Skip to main content
SpringerLink
Log in

On the choice of parameters in the phase field method for simulating crack initiation with experimental validation

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

Abstract

The phase field method is a versatile simulation framework for studying initiation and propagation of complex crack networks without dependence to the finite element mesh. In this paper, we discuss the influence of parameters in the method and provide experimental validations of crack initiation and propagation in plaster specimens. More specifically, we show by theoretical and experimental analyses that the regularization length should be interpreted as a material parameter, and identified experimentally as it. Qualitative and quantitative comparisons between numerical predictions and experimental data are provided. We show that the phase field method can predict accurately crack initiation and propagation in plaster specimens in compression with respect to experiments, when the material parameters, including the characteristic length are identified by other simple experimental tests.

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
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Amor H, Marigo JJ, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57(8):1209–1229

    Article  Google Scholar 

  • Baz̆ant Z, Belytschko T (1985) Wave propagation in strain-softening bar: exact solution. J Eng Mech 111:81–389

    Google Scholar 

  • Baz̆ant Z, Pijaudier-Cabot G (1988) Nonlocal continuum damage, localization instability and convergence. J Appl Mech 55:521–539

    Google Scholar 

  • Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–620

    Article  Google Scholar 

  • Benalla A, Marigo J-J (2007) Bifurcation and stability issues in gradient theories with softening. Model Simul Mater Sci 15(1):S283–S295

    Article  Google Scholar 

  • Bernard PE, Moës N, Chevaugeon N (2012) Damage growth modeling using the thick level set (TLS) approach: efficient discretization for quasi-static loadings. Comput Methods Appl Mech Eng 233:11–27

    Article  Google Scholar 

  • Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95

    Article  Google Scholar 

  • Bourdin B (2007) Numerical implementation of the variational formulation for quasi-static brittle fracture. Interface Free Bound 9(3):411–430

    Article  Google Scholar 

  • Camacho G, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938

    Article  Google Scholar 

  • Cazes F, Moës N (2015) Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture. Int J Numer Methods Eng (in press)

  • Daux C, Moës N, Dolbow J, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Methods Eng 48:1741–1760

    Article  Google Scholar 

  • De Borst R, Sluys lJ, Muhlausanf HB, Pamin J (1993) Fundamental issues in finite element analysis of localization of deformation. Eng Comput 10:99–121

    Article  Google Scholar 

  • Eastgate LO, Sethna JP, Rauscher M, Cretegny T (2002) Fracture in mode i using a conserved phase-field model. Phys Rev E 65(3):036117

    Article  Google Scholar 

  • Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342

    Article  Google Scholar 

  • Hakim V, Karma A (2009) A continuum phase field model for fracture. J Mech Phys Solids 15(2):342–368

    Article  Google Scholar 

  • Hofacker M, Miehe C (2013) A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns. Int J Numer Methods Eng 93(3):276–301

    Article  Google Scholar 

  • Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Frac Mech 77(18):3625–3634

    Article  Google Scholar 

  • Kuhn C, Müller R (2014) Simulation of size effects by a phase field model for fracture. Theor Appl Mech Lett 4:051008

    Article  Google Scholar 

  • Kuhn C, Schlueter A, Müller R (2015) A phase-field description of dynamic brittle fracture. Comput Mater Sci 108:374–384

    Article  Google Scholar 

  • Lasry D, Belytschko T (1988) Localization limiters in transient problems. Int J Solids Struct 24:581–597

    Article  Google Scholar 

  • Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A Solid 21(1):61–72

    Article  Google Scholar 

  • Li J, Zhang XB (2006) A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials. Eng Frac Mech 73:505–523

    Article  Google Scholar 

  • Lorentz E, Benallal A (2005) Gradient constitutive relations: numerical aspects and application to gradient damage. Comput Methods Appl Mech Eng 194:5191–5220

    Article  Google Scholar 

  • Mary S, Vignollet J, de Borst R (2015) A numerical assessment of phase-field models for brittle and cohesive fracture: \(\Gamma \)-convergence and stress oscillations. Eur J Mech A Solids 52:72–84

