Abstract
In this paper, a two-dimensional (2D) microstructure-based modeling method is developed in order to predict the ductility of a thin-walled high pressure die cast magnesium (Mg) by considering the three-dimensional (3D) thru-thickness pore distributions. For this purpose, a series of 3D synthetic microstructure-based finite element models and the corresponding 2D models are first generated with various pore volume fractions, pore size distributions and pore shapes. The input material properties for the 2D models are determined based on the 3D cubic model with a spherical pore and the generalized Neuber’s rule. Based on the resulting ductility of the 3D and 2D models, a 3D/2D ductility correlation curve is developed as a function of the characteristics/shape of the input fracture strain curve used in the 3D model. The validity of the ductility correlation curve is examined with casting samples with actual microstructures. The results show that the suggested 2D modeling methodology can be used together with the ductility correlation curve in predicting the ductility of thin-walled Mg castings.
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References
Abaqus (2016) Analysis user’s guide. Dassault Systèmes Simulia Corp, Johnston
Barker EI, Choi KS, Sun X, Deda E, Allison J, Li M, Forsmark J, Zindel J, Godlewski L (2014) Microstructure based modeling of \(\upbeta \) phase influence on mechanical response of cast AM series Mg alloys. Comput Mater Sci 92:353–361
Brown LM, Embury JD (1973) Initiation and growth of voids at second phase particles. In: Proceedings of the 3rd international conference on microstructure and design of alloys, vol 1. Institute of Metals and Iron and Steel Institute, London, pp 164–169
Cáceres CH (1995) On the effect of macroporosity on the tensile properties of the Al-7%Si-0.4%Mg casting alloy. Scr Metall Mater 32:1851–1856
Cáceres CH, Davidson CJ, Griffiths JR (1995) The deformation and fracture behaviour of an Al–Si–Mg casting alloy. Mater Sci Eng 197A:171–179
Cáceres CH, Selling BI (1996) Casting defects and the tensile properties of an Al–Si–Mg alloy. Mater Sci Eng 220A:109–116
Chadha G, Allison JE, Jones JW (2007) The role of microstructure on ductility of die-cast AM50 and AM60 magnesium alloys. Metall Mater Trans A 38:286–297
Chen G, Shi MF, Tyan T (2011) Fracture modeling of AHSS in component crush tests. SAE Int J Mater Manuf 4:1–9
Choi KS, Li D, Sun X, Li M, Allison J (2013) Effects of pore distributions on ductility of thin-walled high pressure die-cast magnesium. SAE Technical Paper 2013-01-0644. https://doi.org/10.4271/2013-01-0644
Choi KS, Barker E, Cheng G, Sun X, Forsmark J, Li M (2016) Predicting stress vs. strain behaviors of thin-walled high pressure die casting magnesium alloy with actual pore distribution. SAE Int J Mater Manuf 9:361–367
Dahle AK, Lee YC, Nave MD, Schaffer PL, St John DH (2001) Development of the as-cast microstructure in magnesium–aluminium alloys. J Light Met 1:61–72
Deda E, Berman TD, Allison JE (2017) The influence of Al content and thickness on the microstructure and tensile properties in high-pressure die cast magnesium alloys. Metall Mater Trans A 48:1999–2014
Forsmark J, Dowling Z, Gibson K, Mueller C, Godlewski L, Zindel J, Boileau J (2015) An investigation of the effects of cast skin on the mechanical properties of an AM60 die-cast magnesium alloy. SAE Int J Mater Manuf 8:714–721
Gokhale AM, Patel GR (2005) Quantitative fractographic analysis of variability in tensile ductility of a squeeze cast Al–Si–Mg base alloy. Mater Charact 54:13–20
Ghosh AK (1977) Tensile instability and necking in materials with strain hardening and strain-rate hardening. Acta Metall 25:1413–1424
Gu G, Lin S, Meng Y, Xia Y, Zhou Q (2011) Influence of strain rate and stress state on the mechanical behavior of die-casting AM60 magnesium alloy. IMECE Paper 2011-65196. ASME 2011 International Mechanical Engineering Congress & Exposition. Denver, CO, USA
Hoffmann M, Seeger T (1985a) Generalized method for estimating multiaxial elastic-plastic notch stresses and strains. Part 1: theory. J Eng Mater Technol Trans ASME 107:250–254
Hoffmann M, Seeger T (1985b) Generalized method for estimating multiaxial elastic-plastic notch stresses and strains. Part 2: application and general discussion. J Eng Mater Technol Trans ASME 107:255–260
