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International Journal of Mechanical Sciences

journal homepage: www.elsevier.com/locate/ijmecsci

Local sheet thickening by in-plane swaging

S. Wernickea, P. Sieczkareka, P.A.F. Martinsb,⁎, A.E. Tekkayaa

a Institute of Forming Technology and Lightweight Construction, Technical University of Dortmund, Baroper Str. 303, D-44227 Dortmund, Germanyb IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

A R T I C L E I N F O

Keywords:Sheet-bulk metal formingLocal sheet thickeningAnalytical modellingFinite element modellingExperimentation

A B S T R A C T

This paper presents a new sheet-bulk forming process to locally pile-up material in thin sheets for subsequentforming or joining operations. An analytical solution is proposed for explaining the influence of the majorprocess parameters, estimating the thickening of the pile-up material and determining the normal and thrustforces applied by the tools. The approach is built upon the slip-line field theory under plane strain assumptionsand results are compared against finite element predictions and experimental results using Aluminium EN AW-1050A (EN 573-3) sheets with 3 mm thickness. The last part of the paper introduces a modified tool geometrythat is able to control the pile-up material for subsequent mechanical fastening operations.

1. Introduction

The identification of sheet-bulk metal forming (SBMF) as a newmanufacturing technology in which conventional sheet and bulk metalforming processes are combined to plastically deform sheets and plateswith intended three dimensional material flow is attributed to Merkleinet al. [1]. SBMF is aimed at replacing commonly used multi-stagestamping, fine blanking and precision machining operations for theproduction of net shape (or near-net shape) components having a highratio of surface area to thickness and local functional features such asteeth, ribs and solid bosses positioned outside the plane of the sheets orplates from which they are produced. Pulleys, vibration dumpers andtransmission gears of automotive are among the target components ofthis new forming technology.

Earlier developments of special purpose processes to fabricate sheetmetal components with different thicknesses are due to Greisert et al.[2], who introduced flexible rolling to produce sheets with periodicallyvarying thickness and to Merklein et. al. [3], who proposed theutilization of tailored blanks for producing functional elements withdifferent thicknesses. In fact, these two developments are among thefirst solutions towards lightweight and load-adapted design of sheetmetal components with functional features positioned outside theinitial surface of the sheets but they are not flexible enough forproducing components that require local thickening instead of periodi-cally or tailored varying sheet thickness.

From the above said, it is concluded that a major objective in SBMFis the development of simple and effective forming procedures toobtain local thickening of sheets and plates with dimensions up orabove their original thicknesses (Fig. 1). The first steps towards this

objective were taken by Sieczkarek et al. [4] who presented a novel five-axis press concept that is capable of performing different formingsequences such as embossing, rolling and compression. This work wasfollowed by an investigation on the deformation mechanics of sheet-bulk indentation and by presentation of a closed-form analyticalsolution to estimate the pressure and force applied by a flat indentationpunch in the direction perpendicular to the sheet thickness [5].

The present paper extends previous work on local thickening ofsheets by considering in-plane swaging (also designated as ‘local bossforming’) with a cylindrical roll. The main idea is to locally pile-upmaterial in a sheet (Fig. 1a) for subsequent forming or joining offunctional elements. The process can also be applied to localizedthickening of cup walls and tubes (Fig. 1b).

The paper has three major broad objectives besides that ofproposing a new sheet-bulk metal forming process. Firstly, it proposesan analytical model build upon the slip-line field theory to explain theinfluence of the major process parameters, to estimate the thickeningof the pile-up material and to calculate the normal and thrust forcesapplied by the roll. Secondly, it aims to identify the process window andto quantify the deviations of the actual material flow from the planestrain deformation conditions that are assumed by the analyticalmodel. And, thirdly, it proposes a modified tool design to control thegeometry and volume of the pile-up material. The proposed modifica-tion in conjunction with micro-hardness measurements is very im-portant to determine the overall workability of the piled-up material forsubsequent localized forming or joining operations.

http://dx.doi.org/10.1016/j.ijmecsci.2016.10.003Received 23 September 2015; Received in revised form 4 October 2016; Accepted 5 October 2016

⁎ Corresponding author.E-mail address: pmartins@ist.utl.pt (P.A.F. Martins).

