Original Article

A new test for determining themechanical and fracture behavior ofmaterials in sheet-bulk metal forming

CMA Silva, MB Silva, LM Alves and PAF Martins

Abstract

This paper presents a new experimental test for determining the stress–strain curve and the fracture toughness of sheets

to be used in sheet-bulk metal forming (SBMF) applications. The test is based on the utilization of double-notched

specimens loaded in shear and combines the plane stress loading conditions of sheet metal forming with the three-

dimensional plastic flow conditions of bulk metal forming, which are commonly found in SBMF processes. The meth-

odology to obtain the stress–strain curve involves calculation of the shear stresses and strains along the two symmetric

plastic shear zones of the test specimens up to point where cracks start to propagate along the ligaments that connect

each pair of opposite notches. The determination of fracture toughness involves characterization of the evolution of load

with displacement for a number of test cases performed with specimens having different ligaments between the two

symmetric opposite notches. The work is performed on aluminium alloy EN AW 5754 H111 sheets with 5 mm thickness

and the results obtained by means of the new proposed test are compared against those from conventional mechanical

and fracture characterization tests.

Keywords

Sheet-bulk metal forming, in-plane shear test, experimentation, stress–strain curve, fracture toughness

Date received: 22 September 2015; accepted: 16 October 2015

Introduction

The identification of sheet-bulk metal forming(SBMF) as a new manufacturing technology thatdeforms sheets and plates with intended three-dimensional material flow by Merklein et al.,1

opened a whole new field of research for the produc-tion of parts with a high ratio of surface area to thick-ness and geometric details positioned outside thefunctional planes of the sheets or plates from whichthey are produced. The goal in the development ofSBMF is the replacement of complicated and costlymultistage stamping, fine blanking and precisionmachining operations that are commonly utilized inthe production and assembly of synchronizer rings,disk gears, gear drums, and other mechanisms thatinclude complex sheet metal parts.2,3 (Figure 1(a)).

From a product development and manufacturingdesign point of view, typical applications of SBMFrequire application of loading across (refer to direc-tion ‘‘S’’ in Figure 1(b)) and perpendicular (refer totransverse ‘‘T’’ and longitudinal ‘‘L’’ directions inFigure 1(b)) to sheet thickness. Because of this, plasticflow in SBMF is said to be a combination of planestress conditions that are typical of sheet metal

forming and three-dimensional stress settings thatare typical of bulk metal forming.

The directionality of the mechanical and physicalproperties of the materials resulting from the applica-tion of loading in different directions plus the attain-ment of strain levels that are much larger than thoseobtained in standard tensile tests suggests that testingprocedures for the materials used in SBMF must beable to characterize the stress response up to the largestrains that result from the application of loadingacross or perpendicular to the sheet thickness (direc-tions ‘‘S’’, ‘‘T’’, and ‘‘L’’ of Figure 1(b)).

The characterization of the stress–strain behaviorof thick sheets (hereafter designated as ‘‘plates’’) up tolarge strains by means of standard compression testsperformed in specimens that were machined out ofthe plates in transverse ‘‘T’’ and longitudinal ‘‘L’’

IDMEC, Instituto Superior Tecnico, Universidade de Lisboa, Av.

Rovisco Pais, Lisboa, Portugal

Corresponding author:

PAF Martins, IDMEC, Instituto Superior Tecnico, Universidade de

Lisboa, Av. Rovisco Pais, Lisboa 1049-001, Portugal.

Email: pmartins@ist.utl.pt

Proc IMechE Part L:

J Materials: Design and Applications

0(0) 1–11

! IMechE 2015

Reprints and permissions:

sagepub.co.uk/journalsPermissions.nav

DOI: 10.1177/1464420715616140

pil.sagepub.com

by guest on November 11, 2015pil.sagepub.comDownloaded from

directions (Figure 1(b)) has been long investigated dueto fibering of inclusions and formation of crystallo-graphic textures in preferential directions during roll-ing. Test standards, such as ASTM E9,4 provideguidance on the procedure to be utilized for the prep-aration of the compression test specimens.

An alternative procedure based on the utilizationof small test cubes cut out of a plate in various pos-itions was recently proposed by Kitamura andTerano5 to characterize the local properties of plasticanisotropy for loading applications across and per-pendicular to the sheet thickness.

