Skip to main content
SpringerLink
Log in

Study of the transition from strain localization to fracture of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy by experiments and phase-field modeling

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Many metal materials possess the transition from strain localization to fracture, the so-called post-necking behavior, during large deformation under tensile load. It is crucial to understand and characterize the transition for the application of these materials. In this paper, the stress state dependence of the transition from strain localization to fracture of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy is characterized and analyzed by carrying out experiments and phase-field modeling. Firstly, tensile tests for smooth and notched round bars were conducted, in which the notched specimens have different notch radius. It was observed in the tests that the sharper the notch, the shorter the transition process, which can be explained as that high stress triaxiality would shorten the transition process. To further quantify the effects of stress triaxiality in the transition process, the phase-field fracture model involving the nucleation, growth and coalescence of micro-voids is developed to simulate and characterize the damage evolution observed in experiments. The simulations show that as the stress triaxiality increases, the material undergoes less plastic deformation, whether in the initiation of strain localization or the transition process. More interestingly, it is found that there exists a critical value of stress triaxiality, which can be considered the characteristic point of brittle-ductile transition. Above this point, the material has almost no plastic deformation before localization, and brittle fracture occurs directly. This work is meaningful for evaluating the safety of metal structures under complex loads.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Aldakheel F, Wriggers P, Miehe C (2018) A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling. Comput Mech 62:815–833

    Article  Google Scholar 

  • Alexandrov SE, Goldstein RV (1998) Distributions of stress and plastic strain in notched tensile bars. Int J Fract 91:1–11

    Article  Google Scholar 

  • Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55:1017–1040

    Article  Google Scholar 

  • Anvari M, Liu J, Thaulow C (2007) Dynamic ductile fracture in aluminum round bars: experiments and simulations. Int J Fract 143:317–332

    Article  CAS  Google Scholar 

  • Areias P, Rabczuk T, Msekh MA (2016) Phase-field analysis of finite-strain plates and shells including element subdivision. Comput Methods Appl Mech Eng 312:322–350

    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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98

    Article  Google Scholar 

  • Becker R, Needleman A, Richmond O, Tvergaard V (1988) Void growth and failure in notched vars. J Mech Phys Solids 36:317–351

    Article  Google Scholar 

  • Benzerga A (2002) Micromechanics of coalescence in ductile fracture. J Mech Phys Solids 50:1331–1362

    Article  Google Scholar 

  • Benzerga A, Leblond JB, Needleman A, Tvergaard V (2016) Ductile failure modeling. Int J Fract 201:29–80

    Article  Google Scholar 

  • Borden MJ, Hughes TJR, Landis CM, Anvari A, Lee IJ (2016) A phase-field formulation for fracture in ductile materials: finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Comput Methods Appl Mech Eng 312:130–166

    Article  Google Scholar 

  • Bourdin B (2007) Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces Free Bound 9:411–430

    Article  Google Scholar 

  • Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48:797–826

    Article  Google Scholar 

  • Brünig M, Chyra O, Albrecht D, Driemeier L, Alves M (2008) A ductile damage criterion at various stress triaxialities. Int J Plast 24:1731–1755

    Article  CAS  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 

  • Chu D, Li X, Liu Z (2017) Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling. Int J Fract 208:115–130

    Article  Google Scholar 

  • Chu D, Li X, Liu Z, Cheng J, Wang T, Li Z, Zhuang Z (2019) A unified phase field damage model for modeling the brittle-ductile dynamic failure mode transition in metals. Eng Fract Mech 212:197–209

    Article  Google Scholar 

  • Coppieters S, Cooreman S, Sol H, Houtte PV, Debruyne D (2011) Identification of the post-necking hardening behaviour of sheet metal by comparison of the internal and external work in the necking zone. J Mater Process Technol 211:545–552

    Article  CAS  Google Scholar 

  • Driemeier L, Moura RT, Machado IF, Alves M (2015) A bifailure specimen for accessing failure criteria performance. Int J Plast 71:62–86

    Article  Google Scholar 

  • Farren WS, Taylor GI (1925) The heat developed during plastic extension of metals. Proc Roy Soc Lond A 107:422–451

    Article  Google Scholar 

  • Goswami S, Anitescu G, Chakraborty S, Rabczuk T (2020) Transfer learning enhanced physics informed neural network for phase-field modeling of fracture. J Theor Appl Mech 106:102447

