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Study on coexistence of brittle and ductile fractures in nano reinforcement composites under different loading conditions

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Abstract

Experimental study on high volume fraction of metallic matrix nano composites (MMNCs) was conducted, including uniaxial tension, uniaxial compression, and three-point bending. The example materials were two magnesium matrix composites reinforced with 10 and 15% vol. SiC particles (50 nm size). Brittle fracture mode was exhibited under uniaxial tension and three-point bending, while shear dominated ductile fracture mode (up to 12% fracture strain) was observed under uniaxial compression. The original Modified Mohr–Coulomb (MMC) fracture model (Bai and Wierzbicki in Int J Fract 161:1–20, 2010; in a mixed space of stress invariants and equivalent strain) was transferred into a stress based MMC (sMMC) model. This model was demonstrated to be capable of predicting the coexistence of brittle and ductile fracture modes under different loading conditions for MMNCs. A material post-failure softening model was postulated along the damage accumulation to capture the above two different failure modes. This model was implemented to the Abaqus/Explicit as a material subroutine. Numerical simulations using finite element method well duplicated the material strength, fracture initiation sites and crack propagation modes of the Mg/SiC nano composites with a good accuracy. The proposed model has a good potential to predict fracture for a wide range of material with strength asymmetry and coexistence of brittle and ductile fractures modes.

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References

  • An L, Qu J, Luo J, Fan Y, Zhang L, Liu J, Xu C, Blau PJ (2011) Aluminum nanocomposites having wear resistance better than stainless steel. J Mater Res 26(19):2479–2483

    Article  Google Scholar 

  • Arsenault RJ, Shi N (1986) Dislocation generation due to differences between the coefficients of thermal expansion. Mater Sci Eng 81:175–187

    Article  Google Scholar 

  • Arsenault RJ, Wang L, Feng CR (1991) Strengthening of composites due to microstructural changes in the matrix. Acta Mater 39:47–57

    Article  Google Scholar 

  • Ashby MF (1971) Strengthening methods in crystals. Elsevier, Amsterdam

    Google Scholar 

  • Azizi R, Legarth BN, Niordson CF (2013) A new macroscopically anisotropic pressure dependent yield function for metal matrix composite based on strain gradient plasticity for the microstructure. J Mech Phys Solids 61(4):991–1009

    Article  Google Scholar 

  • Bai Y, Wierzbicki T (2008) A new model of metal plasticity and fracture with pressure and lode dependence. Int J Plast 24:1071–1096

    Article  Google Scholar 

  • Bai Y, Wierzbicki T (2010) Application of extended Mohr–Coulomb criterion to ductile fracture. Int J Fract 161:1–20

    Article  Google Scholar 

  • Barai P, Weng GJ (2011) A theory of plasticity for carbon nanotube reinforced composites. Int J Plast 27(4):539–559

    Article  Google Scholar 

  • Beese AM, Luo M, Li Y, Bai Y, Wierzbicki T (2010) Partially coupled anisotropic fracture model for aluminum sheets. Eng Fract Mech 77(7):1128–1152

    Article  Google Scholar 

  • Brown E, Bray J, Santarelli F (1989) Influence of stress-dependent elastic moduli on stresses and strains around axisymmetric boreholes. Rock Mech Rock Eng 22(3):189–203

    Article  Google Scholar 

  • Brünig M, Gerke S, Hagenbrock V (2013) Micro-mechanical studies on the effect of the stress triaxiality and the lode parameter on ductile damage. Int J Plast 50:49–65

    Article  Google Scholar 

  • Cazacu O (1999) On the choice of stress-dependent elastic moduli for transversely isotropic solids. Mech Res Commun 26(1):45–54

    Article  Google Scholar 

  • Clyne TW, Withers PJ (1995) An introduction to metal matrix composites. Cambridge University Press, Cambridge

    Google Scholar 

  • Ferkel H, Mordike B (2001) Magnesium strengthened by SiC nanoparticles. Mater Sci Eng A 298(1):193–199

    Article  Google Scholar 

  • Fishman SG (1986) Interfaces in composites. J Miner Met Mat Soc 38(3):26–27

  • Flom Y, Arsenault RJ (1985) Deformation in Al–SiC composites due to thermal stresses. Mater Sci Eng 75:151–167

    Article  Google Scholar 

  • Fritzen F, Forest S, Böhlke T, Kondo D, Kanit T (2012) Computational homogenization of elasto-plastic porous metals. Int J Plast 29:102–119

    Article  Google Scholar 

  • Gurson AL (1975) Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth and interaction. Doctoral dissertation, Brown University, Providence

  • 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

    Article  Google Scholar 

  • Gustafson TW, Panda PC, Song G, Raj R (1997) Influence of microstructural scale on plastic flow behavior of metal matrix composites. Acta Mater 45:1633–1643