International Journal of Mechanical Sciences 119 (2016) 59–67

0020-7403/ © 2016 Elsevier Ltd. All rights reserved.Available online 06 October 2016

crossmark

2. Analytical model

Fig. 2 presents the pile-up of material by combination of indenta-tion and in-plane swaging of a sheet with a cylindrical punch. The basiccomponents of the process are; (i) the sheet blank, (ii) the cylindricalroll and (iii) the fixture system that clamps the sheet blank to themachine worktable.

The analytical model to be developed is focused on the in-planeswaging that follows the initial indentation stage. From a deformationmechanics point of view, during in-plane swaging the roll movesperpendicular to sheet thickness and plastic flow is three-dimensionaldue to the increase in width w of the pile-up material (hereafterdesignated as ‘pile-up spread’). However, in the proposed analyticalmodel it is assumed that the pile-up spread s w w w= ( − )/ ≈ 01 , wherew1 is the final width of the pile-up material and w is the width of theroll. This allows analysing plastic flow under plane strain deformationconditions and to develop an analytical solution based in the slip-linefield theory for steady-state deformation conditions. The analysis of thetransient plastic flow associated to the early deformation stages will notbe addressed, although an analytical model for the initial indentationstage could easily be setup from previous work on indentation bymeans of frictionless cylindrical punches carried out by Hill [6] in1948.

Under these conditions, the main process parameters that will beincluded in the proposed analytical model are; (i) the sheet thickness t ,(ii) the radius R of the roll, (iii) the width w of the roll and (iii) theindentation depth i. The mechanical behaviour of the material is leftout of the process parameters because the slip-line field theory requiresmaterial to be rigid-ideally plastic (i.e. no strain hardening effects aretaken into account).

The two other assumptions derived from the application of slip-linetheory are; (i) the material is isotropic and homogeneous, and (ii) theeffects of temperature and strain rate are ignored. In addition to this,

authors also assumed the coefficient of friction μ (defined as the ratio ofshear and normal stresses) to vary along the contact interface betweenthe sheet and the roll.

Fig. 3a–c, shows the proposed slip-line fields for the initial (Fig. 3a),transient beginning (Fig. 3b) and the transition to steady-state in-planeswaging (Fig. 3c). As seen in the figures, the shape of the slip-line fieldchanges as deformation continuous up to the instant of time when thepile-up material detaches from the surface of the roll and steady-stateplastic deformation conditions are attained (Fig. 3c).

All the three slip-line fields make use of a centred-fan with equalradius, but while in Fig. 3a the origin of the centred-fan is a singularitypoint O located on the surface of the roll, in case of Fig. 3b and c theorigin of the centred-fan P OPI I1, 3, is located outside the plasticdeformation region. As a result of this, the slip-line field consists ofan extended centred-fan with α (clockwise maximum shear lines) and β(anticlockwise maximum shear lines) meeting orthogonally at the rollsurface but with different inclination angles γ to the roll surface. In fact,the proposed solution assumes γ to decrease from π /4 (frictionlesscondition) at P II1, to ψ π− /4 at P I3, , where ψ represents the contactangle for the pile-up material detaching from the roll.

The decrease in γ replicates the increase in the friction coefficient μthat is expected to occur along the contact interface between the sheetand the roll when we move from point P II1, where the pile-up materialdetaches from the roll to point P I3, where the roll is tangent to theplastically deformed surface of the sheet.

The remaining fields are made of straight lines of constant averagestress (for example, P P PI I II0, 1, 1, in Fig. 3b and c). The dashed linelimiting the straight lines of constant average stress in the leftmostregion of Fig. 3b and c represent a discontinuity in stress between therigid material and the plastically deforming regions. In connection tothe volume elements included in Fig. 3c it is worth noting that σ k= 2Y ,where σY is the flow stress and k is the shear yield stress according toTresca’s yield criterion.

Now, by focusing on the slip-line field corresponding to steady-stateplastic deformation conditions and taking into account the angularrelationships that are given in Fig. 3d it is possible to write the radiusRsl of the extended centred-fan with a centre in point O as a function ofthe radius R of the roll as follows,

⎛

⎝⎜⎜

⎞

⎠⎟⎟R R ψ

π ψR R ψ

π ψ= 1

2sin

cos ( − )+ − cos

sin ( − )sl 3

434 (1)

The enlarged detail of Fig. 3d gives the thickness tp of the pile-upmaterial as a function of the radius R of the roll and of the indentationdepth i,

Fig. 1. Local thickening of (a) a sheet (or plate) and of (b) a cup wall (or tube) by in-plane swaging with a cylindrical roll.