However, the mechanical characterization ofmaterials for SBMF is more complicated becauseraw materials generally consist of sheets with smallthickness from which it is not possible to machineout compression test specimens. The first investiga-tion focused on the characterization of the stress–strain behavior of sheets subjected to loading acrossthe thickness direction ‘‘S’’ (Figure 1(c)) was per-formed by Pawelski6 who developed the stack com-pression test for determining the flow curve ofmaterials supplied in the form of sheets. The stackcompression test makes use of circular discs that arecut out of the sheets and piled to form a cylindricaltest specimen with an aspect ratio in the range of solidcylinders that are employed in the standard compres-sion test (Figure 1(c)). Recent publications byMerklein and Kuppert7 and Alves et al.8 investigatedthe utilization of the stack compression test to deter-mine the stress–strain curve of anisotropic sheets andto compare the deformation mechanics of multi-layered stacked test specimens against that of solidcylindrical test specimens, respectively.

In what regards determination of the stress–straincurve along the transverse ‘‘T’’ and longitudinal ‘‘L’’

directions (i.e. perpendicular to the thickness direction‘‘S’’), the alternative to standard tensile tests is theutilization of shear tests according to ASTM B831.9

Figure 1(d) includes a schematic drawing of the cor-responding test specimens, which are characterized fordeveloping a single plastic shear zone when loadedwith a tensile force in a standard universal testingmachine. This test is known to perform well forsmall strains but may experience some difficulties forlarge strain levels due to rotation of the plastic shearzone during the application of the tensile load.

The characterization of fracture toughness insheets to be employed in SBMF can be easilyaccomplished by means of double-notched test speci-mens loaded in tension (Figure 2(a)) and shear

Figure 1. Loading directions and orientation in sheet-bulk metal forming (SBMF): (a) schematic drawing of a typical part produced by

SBMF; (b) compression test specimens to be cut out of sheets with large thickness (plates); (c) stack compression test specimens to be

cut of sheets with small thickness; (d) shear test specimens to be cut out of sheets with small thickness.

Figure 2. Conventional test specimens that are utilized to

determine fracture toughness in thin sheets: (a) double-

notched tensile test specimen; (b) double-notched shear

test specimen.

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

by guest on November 11, 2015pil.sagepub.comDownloaded from

(Figure 2(b)) following the methodology for determin-ing the specific work of fracture that was originallyproposed by Cotterell and Reddel.10 The specimensshown in Figure 2(a) and (b) lead to crack openingby tension (mode I) and by in-plane shear (mode II),but the double-notched shear test specimen shown inFigure 2(b) is also influenced by rotation of the plasticshear area during crack propagation.

This paper is focused on the mechanical and frac-ture characterization of sheets for SBMF applica-tions. The aim and objectives of the paper aretwofold: (i) to present a new experimental shear testthat allows simultaneous determination of the stress–strain curve and fracture toughness along transverse‘‘T’’ and longitudinal ‘‘L’’ directions and (ii) to valid-ate these results against standard mechanical and frac-ture characterization procedures that require theutilization of test specimens machined out of thesheets along different directions.

The new proposed experimental shear test is per-formed under compression loading and employs spe-cimens with geometry different from that specified inthe ASTM B831 standard in order to minimize theabove mentioned rotation effects of the plastic shearzones. The new test is expected to complement theutilization of the stack compression test in situationswhere anisotropy requires mechanical characteriza-tion of the material to be performed in the transverse‘‘T’’, longitudinal ‘‘L’’, and thickness ‘‘S’’ directions.

The work is performed on aluminium alloy ENAW 5754 H111 sheets with 5mm thickness and theresults obtained by means of the new proposed sheartest are compared against those obtained by means ofconventional mechanical and fracture characteriza-tion tests.

Theoretical background

The new proposed shear test for the mechanical andfracture characterization of sheets for SBMF appli-cations is schematically illustrated in Figure 3(a).

The geometry of the specimens to be utilized in thetest was inspired by the geometry of double-notchedbars loaded in shear that were employed by Atkins11

to determine fracture toughness in plane straindeformation conditions.

As seen in Figure 3(a), the geometry of the double-notched shear test specimens and of the punch anddies are such that the width w of the specimens doesnot undergo any change during the test. The test isperformed under plane stress conditions and the com-pression force F applied by the punch on the centralpart of the specimens gives rise to shearing along thetwo symmetric ligaments l that connect each pair ofopposite notches.