    Article  Google Scholar 

  • Habibi M, Hamouda A, Gupta M (2012) Enhancing tensile and compressive strength of magnesium using ball milled Al+ CNT reinforcement. Compos Sci Technol 72(2):290–298

    Article  Google Scholar 

  • Hamilton R, Efstathiou C, Sehitoglu H, Chumlyakov Y (2006) Thermal and stress-induced martensitic transformations in NiFeGa single crystals under tension and compression. Scr Mater 54(3):465–469

    Article  Google Scholar 

  • 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(2–3):147–160

    Article  Google Scholar 

  • Hesabi ZR, Simchi A, Reihani SMS (2006) Structural evolution during mechanical milling of nanometric and micrometric Al\(_{2}\)O\(_{3}\) reinforced Al matrix composites. Mater Sci Eng A 428:159–168

    Article  Google Scholar 

  • Hong SJ, Kim HM, Huh D, Suryanarayana C, Chun BS (2003) Effect of clustering on the mechanical properties of SiC particulate-reinforced aluminum alloy 2024 metal matrix composites. Mater Sci Eng A 347:198–204

    Article  Google Scholar 

  • Ibrahim IA, Mohamed FA, Lavernia EJ (1991) Particle reinforced metal matrix composites—a review. J Mater Sci 26:1137–1156

    Article  Google Scholar 

  • Jarausch K, Kiely J, Houston JE, Russell P (2000) Defect-dependent elasticity: nanoindentation as a probe of stress state. J Mater Res 15(08):1693–1701

    Article  Google Scholar 

  • Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21(1):31–48

    Article  Google Scholar 

  • Jones RM (1977) Stress–strain relations for materials with different moduli in tension and compression. AIAA J 15(1):16–23

    Article  Google Scholar 

  • Kamat SV, Rollett AD, Hirth JP (1991) Plastic-deformation in Al-alloy matrix-alumina particulate composites. Scr Metal Mater 25:27–32

    Article  Google Scholar 

  • Kang Y, Chan SLI (2004) Tensile properties of nanometric Al\(_{2}\)O\(_{3}\) particle-reinforced aluminum matrix composites. Mater Chem Phys 85:438–443

    Article  Google Scholar 

  • Kim KT, Cha SI, Hong SH, Hong SH (2006) Microstructures and tensile behavior of carbon nanotube reinforced Cu matrix nanocomposites. Mater Sci Eng A 430(1–2):27–33

    Article  Google Scholar 

  • Kim KT, Eckert J, Menzel SB, Gemming T, Hong SH (2008) Grain refinement assisted strengthening of carbon nanotube reinforced copper matrix nanocomposites. Appl Phys Lett 92(12):121901–121903

    Article  Google Scholar 

  • Kim J-Y, Jang D, Greer JR (2012) Crystallographic orientation and size dependence of tension-compression asymmetry in molybdenum nano-pillars. Int J Plast 28(1):46–52

    Article  Google Scholar 

  • Kouzeli M, Mortensen A (2002) Size dependent strengthening in particle reinforced aluminum. Acta Mater 50:39–51

    Article  Google Scholar 

  • Kouzeli M, Weber L, Marchi CS, Mortensen A (2001) Quantification of microdamage phenomena during tensile straining of high volume fraction particle reinforced aluminum. Acta Mater 49:497–505

    Article  Google Scholar 

  • Lecarme L, Tekog C, Pardoen T (2011) Void growth and coalescence in ductile solids with stage III and stage IV strain hardening. Int J Plast 27(8):1203–1223

    Article  Google Scholar 

  • Lei X, Lissenden CJ (2007) Pressure sensitive nonassociative plasticity model for DRA composites. J Eng Mater Technol 129(2):255–264

    Article  Google Scholar 

  • Li Y, Ramesh KT, Chin ESC (2000) The compressive viscoplastic response of an A359/SiCp metal-matrix composite and of the A359 aluminum alloy matrix. Int J Solids Struct 37(51):7547–7562

  • Li Y, Ramesh KT, Chin ESC (2004) Comparison of the plastic deformation and failure of A359/SiC and 6061–T6/Al2O3 metal matrix composites under dynamic tension. Mater Sci Eng A 371(1–2):359–370

    Article  Google Scholar 

  • Li X, Yang Y, Weiss D (2008) Theoretical and experimental study on ultrasonic dispersion of nanoparticles for strengthening cast aluminum alloy A356. Metal Sci Technol 26(2):12–20

    Google Scholar 

  • Li Y, Luo M, Gerlach J, Wierzbicki T (2010) Prediction of shear-induced fracture in sheet metal forming. J Mater Process Technol 210(14):1858–1869