Fig. 2. Local thickening of sheet by in-plane swaging. (a) Schematic evolution of the pile-up material from the initial indentation stage up to steady-state plastic deformation conditions;(b) Top schematic view of the experimental setup; (c) Photograph showing the pile-up material in an experiment performed with aluminium EN AW-1050A.

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⎛⎝⎜

⎞⎠⎟t b π χ= cos

4−p

(2)

where, the angle χ is obtained from,

⎛⎝⎜

⎞⎠⎟χ c

b= arccos

(3)

and the lengths b and c are obtained from (refer to the enlarged detailin Fig. 3d),

Fig. 3. Slip-line field solutions for the in-plane swaging of a sheet blank. (a) Incipient slip-line field at the beginning of the process; (b) Unsteady slip-line field (corresponding to aparticular instant of time) at the transient beginning to in-plane swaging; (c) Steady-state slip-line field; (d) Geometric relationships in the steady-state slip-line field.

Fig. 4. Mohr circles in the stress plane for the steady-state slip-line solution in case of two different contact angles ψ where the pile-up material detaches from the roll. (a) General

contact angle ψ ; (b) Limiting contact angle ψ π= /2.

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⎛⎝⎜⎜

⎞⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟c R R ψ

π ψb a c i

ψR R ψ

π ψ= − cos

sin ( − )= + =

sin ( − )+ − cos

sin ( − )π34

2 2

4

2

34

2

(4)

In the above expressions a is given by,

a iψ

=sin ( − )π

4 (5)

The value of the contact angle ψ where the pile-up materialdetaches from the roll may be obtained from experiments or estimatedby minimizing the thickness tp of the pile-up material ( t ψ∂ /∂ = 0p ). Thisminimization procedure shares some similarities with that used inorthogonal metal cutting to determine the shear plane angle becausefrom an energy point of view the contact angle ψ for material to detachfrom the roll should be the one ensuring a minimum thickness tp of thepile-up material. Results from the minimization procedure for typicalprocess parameters will be given in the section entitled ‘Results anddiscussion’.

In connection to what was mentioned above, it is worth noticingthat the contact angle ψ is bracketed in the interval π π[ /4, /2] by twodifferent boundary conditions. The lower value of ψ is obtained fromcombination of Eqs. (2) and (4) and determines that the thickness tp ofthe pile-up material tends to infinity (t → ∞p ) when ψ π= /4. This resultis understandable because the radius Rsl of the extended centred-fanbecomes infinity when ψ π= /4 (refer to Eq. (1)). The upper valueψ π= /2 results from the kinematic boundary condition that requiresvelocity of the detached pile-up material to be tangent to the rollsurface.

Fig. 4a presents the stress field in the Mohr plane for the steady-state slip-line field solution corresponding to a general contact angle ψwhere the pile-up material detaches from the roll, whereas Fig. 4bpresents the same result for the limiting special case of a contact angleψ π= /2.

As seen in Fig. 4, the discontinuities in stress separate the rigidmaterial from the plastically deforming regions defined by straight αand β slip-lines undergoing pure compression. As a result of this, thestress field in this region (for example, in point P I1, ) is given by therightmost Mohr circles in Fig. 4a and b. Then, as one moves along the βlines of the extended centred-fan from point P I1, to point P I3, the changein the average stress Δσm is computed by means of Hencky’s equation[7] as follows,

⎛⎝⎜

⎞⎠⎟Δσ k ψ π= −2 2 −

2m(6)

This result allows determining the normal pressure p acting at thetwo contact ends of the roll surface as follows (refer to the detail inFig. 4a, and notice that the stress field in P I1, is identical to that in P II1, ),

p k

p k k ψ ρ k

= −2= −[ + 2 (2 − ) + ]

I

Iπ

1,

3, 2 (7)

where ρ is a fraction of the shear yield stress k given by (refer toFig. 4a),

ρ π ψ= cos ( − 2 ) (8)