The two dark blue regions in Figure 3(b) representthe material undergoing shear deformation along theligaments. Both regions with volumeVp are assumed tobe confined by rectangular patches (trapezoidalpatches, after deformation) with a geometry approxi-mately equal to ld, where the width d ¼ � l of thenotches is assumed to be a fraction � of the ligament l.

Stress–strain curve

The determination of the stress–strain curve of thematerial by means of the new proposed shear test isbased on two major assumptions. Firstly, plastic workis considered to be totally consumed by sheardeformation inside the two rectangular patches ofFigure 3(b). The remaining parts of the specimenare assumed to be rigid because the contribution ofelastic deformation is negligible. Secondly, the shearstresses and strains are considered to be uniformlydistributed inside the two shear deformation regions.

Under these circumstances, the shear strain � of theshear deformation zones for a punch displacementequal to � is given by (Figure 3(b))

� ffi tan � ¼�

dð1Þ

Figure 3. The proposed shear test for the mechanical and fracture characterization of sheets: (a) schematic illustration of the tooling

apparatus and of the double-notched shear test specimen; (b) detailed of the plastic shear zone (original and deformed) with notation.

Silva et al. 3

by guest on November 11, 2015pil.sagepub.comDownloaded from

The corresponding shear stress � is calculated from

� ¼F

2 ltð2Þ

where the punch compression force F is divided by 2due to the existence of two symmetric shear deform-ation zones. The shear stress � derived from the pre-vious equation may be seen as an average value of theshear stresses acting in both shear deformation zonesbecause it is impossible to separate the exact value offorce acting on each zone alone from the experimentalevolution of force with displacement (Figure 4(a)and (b)).

From the curve �ð�Þ derived from equations (1)and (2) it is possible to determine the flow stressusing the von Mises’s expressions for the effectivestress �� and effective strain �"

�" ¼�ffiffiffi3p �� ¼

ffiffiffi3p

� ð3Þ

The overall method and procedure to determinethe stress–strain curve is schematically outlined inFigure 4(c) and the experimental values of force anddisplacement can be used up to the point where cracksare triggered and start to propagate. Test specimens

with different ligament sizes l can be utilized.However, no experimental results should be takenfrom test specimens with large ligaments that giverise to plastic deformation extending outside of thepreviously mentioned shear deformation regions.

Fracture toughness

The determination of fracture toughness is based onthe methodology for calculating the specific essentialwork of fracture wf that was originally proposed byCotterell and Reddel10 for double-notched test speci-mens loaded in tension (mode I of fracture mech-anics), and recently extended by Isik et al.12 fordouble-notched circular test specimens loaded inplane torsion.

Similarly to what was done in the twoabovementioned references, crack propagation indouble-notched test specimens loaded in shear isassumed to be generally preceded by extensive plas-tic deformation in the two symmetric shear deform-ation regions. The total work WT consumed by theend of the test (assuming material as rigid-plastic) isgiven by

WT ¼ Fd� ¼ 2wpdVp þ 2RdA ð4Þ

Figure 4. The new proposed shear test: (a) schematic representation of the specimen and of test operating conditions;

(b) force–displacement evolution as a function of the ligament 2l; (c) method and procedure to determine the stress–strain curve ��ð �"Þup to the point where cracks are triggered; (d) method and procedure to determine fracture toughness R.

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

by guest on November 11, 2015pil.sagepub.comDownloaded from

where wp is the plastic work per unit of volume and Ris fracture toughness, defined as the specific essentialwork of fracture wf that is necessary to open a crackof area A in each shear deformation region.

