Figure 5. Sheet-bulk indentation of rectangular blanks by a flat punch: (a) experimental and finite element evolutions of the force vs. displacement for AA5754-H111 and PC; and (b) details of the indentations in AA5754-H111 (top) and PC (bottom) at the end of punch stroke. The left pictures show the real specimens while the right pictures show the corresponding finite element models. FEM: finite element method; EXP: experimental. In the above functional, is the effective stress, _ " is the effective strain rate, _" v is the volumetric strain rate, K is a large positive constant imposing the incompressibility of volume V, T i and u i are the surface tractions and velocities on surface S T, f and u r are the friction shear stress and the relative velocity on the contact interface S f between the blank and the tool. Friction is modeled through the utilization of the law of constant friction. Details of the computer implementation with special emphasis on the explicit time integration algorithm, minimization of the residual force, and remeshing procedure are available elsewhere. 14 The numerical simulation of the sheet-bulk indentation of the PC blanks made use of the extended finite element flow formulation 15 that utilizes the following yield function Fð ij Þ proposed by Caddell et al. 16 F ij ¼ 2 C T þð C T Þ kk ¼ 0 ð3þ In the above equation, T and C are the tensile and compressive flow stresses, which account for the strength differential effect of pressure-sensitive materials like PC. The symbol kk ¼ ij ij is the hydrostatic pressure, where ij is the Kronecker delta. The numerical simulation of the sheet-bulk indentations was performed in plane stress conditions because the blanks are thin and their thickness is smaller than the length of the plastically deforming region. The blanks were discretized by means of 12,000 quadrilateral elements and the tools were modeled as rigid objects and discretized by means of linear contact-friction elements (Figure 4). The overall central processing unit (CPU) time for a typical indentation requiring six intermediate remeshing was approximately equal to 25 min on a computer equipped with an Intel i7-6700hq Processor (2.6 GHz). Results and discussion Sheet-bulk indentations with flat, curved, and gear tooth punches Figure 5(a) shows the experimental and finite element evolution of the force with displacement for the

5 Magrinho et al. 5 Figure 6. Sheet-bulk indentation of rectangular and circular blanks of AA5754-H111: (a) schematic representation of the contact length and of the plastically deformed region in the indentation of blanks by flat and curved punches; (b) experimental and finite element evolutions of the force vs. displacement for the flat punch; (c) experimental and finite element evolutions of the force vs. displacement for the curved punch; and (d) experimental and finite element evolutions of the force vs. displacement for the gear tooth punch. FEM: finite element method; EXP: experimental. sheet-bulk indentation of AA 5754-H111 and PC rectangular blanks by a flat punch. The force in the AA 5754-H111 blank shows a monotonic increase with displacement due to combination of strain hardening and growing contact area between the punch and the blank. The contact between the punch and the blank is also responsible for thickening of the plastically deforming region. The force displacement evolution of PC is similar to that of AA 5754-H111, apart from a small drop in the force at approximately 1.4 mm of punch displacement. This drop is caused by the transition between the viscoelastic and plastic regimes of the polymer as it was previously mentioned in the stress strain curve of PC (Figure 1). The maximum forces at the end of the punch stroke are equal to 35 kn in AA 5754-H111 and to 8 kn in PC and reflect the differences in material strength. The agreement between experimental and finite element predictions is good as can be further seen in the details of the real and numerically computed geometries of AA 5754-H111 and PC at the end of the punch stroke. Measurements and predictions of the final thickness of the blanks in the plastically deformed region allow concluding that maximum thickening is approximately equal to 50% and 40.8% for the AA 5754-H111 and PC specimens, respectively. Figure 6 shows a resume of the first set of tests performed with different punch geometries (flat, curved, and gear tooth) and different blank shapes (rectangular and circular) for AA5754-H111. As seen, the agreement between experimental results and finite element predictions is excellent and the influence of material strain hardening in the force displacement evolution is clearly observed in the indentation of rectangular blanks by flat and curved punches (Figure 6(b) and (c)). In fact, despite the contact length s of the curved punch being larger than that of the flat punch (2R) at the end of the punch stroke, the extent of the plastically deforming region and, therefore, the amount of strain hardening is larger in case of the flat punch (Figure 6(a)). This explains the reason why the compression force of the flat punch is larger at the end of stroke.! c s ¼ arcsin h þ c2 h þ c2 4h 4h ¼ 16:3 mm4 2R ¼ 15 mm sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c ¼ R h 8h ¼ 13:3 mm 2 In the above equation, h ¼ 4 mm is the displacement at the end of the punch stroke and R ¼ 7:5 mm is the half-length of the flat punch (and ð4þ

