Original article

Sheet-bulk forming of three-dimensionalfeatures in metal and polymer blanks

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 com-

plicate 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 andmechanisms has been stimulating the development ofnew fabrication processes that allow minimizing thenumber of parts, reduce weight, and cut assembly andmaintenance costs by combining two or more func-tional features together in a single sheet metal part.

The combination of different functional featureswith tight geometric tolerances and the specificationof variable thicknesses to reduce weight often incursin sheet metal parts with increasing geometric com-plexity, ineffective material utilization, and substantialmanufacturing costs.1 In addition, the technical spe-cifications of these parts may also not fall within thescope of applicability of conventional manufacturingprocesses.

These challenges encouraged the development of anew group of advanced metal forming processesdesignated as sheet-bulk forming by Merklein et al.2

and plate forging by Mori and Nakano,3 which com-bines plane-stress conditions of sheet forming andthree-dimensional stress settings of bulk forming.The goal in sheet-bulk forming is to produce sheetparts with massive local shape changes and smallersurface-to-volume ratios than the original blanks.The changes in surface-to-volume ratios result frommaking geometric details outside the plane of theblanks from which they are produced.

In case of sheet metal parts with gear features, sev-eral sheet-bulk forming processes have been proposedin which compression is combined with drawing and

ironing,4 compression is combined with flanging,5 andforging is combined with fine blanking,6 among othersthat are comprehensively described in the state-of-the-art review by Merklein et al.7

In contrast to the above sheet-bulk forming pro-cesses that aim to produce sheet metal parts in a singleor a limited number of press strokes, there are situ-ations in which small batches and customized produc-tion requirements demand the use of incrementalsheet-bulk metal forming processes that circumventthe utilization of complex and expensive tool systemsinstalled in large capacity presses. The first step in thisdirection was given by Sieczkarek et al.,8 who pro-posed the fabrication of functional features in sheetmetal parts by incremental compression in the direc-tion perpendicular to thickness. The deformationmechanics of this process and its application to thefabrication of disk gears made from DC04 steel weresubsequently investigated by Sieczkarek et al.9,10

This paper revisits the incremental sheet-bulkforming of metals by investigating material flow andforce requirements in the indentation of rectangularand circular aluminum blanks by flat, curved, and

IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Lisbon,

Portugal

Corresponding author:

PAF Martins, IDMEC, Instituto Superior Tecnico, Universidade de

Lisboa, Av. Rovisco Pais, Tecnologia Mecanica, Lisbon 1049-001,

Portugal.

Email: pmartins@tecnico.ulisboa.pt

Proc IMechE Part L:

J Materials: Design and Applications

0(0) 1–9

! IMechE 2018

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DOI: 10.1177/1464420718796692

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gear tooth punches, and gives the first steptowards the extension of sheet-bulk forming topolymers. The potential of producing polymer gearsby incremental sheet-bulk forming is investigatedand comparisons are made with gears fabricated inaluminum. Results show that incremental sheet-bulkforming of polymers can be successfully appliedto low-volume production, at room temperature,of gears that are widely used in machines andmechanisms.

Experimentation

Materials and mechanical characterization

The work was carried out in aluminum AA5754-H111and polycarbonate (PC) sheets with 5mm of thickness.The mechanical characterization of the aluminum alloywas performed by means of stack compression tests11

in specimens that were assembled by pilling up threecircular discs with 15mm diameter and 5mm thicknessmachined out of the supplied sheets. No tensile testswere performed because the stack compression test isable to provide the mechanical characterization of thealuminum alloy for larger strains than the onset ofnecking in tension.

The mechanical characterization of PC was per-formed by means of tensile and stack compressiontests, because the material is pressure sensitive and pro-vides different stress response in tension and compres-sion. The tensile specimens were machined out ofthe supplied sheets in accordance to the ASTM D638-10 standard,12 whereas the stack compression spe-cimens were prepared in a similar manner to that ofaluminum.

The tensile and stack compression tests were car-ried out at room temperature in a hydraulic testingmachine (Instron SATEC 1200 kN) with a cross-headspeed of 5mm/min. The resulting stress–strain curvesare shown in Figure 1 and the local drop in stress thatis observed in the PC stress–strain curves is attributedto the transition between viscoelastic and plasticmaterial flow regimes.