From the definition of plastic work per unit ofvolume, equation (4) can be rewritten as

WT ¼ 2

Z �"

0

��d �"

� �ld tþ 2R tl ð5Þ

where ld ¼ � l2 is the area of each shear deformationregion of the specimen and � is a constant that allowsexpressing the width d of the notches as a function ofthe length l of the ligaments. Dividing the above equa-tion by 2tl, we obtain the following relation for thetotal specific work wT

wT ¼

Z �"

0

��d �"

� �� lþ R ð6Þ

By taking into consideration that shear stresses andstrains are uniformly distributed inside the sheardeformation regions it is possible to approximatethe integral in equation (6) by the product betweenthe mean flow stress ��mean and the final average valueof the plastic strain �"av for the entire deformation ofthe specimen. This allows rewriting equation (6) asfollows

wT ¼1

2��mean �"av� 2lþ R ð7Þ

where the mean flow stress ��mean is calculated byintegration of the stress–strain curve between the ini-tial and final average experimental values of plasticstrain �"av

��mean ¼ ð1= �"avÞ

Z �"av

0

��d �" ð8Þ

From equation (7) it is possible to conclude that thetotal specific work wT can be split into two differentterms; (i) the specific nonessential plastic workwp ¼ ��mean �"av� l and (ii) the specific essential work offracture wf ¼ R (fracture toughness).

Figure 4 outlines the procedure to determinefracture toughness from the experimental evolutionof force with displacement for different test specimenswith different ligaments. As seen, the evolution ofthe force F with displacement � is first registeredfor a number of test cases performed with speci-mens having different starting lengths 2l of the twosymmetric ligaments (Figure 4(a) and (b)). Then,the total energy WT required by each test case iscalculated by integrating the evolution of the forcewith displacement until separation of the specimeninto two parts. Finally, the total energy WT requiredby each test is normalized by 2tl and plotted as afunction of the starting length 2l of the two symmetric

ligaments by means of a straight line (Figure 4(d)).The overall procedure is easy to understandbecause the specific total work in equation (7) varieslinearly with the starting length 2l of the two liga-ments. Fracture toughness R is the y-intercept ofthis line.

The application of the methods and procedures fordetermining the stress–strain curve and fracturetoughness by means of the new proposed shear testis provided in ‘‘Results and discussion’’ section. Thenext section provides details on the experimentalworkplan with emphasis on the tensile, compressionand stack compression tests, and on the double-notched fracture test specimens loaded in tensionthat were performed to validate the results providedby the new proposed shear test.

Experimentation

Mechanical characterization

The experimental work was carried out on aluminiumalloy EN AW 5754 H111 sheets with 5mm thicknessand the mechanical characterization of the materialwas performed by means of standard tensile and com-pression tests, stack compression tests and by meansof the new proposed double-notched shear test.Table 1 presents a summary of the main geometricalfeatures of the specimens and of the operative testingconditions.

The specimens were cut out of the suppliedsheets by machining and by wire electrical dischargemachining (EDM). The tests were performed atroom temperature on an INSTRON 4507 universaltesting machine with a cross-head speed equal to10mm/min.

Fracture toughness characterization

The experimental work plan on fracture toughnesscomprised two different types of tests. The conven-tional tests performed on double-notched specimensloaded in tension, which lead to crack opening bytension (mode I of fracture mechanics) and the newproposed test performed on double-notched speci-mens loaded in shear, which lead to crack openingby in-plane shear (mode II of fracture mechanics).Table 2 presents a summary of the main geometricalfeatures of the specimens and of the operative testingconditions.

The specimens were cut out of the supplied sheetsby wire EDM and the tests were performed at roomtemperature on the same universal testing machinewhere the mechanical characterization tests wereperformed. The influence of the loading direction(transverse ‘‘T’’ and longitudinal ‘‘L’’) was nottaken into consideration due to the results obtainedfrom the mechanical characterization of the material(Table 3).

Silva et al. 5

by guest on November 11, 2015pil.sagepub.comDownloaded from

Table 1. Summary of the geometrical and operative conditions utilized in the tests for determining the stress–strain curve (all units

in (mm)).

(a) (b) (c)

(a) Tensile tests (TT); (b) Compression tests (CT) and stack compression tests (SCT) with 2 and 3 disks; (c) New proposed double-notched shear test

(DNST).

Table 2. Summary of the geometrical and operative conditions utilized in the tests for determining fracture toughness (all units

in (mm)).

(a) (b)

(a) Double-notched tensile test (DNTT); (b) New proposed double-notched shear test (DNST).

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

by guest on November 11, 2015pil.sagepub.comDownloaded from

Results and discussion

Stress–strain curve

Figure 5 shows the stress–strain curves obtained fromtensile tests performed in specimens cut out from thesupplied sheets at 0�, 45�, and 90� with respect to therolling direction.