6 6 Proc IMechE Part L: J Materials: Design and Applications 0(0) Figure 7. Multiple sheet-bulk indentations in an AA5754-H111 rectangular blank to fabricate a rack gear: (a) schematic representation of the multiple sheet-bulk indentation process; (b) experimental and finite element evolutions of the force vs. displacement for the first, second, and third indentations; and (c) details of the indentations at the end of the punch stroke. The left picture shows the real specimen while the right picture shows the corresponding finite element model. FEM: finite element method; EXP: experimental. also, the radius of the curved punch), according to Figures 2(b) and 6(a). The influence of the growing rate of the contact area between the punch and the blank can be analyzed by observing the results of the indentation of rectangular and circular blanks by a flat punch (Figure 6(b)). In fact, because contact starts at the center of the punch and progressively extends to its full length in case of circular blanks, whereas it starts with full length in case of rectangular blanks, it follows that thickening of the plastically deforming region is reduced and force growing rate is smaller at the beginning of the indentation. However, the growing rates become identical for larger indentation depths because the amount of material undergoing plastic deformation and thickening becomes similar. The influence of the growing rate of the contact area between the punch and the blank is not significant in case of indentations with curved punches (Figure 6(c)), because the initial contact length is very small s 2R. Similar results were obtained for PC blanks. The localized deformation below the wedges of the gear tooth punch at the beginning of the indentation is also the reason why rectangular and circular blanks provide almost identical results (Figure 6(d)). This justifies the reason why the next section of the paper that is focused on multiple sheet-bulk indentations with a gear tooth punch will be exclusively focused on rectangular blanks. Multiple sheet-bulk indentations with a gear tooth punch Figure 7(a) shows a schematic representation of the multiple sheet-bulk indentations in a rectangular

7 Magrinho et al. 7 Figure 8. Multiple sheet-bulk indentations in a PC rectangular blank to fabricate a rack gear: (a) experimental and finite element evolutions of the force vs. displacement for the first, second, and third indentations; and (b) details of the indentations at the end of the punch stroke. The left picture shows the real specimen while the right picture shows the corresponding finite element model. FEM: finite element method; EXP: experimental. blank by a gear tooth punch to fabricate a rack gear. The experimental and finite element predicted evolutions of the force with displacement for the first, second, and third indentations of AA 5754-H111 are disclosed in Figure 7(b). As seen, the evolution of the force with displacement for the first indentation is equal to that shown in Figure 6(d), because the process is identical to a single indentation of a rectangular blank in the direction perpendicular to thickness. The second indentation is also a compression in the direction perpendicular to thickness but only half of the gear tooth punch is plastically deforming the material (refer to the finite element models placed inside Figure 7(b)), because the step size between the first and second indentations (4.72 mm) is identical to the pitch p. Also, for this reason, the evolution of the force with displacement in the second indentation (up to a punch displacement of approximately 2.8 mm) is half of the force measured in the first indentation, during which both the left and right punch wedges were plastically deforming the material. Beyond a punch displacement of 2.8 mm, the force starts growing faster because the left wedge of the gear tooth punch gets in contact with the material being formed by the right wedge and confine the material to its final shape. At the end of the second indentation, the force becomes equal to that of the first indentation because the left wedge of the gear tooth punch also gets in full contact with the blank. Subsequent indentations (third, fourth, etc.) are similar to the second indentation, because the deformation mechanism is identical. For this reason, the corresponding force displacement evolutions are equal to that of the second indentation. Figure 7(c) shows details of the final rack gear at the end of the sheet-bulk indentation process and the corresponding finite element predicted geometry. As seen, both real and numerical predicted geometries of the first indentation lead to under filling of the punch cavity, due to a significant material flow constraint originated by the adjacent volume of the nondeforming material. The same phenomenon had been previously observed in case of disk gears made from DC04 steel and the solution is to use a tailored blank with additional volume in the region where the first indentation will take place. 10 Figure 8(a) shows the experimental and finite element evolutions of the force with displacement