The knowledge of the normal pressure p acting on the roll surfaceallows determining the normal (horizontal) Fn and thrust (vertical) Ft

forces as follows (refer to the detail of Fig. 4a),

∫

∫

F p wR θ dθ

F p wR θ dθ

= cos

= sin

n ψ

π

t ψ

π−2

−2

π

π

2

2 (9)

A rough estimate of these forces can be obtained by assuming alinear variation of the normal pressure p along the contact surface andintroducing an average normal pressure p given by,

⎡⎣⎢

⎤⎦⎥p

p pk π ψ π ψ=

+2

= −2 − 34

+4

− − 14

cos ( − 2 )I I1, 3,

(10)

In case, for example, of the limiting contact angle ψ π= /2, theaverage normal pressure is given by p k π= −2 (1 + /4) and the normalFn and thrust Ft forces are obtained from integration of Eq. (9) asfollows,

⎛⎝⎜

⎞⎠⎟F F k π Rw= ≅ 2 1 +

4n t(11)

The estimates of the normal Fn and thrust Ft forces derived from therigid-ideally plastic assumption of the proposed slip-line field will alsobe checked against experimental values in the section entitled ‘Resultsand discussion’.

To conclude the presentation of the analytical model it is worthmentioning its relevance for understanding the influence of two of themost important process parameters - the radius R of the roll and the

Fig. 5. Schematic analysis of the influence of the (a) indentation depth and of the (b) radius of the roll in the final thickness of the pile-up material.

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indentation depth i. In fact, observation of Fig. 5 under the assumptionthat the contact angle ψ remains constant, allows concluding that anincrease in the indentation depth from i0 to i1 as well as an increase inthe radius of the roll from R0 to R1 will result in an increase of thethickness tp of the pile-up material.

3. Experimentation

3.1. Material characterization

The experiments were performed in aluminium EN AW-1050A (EN573-3) sheets with 3 mm thickness. The stress-strain curve wasdetermined by means of stack compression tests using specimens thatwere assembled by pilling-up 3 discs with 12 mm diameter, which werecut from the supplied sheets by laser. The tests were carried out on aZwickZ250 universal testing machine with a cross-head speed equal to0.1 mm/s by pressing the specimens between two flat polished, well-lubricated, parallel platens at room temperature. The resulting stress-strain curve was approximated by the following Ludwik–Hollomon’sstrain hardening model,

σ ε= 131 (MPa)0.29 (12)

Further details on the utilization of stack compression tests for themechanical characterization of materials for sheet-bulk metal formingapplications are provided by Sieczkarek et al. [5].

3.2. Experimental work plan

The experiments were performed on the five-axis press that isshown in Fig. 6a. This prototype machine was developed for incre-mental sheet-bulk metal forming applications by Sieczkarek et al. [4]and is equipped with four hydraulic linear axes and a turntable rotaryaxis.

Twelve different rolls made from a powder metallurgy high-speedsteel ASP2023 (WN 1.3344) with radius R varying from 5 to 12.5 mmand widths w varying from 5 to 15 mm were utilized. The rolls werevacuum hardened in order to ensure a surface hardness of approxi-mately 60 HRc and were positioned perpendicular to the sheet surfacein order to attain the desired indentation. After attaining the desiredindentation the worktable was moved longitudinally against the rolls inorder to ensure a linear relative displacement l between the sheet andthe rolls (Fig. 6).

The sheets were clamped to the worktable by means of a fixturesystem that prevented slipping and lifting-off during the formingprocess. The fixture system was secured to the worktable by screwsand consisted of a blank holder with a central longitudinal gap to allowthe linear movement of the roll (Fig. 6b). The central longitudinal gap

was made 0.5 mm wider than the rolls in order to avoid contact withthe blank holder. This clearance was small enough to limit the amountof flash that was formed between the roll and the blank holder to aminimum.

4. Results and discussion

4.1. Assessment of the analytical model

Fig. 7 shows a comparison between the slip-line field solution of theproposed analytical model and the distribution of effective strain rateobtained from finite element analysis using the commercial softwareSimufact.forming12 under frictionless, rigid-ideally plastic, planestrain loading conditions.