    Google Scholar 

  • 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 

  • Hakim V, Karma A (2009) Laws of crack motion and phase-field models of fracture. J Mech Phys Solids 57:342–368

    Article  CAS  Google Scholar 

  • Hodowany J, Ravichandran G, Rosakis AJ, Rosakis P (2000) Partition of plastic work into heat and stored energy in metals. Exp Mech 40:113–123

    Article  CAS  Google Scholar 

  • Huang LJ, Geng L, Li AB, Wang GS, Cui XP (2008) Effects of hot compression and heat treatment on the microstructure and tensile property of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy. Mater Sci Eng A 489:330–336

    Article  CAS  Google Scholar 

  • Ji Z, Chen Y, Qiang Y, Shen C, Li H (2018) Effect of deformation of constituent phases on mechanical properties of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si titanium alloy. Mater Sci Eng A 723:29–37

    Article  CAS  Google Scholar 

  • Kim JH, Serpantié A, Barlat F, Pierron F, Lee MG (2013) Characterization of the post-necking strain hardening behavior using the virtual fields method. Int J Solids Struct 50:3829–3842

    Article  Google Scholar 

  • Knysh P, Korkolis YP (2017) Identification of the post-necking hardening response of rate- and temperature-dependent metals. Int J Solids Struct 115–116:149–160

    Article  CAS  Google Scholar 

  • Koplik J, Needleman (1988) Void growth and coalescence in Porous plastic solids. Int J Solids Struct 24:835–853

    Article  Google Scholar 

  • Li Y, Wierzbicki T (2010) Prediction of plane strain fracture of AHSS sheets with post-initiation softening. Int J Solids Struct 47:2316–2327

    Article  CAS  Google Scholar 

  • Lu S, Bao R, Wang K, Liu D, Wu Y, Fei B (2017) Fatigue crack growth behavior in laser melting deposited Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy. Mater Sci Eng A 690:378–386

    Article  CAS  Google Scholar 

  • Macdougall D (2000) Determination of the plastic work converted to heat using radiometry. Exp Mech 40:298–306

    Article  CAS  Google Scholar 

  • Mason JJ, Rosakis AJ, Ravichandran G (1994) On the strain and strain rate dependence of the faction of plastic work converted to heat: an experimental study using high speed infrared dectoctora and the Kolsky bar. Mech Mater 17:135–145

    Article  Google Scholar 

  • McAuliffe C, Waisman H (2015) A unified model for metal failure capturing shear banding and fracture. Int J Plast 65:131–151

    Article  Google Scholar 

  • McAuliffe C, Waisman H (2016) A coupled phase field shear band model for ductile-brittle transition in notched plate impacts. Comput Methods Appl Mech Eng 305:173–195

    Article  Google Scholar 

  • Miehe C, Hofacker M, Welschinger F (2010a) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199:2765–2778

    Article  Google Scholar 

  • Miehe C, Welschinger F, Hofacker M (2010b) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Numer Methods Eng 83:1273–1311

    Article  Google Scholar 

  • Miehe C, Hofacker M, Schanzel LM, Aldakheel F (2015) Phase field modeling of fracture in mulTi–physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermos-elastic-plastic solids. Comput Methods Appl Mech Eng 294:486–522

    Article  Google Scholar 

  • Miehe C, Aldakheel F, Raina A (2016) Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory. Int J Plast 84:1–32

    Article  Google Scholar 

  • Mirone G, Corallo D (2010) A local viewpoint for evaluating the influence of stress triaxiality and Lode angle on ductile failure and hardening. Int J Plast 26:348–371

    Article  CAS  Google Scholar 

  • Moftakhar A, Buczynski A, Glinka G (1995) Calculation of elasto-plastic strains and stresses in notches under multiaxial loading. Int J Fract 70:357–373

    Article  Google Scholar 

  • Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32:461–490

    Article  Google Scholar 

  • Pardoen T, Hutchinson JW (2000) An extended model for void growth and coalescence. J Mech Phys Solids 48:2467–2512

    Article  Google Scholar 

  • Pineau A, Benzerga A, Pardoen T (2016) Failure of metals I: Brittle and ductile fracture. Acta Mater 107:424–483

    Article  CAS  Google Scholar 

  • Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61:2316–2343

    Article  Google Scholar 

  • Ren H, Zhuang X, Cai Y, Rabczuk T (2016) DuAl–horizon peridynamics. Int J Numer Methods Eng 108:1451–1476

