Abstract
The plastic anisotropy and ductile fracture behavior of an Al–Si–Mg die-cast alloy (AA365-T7, or Aural-2) is probed using a combination of experiments and analysis. The plastic anisotropy is assessed using uniaxial tension, plane-strain tension and disc compression experiments, which are then used to calibrate the Yld2004-3D anisotropic yield criterion. The fracture behavior is investigated using notched tension, central hole and shear specimens, with the latter employing a geometry that was custom-designed for this material. Digital image correlation is used to assess the full strain fields for these experiments. However, fracture is expected to initiate at the through-thickness mid-plane of the specimens and thus it cannot be measured directly from experiments. Instead, the stresses and strains at the onset of fracture are estimated using finite element modeling. The loading path and the resulting fracture locus were found to be sensitive to the yield criterion employed, which underscores the importance of an adequate modeling of plastic anisotropy in ductile fracture studies. Based on the finite element modeling, the fracture locus is represented with three common criteria (Oyane, Johnson–Cook and Hosford–Coulomb), as well as a newly proposed one as the linear combination of the first two. However, beyond that, it is still questionable if all of these experiments are probing the same fracture locus, since the predicted loading paths of notched tension specimens are highly evolving compared to those of central hole and shear ones.
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References
Abedini A, Butcher C, Worswick MJ (2017) Fracture characterization of rolled sheet alloys in shear loading: studies of specimen geometry, anisotropy, and rate sensitivity. Exp Mech 57:75–88. https://doi.org/10.1007/s11340-016-0211-9
Abi-Akl R, Mohr D (2017) Paint-bake effect on the plasticity and fracture of pre-strained aluminum 6451 sheets. Int J Mech Sci 124–125:68–82. https://doi.org/10.1016/j.ijmecsci.2017.01.002
Banabic D (2010) Sheet metal forming processes: constitutive modelling and numerical simulation. Springer, Berlin
Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98. https://doi.org/10.1016/j.ijmecsci.2004.02.006
Baral M (2015) Experimental investigation of plastic anisotropy of commercially-pure titanium. MS Thesis. University of New Hampshire
Baral M, Hama T, Knudsen E, Korkolis YP (2018) Plastic deformation of commercially-pure titanium: experiments and modeling. Int J Plast 105:164–194. https://doi.org/10.1016/j.ijplas.2018.02.009
Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi S-H, Chu E (2003) Plane stress yield function for aluminum alloy sheets–part 1: theory. Int J Plast 19:1297–1319. https://doi.org/10.1016/S0749-6419(02)00019-0
Barlat F, Aretz H, Yoon JW, Karabin ME, Brem JC, Dick RE (2005) Linear transfomation-based anisotropic yield functions. Int J Plast 21:1009–1039. https://doi.org/10.1016/j.ijplas.2004.06.004
Basu S, Benzerga AA (2015) On the path-dependence of the fracture locus in ductile materials: experiments. Int J Solids Struct 71:79–90. https://doi.org/10.1016/j.ijsolstr.2015.06.003
Benzerga AA, Leblond J-B (2010) Ductile fracture by void growth to coalescence. In: Advances in applied mechanics, pp 169–305. https://doi.org/10.1016/S0065-2156(10)44003-X
Benzerga AA, Besson J, Pineau A (2004) Anisotropic ductile fracture. Acta Mater 52:4623–4638. https://doi.org/10.1016/j.actamat.2004.06.020
Benzerga AA, Surovik D, Keralavarma SM (2012) On the path-dependence of the fracture locus in ductile materials—analysis. Int J Plast 37:157–170. https://doi.org/10.1016/j.ijplas.2012.05.003
Clift SE, Hartley P, Sturgess CEN, Rowe GW (1990) Fracture prediction in plastic deformation processes. Int J Mech Sci 32:1–17. https://doi.org/10.1016/0020-7403(90)90148-C
Cockcroft MG, Latham DJ (1968) Ductility and the workability of Metals. J Inst Met 96:33–39 https://doi.org/citeulike-article-id:4789874
Coppieters S, Kuwabara T (2014) Identification of post-necking hardening phenomena in ductile sheet metal. Exp Mech 54:1355–1371. https://doi.org/10.1007/s11340-014-9900-4