8 8 Proc IMechE Part L: J Materials: Design and Applications 0(0) for the first, second, and third indentations of a PC rectangular blank by a gear tooth punch. The agreement between the experimental and finite element predictions of the force-displacement evolution and of the final geometries is good (Figure 8(a) and (b)). Similar to AA 5754-H111, there is underfilling of the punch cavity during the first indentation due to a significant material flow constraint imposed by the adjacent volume of the nondeforming material. The results obtained for PC demonstrate that multiple sheet-bulk indentations of a polymer blank can be utilized to fabricate rack and disk gears. However, in case of polymers it is necessary to account for the elastic recovery of the material due to the small values of the elasticity modulus (approximately 2 GPa in case of PC). This means that the final indentation depths must be set larger than in metals in order to compensate for the elastic recovery and also indicates that numerical modeling must include the elastic recovery between two consecutive indentations. In fact, all the simulations presented in this paper took into consideration the elastic recovery at the end of the indentations. Conclusions The indentation of sheets in the direction perpendicular to thickness can be successfully utilized to produce three-dimensional features that are positioned outside the functional planes of the blanks from which they were formed. Single indentations of aluminum AA-5754-H111 and polycarbonate rectangular and circular blanks by means of flat, curved, and tooth gear punches allowed understanding the influence of the material, blank geometry, and shape of the punches in plastic material flow and force requirements. The experimental and numerical simulation work carried out in polycarbonate confirmed the potential of this material to be utilized in sheet-bulk forming applications, at room temperature. Multiple indentations in rectangular blanks by a gear tooth punch prove effective to fabricate rack gears by incremental sheet-bulk forming. The compression forces to plastically deform the material and the overall cost of tooling to produce gears by incremental sheet-bulk forming are smaller than those required by alternative processes that attempt to produce the gears in a single or a limited number of press strokes. The flexibility of the incremental sheet-bulk forming process and the possibility of permitting low-volume production, at room temperature, of complicated polymer parts for machines and mechanisms is an important advantage over conventional polymer processing that are based on heating shaping cooling manufacturing routes and are closely linked to mass production due to economic limitations. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by the support provided by Fundac a o para a Cieˆ ncia e a Tecnologia of Portugal and IDMEC under LAETA-UID/EMS/50022/ 2013 and PDTC/EMS-TEC/0626/2014. ORCID id PAF Martins References 1. Merklein M, Koch J, Opel S, et al. Fundamental investigation on the material flow at combined sheet and bulk metal forming processes. CIRP Ann - Manuf Technol 2011; 60: Merklein M, Koch J, Schneider T, et al. Manufacturing of complex functional components with variants by using a new sheet metal forming process. In: Proceedings of the 42nd plenary meeting of the International Cold Forging Group, Chinese Society for Technology of Plasticity, Shanghai, China, 2009, pp Mori K and Nakano T. State-of-the-art of plate forging in Japan. Prod Eng Res Dev 2016; 10: Nakano T, Ashihara K, Ishinaga N, et al. Development of combined forming of cold forging and thick sheet metal forming. J Jpn Soc Technol Plast 2006; 47: Maeda A and Araki K. Plate gear. Japanese Patent, , Hayashi K. Tool engineering for fine blanking and sheet metal forging complex work. J Jpn Soc Technol Plast 2006; 47: Merklein M, Allwood JM, Behrens BA, et al. Bulk forming of sheet metal. CIRP Ann - Manuf Technol 2012; 61: Sieczkarek P, Kwiatkowski L, Tekkaya AE, et al. Improved tool surfaces for incremental bulk forming processes of sheet metals. Key Eng Mater 2012; : Sieczkarek P, Isik K, Khalifa NB, et al. Mechanics of sheet-bulk indentation. J Mater Process Technol 2014; 214: Sieczkarek P, Wernicke S, Gies S, et al. Incipient and repeatable plastic flow in incremental sheet-bulk forming of gears. Int J Adv Manuf Technol 2016; 86: Alves LM, Nielsen CV and Martins PAF. Revisiting the fundamentals and capabilities of the stack compression test. Exp Mech 2011; 51:

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