    Article  Google Scholar 

  • Li H, Fu M, Lu J, Yang H (2011a) Ductile fracture: experiments and computations. Int J Plast 27(2):147–180

  • Li Y, Wierzbicki T, Sutton M, Yan J, Deng X (2011b) Mixed mode stable tearing of thin sheet AI 6061–T6 specimens: experimental measurements and finite element simulations using a modified Mohr–Coulomb fracture criterion. Int J Fract 168:53–71

  • Lloyd DJ (1994) Particle reinforced aluminium and magnesium matrix composites. Int Mater Rev 39(1):1–23

    Article  Google Scholar 

  • Long X, Bai Y, Algarni M, Choi Y, Chen Q (2015) Study on the strengthening mechanisms of Cu/CNT nano-composites. Mater Sci Eng A 645:347–356

    Article  Google Scholar 

  • Lui J, Yu B, Weber K (1999) Coexisting brittle-ductile fracturing mechanisms in fault zones of the upper crust level. Chin Sci Bull 44(22):2107–2112

    Article  Google Scholar 

  • Luo M, Wierzbicki T (2010) Numerical failure analysis of a stretch-bending test on dual-phase steel sheets using a phenomenological fracture model. Int J Solids Struct 47(22–23):3084–3102

    Article  Google Scholar 

  • Luo M, Dunand M, Mohr D (2012) Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading—part II: ductile fracture. Int J Plast 32–33:36–58

    Article  Google Scholar 

  • Malcher L, Pires FA, De Sá JC (2014) An extended GTN model for ductile fracture under high and low stress triaxiality. Int J Plast 54:193–228

    Article  Google Scholar 

  • Manoharan M, Lim S, Gupta M (2002) Application of a model for the work hardening behavior to Mg/SiC composites synthesized using a fluxless casting process. Mater Sci Eng A 333(1):243–249

    Article  Google Scholar 

  • McClintock FA (1968) A criterion of ductile fracture by the growth of holes. J Appl Mech 35:363–371

    Article  Google Scholar 

  • Miracle DB (2005) Metal matrix composites—from science to technological significance. Compos Sci Technol 65(15–16):2526–2540

    Article  Google Scholar 

  • Mortensen A, Llorca J (2010) Metal matrix composites. Ann Rev Mater Res 40:243–270

    Article  Google Scholar 

  • Mula S, Padhi P, Panigrahi SC, Pabi SK, Ghosh S (2009) On structure and mechanical properties of ultrasonically cast Al-2%Al\(_2\)O\(_3\) nanocomposites. Mater Res Bull 44:1154–1160

    Article  Google Scholar 

  • Mummery P, Derby B (1991) The Influence of microstructure on the fracture behavior of particulate metal matrix composites. Mater Sci Eng A 135:221–224

    Article  Google Scholar 

  • Nan CW, Clarke DR (1996) The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites. Acta Mater 44:3801–3811

    Article  Google Scholar 

  • Ohr SM, Chang SJ, Park CG, Thomson R (1985) Coexistence of ductile and brittle fracture in metals. Oak Ridge National Laboratory, Oak Ridge, Tennessee

  • Pozdnyakova I, Bruno G, Efremov AM, Clausen B, Hughes D (2009) Stress-dependent elastic properties of porous microcracked ceramics. Adv Eng Mater 11(12):1023–1029

    Google Scholar 

  • Prabhu B, Suryanarayana C, An L, Vaidyanathan R (2006) Synthesis and characterization of high volume fraction Al–Al\(_{2}\)O\(_{3}\) nanocomposite powders by high-energy milling. Mater Sci Eng A Struct Mater Prop Microstruct Process 425:192–200

    Article  Google Scholar 

  • Prangnell PB, Downes T, Stobbs WM, Withers PJ (1994) The deformation of discontinuously reinforced MMCs-I. The initial yielding behavior. Acta Mater 10:3425–3436

    Article  Google Scholar 

  • Ran J, Fu M, Chan W (2013) The influence of size effect on the ductile fracture in micro-scaled plastic deformation. Int J Plas 41:65–81

    Article  Google Scholar 

  • Ravichandran KS (1994) A simple model of deformation behavior of two phase composites. Acta Metall Mater 42:1113–1123

    Article  Google Scholar 

  • Rice JR, Tracey DM (1969) On the ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:201–217

    Article  Google Scholar 

  • Saravanan R, Surappa M (2000) Fabrication and characterisation of pure magnesium-30 vol.% SiC P particle composite. Materials Science and Engineering: A 276(1):108–116

    Article  Google Scholar 

  • Schleicher F (1926) Der spannonggszustand and der flieffgrenze plastizitatsbedingqung. Z Angew Math Mech 6:199–216