Work plan, methods, and procedures

The tool utilized in the experiments is schematicallyshown in Figure 2(a) and was installed in the hydrau-lic testing machine where material characterizationtests were performed. Its design is an evolution of aconcept originally proposed by Silva et al.13 to allowforming both rectangular and circular blanks with dif-ferent punch shapes (Figure 2(b) and (c)).

The main components of the tool are: (a) the punchholder, (b) the blank holders, (c) the die shoe, and (d)the guide rails. The punch holder moves verticallywith the press ram and securely fastens the sheet-bulk forming punches. The forming punches havethree different shapes (Figure 2(b)) and are made

from a tool steel C265, which was tempered toensure a surface hardness of approximately 64 HRC.

The blank holders are made from PM400 steel platesand include screws to clamp the blanks firmly in pos-ition during the indentations. The die shoe is also madefrom PM400 steel and holds and ensures the alignmentof the blank holders for thicknesses up to 10mm.

The guide rails allow the die shoe to slide horizon-tally in order to move the blanks with the requiredpitch length to fabricate rack gears made of a series ofstraight teeth. In case of disk gears, the blanks arerotated by means of a small rod inserted through ahole in the blank holder.

All the blanks were positioned with 20mm abovethe surface of the blank holders in order to ensure freethickening of the plastically deforming region duringthe entire sheet-bulk indentation depths (formingdepths).

The experimental work plan consisted of two dif-ferent sets of tests. The first set of tests involved theindentation of rectangular and circular blanks in thedirection perpendicular to thickness by flat, circular,and gear tooth punches. The geometry of the geartooth punch was defined in accordance to the DIN867 profile, module 1.5.

The main objective of these tests was the charac-terization of plastic flow in sheet-bulk indentation andthe overall work is an extension to polymers of a pre-vious investigation in aluminum EN AW-1050A.9 Thetests performed in AA5754-H111 were utilized for ref-erence purposes.

The second set of tests involved multiple indenta-tions to produce rack and disk gears. For this pur-pose, the blanks were moved horizontally by adistance corresponding to the pitch p (in case ofrack gears, Figure 3(a)) or, were rotated by an angle� (in case of disk gears, Figure 3(b)) after each inden-tation. The angle � of the circular pitch was deter-mined from

� ¼p

Rpð1Þ

where Rp is the radius of the pitch circle (Figure 3(b)).

Finite element modeling

The sheet-bulk indentation of rectangular and circularblanks was numerically simulated with the in-housefinite element computer program i-form. The programis based on the irreducible finite element flow formu-lation and accounts for the contact with frictionbetween rigid and deformable objects

� ¼

ZV

�� _�" dVþ 12K

ZV

_"2v dV�

ZST

Tiui dS

þ

ZSf

Z jurj0

�fdur

� �dS ð2Þ

2 Proc IMechE Part L: J Materials: Design and Applications 0(0)

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.

Magrinho et al. 3

In the above functional, �� is the effective stress, _�" isthe effective strain rate, _"v is the volumetric strain rate,K is a large positive constant imposing the incom-pressibility of volume V, Ti and ui are the surfacetractions and velocities on surface ST, �f and ur arethe friction shear stress and the relative velocity on thecontact interface Sf between the blank and the tool.Friction is modeled through the utilization of the lawof constant friction.

Details of the computer implementation with spe-cial emphasis on the explicit time integration algo-rithm, minimization of the residual force, andremeshing procedure are available elsewhere.14

The numerical simulation of the sheet-bulk indenta-tion of the PC blanks made use of the ‘‘extended finiteelement flow formulation’’15 that utilizes the followingyield function Fð�ijÞ proposed by Caddell et al.16

F �ij� �¼ ��2 � �C � �T þ ð�C � �TÞ �kk ¼ 0 ð3Þ

In the above equation, �T and �C are the tensileand compressive flow stresses, which account for thestrength differential effect of pressure-sensitive

materials like PC. The symbol �kk ¼ �ij�ij is the hydro-static pressure, where �ij is the Kronecker delta.

The numerical simulation of the sheet-bulk inden-tations was performed in plane stress conditionsbecause the blanks are thin and their thickness issmaller than the length of the plastically deformingregion. The blanks were discretized by means of12,000 quadrilateral elements and the tools were mod-eled as rigid objects and discretized by means of linearcontact-friction elements (Figure 4).