As shown in the proposed slip-line field solution, there is a slightincrease of friction along the roll surface from point P II1, , correspondingto the contact angle ψ where the pile-up material detaches from theroll, to point P I3, where the roll is tangent to the deformed surface of thesheet. The increase in friction is due to a decrease in angle γ (refer toFig. 3d) from π /4 at P1, II to ψ π− /4 at P3,I, which for a typical ratio R i/between the roll radius R and the amount of indentation i correspondsto values in the range of π(1~0.65) /4. These values of γ are significantlydifferent from those of sticking boundary conditions (0 or π /2) andjustify the reason why the analytical and the frictionless finite elementestimates of the plastic deformation region are similar. In fact, bothsolutions disclose linear and circular velocity discontinuity contoursthat separate the plastic deformation region from the remaining non-deformed (or already deformed) material.

Fig. 8 presents the analytical evolution of the thickness of the pile-up material with the contact angle for selected combinations of processparameters (tool radius R and indentation depth i). The curves wereobtained from Eq. (2) and the analytical estimate of the contact angleψ , where the pile-up material detaches from the roll surface, shouldcorrespond to the minimum thickness tp of the pile-up material, as itwas previously mentioned in the section entitled ‘Analytical model’.The extra points in Fig. 8 (refer to the square and triangular markers)are included for comparison purposes and correspond to finite elementestimates under rigid-ideally plastic, plane strain loading conditionsbecause the estimate of the contact angle ψ derived from the analyticalmodel is independent from material flow stress. The square markerscorrespond to frictionless boundary conditions and the triangularmarkers correspond to a constant friction factor m = 0.5 along the rollsurface.

The overall agreement between finite element estimates andanalytical results is fair. The contact angles ψ obtained from theminimum values of the curves show a good agreement with thoseobtained from finite element analysis but the corresponding values of

Fig. 6. Detail of the (a) five axis press and of the (b) experimental setup that was utilized in the investigation on local thickening by in-plane swaging.

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the minimum thickness tp of the pile-up material are overestimated.However, this agreement improves when the finite element estimatestake friction into account because the proposed slip-line field alsoconsiders the existence of friction along the roll surface.

The vertical dashed lines at 45° and 90° (Fig. 8) correspond to thelower and upper bracketing values of the contact angle ψ in accordanceto what was previously mentioned in Section 2 (‘Analytical model’).

The overall validity of the plane strain deformation assumption isdiscussed in Fig. 9 where the normalized volume of the pile-up spreadV V/s is plotted as a function of the longitudinal displacement l of theroll for a selected experimental test case. The procedure utilized forobtaining the ratioV V/s involves determination of volumeVp of the pile-up material (for different longitudinal displacements of the roll) byimprinting the in-plane swaged sheets in plasticine and by subse-quently filling up the region of the piled-up material with water using apipette. The volume Vs of the pile-up spread corresponds to thedifference between the total volume V that was displaced by the rollduring its movement (obtained from the product between the crosssectional area and the length of the rolling track for longitudinaldisplacements corresponding to the positions where the plasticine

imprints were taken) and the volume Vp of the corresponding pile-upmaterial.

As seen in the figure, the normalized volume of the pile-up spreadV V/s is less than 10% and justifies the reason why plastic flow during in-plane swaging can be analysed under plane strain deformation

Fig. 7. Comparison between (a) the proposed slip-line field and (b) the finite element distribution of effective strain rate for a test case with R = 10 mm, t = 3 mm and i = 1.5 mm at aninstant of time corresponding to steady-state plastic deformation conditions.

Fig. 8. Evolution of the thickness of the pile-up material with the contact angle for selected combinations of the main process parameters under steady-state forming conditions. Theresults obtained from finite element analysis under frictionless (square markers) and friction (m = 0.5, triangular markers) are included for reference purposes.

Fig. 9. Normalized volume of the pile-up spread as a function of the longitudinaldisplacement l of the roll for an experimental test case corresponding to (R = 7.5 mm,w = 5 mm and i = 1.5 mm).

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assumptions.

4.2. Evolution and prediction of forces

Fig. 10 shows how the experimental values of the normal Fn andthrust Ft forces evolve with time in case of successful and non-successful local thickening of sheets by in-plane swaging.