    Article  Google Scholar 

  • Shao J, Xiao B, Wang Q, Ma Z, Yang K (2011) An enhanced FEM model for particle size dependent flow strengthening and interface damage in particle reinforced metal matrix composites. Compos Sci Technol 71(1):39–45

    Article  Google Scholar 

  • Shen J, Yin W, Wei Q, Li Y, Liu J, An L (2013) Effect of ceramic nanoparticle reinforcements on the quasistatic and dynamic mechanical properties of magnesium-based metal matrix composites. J Mater Res 28(13):1835–1852

    Article  Google Scholar 

  • Shi N, Arsenault RJ (1994) Plastic-flow In SiC/Al composites-strengthening and ductility. Ann Rev Mater Sci 24:321–357

    Article  Google Scholar 

  • Tang F, Hagiwara M, Schoenung JM (2005) Microstructure and tensile properties of bulk nanostructured Al-5083/SiCp composites prepared by cryomilling. Mater Sci Eng 407:306–314

    Article  Google Scholar 

  • Tvergaard V (1989) Material failure by void growth to coalescence. Adv Appl Mech 27:83–151

  • Tvergaard V, Hutchinson JW (2002) Two mechanisms of ductile fracture: void by void growth versus multiple void interaction. Int J Solids Struct 39(13–14):3581–3597

    Article  Google Scholar 

  • Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Mater 32:157–169

    Article  Google Scholar 

  • Vasudevan AK, Richmond O, Zok F, Embury JD (1989) The influence of hydrostatic pressure on the ductility of Al–SiC composites. Mater Sci Eng A 107:63–69

    Article  Google Scholar 

  • von Mises R (1913) Gottinger Nachrichten Math. Phys Klasse 582

  • Wu JM, Li ZZ (2000) Nanostructured composites obtained by mechanically driven reduction reaction of CuO and Al powder mixture. J Alloys Compd 299:9–16

    Article  Google Scholar 

  • Xu Q, Qu S (2015) Irreversible deformation of metal matrix composites: a study via the mechanism-based cohesive zone model. Mech Mater 89:72–84

    Article  Google Scholar 

  • Yang Y, Li X (2007) Ultrasonic cavitation-based nanomanufacturing of bulk aluminum matrix nanocomposites. Trans ASME 129:252–255

    Article  Google Scholar 

  • Yang Y, Lan J, Li X (2004) Study on bulk aluminum matrix nanocomposite fabricated by ultrasonic dispersion of nano-sized SiC particles in molten aluminum alloy. Mater Sci Eng A 380:378–383

    Article  Google Scholar 

  • Yar AA, Montazerian M, Abdizadeh H, Baharvandi HR (2009) Microstructure and mechanical properties of aluminum alloy matrix composite reinforced with nano-particle MgO. J Alloys Compd 484:400–404

    Article  Google Scholar 

  • Yokobori T, Ichikawa M (1994) An interpretation of the scatter in brittle-ductile transition region as a statistical event as a result of the two different populations. ASTM Int Fract Mech 24

  • Yuan M, Yang Y, Li C, Heng P, Li L (2012) Numerical analysis of the stress–strain distributions in the particle reinforced metal matrix composite SiC/6064Al. Mater Des 38:1–6

    Article  Google Scholar 

  • Yu S, Dakoulas P (1993) General stress-dependent elastic moduli for cross-anisotropic soils. J Geotech Eng 119(10):1568–1586

    Article  Google Scholar 

  • Zhang H, Maljkovic N, Mitchell BS (2002) Structure and interfacial properties of nanocrystalline aluminum/mullite composites. Mater Sci Eng A 326:317–323

    Article  Google Scholar 

  • Zhang H, Ramesh KT, Chin ESC (2005) Effects of interfacial debonding on the rate-dependent response of metal matrix composites. Acta Mater 53(17):4687–4700

    Article  Google Scholar 

  • Zhang H, Ramesh KT, Chin ESC (2008) A multi-axial constitutive model for metal matrix composites. J Mech Phys Solids 56(10):2972–2983

    Article  Google Scholar 

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Acknowledgements

Thanks due to Dr. Shankar Mall of Air Force Institute of Technology for providing great insight into the research on MMNCs. Help from Dr. Heath Misak and Dr. Victor Perel on the test image analysis are appreciated. The authors appreciate Dassault Systèmes for providing software license of Abaqus (Simulia). Partial financial support from SFFP fellowship is deeply acknowledged.

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Qiao, Y., Liu, J., Jia, Y. et al. Study on coexistence of brittle and ductile fractures in nano reinforcement composites under different loading conditions. Int J Fract 204, 205–224 (2017). https://doi.org/10.1007/s10704-016-0174-y

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  • DOI: https://doi.org/10.1007/s10704-016-0174-y

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