The tests were performed in accordance to theASTM standard E8/E8M–0913 and the stress responsewas characterized up to a strain of approximately 0.16because the specimens began to neck and the elong-ation was no longer uniform beyond this level of strain.

The average stress–strain curve resulting from theexperimental data plotted in Figure 5 was approxi-mated by the following Ludwik–Hollomon’s equation

� ¼ 398:8"0:27 MPað Þ ð9Þ

Table 3 provides a summary of the mechanical prop-erties of aluminium EN AW 5754 H111 obtainedfrom the aforementioned tensile tests. The normal �rand planar �r anisotropy coefficients were calculatedfrom

�r ¼r0 þ 2r45 þ r90

4�r ¼

r0 � 2r45 þ r902

ð10Þ

where r0, r45, and r90 are the anisotropy coefficientsobtained from specimens cut out from the suppliedsheets at 0�, 45�, and 90� with respect to the rollingdirection by using a transverse extensometer.

As seen in both Figure 5 and Table 3 there is nosignificant differences in the results obtained from thetests performed with different orientation of the spe-cimens. In particular, the anisotropy within the planeof sheet material �r ¼ �0:22 reveals that typicalapplications of SBMF that require application ofloading perpendicular to sheet thickness (e.g. alongtransverse ‘‘T’’ and longitudinal ‘‘L’’ directions ofFigure 1(b)) of the material utilized in this investiga-tion should provide similar stress responses.

The mechanical behavior of the material acrossthickness is also similar. In fact, the results obtainedfrom standard tensile tests (TT) and from stack com-pression tests (SCT) are similar up to an effectivestrain �" ffi 0:16 (refer to the vertical dashed line inFigure 6). The stress response obtained from standardtensile tests (TT) for effective strain values �"4 0:16was extrapolated from the average stress–straincurve in equation (9) or directly plotted from theexperimental values obtained by means of stack com-pression tests (in case of SCT_2 and SCT_3 inFigure 6). As seen, the extrapolation of the stressresponse from standard tensile tests (TT) leads to

Figure 5. Stress–strain evolutions obtained from standard tensile tests performed in specimens cut out from the supplied sheets at

0� (L), 45� (LT), and 90� (T) with respect to the rolling direction.

Table 3. Summary of the mechanical properties of aluminium EN AW 5754 H111 sheets with 5 mm thickness.

Modulus of

elasticity (GPa)

Yield strength

(MPa)

Ultimate tensile

strength (MPa)

Elongation at

break (%)

Anisotropy

coefficient

0� RD 71,760 103.14 213.09 22.67 0.62

45� RD 72,072 95.96 203.87 27.50 0.81

90� RD 71,822 99.08 210.50 27.50 0.73

Average 71,931 98.54 207.73 26.29 �r ¼0.74

Silva et al. 7

by guest on November 11, 2015pil.sagepub.comDownloaded from

significant deviations from stack compression tests(SCT) for large values of strain.

The differences in stress response that wereobtained from stack compression test specimensassembled by piling up two (SCT_2) or three(SCT_3) discs are due to the fact that the aspectratio h=d of the two disc assembly drops to verysmall values h=d ffi 0:2 at the end of the compressiontest. In fact, taken into account that friction causesthe normal pressure to increase exponentially towardsthe center of the specimens in inverse proportion tothe aspect ratio h=d (in agreement with the ‘‘frictionhill’’ analogy of the slab method of analysis), it fol-lows that even the smallest amount of friction or thesmallest increase in the amount of friction will inevit-ably give rise to a significant build-up of pressure incase of test specimens with very small aspect ratios.This situation may cause lubricant breakdown,followed by an increase in friction and in the corres-ponding stress response shifting conditions from thehomogeneous material flow of the standard (friction-less) compression test.

Nevertheless, it is worth noting that stack compres-sion tests are capable of determining the stress straincurve for strain levels that are more than three timeslarger than those obtained by means of standardtensile tests. This aptitude to characterize the stress–strain curve of sheets for large strain values is particu-larly important for SBMF applications.