The overall central processing unit (CPU) time fora typical indentation requiring six intermediateremeshing was approximately equal to 25 min on acomputer equipped with an Intel i7-6700HQProcessor (2.6GHz).

Results and discussion

Sheet-bulk indentations with flat, curved, and geartooth punches

Figure 5(a) shows the experimental and finite elementevolution of the force with displacement for the

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.

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.

4 Proc IMechE Part L: J Materials: Design and Applications 0(0)

sheet-bulk indentation of AA 5754-H111 and PC rect-angular blanks by a flat punch.

The force in the AA 5754-H111 blank shows amonotonic increase with displacement due to combin-ation of strain hardening and growing contact areabetween the punch and the blank. The contactbetween the punch and the blank is also responsiblefor thickening of the plastically deforming region.

The force–displacement evolution of PC is similar tothat of AA 5754-H111, apart from a small drop in theforce at approximately 1.4mm of punch displacement.This drop is caused by the transition between the visco-elastic and plastic regimes of the polymer as it was previ-ously mentioned in the stress–strain curve of PC(Figure 1). The maximum forces at the end of the punchstroke are equal to 35 kN in AA 5754-H111 and to 8kNin PC and reflect the differences in material strength.

The agreement between experimental and finiteelement predictions is good as can be further seen inthe details of the real and numerically computed geo-metries of AA 5754-H111 and PC at the end of thepunch stroke. Measurements and predictions of thefinal thickness of the blanks in the plastically deformedregion allow concluding that maximum thickening isapproximately equal to 50% and 40.8% for the AA5754-H111 and PC specimens, respectively.

Figure 6 shows a resume of the first set of testsperformed with different punch geometries (flat,

curved, and gear tooth) and different blank shapes(rectangular and circular) for AA5754-H111. Asseen, the agreement between experimental resultsand finite element predictions is excellent and theinfluence of material strain hardening in the force–displacement evolution is clearly observed in theindentation of rectangular blanks by flat and curvedpunches (Figure 6(b) and (c)). In fact, despite the con-tact length s of the curved punch being larger thanthat of the flat punch (2R) at the end of the punchstroke, the extent of the plastically deforming regionand, therefore, the amount of strain hardening islarger in case of the flat punch (Figure 6(a)). Thisexplains the reason why the compression force ofthe flat punch is larger at the end of stroke.

s ¼ arcsinc

hþ c2

4h

� � !

hþc2

4h

� �

¼ 16:3 mm4 2R ¼ 15 mm

c ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR�

h

2

� �8h

s¼ 13:3 mm

ð4Þ

In the above equation, h ¼ 4mm is the displace-ment at the end of the punch stroke andR ¼ 7:5mm is the half-length of the flat punch (and

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.

Magrinho et al. 5

also, the radius of the curved punch), according toFigures 2(b) and 6(a).

The influence of the growing rate of the contactarea between the punch and the blank can be analyzedby observing the results of the indentation of rect-angular and circular blanks by a flat punch(Figure 6(b)). In fact, because contact starts at thecenter of the punch and progressively extends to itsfull length in case of circular blanks, whereas it startswith full length in case of rectangular blanks, it fol-lows that thickening of the plastically deformingregion is reduced and force growing rate is smallerat the beginning of the indentation. However, thegrowing rates become identical for larger indentationdepths because the amount of material undergoingplastic deformation and thickening becomes similar.

The influence of the growing rate of the contactarea 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 verysmall s� 2R. Similar results were obtained for PCblanks.

The localized deformation below the wedges of thegear tooth punch at the beginning of the indentationis also the reason why rectangular and circular blanksprovide almost identical results (Figure 6(d)). Thisjustifies the reason why the next section of the paperthat is focused on multiple sheet-bulk indentationswith a gear tooth punch will be exclusively focusedon rectangular blanks.

Multiple sheet-bulk indentations with a gear toothpunch

Figure 7(a) shows a schematic representation of themultiple sheet-bulk indentations in a rectangular

Figure 7. Multiple sheet-bulk indentations in an AA5754-H111 rectangular blank to fabricate a rack gear: (a) schematic represen-

tation 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.

6 Proc IMechE Part L: J Materials: Design and Applications 0(0)

blank by a gear tooth punch to fabricate a rack gear.The experimental and finite element predicted evolu-tions of the force with displacement for the first,second, and third indentations of AA 5754-H111 aredisclosed in Figure 7(b).