Two different regions can be identified in Fig. 10a. The first regioncorresponds to the initial indentation stage where the upper sheetsurface is compressed by the roll across thickness. During indentationthe applied force is vertical and increases steeply up to the desiredindentation depth i. In order to ensure consistency with the notationthat is being utilized for in-plane swaging, the vertical indentation forcewill be designated as the thrust force Ft (refer to Fig. 4).

The second region corresponds to the local thickening of sheets byin-plane swaging and is characterized by a monotonic increase of thenormal Fn and thrust Ft forces towards steady-state plastic deformationconditions as the pile-up material starts to build-up in front of the roll.

In case of Fig. 10b, the second region presents a different shape andreveals the existence of local peaks in close agreement to what iscommonly observed in the thrust force Ft of orthogonal metal cutting atthe instant of time when a crack is initiated to allow material separationat the tip of the tool [8].

The absence of local peaks in Fig. 10a allows concluding that in-plane swaging is a plasticity and friction only based metal formingprocess. There is no crack opening and propagation if the processparameters are chosen in accordance to the process window shown inthe next sub-section of this paper.

Fig. 11 presents a comparison between the experimental values ofthe normal Fn and thrust Ft forces and the analytical estimates providedby Eq. (11), under the limiting extreme condition of the contact angle ψwhere the pile-up material detaches from the roll being equal to π /2.

The analytical estimates of the normal Fn and thrust Ft forces madeuse of a shear yield stress k = 80 MPa after observation from finiteelement results that effective strain ε > 1.0 during in-plane swagingunder steady-state conditions. The utilization of the limiting extremecondition ψ π= /2 ensures that the estimates of Fn and Ft are the highestpossible.

As seen in Fig. 11, the overall agreement is good and the utilizationof Eq. (11) explains the reason why the analytical estimates of thenormal Fn and thrust Ft forces are identical whereas the correspondingexperimental values are different. The utilization of the limitingextreme condition ψ π= /2 further explains the reason why theanalytical model predicts larger forces as compared to experimentaldata, though strain hardening was not modelled as slip-line field theoryrequires rigid-ideally plastic material modelling. In fact, if intermediatevalues of the contact angle ψ (in the range π /3 to π /2) had been chosenfrom Fig. 8 the analytical estimates of Fn and Ft would have been

smaller than the experimental values included in Fig. 11.To conclude, it is worth mentioning that the analytical model is also

able to replicate the increase of the normal Fn and thrust Ft forces whenthe radius R and the width w of the rolls increase, or when theindentation depth i increases.

4.3. Process window

The experiments carried out for the entire range of processparameters listed in Table 1 allowed establishing the process windowas a function of the radius R of the rolls, the compression ratio i t/between the indentation depth i and the sheet thickness t , and theslenderness ratio w w/ sheet between the width of the roll w and the widthof the sheet wsheet. As seen in Fig. 12, large compression ratiosperformed with large slenderness ratios give rise to the occurrence ofcracks even before attaining steady-state forming conditions (ex. forlongitudinal displacements l = 25 mm), when using the largest roll(R = 10 mm). This justifies the reason why the dashed line separatingthe acceptable from the non-acceptable process working conditions isan inclined line falling from left to right.

4.4. Modified tool design

The last section of this paper introduces a modified tool design thatis aimed at controlling the geometry of the piled-up material. The newtool shown in Fig. 13a takes advantage of the increase formability ofsmall radius R (refer to Fig. 12) and constrains the free rise ht of thepile-up material in order to obtain an adequate geometry and volumefor a subsequent mechanical fastening that uses the thin sheet as acarrier (Fig. 13b).

The finite element computed evolution of the geometry of the piled-up material from the beginning up to the instant of time correspondingto the photograph shown in Fig. 13b is disclosed in Fig. 13d. A smallfold (or flaw) caused by buckling of the upper region of the pile-upmaterial during compression against the flat contour of the modifiedtool design is observed both in finite element analysis and in the crosssection image of the pile-up material (Fig. 13c).

The finite element analysis in Fig. 13d was performed under three-dimensional plastic flow conditions. The sheet was discretized bymeans of tetrahedral elements and took into account the longitudinalsymmetry conditions of the process. The mechanical behaviour of thematerial was characterized by means of the stress-strain curve of Eq.(12). The tools were considered as rigid objects.