The utilization of standard compression tests (CT)with solid cylindrical test specimens that weremachined out of sheets along ‘‘S’’, ‘‘T’’, and ‘‘L’’ dir-ections of Figure 1(b) is not an option for thin sheets.However, because the supplied sheets used in thisinvestigation have 5mm thickness it was possible toproduce small compression tests with aspect ratioh=d ¼ 1 that were employed to further confirm and

validate the results that were previously obtained bymeans of tensile and stack compression tests. Theresults are shown in Figure 7 and the agreementwith previous average stress–strain curves obtainedfrom standard tensile tests (TT) and stack compres-sion tests (SCT) is very good. The deviations in theaverage stress–strain curve derived from standard ten-sile tests (TT) are due to the previously mentionedextrapolation procedure for effective strain values�"4 0:16.

Now, remembering that our goal is to establish aset of experimental procedures that are able to char-acterize the stress–strain curve of thin sheets to beused in SBMF applications, it may be concludedthat stack compression tests (SCT) are capable ofproviding adequate stress responses up to highstrain levels in loading conditions across the thicknessof the sheets (direction ‘‘S’’ in Figure 1). However, inthe case of anisotropic raw materials subjected toloading conditions perpendicular to the sheet thick-ness (transverse ‘‘T’’ and longitudinal ‘‘L’’ directionsin Figure 1), there is a need to utilize additional test-ing procedures. Standard tensile tests are not appro-priate because they are generally limited to smallvalues of strain.

The new proposed shear test provides an effectiveanswer to the above mentioned needs, as can beobserved from the experimental evolution of thestress–strain curve obtained from double-notchedtest specimens loaded in tension that are plotted inFigure 8. The average stress–strain curve derivedfrom the SCT is included for reference purposes.

As seen in Figure 8, the size of the ligaments 2lmust be kept small (say, below 10mm) because theincrease in the size of the ligament allows plasticdeformation to extend outside the region placed inbetween the notches. This causes the stress state to

Figure 6. Stress–strain evolutions obtained from standard tensile tests (TT) and from stack compression tests (SCT_2 and SCT_3)

built upon two and three circular discs piled up to form cylindrical test specimens.

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

by guest on November 11, 2015pil.sagepub.comDownloaded from

deviate from pure shear material flow conditions.Similar caution must be taken in the fracture testsperformed with the new proposed shear test, as willbe discussed in the next sub-section.

Fracture toughness

The method and procedure to determine fracturetoughness in crack opening mode I is similar to thatpreviously described for the new proposed test per-formed with double-notched specimens loaded inshear (refer to sub-section ‘‘Fracture toughness’’).

Figure 9 shows the experimental evolution of theforce with displacement for the different fracture tests

specimens listed in Table 2. As seen, the force-displacement evolution exhibits a gradual increase toa maximum peak value (where cracks are triggered)and a gradual decrease from this peak value, whichchanges as a function of the size l of the ligaments.The area under each curve is the total work WT con-sumed during the test, which after being normalizedby lt (or by 2lt, in case of the new proposed shear test)may be split into the sum of the plastic work per unitof volume wp due to shearing with the specific essen-tial work of fracture wf. Fracture toughness R isobtained from the y-intercept of the straight linethat interpolates the variation of the normalizedtotal work wT as a function of the ligament length l

Figure 8. Stress–strain evolutions obtained from the new proposed shear test performed with double notched test specimens with

different ligament sizes 2l. The stress–strain curve of the stack compression test (SCT) is included for reference purposes.

Figure 7. Stress–strain evolutions obtained from standard tensile tests, from stack compression tests and from standard

compression tests machined out the ‘‘S’’, ‘‘T’’, and ‘‘L’’ directions of Figure 1(b).

Silva et al. 9

by guest on November 11, 2015pil.sagepub.comDownloaded from

of the specimens. The theoretical background for theabove described procedure is outlined in Figure 4 andthe results are given in Figure 10.

As seen in Figure 10, the values of fracture tough-ness R obtained from the two different fracture testsare similar (R ffi 200 kJ/m2) and demonstrate the cap-ability of the new proposed shear test to simultan-eously determine the stress–strain curve and thefracture toughness of metal sheets. Results alsoshow that the ligament length l of the specimensshould be smaller than a critical threshold value �d,where � � 8 for double-notched test specimens loadedin tension and � � 1:5 for double-notched test speci-mens loaded in shear, in order to ensure plastic flowto be restricted to the region placed in between thenotches. This constraint is needed because the deter-mination of fracture toughness R from test specimens

with very large ligament lengths is overestimated dueto the fact that total work includes plastic workperformed in regions other than the ligament. Therightmost grey points included in Figure 10(a) and(b) illustrate this problem.

