In this paper we are going to investigate the ductile fracture in cold forming of
nanostructured Al - 6082 alloy material during axi-symmetric collar
(flanged) tests and cylindrical upsetting tests by using eight types of
fracture criteria. The material of specimens were taken out of ECAP was made by one, four,
and eight passes (route C) in three perpendicular axes. The material has
ultrafine grain size and an anisotropic behaviour. A simple yield criterion
and material law are used to describe the plastic deformation of the
nanostructured material. The collar tests and cylindrical upsetting tests
produced typical ductile fractures in all types of specimens

Krállics, György

S. M. Agena, Ahmed

English

Periodica Polytechnica (Budapest University of Technology and Economics)

PERIODICA POLYTECHNICA SER. MECH. ENG. VOL. 50, NO. 2, PP. 89–97 (2006)INVESTIGATION OF DUCTILE FRACTURE OFNANOSTRUCTURED AL-6082 MATERIALGyörgy KRÁLLICS∗ and Ahmed S. M. AGENA∗∗Department of Materials Science and Engineering,Budapest University of Technology and Economics,H–1111 Budapest, Bertalan L u.7.* Tel: (1) 463 1445,*e-mail: krallics@eik.bme.hu** Tel: (6) 70-502-9031,e-mail: ahmedajina@yahoo.comReceived: Sept. 14, 2004AbstractIn this paper we are going to investigate the ductile fracture in cold forming of nanostructured Al- 6082 alloy material during axi-symmetric collar (flanged) tests and cylindrical upsetting tests byusing eight types of fracture criteria. The material of specimens were taken out of ECAP was madeby one, four, and eight passes (route C) in three perpendicular axes. The material has ultrafine grainsize and an anisotropic behaviour. A simple yield criterion and material law are used to describe theplastic deformation of the nanostructured material. The collar tests and cylindrical upsetting testsproduced typical ductile fractures in all types of specimens.Keywords: nanostructured Al-6082 alloy, upsetting test, ductile fracture criteria.1. IntroductionMost of previous studies have dealt with workability of isotropic materials whichis easier to define by mechanical and physical properties. In recent years, bulknanostructured materials (NSM) processed by several plastic deformations (SPD)have been investigated by a few literature and it is still limited.Generally, nanostructured materials produced by (ECAP) process, the worka-bility parameters depend on the number of passes, the type of route, and the directionof the specimen’s axis and it refers to the relative ease with which the material canbe shaped through plastic deformation and it is a function of the material and theprocess. A large number of tests are currently used to evaluate the ductility of nanos-tructured materials such as tension, torsion, and compression tests. The initiationof ductile fracture is a major factor influencing the limit of deformability in manymetalworking operations [1]. In this work, several upsetting tests were carried outto evaluate the formability of nanostructured Al -6082 alloy by using cylindricaland flanged specimens (Fig. 1) and the flow curves for all types of specimens wereplotted.90 GY. KRÁLLICS and A. S. M. AGENA2. Ductile Fracture CriteriaWorkability is usually thought as being limited by the onset of the fracture. Greaterworkability of the material allows greater deformation. In this study many types ofductile fracture criteria were used to determine the limit of the bulk deformation.The empirical formulas of these criteria are described below [2, 3, 4].102O 14O 10O 1010All Dimension in mmFig. 1. Geometry of work piece (a) Flanged specimen (b) cylindrical specimen2.1. Cockcroft and Latham Fracture CriterionThis criterion is based on true ductility and it is suggesting that the fracture occurswhen the tensile strain energy reaches a critical value :1σyε̄f∫0σ1dε̄ = C1 (1)where σ1 is the maximum tensile stress and σy is the yield stress.2.2. Brozzo et al. Fracture CriterionBrozzo et al. have made a modification to the Cockcroft and Latham criterion(Eq. (1)). This criterion depends on the maximum tensile stress σ1 and hydrostaticDUCTILE FRACTURE OF NANOSTRUCTURED AL-6082 MATERIAL 91(mean) stress σm:ε̄f∫02σ13 (σ1 − σm)dε̄ = C2 (2)2.3. Freudenthal Fracture CriterionIt is assuming that the total plastic work to fracture is constant:1σyε̄f∫0σ̄ dε̄ = C3 (3)where σ̄ is the effective stress, ε̄ is the effective strain at fracture and σy is the yieldstress.2.4. Im and Argan Fracture