The finite element predicted distribution of effective strain at therightmost image of Fig. 13d shows high values increasing towards thetool surface and decreasing towards the undeformed sheet materialplaced ahead of the plastic deformation region. This distribution ofeffective strain is in good agreement with the micro-hardness measure-

Fig. 10. Experimental values of the normal Fn and thrust Ft forces as a function of time for two selected testing conditions corresponding to (aluminium EN AW-1050A). (a) Successful

local thickening (R=10 mm, w=5 mm, i=1 mm); (b) Non-successful local thickening due to the occurrence of cracks (R=10 mm, w=15 mm, i=1.5 mm).

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ments (HV 0.01) carried out on a predetermined set of grid points of

the pile-up material (refer to Fig. 13c). As seen in Fig. 13c and d, thehighest values of micro-hardness and effective strain are found at thevicinity of the contact surface between material and tool.

The importance of knowing the distribution of hardness and strainis relevant because it helps deciding if additional heat treatments areneeded for the utilization of these zones as potential functionalelements (such as, load carriers).

5. Conclusions

This paper presented a new sheet-bulk metal forming process for

Fig. 11. Experimental and analytical values of the normal Fn and thrust Ft forces for selected testing conditions (units of R, w and i in [mm], material: aluminium EN AW-1050A).

Table 1Summary of the process parameters that were utilized in the experiments.

Parameter Values

Tool radius R 5, 7.5, 10, 12.5 [mm]Indentation i 0.5, 1, 1.5 [mm]Tool width w 5, 10 ,15 [mm]Distance l 25, 50, 100 [mm]Velocity 10 [mm/s]

Fig. 12. Process window for in-plane swaging of aluminium EN AW-1050A sheets with 3 mm thickness as a function of the major process parameters.

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local thickening of sheets by means of in-plane swaging. An analyticalmodel built upon the slip-line filed theory was proposed to predict theprocess behaviour across a useful range of operating conditions and toestimate the normal Fn and thrust Ft forces, the thickness tp of the pile-up material and the contact angle ψ , where material detaches from theroll.

The comparison of the analytical estimates of the thickness tp of thepile-up material and of the contact angle ψ against finite elementresults revealed a generalized fair agreement. According to theanalytical model these values should be independent from the materialflow stress and only influenced by the remaining process parameters(roll radius R, indentation depth i and sheet thickness t), Calculationsfor typical values of roll radius R and indentation depths i revealed thatmaterial detaches from the roll surface at typical contact angles

ψ60º ≤ ≤ 75º in order to minimize the sheet thickness tp of the pile-up material.

The comparison against normal Fn and thrust Ft experimental forcesretrieved from test cases performed in aluminium EN AW-1050Asheets with 3 mm thickness not only reveals good agreement with theanalytical estimates as it unveils that both forces have similar values.This observation is different from what is commonly found in metalcutting processes where the normal forces Fn are significant larger thanthe thrust forces Ft . The justification for these differences is attributedto the fact that deformation mechanics of in-plane swaging is solelybased in plasticity and friction in contrast to that of metal cutting,which additionally requires material separation by cracking at the tip ofthe tool in order to allow the tool to move along its cutting path.

The utilization of a modified tool design for controlling thegeometry of the pile-up material shows potential for subsequent localforming and joining operations but further research is needed to avoidthe occurrence of folds and to extend results to other materials thanaluminium.

Acknowledgments

This work was supported by the German Research Foundation(DFG) within the scope of the Transregional Collaborative ResearchCentre on sheet-bulk metal forming (SFB/TR 73) in the subproject A4‘Fundamental research and process development for manufacturing ofload optimized parts with incremental forming of thick sheets’. PauloMartins would also like to acknowledge the support provided byFundação para a Ciência e a Tecnologia of Portugal under LAETA –

UID/EMS/50022/2013 and PDTC/EMS-TEC/0626/2014.

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Fig. 13. Mechanical fastening using the pile-up material of an aluminium EN AW-1050A sheet with 3 mm thickness as a carrier. (a) The modified tool design(R = 5 mm,r = 3 mm,L = 14 mm,h = 8 mm) under process conditions of t = 3 mm, and i = 1.5 mm; (b) Photograph of the screw fastened in the pile-up material; (c)Microhardness indentation points in the cross section of the pile-up material; (d) Finite element predicted distribution of effective strain for different tool displacements.

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