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. Int J Numer Methods Eng 83(10):1273–1311

    Article  Google Scholar 

  • Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  Google Scholar 

  • Nguyen TT, Yvonnet J, Zhu Q-Z, Bornert M, Chateau C (2015) A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure. Eng Fract Mech 139:18–39

    Article  Google Scholar 

  • Nguyen TT, Yvonnet J, Zhu Q-Z, Bornert M, Chateau C (2016) A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography. Comput Methods Appl Mech Eng. doi:10.1016/j.cma.2015.10.007

  • Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree HPJ (1996) Gradient-enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39(39):3391–3403

    Article  Google Scholar 

  • Pham K, Marigo J-J, Maurini C (2011) The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models. J Mech Phys Solids (6)

  • Pietruszczak S, Mroz S (1981) Finite element analysis of deformation of strain-softening materials. Int J Numer Methods Eng 17:327–334

    Article  Google Scholar 

  • Pijaudier-Cabot G, Baz̆ant Z (1987) Nonlocal damage theory. J Eng Mech 113:1512–1533

    Article  Google Scholar 

  • Romani R (2013) Rupture en compression des structures hétérogènes á base de materiaux quasi-fragiles. PhD thesis, Université Pierre et Marie Curie

  • Romani R, Bornert M, Leguillon D, Roy RL, Sab K (2015) Detection of crack onset in double cleavage drilled specimens of plaster under compression by digital image correlation-theoretical predictions based on a coupled criterion. Eur J Mech A Solid 51:172–182

    Article  Google Scholar 

  • Sammis CG, Ashby WF (1986) The failure of brittle porous solids under compressive stress states. Acta Metall 34(3):511–526

    Article  Google Scholar 

  • Spatschek R, Hartmann M, Brener E, Müller KH, Kassner K (2006) Phase field modeling of fast crack propagation. Phys Rev Lett 96(1):015502

    Article  Google Scholar 

  • Triantafyllidis N, Aifantis EC (1986) A gradient approach to localization of deformation: I. Hyperelastic materials. J Elast 16:225–237

    Article  Google Scholar 

  • Wong RHC, Lin P, Tang CA (2006) Experimental and numerical study on splitting failure of brittle solids containing single pore under uniaxial compression. Mech Mater 38:142–159

    Article  Google Scholar 

  • Xu X-P, Needleman A (1994) Numerical simulation of fast crack growth in brittle solids. J Mech Phys Solids 42(9):1397–1434

    Article  Google Scholar 

  • Zhou F, Molinari JF (2004) Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. Int J Numer Methods Eng 59:1–24

    Article  Google Scholar 

Download references

Acknowledgments

This work has benefited from a French government grant managed by ANR within the frame of the national program Investments for the Future ANR-11-LABX-022-01. The financial support of J. Yvonnet from IUF (Institut Universitaire de France) is gratefully acknowledged. We thank the support from the Federeation Francilienne de Mecanique to conduct the experimental program.

Author information

Authors and Affiliations

  1. Laboratoire Modélisation et Simulation Multi Échelle MSME UMR 8208 CNRS, Université Paris-Est, 5 bd Descartes, 77454, Marne-la-Vallée, France

    T. T. Nguyen & J. Yvonnet

  2. Laboratoire Navier, CNRS UMR8205, ENPC, IFSTTAR, Université Paris-Est, 6 et 8 avenue Blaise Pascal, 77455, Marne-la-Vallée, Cedex, France

    T. T. Nguyen, M. Bornert, C. Chateau, K. Sab, R. Romani & R. Le Roy

Authors
  1. T. T. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Yvonnet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Bornert
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Chateau
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. K. Sab
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. R. Romani
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. R. Le Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Yvonnet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nguyen, T.T., Yvonnet, J., Bornert, M. et al. On the choice of parameters in the phase field method for simulating crack initiation with experimental validation. Int J Fract 197, 213–226 (2016). https://doi.org/10.1007/s10704-016-0082-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-016-0082-1

Keywords

Search

Navigation