Coppola T, Cortese L, Folgarait P (2009) The effect of stress invariants on ductile fracture limit in steels. Eng Fract Mech 76:1288–1302. https://doi.org/10.1016/j.engfracmech.2009.02.006
Deng N, Kuwabara T, Korkolis YP (2015) Cruciform specimen design and verification for constitutive identification of anisotropic sheets. Exp Mech 55:1005–1022. https://doi.org/10.1007/s11340-015-9999-y
Dick CP, Korkolis YP (2015) Anisotropy of thin-walled tubes by a new method of combined tension and shear loading. Int J Plast 71:87–112. https://doi.org/10.1016/j.ijplas.2015.04.006
Dunand M, Mohr D (2010) Hybrid experimental-numerical analysis of basic ductile fracture experiments for sheet metals. Int J Solids Struct 47:1130–1143. https://doi.org/10.1016/j.ijsolstr.2009.12.011
Dunand M, Mohr D (2011) Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading. Eng Fract Mech 78:2919–2934. https://doi.org/10.1016/j.engfracmech.2011.08.008
Ghahremaninezhad A, Ravi-Chandar K (2011) Ductile failure in polycrystalline OFHC copper. Int J Solids Struct 48:3299–3311. https://doi.org/10.1016/j.ijsolstr.2011.07.001
Ghahremaninezhad A, Ravi-Chandar K (2012) Ductile failure behavior of polycrystalline Al 6061–T6. Int J Fract 174:177–202. https://doi.org/10.1007/s10704-012-9689-z
Giagmouris T, Kyriakides S, Korkolis YP, Lee L-H (2010) On the localization and failure in aluminum shells due to crushing induced bending and tension. Int J Solids Struct 47:2680–2692. https://doi.org/10.1016/j.ijsolstr.2010.05.023
Gologanu M, Leblond J-B, Devaux J (1993) Approximate models for ductile metals containing non-spherical voids–case of axisymmetric prolate ellipsoidal cavities. J Mech Phys Solids 41:1723–1754. https://doi.org/10.1016/0022-5096(93)90029-F
Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I-yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99:2–15
Ha J, Baral M, Korkolis YP (2018) Plastic anisotropy and ductile fracture of bake-hardened AA6013 aluminum sheet. J Solids Struct Int 155:123–139. https://doi.org/10.1016/J.IJSOLSTR.2018.07.015
Haltom SS, Kyriakides S, Ravi-Chandar K (2013) Ductile failure under combined shear and tension. Int J Solids Struct 50:1507–1522. https://doi.org/10.1016/j.ijsolstr.2012.12.009
Hancock JW, Mackenzie AC (1976) On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J Mech Phys Solids 24:147–160. https://doi.org/10.1016/0022-5096(76)90024-7
Hartlieb M (2013) High integrity diecasting for structural applications. IMDC meeting, Worcester, MA
Hershey AV (1954) The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals. J Appl Mech ASME 21:241–249
Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A Math Phys Eng Sci 193:281–297
Hosford WF (1972) A generalized isotropic yield criterion. J Appl Mech 39:607–609
Hosford WF, Caddell RM (1993) Metal forming: mechanics and metallurgy. Prentice Hall, Englewood Cliffs
Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48. https://doi.org/10.1016/0013-7944(85)90052-9
Kim J, Gao X, Srivatsan TS (2004) Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Eng Fract Mech 71:379–400. https://doi.org/10.1016/S0013-7944(03)00114-0
Korkolis YP, Kyriakides S (2008a) Inflation and burst of aluminum tubes. Part II: an advanced yield function including deformation-induced anisotropy. Int J Plast 24:1625–1637. https://doi.org/10.1016/j.ijplas.2008.02.011
Korkolis YP, Kyriakides S (2008b) Inflation and burst of anisotropic aluminum tubes for hydroforming applications. Int J Plast 24:509–543. https://doi.org/10.1016/j.ijplas.2007.07.010
Korkolis YP, Kyriakides S (2009) Path-dependent failure of inflated aluminum tubes. Int J Plast 25:2059–2080. https://doi.org/10.1016/j.ijplas.2008.12.016
Korkolis YP, Kyriakides S (2011) Hydroforming of anisotropic aluminum tubes: part I experiments. Int J Mech Sci 53:75–82. https://doi.org/10.1016/j.ijmecsci.2010.11.003
Korkolis YP, Kyriakides S, Giagmouris T, Lee L-H (2010) Constitutive modeling and rupture predictions of Al-6061-T6 tubes under biaxial loading paths. J Appl Mech Trans ASME 77:064501. https://doi.org/10.1115/1.4001940