Hooputra H, Gese H, Dell H, Werner H (2004) A comprehensive failure model for crachworthiness simulation of aluminum extrusions. Int J Crashworthiness 9:449–463
Jung IY (2002) Prediction of tensile ductility in porous materials. Philos Mag 82A:2263–2268
Lee CD (2007a) Dependence of tensile properties of AM60 magnesium alloy on microporosity and grain size. Mater Sci Eng A 454–455:575–580
Lee CD (2007b) Tensile properties of high-pressure die-cast AM60 and AZ91 magnesium alloys on microporosity variation. J Mater Sci 42:10032–10039
Lee SG, Patel GR, Gokhale AM, Sreeranganathan A, Horstemeyer MF (2005) Variability in the tensile ductility of high-pressure die-cast AM50 Mg-alloy. Scr Mater 53:851–856
Lee SG, Gokhale AM, Patel GR, Evans M (2006a) Effect of process parameters on porosity distributions in high-pressure die-cast AM50 Mg-alloy. Mater Sci Eng 427A:99–111
Lee SG, Patel GR, Gokhale AM, Sreeranganathan A, Horstemeyer MF (2006b) Quantitative fractographic analysis of variability in the tensile ductility of high-pressure die-cast AE44 Mg-alloy. Mater Sci Eng 427A:255–262
Mayer H, Papakyriacou M, Zettl B, Stanzl-Tschegg SE (2003) Influence of porosity on the fatigue limit of die cast magnesium and aluminium alloys. Int J Fatigue 25:245–256
Mordike BL, Ebert T (2001) Magnesium: properties-applications-potential. Mater Sci Eng 302A:37–45
Song J, Xiong SM, Li M, Allison J (2009) The correlation between microstructure and mechanical properties of high-pressure die-cast AM50 alloy. J Alloys Compd 477:863–869
Sun X (2014) Mechanistic-based ductility prediction for complex magnesium castings. In: 2014 DOE vehicle technologies program annual merit review and peer evaluation meeting, DC, USA
Sun X (2015) Mechanistic-based ductility prediction for complex magnesium castings. In: 2015 DOE vehicle technologies program annual merit review and peer evaluation meeting, DC, USA
Sun X, Choi KS, Li DS (2013) Predicting the influence of pore characteristics on ductility of thin-walled high pressure die casting magnesium. Mater Sci Eng 572A:45–55
Surappa MK, Blank E, Jaquet JC (1986) Effect of macro-porosity on the strength and ductility of cast Al-7Si-0. 3Mg alloy. Scr Metall 20:1281–1286
Wang QZ (2002) Simple formulae for the stress concentration factor for two- and three-dimensional holes in finite domains. J Strain Anal Eng Des 37:259–264
Wang K, Deng Y-C, Rao V, Yang X (2011) An engineering approach to predict fracture and tearing. SAE Technical Paper 2011-01-0002. https://doi.org/10.4271/2011-01-0002
Weiler JP, Wood JT (2009a) Modeling fracture properties in a die-cast AM60B magnesium alloy I—analytical failure model. Mater Sci Eng 527A:25–31
Weiler JP, Wood JT (2009b) Modeling fracture properties in a die-cast AM60B magnesium alloy II—the effects of the size and location of porosity determined using finite element simulations. Mater Sci Eng 527A:32–37
Weiler JP, Wood JT (2012) Modeling the tensile failure of cast magnesium alloys. J Alloys Compd 537:133–140
Weiler JP, Wood JT, Klassen RJ, Maire E, Berkmortel R, Wang G (2005) Relationship between internal porosity and fracture strength of die-cast magnesium AM60B alloy. Mater Sci Eng 395A:315–322
Wierzbicki T, Bao Y, Lee Y-W, Bai Y (2005) Calibration and evaluation of seven fracture models. Int J Mech Sci 47:719–743
Zhu H, Zhu X (2011) A mixed-mode fracture criterion for AHSS cracking prediction at large strain. SAE Int J Mater Manuf 4:10–26
Acknowledgements
Pacific Northwest National Laboratory is operated by Battelle Memorial Institute for the US Department of Energy under Contract No. DEAC05- 76RL01830. Oak Ridge National Laboratory is operated by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725. This work was funded by the Department of Energy Office of FreedomCar and Vehicle Technologies under the Automotive Lightweighting Materials Program managed by Mrs. Sarah Kleinbaum.
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Choi, K.S., Barker, E.I., Sun, X. et al. An integrated two-dimensional modeling method for predicting ductility of thin-walled die cast magnesium. Int J Fract 219, 203–220 (2019). https://doi.org/10.1007/s10704-019-00390-w
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DOI: https://doi.org/10.1007/s10704-019-00390-w