CriterionThis criterion assumes that the integration of the amount of hydrostatic stress andeffective stress is constant:1σyεf∫0(σm + σ̄ )dε̄ = C4 (4)2.5. Oyane et al. Fracture CriterionThis criterion assumes that the fracture occurs at a critical volumetric strain:εf∫0(1 +σmAσ̄)dε̄ = C5 (5)where A = 2/3 (i.e. between unixial and triaxil stress states).92 GY. KRÁLLICS and A. S. M. AGENA2.6. Oh and Kobayashi CriterionIt assumes that the ratio of the maximum tensile stress and effective strain is equalto constant:ε̄f∫0σ1σ̄dε̄ = C6 (6)2.7. Shabaic and Vujovic CriterionThis criterion considers the ratio of mean stress and effective stress and it gives thefollowing fracture model:(3σmσ̄)= C7 (7)2.8. Tresca Energy Fracture CriterionThis is a simple criterion. Considering the difference between tensile and compres-sion stresses, it is as follows:1σyεf∫0(σ1 − σ22)dε̄ = C8 (8)where σ1 is the maximum tensile stress, σ2 is the maximum compression stress andσy is the yield stress.C1, C2, C3, C4, C5, C6, C7 and C8 are constants.3. Calculation of Ductile Fracture Criterion ConstantsIn order to calculate ductile fracture criteria we need at least a certain kind ofdestructive test. In this work we carried out compression tests, and results weresimulated using computer programme to determine anisotropic parameters. Eachductile fracture criterion needs to calculate stress state and effective stress.DUCTILE FRACTURE OF NANOSTRUCTURED AL-6082 MATERIAL 934. Theoretical BackgroundThe continuum theory of plasticity (continuum mechanics) attempts to describethe stress –strain behaviour of a continuum on the basis of postulated yield criteriawithout regard to internal structure. Continuum mechanics also bypasses all ofdetails involved in dislocation mechanics.Mathematical modelling of bulk forming operation requires a yield criterionthat describes the anisotropic yielding behaviour of the bulk metal.Plasticity continuum theory was originally developed for an isotropic mater-ial. The theory was then modified by many anisotropic yield criteria such as: Hillcriterion to explain the effects of anisotropy on the forming processes by incorpo-rating the ‘parameters of anisotropic plasticity’ or the ‘coefficients of anisotropy’.HILL [13] extended the theoretical framework of Von Mises criterion to includeanisotropy and expressed his criterion as:F(σ22 − σ33)2 + G(σ33 − σ11)2 + H(σ11 − σ22)2+2Lσ 223 + 2Mσ 231 + 2Nσ 212 = 1(9)where F,G,…..,N are anisotropy parameters.0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.00.20.40.60.81.01.21.41.61.8Longitudinal Directionm3m1Zero Directionm2900 Directionln(b/a)ln(h0/h)Fig. 2. Values of m1, m2and m3. Fig. 3. Ellipse axes of deformed specimenFrom this criterion the equivalent stress can be expressed as [8]:σ̄eq =( √32√(FH+FG+GH)[F(σ22 − σ33)2 + G(σ33 − σ11)2 + H(σ11 − σ22)2++2Lσ 223 + 2Mσ 231 + 2Nσ 212] )12(10)In the case of the upsetting test of collar workpiece, at the free surface one ofthe three components of the stress is equal to zero and the shear stresses are equalto zero, too.σ12 = σ23 = σ31 = 0.94 GY. KRÁLLICS and A. S. M. AGENAThe above equation becomes:F(σ22 − σ33)2 + G(σ33 − σ11)2 + H(σ11 − σ22)2 = 1 (11)But in all directions there is only one of stress components then:σ11 = σ22 = 0and the equivalent stress becomes:σ̄eq =( √3[σ 233(F+G)]2√(FH+FG+GH))12(12)The equivalent strain can be expressed as :ε̄ =√6 (F + G + H) ×√(G2+HF+GH)2F+G × lnh0h3 (HF + FG + GH)(13)The values of anisotropy parameters can be calculated by solving these equations:(F + G)σy = m1 (14)G − HG + H= m2 (15)H − FF + H= m3 (16)where σy is the yield stress and m1, m2and m3 are the slope of the curve lines in theFig. 2 where a and b are principal axes of the ellipse of deformed specimen (Fig.3).The three components of strain rate can be calculated from the flow ruleequation as:ε̇ij = λ̇∂f∂σij(17)andεii = aii(lnhh0)b0(18)ε̇ii =∂εii∂h∂h∂t=∂εii∂hν (19)where ν ìs the velocity of the punch, h0 is the initial height of the work piece, a andb are approximation parameters i = 2, 3 ….DUCTILE FRACTURE OF NANOSTRUCTURED AL-6082 MATERIAL 95And the equivalent strain rate ¯̇ε can be calculated as¯̇ε =ε̇22σ22 + ε̇33σ33σ̄(20)andλ̇ =¯̇εσ̄4(21)Repeating equations (17) and (19) we can calculate the real values of σ22 and σ33.Fig. 4 is illustrating the equivalent stress for one, four, and eight passes.0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2 1 .4 1 .6200225250275300325Equivalent