Korkolis YP, Barlat F, Kuwabara T (2017) Simplified representations of multiaxial test results in plasticity. In: 5th international conference on material modeling (ICMM5). Rome, Italy
Leblond J-B, Perrin G, Devaux J (1995) An improved Gurson-type model for hardenable ductile metals. Eur J Mech A Solids 14:499–527
Logan RW, Hosford WF (1980) Upper-bound anisotropic yield locus calculations assuming \(\langle 111\rangle \)-pencil glide. Int J Mech Sci 22:419–430. https://doi.org/10.1016/0020-7403(80)90011-9
Lou Y, Huh H (2013) Extension of a shear-controlled ductile fracture model considering the stress triaxiality and the Lode parameter. Int J Solids Struct 50:447–455. https://doi.org/10.1016/j.ijsolstr.2012.10.007
Lou Y, Yoon JW (2017) Anisotropic ductile fracture criterion based on linear transformation. Int J Plast 93:3–25. https://doi.org/10.1016/J.IJPLAS.2017.04.008
Lou Y, Huh H, Lim S, Pack K (2012) New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals. Int J Solids Struct 49:3605–3615. https://doi.org/10.1016/j.ijsolstr.2012.02.016
Mae H, Teng X, Bai Y, Wierzbicki T (2007) Calibration of ductile fracture properties of a cast aluminum alloy. Mater Sci Eng A 459:156–166. https://doi.org/10.1016/J.MSEA.2007.01.047
McClintock FA (1968) A criterion for ductile fracture by the growth of holes. J Appl Mech 35:363–371
Meyers MA, Chawla KK (1984) Mechanical metallurgy: principles and applications. Prentice-Hall, Englewood Cliffs
Miyauchi K (1984) A proposal for a planar simple shear test in sheet metals. Sci Pap RIKEN 81:27–42
Mohr D, Henn S (2007) Calibration of stress-triaxiality dependent crack formation criteria: a new hybrid experimental-numerical method. Exp Mech 47:805–820. https://doi.org/10.1007/s11340-007-9039-7
Mohr D, Marcadet SJ (2015) Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities. Int J Solids Struct 67–68:40–55. https://doi.org/10.1016/j.ijsolstr.2015.02.024
Nahshon K, Hutchinson JW (2008) Modification of the Gurson Model for shear failure. Eur J Mech A/Solids 27:1–17. https://doi.org/10.1016/j.euromechsol.2007.08.002
Oh SI, Chen CC, Kobayashi S (1979) Ductile fracture in axisymmetric extrusion and drawing-Part2: workability in extrusoin and drawing. J Eng Ind 101:36–44. https://doi.org/10.1115/1.3439471
Oyane M, Sato T, Okimoto K, Shima S (1980) Criteria for ductile fracture and their applications. J Mech Work Technol 4:65–81. https://doi.org/10.1016/0378-3804(80)90006-6
Pack K, Marcadet SJ (2016) Numerical failure analysis of three-point bending on martensitic hat assembly using advanced plasticity and fracture models for complex loading. Int J Solids Struct 85–86:144–159. https://doi.org/10.1016/J.IJSOLSTR.2016.02.014
Papasidero J, Doquet V, Mohr D (2015) Ductile fracture of aluminum 2024–T351 under proportional and non-proportional multi-axial loading: Bao–Wierzbicki results revisited. Int J Solids Struct 69–70:459–474. https://doi.org/10.1016/j.ijsolstr.2015.05.006
Pardoen T, Hutchinson J (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2467–2512. https://doi.org/10.1016/S0022-5096(00)00019-3
Paredes M, Lian J, Wierzbicki T, Cristea ME, Münstermann S, Darcis P (2018) Modeling of plasticity and fracture behavior of X65 steels: seam weld and seamless pipes. Int J Fract 213:17–36. https://doi.org/10.1007/s10704-018-0303-x
Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217. https://doi.org/10.1016/0022-5096(69)90033-7
Roth CC, Mohr D (2014) Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: experiments and modeling. Int J Plast 56:19–44. https://doi.org/10.1016/j.ijplas.2014.01.003
Roth CC, Mohr D (2016) Ductile fracture experiments with locally proportional loading histories. Int J Plast 79:328–354. https://doi.org/10.1016/j.ijplas.2015.08.004
Scales M, Tardif N, Kyriakides S (2016) Ductile failure of aluminum alloy tubes under combined torsion and tension. Int J Solids Struct 97–98:116–128. https://doi.org/10.1016/J.IJSOLSTR.2016.07.038
Sharpe W (ed) (2010) Handbook of experimental solid mechanics. Springer, Berlin
Shukla A, Dally JW (2010) Experimental solid mechanics. College House Enterprises, Knoxville
