Advertisement

International Journal of Fracture

, Volume 215, Issue 1–2, pp 105–128 | Cite as

A new bond failure criterion for ordinary state-based peridynamic mode II fracture analysis

  • Yong Zhang
  • Pizhong QiaoEmail author
Original Paper

Abstract

Peridynamics is a nonlocal theory, and it has been applied to a series of fracture problems based on its two main bond failure criteria: the critical stretch criterion and the critical energy density criterion. In this paper, a new criterion, the critical skew criterion, corresponding to the shear deformation, is for the first time proposed specifically for ordinary state-based peridynamic mode II fracture analysis. The necessity of the critical skew criterion is demonstrated by limitations and inaccuracy of the existing critical stretch and energy density criteria in theoretical and numerical mode II fracture analysis. The validity of the proposed critical skew criterion is illustrated by quantitative analysis of the captured behaviors of the typical mode II fracture tests. The results obtained by the critical skew criterion agree well with the benchmark data from the linear elastic theory, the virtual crack closure technique, and the Griffith’s theory in different aspects of analysis. A simplified formula of the bond energy density is also derived and verified, and it can serves as a fundamental tool in peridynamic fracture analysis.

Keywords

Peridynamics Mode II fracture Bond energy density Failure criterion Critical skew 

Notes

Acknowledgements

The authors would like to acknowledge the partial financial support from the National Natural Science Foundation of China (NSFC Grant Nos. 51478265 and 51679136).