As seen, the evolution of the force with displace-ment for the first indentation is equal to that shown inFigure 6(d), because the process is identical to a singleindentation of a rectangular blank in the directionperpendicular to thickness.

The second indentation is also a compressionin the direction perpendicular to thickness butonly half of the gear tooth punch is plasticallydeforming the material (refer to the finite elementmodels placed inside Figure 7(b)), because the stepsize between the first and second indentations(4.72mm) is identical to the pitch p. Also, for thisreason, the evolution of the force with displacementin the second indentation (up to a punch displacementof approximately 2.8mm) is half of the force mea-sured in the first indentation, during which both theleft and right punch wedges were plastically deform-ing the material.

Beyond a punch displacement of 2.8mm, the forcestarts growing faster because the left wedge of the gear

tooth punch gets in contact with the material beingformed by the right wedge and confine the material toits final shape. At the end of the second indentation,the force becomes equal to that of the first indentationbecause the left wedge of the gear tooth punch alsogets in full contact with the blank. Subsequent inden-tations (third, fourth, etc.) are similar to the secondindentation, because the deformation mechanism isidentical. For this reason, the corresponding force–displacement evolutions are equal to that of thesecond indentation.

Figure 7(c) shows details of the final rack gear atthe end of the sheet-bulk indentation process and thecorresponding finite element predicted geometry. Asseen, both real and numerical predicted geometries ofthe first indentation lead to under filling of the punchcavity, due to a significant material flow constraintoriginated by the adjacent volume of the nondeform-ing material. The same phenomenon had been previ-ously observed in case of disk gears made from DC04steel and the solution is to use a tailored blank withadditional volume in the region where the first inden-tation will take place.10

Figure 8(a) shows the experimental and finiteelement evolutions of the force with displacement

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.

Magrinho et al. 7

for the first, second, and third indentations of aPC rectangular blank by a gear tooth punch.The agreement between the experimental andfinite element predictions of the force-displacementevolution 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 thefirst indentation due to a significant material flow con-straint imposed by the adjacent volume of the nonde-forming material.

The results obtained for PC demonstrate that mul-tiple sheet-bulk indentations of a polymer blank canbe utilized to fabricate rack and disk gears. However,in case of polymers it is necessary to account for theelastic recovery of the material due to the small valuesof the elasticity modulus (approximately 2GPa in caseof PC). This means that the final indentation depthsmust be set larger than in metals in order to compen-sate for the elastic recovery and also indicates thatnumerical modeling must include the elastic recoverybetween two consecutive indentations. In fact, allthe simulations presented in this paper took into con-sideration the elastic recovery at the end of theindentations.

Conclusions

The indentation of sheets in the direction perpendicu-lar to thickness can be successfully utilized to producethree-dimensional features that are positioned outsidethe functional planes of the blanks from which theywere formed.

Single indentations of aluminum AA-5754-H111and polycarbonate rectangular and circular blanksby means of flat, curved, and tooth gear punchesallowed understanding the influence of the material,blank geometry, and shape of the punches in plasticmaterial flow and force requirements. The experimen-tal and numerical simulation work carried out in poly-carbonate confirmed the potential of this material tobe utilized in sheet-bulk forming applications, atroom temperature.

Multiple indentations in rectangular blanks by agear tooth punch prove effective to fabricate rackgears by incremental sheet-bulk forming. The com-pression forces to plastically deform the materialand the overall cost of tooling to produce gears byincremental sheet-bulk forming are smaller than thoserequired by alternative processes that attempt to pro-duce the gears in a single or a limited number of pressstrokes.

The flexibility of the incremental sheet-bulkforming process and the possibility of permittinglow-volume production, at room temperature, ofcomplicated polymer parts for machines and mech-anisms is an important advantage over conven-tional polymer processing that are based on

heating–shaping–cooling manufacturing routes andare closely linked to mass production due to economiclimitations.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication ofthis article.

Funding

The author(s) disclosed receipt of the following financialsupport for the research, authorship, and/or publicationof this article: This study was funded by the support pro-

vided by Fundacao para a Ciencia e a Tecnologia ofPortugal and IDMEC under LAETA-UID/EMS/50022/2013 and PDTC/EMS-TEC/0626/2014.

ORCID iD

PAF Martins http://orcid.org/0000-0002-2630-4593

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