The same conclusion applies to the determinationof the stress–strain curve.

Conclusions

This paper introduces a new experimental test for thesimultaneous determination of stress–strain curvesand fracture toughness of metal sheets. The testmakes use of double-notched test specimens loadedin shear and combines the plane stress loading condi-tions typical of sheet metal forming with the three-dimensional plastic flow conditions resulting from

Figure 9. Experimental evolution of the force with displacement for: (a) double-notched test specimens loaded in tension and

(b) double-notched test specimens loaded in shear (Table 2).

Figure 10. Evolution of the normalized total work with ligament length for: (a) double-notched test specimens loaded in tension and

(b) double-notched test specimens loaded in shear. Fracture toughness R is obtained from the y-intercepts of the straight lines.

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

by guest on November 11, 2015pil.sagepub.comDownloaded from

compressing in the direction perpendicular to thesheet thickness that are typical of bulk metal forming.

Experiments performed on aluminium alloy ENAW 5754 H111 sheets with 5mm thickness demon-strate that the new proposed shear test can effectivelybe utilized to determine the stress–strain curve of thematerials up to higher strain levels than those attainedin standard tensile tests. The procedure to determinefracture toughness makes use of these tests performedwith ligaments l5 1:5d in order to ensure that plasticwork is totally consumed in the shear deformationregion located in between the notches of the double-notched test specimens. Ligament lengths larger thanthe above mentioned threshold value will overesti-mate fracture toughness due to the fact that totalwork will include plastic work performed in regionsother than those located in between the notches.

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: The authors would like to acknowledge the

support provided by Fundacao para a Ciencia e aTecnologia of Portugal and IDMEC under LAETA –UID/EMS/50022/2013, PDTC/EMS-TEC/0626/2014 and

SFRH/BSAB/105959/2015. The support of MCG – Mindfor Metal, Carregado, Portugal and the work of JoaoRicardo are gratefully acknowledged.

References

1. Merklein M, Koch J, Schneider T, et al. Manufacturingof complex functional components with variants by using

a new metal forming process – sheet-bulk metal form-ing. Int J Mater Form 2010; 3: 347–350.

2. Merklein M, Allwood JM, Behrens BA, et al. Bulkforming of sheet metal. CIRP Ann Manuf Technol

2012; 61: 725–745.3. Sieczkarek P, Isik K, Ben Khalifa N, et al. Mechanics of

sheet-bulk indentation. J Mater Process Technol 2014;

214: 2387–2394.4. ASTM E9: 2009. Standard test methods of compression

testing of metallic materials at room temperature. West

Conshohocken, PA: ASTM International, 2009.5. Kitamura K and Terano M. Determination of local

properties of plastic anisotropy in thick plate by

small-cube compression test for precise simulation ofplate forging. CIRP Ann -Manuf Technol 2014; 63:293–296.

6. Pawelski O. Uber das stauchen von holzylindern und

seine eignung zur bestimmung der formanderungsfestig-keit dunner bleche. Arch Eisenhuttenwes 1967; 38:437–442.

7. Merklein M and Kuppert A. A method for the layercompression test considering the anisotropic materialbehavior. Int J Mater Form 2009; 12: 483–486.

8. Alves LM, Nielsen CV and Martins PAF. Revisiting thefundamentals and capabilities of the stack compressiontest. Exp Mech 2011; 51: 1565–1572.

9. ASTM B831: 2014. Standard test method for shear

testing of thin aluminum alloy products. WestConshohocken, PA: ASTM International, 2014.

10. Cotterell B and Reddel JK. The essential work of plane

stress fracture. Int J Fract 1977; 13: 267–277.11. Atkins AG. Ductile shear fracture mechanics. Key Eng

Mater 2000; 177–180: 59–68.

12. Isik K, Silva MB, Atkins AG, et al. A new test fordetermining fracture toughness in plane stress in modeII. J Strain Anal Eng Des 2015; 50: 221–231.

13. ASTM E8/E8M: 2013. Standard test methods for tensiontesting of metallic materials. West Conshohocken, PA:ASTM International, 2013.

Silva et al. 11

by guest on November 11, 2015pil.sagepub.comDownloaded from