Stress (MPa)E q u iv a le n t S tra in 1  p a s s 4  p a s s 8  p a s s R a w  m a te r ia lFig. 4. Equivalent stress – Equivalent strain curves     a      b Fig. 5. Crack on the specimens. (a) Flanged specimen (b). Cylindrical specimen96 GY. KRÁLLICS and A. S. M. AGENA00.511.522.531-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-9000.511.522.531-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-90Fig.6-a. Constant value of Brozzofracture criterionFig.6-b. Constant value of Cock-croft and Latham fracture criterion01234561-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-9000.10.20.30.40.50.61-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-90Fig.6-c. Constant value of Im&Argane fracture criterionFig.6-d. Constant value of Cock-croft and Latham fracture criterion00.20.40.60.811.21.41.61-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-9000.511.522.531-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-90Fig.6-e. Constant value of Oyaneel al. fracture criterionFig.6-f. Constant value of Oh andKobayashi criterion00.511.522.531-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-9000.10.20.30.40.50.61-long1-zerop-1-904-long4-zerop4-90 8-long8-zerop8-90Fig.6-g. Constant value ofFreudenthal fracture criterionFig.6-h. Constant value ofShabaic and Vujovic criterionDUCTILE FRACTURE OF NANOSTRUCTURED AL-6082 MATERIAL 975. Results and DiscussionCracks appeared on all types of the specimens after certain value of deformation(Fig. 5). Many criteria have been developed to predict ductile fracture. In thispaper we apply the above eight types of fracture criteria. To apply these formulaswe need a relation equation between criteria parameters and equivalent strain thatcan be created from the curves by using special computer program and take theintegration. Fig. 6 shows that the values of criteria constants are changing like azigzag path.From the results of experimental tests we concluded that the minimum value ofductile fracture criteria occurred at pass four in longitudinal direction of specimen’saxes and the maximum value of ductile fracture outcame at pass one in longitudinaldirection. The reasons for that are may be the fact that the value of effective strainat fracture in pass four is the lowest.6. Summary and ConclusionsThe properties of Al 6082 alloy changed when the material was subjected to ECAPprocess, they turned into anisotropic and the microstructure of materials transferredto nanostructured one as well as flow stresses became greater than those beforeECAP method. After deformation the initial circular cross section of specimenschanged to elliptical shape. It is reported that the minimum value of constant offracture criteria occurred in pass four of ECAP in longitudinal direction.References[1] VENUGOPAL RAO, A. – RAMAKRISHNAN, N. – KRISHNA KUMAR, R., A ComparativeEvaluation of The Theoretical Failure Criteria for Workability in Cold Forging: Journal ofMaterial Process Technology 142 (2003) pp. 29–42.[2] FAHRETTIN OZTURK – DAEYONG LEE, Analysis of Forming Limits Using Ductile FractureCriteria: Journal of Material Process Technology 147 (2004) pp. 397–404.[3] NARAYANA, S.V.S– MURTY, B.–NAGESWARA RAO,–KASHYAP, B.P., Improved DuctileFracture Criterion for Cold Forming of Spheroidised Steel, Journal of Material Process Tech-nology, 142 (2004) pp. 94–101.[4] LANDRE, J.–PERTENCE, A.– CETLIN, P.R.– RODRIGUES, J.M.C. –MARTINS, P.A.F., Onthe Utilization of Ductile Fracture Criteria in Cold Forging, Journal of Finite Element in Analysisand Design, 39 (2003) pp. 175–186 .[5] WEILONG HU, An Orthotropic Yield Criterion in 3-D General Stress State: InternationalJournal Plasticity 21 (2005) pp. 1771–1796.[6] KRÁLLICS, G. – FODOR, A. – AGENA, A., Anisotropic Mechanical Properties of Ultra-fineGrained Aluminum Alloy. Under publication paper[7] LIU, C.–HUNG, Y.– STOUT M. G., On The A Symmetric Yield Surface of Plastically Or-thotropic Materials :A Phenomenological Study. Acta Mater 45 N0.6: P. 2397-2406 1997.[8] MONTMITONNET, P. – CHENOT, J. L., Introduction of Anisotropy in Viscoplastic 2D and 3DFinite-element Simulations of Hot Forging, Journal of Materials Processing Thechnology 53(1995) pp. 662–683.

Investigation of Ductile Fracture of Nanostructured Al-6082 Material

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Investigation of Ductile Fracture of Nanostructured Al-6082 Material

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