    Article  Google Scholar 

  • Ren H, Zhuang X, Anitescu C, Rabczuk T (2019) An explicit phase field method for brittle dynamic fracture. Comput Struct 217:45–56

    Article  Google Scholar 

  • Rosa GL, Mirone G, Risitano A (2003) Postnecking elastoplastic characterization: degree of approximation in the Bridgman method and properties of the flow-stress/true-stress ratio. Met Mater Trans A 34A:615–624

    Article  Google Scholar 

  • Roth CC, Mohr D (2018) Determing the strain to fracture for simple shear for a wide range of sheet metals. Int J Mech Sci 149:224–240

    Article  Google Scholar 

  • Spencer K, Corbin SF, Lloyd DJ (2002) The influence of iron content on the plane strain fracture behavior of AA 5754 Al–Mg sheet alloys. Mater Sci Eng A 325:394–404

    Article  Google Scholar 

  • Taylor GI, Quinney H (1937) The latent heat remaining in a metal after cold working. Proc Roy Soc Lond A 163:157–181

    Article  Google Scholar 

  • Tekoǧlu C, Hutchinson JW, Pardoen T (2015) On localization and void coalescence as a precursor to ductile fracture. Phil Trans R Soc A 373:20140121

    Article  Google Scholar 

  • Wang L, Tong W (2015) Identification of post-necking strain hardening behavior of thin sheet metals from image-based surface strain data in uniaxial tension tests. Int J Solids Struct 75–76:12–31

    Article  CAS  Google Scholar 

  • Wang T, Liu Z, Cui Y, Ye X, Liu X, Tian R, Zhuang Z (2020a) A thermo–elastic-plastic phase-field model for simulating the evolution and transition of adiabatic shear band. Part I. Theory and model calibration. Eng Fract Mech 232:107028

    Article  Google Scholar 

  • Wang T, Ye X, Liu Z, Liu X, Chu D, Zhuang Z (2020b) A phase-field model of therMo–elastic coupled brittle fracture with explicit time integration. Comput Mech 65:1305–1321

    Article  Google Scholar 

  • Xue Z, Pontin MG, Zok FW, Hutchinson JW (2010) Calibration procedures for a computational model of ductile fracture. Eng Fract Mech 77:492–509

    Article  Google Scholar 

  • Zhang B, Lei LM, Jiang XL, Song ZM, Huang X, Zhang GP (2013) On temperature and strain rate dependent strain localization behavior in Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy. J Mater Sci Technol 29:273–278

    Article  CAS  Google Scholar 

  • Zhu Y, Liu D, Tian X, Tang H, Wang H (2014) Characterization of microstructure and mechanical properties of laser melting deposited Ti–6.5Al–3.5Mo–1.5Zr–0.3Si titanium alloy. Mater Des 56:445–453

    Article  CAS  Google Scholar 

  • Zong X, Li Z, Li J, Cheng X, Chen R, Tan CW, Wang HM (2019) High strain rate response of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si titanium alloy fabricated by laser additive manufacturing. J Alloys Compd 781:47–55

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China, under Grant Nos. 12002181, 11921002, 11972205 and 11722218, Beijing Municipal Science & Technology Commission (Z191100002019013) and the Open Research Fund from Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, Beijing Tongren Hospital, Beihang University & Capital Medical University (BHTR-KFJJ-202004). The authors also would like to thank the Ministry of Industry and Information Technology of China under Grant No. MJ-2017-F-20 for the financial support.

Author information

Authors and Affiliations

  1. Applied Mechanics Lab., Dept. of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Yigang Wang, Dongyang Chu & Zhanli Liu

  2. Beijing Tongren Eye Center, Beijing Tongren Hospital, Capital Medical University, Beijing Ophthalmology & Visual Sciences Key Lab, Beijing, China

    Kaijie Wang

  3. Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, Beihang University & Capital Medical University, Beijing Tongren Hospital, Beijing, China

    Kaijie Wang

  4. State Key Laboratory Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Tao Wang

Authors
  1. Yigang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaijie Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongyang Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhanli Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Kaijie Wang or Zhanli Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Wang, K., Wang, T. et al. Study of the transition from strain localization to fracture of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy by experiments and phase-field modeling. Int J Fract 231, 95–108 (2021). https://doi.org/10.1007/s10704-021-00567-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-021-00567-2

Keywords

Search

Navigation