Sung JH, Kim JH, Wagoner RH (2010) A plastic constitutive equation incorporating strain, strain-rate, and temperature. Int J Plast 26:1746–1771. https://doi.org/10.1016/j.ijplas.2010.02.005
Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1:1–18. https://doi.org/10.1016/0022-5096(52)90002-1
Tardif N, Kyriakides S (2012) Determination of anisotropy and material hardening for aluminum sheet metal. Int J Solids Struct 49:3496–3506. https://doi.org/10.1016/j.ijsolstr.2012.01.011
Thomason PF (1990) Ductile fracture of metals. Pergamon Press, New York
Tian H, Brownell B, Baral M, Korkolis YP (2017) Earing in cup-drawing of anisotropic Al-6022-T4 sheets. Int J Mater Form 10:329–343. https://doi.org/10.1007/s12289-016-1282-y
Till E, Hackl B (2013) Calibration of plasticity and failure models for AHSS sheets. In: Proceedings of the international deep drawing research conference IDDRG 2013
Toda H, Oogo H, Tsuruta H, Horikawa K, Uesugi K, Takeuchi A, Suzuki Y, Kobayashi M (2012) Origin of ductile fracture in aluminum alloys. In: ICAA13 Pittsburgh. Springer International Publishing, Cham, pp 565–570. https://doi.org/10.1007/978-3-319-48761-8_83
Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32:157–169. https://doi.org/10.1016/0001-6160(84)90213-X
Wang K, Greve L, Wierzbicki T (2015) FE simulation of edge fracture considering pre-damage from blanking process. Int J Solids Struct 71:206–218. https://doi.org/10.1016/j.ijsolstr.2015.06.023
Water S (2000) Standard test method for shear testing of thin aluminum alloy products 11:11–14. https://doi.org/10.1520/B0831-05
Yin Q, Zillmann B, Suttner S, Gerstein G, Biasutti M, Tekkaya AE, Wagner MF-X, Merklein M, Schaper M, Halle T, Brosius A (2014) An experimental and numerical investigation of different shear test configurations for sheet metal characterization. Int J Solids Struct 51:1066–1074. https://doi.org/10.1016/J.IJSOLSTR.2013.12.006
Yoon JW, Barlat F, Dick RE, Karabin ME (2006) Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function. Int J Plast 22:174–193. https://doi.org/10.1016/j.ijplas.2005.03.013
Zhang X, Wierzbicki T (2015) Characterization of plasticity and fracture of shell casing of lithium-ion cylindrical battery. J Power Sources 280:47–56. https://doi.org/10.1016/j.jpowsour.2015.01.077
Zhang K, Bai J, François D (2001) Numerical analysis of the influence of the Lode parameter on void growth. Int J Solids Struct 38:5847–5856. https://doi.org/10.1016/S0020-7683(00)00391-7
Acknowledgements
Support of this work from an industrial sponsor is acknowledged with thanks. We also wish to thank Scott Campbell for his help with preparing some of the specimens. Finally, it is a pleasure to acknowledge the help of 2nd Lt. Moritz Dirian, a visiting student from Universität der Bundeswehr, Munich, Germany in this work.
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Appendices
Appendix A
The microstructure images of the die-cast alloy taken using the optical microscope are shown in Fig. 19. The specimen surface was polished mechanically with sheet sandpaper up to 2400-grit, and the precipitation on the surface was naturally oxidized by water.
Microstructure images of AA365-T7 die cast alloy at two different magnifications
Appendix B
The specimen geometries for plasticity specimens are shown in Fig. 20.
Specimen geometries for plasticity specimens (units \(=\) mm)
Appendix C
The specimen geometries for fracture specimens are shown in Fig. 21, with a zoomed-in gage section for SH specimen in Fig. 22.
Specimen geometries for fracture specimens (units \(=\) mm)
Appendix D
The yield locus for Yld2000-2D and Yld2004-3D are shown together in Fig. 23.
Detailed geometry of the notch section for the SH specimen (units \(=\) mm)
Comparison of yield locus predicted by Yld2000-2D and Yld2004-3D criteria
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Baral, M., Ha, J. & Korkolis, Y.P. Plasticity and ductile fracture modeling of an Al–Si–Mg die-cast alloy. Int J Fract 216, 101–121 (2019). https://doi.org/10.1007/s10704-019-00345-1
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DOI: https://doi.org/10.1007/s10704-019-00345-1