References

  1. Aksoy HG, Senocak E (2011) Discontinuous Galerkin method based on peridynamic theory for linear elasticity. Int J Numer Methods Eng 88:673–692CrossRefGoogle Scholar
  2. Anderson TL (2017) Fracture mechanics: fundamentals and applications, 4th edn. Taylor & Francis, BostonCrossRefGoogle Scholar
  3. Bidokhti AA, Shahani AR, Fasakhodi MRA (2017) Displacement-controlled crack growth in double cantilever beam specimen: a comparative study of different models. Proc Inst Mech Eng Part C J Mech Eng Sci 231:2835–2847CrossRefGoogle Scholar
  4. Bobaru F, Foster JT, Geubelle PH, Silling SA (2016) Handbook of peridynamic modeling. Taylor & Francis, BostonGoogle Scholar
  5. Breitenfeld MS, Geubelle PH, Weckner O, Silling SA (2014) Non-ordinary state-based peridynamic analysis of stationary crack problems. Comput Methods Appl Mech Eng 272:233–250CrossRefGoogle Scholar
  6. Chen X, Gunzburger M (2011) Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Comput Methods Appl Mech Eng 200:1237–1250CrossRefGoogle Scholar
  7. Chisholm DB, Jones DL (1977) An analytical and experimental stress analysis of a practical mode II fracture test specimen. Exp Mech 17:7–13CrossRefGoogle Scholar
  8. Dipasquale D, Sarego G, Zaccariotto M, Galvanetto U (2017) A discussion on failure criteria for ordinary state-based peridynamics. Eng Fract Mech 186:378–398CrossRefGoogle Scholar
  9. Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85:519–525CrossRefGoogle Scholar
  10. Foster JT, Silling SA, Chen W (2011) An energy based failure criterion for use with peridynamic states. J Multiscale Comput Eng 9:675–687CrossRefGoogle Scholar
  11. Gerstle W, Sau N, Silling SA (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237:1250–1258CrossRefGoogle Scholar
  12. Gillis PP, Gilman JJ (1964) Double cantilever cleavage mode of crack propagation. J Appl Phys 35:647–658CrossRefGoogle Scholar
  13. Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162:229–244CrossRefGoogle Scholar
  14. Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78:1156–1168CrossRefGoogle Scholar
  15. Hu Y, Madenci E (2016) Bond-based peridynamics with an arbitrary Poisson’s ratio. In: 57th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conferenceGoogle Scholar
  16. Hu W, Ha YD, Bobaru F, Silling SA (2012) The formulation and computation of the nonlocal J-integral in bond-based peridynamics. Int J Fract 176:195–206CrossRefGoogle Scholar
  17. Hu YL, De Carvalho NV, Madenci E (2015) Peridynamic modeling of delamination growth in composite laminates. Compos Struct 132:610–620CrossRefGoogle Scholar
  18. Huang D, Lu G, Wang C, Qiao P (2015) An extended peridynamic approach for deformation and fracture analysis. Eng Fract Mech 141:196–211CrossRefGoogle Scholar
  19. Jung J, Seok J (2017) Mixed-mode fatigue crack growth analysis using peridynamic approach. Int J Fatigue 103:591–603CrossRefGoogle Scholar
  20. Kilic B, Madenci E (2010) An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory. Theor Appl Fract Mech 53:194–204CrossRefGoogle Scholar
  21. Kitagawa G, Gersch W (1996) Smoothness priors analysis of time series. In: Lecture notes in statistics. SpringerGoogle Scholar
  22. Le QV, Bobaru F (2018a) Surface corrections for peridynamic models in elasticity and fracture. Comput Mech 61:499–518CrossRefGoogle Scholar
  23. Le QV, Bobaru F (2018b) Objectivity of state-based peridynamic models for elasticity. J Elast 131:1–17CrossRefGoogle Scholar
  24. Le QV, Chan WK, Schwartz J (2014) A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. Int J Numer Methods Eng 98:547–561CrossRefGoogle Scholar
  25. Lee J, Oh SE, Hong JW (2017) Parallel programming of a peridynamics code coupled with finite element method. Int J Fract 203:99–114CrossRefGoogle Scholar
  26. Liu W, Hong JW (2012) Discretized peridynamics for linear elastic solids. Comput Mech 50:579–590CrossRefGoogle Scholar
  27. Macek RW, Silling SA (2007) Peridynamics via finite element analysis. Finite Elements Anal Des 43:1169–1178CrossRefGoogle Scholar
  28. Madenci E, Oterkus E (2014) Damage prediction. In: Peridynamic theory and its applications. Springer, pp 115–124Google Scholar
  29. Madenci E, Oterkus S (2016) Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening. J Mech Phys Solids 86:192–219CrossRefGoogle Scholar
  30. Madenci E, Colavito K, Phan N (2016) Peridynamics for unguided crack growth prediction under mixed-mode loading. Eng Fract Mech 167:34–44CrossRefGoogle Scholar
  31. Oterkus E, Madenci E (2012) Peridynamic analysis of fiber-reinforced composite materials. J Mech Mater Struct 7:45–84CrossRefGoogle Scholar
  32. Oterkus S, Madenci E (2015) Peridynamics for antiplane shear and torsional deformations. J Mech Mater Struct 10:167–193CrossRefGoogle Scholar
  33. Parks ML, Littlewood DJ, Mitchell JA, Silling SA (2012) Peridigm users’ guide, Tech. report SAND2012-7800. Sandia National LaboratoriesGoogle Scholar
  34. Rao Q, Sun Z, Stephansson O, Li C, Stillborg B (2003) Shear fracture (Mode II) of brittle rock. Int J Rock Mech Min Sci 40:355–375CrossRefGoogle Scholar
  35. Ren H, Zhuang X, Rabczuk T (2016) A new peridynamic formulation with shear deformation for elastic solid. J Micromech Mol Phys 1:1–24CrossRefGoogle Scholar
  36. Ren B, Wu CT, Askari E (2017) A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis. Int J Impact Eng 99:14–25CrossRefGoogle Scholar
  37. Sarego G, Le QV, Bobaru F, Zaccariotto M, Galvanetto U (2016) Linearized state-based peridynamics for 2-D problems. Int J Numer Methods Eng 108:1174–1197CrossRefGoogle Scholar
  38. Seleson P (2014) Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations. Comput Methods Appl Mech Eng 282:184–217CrossRefGoogle Scholar
  39. Seleson P, Parks M (2011) On the role of the influence function in the peridynamic theory. Int J Multiscale Comput Eng 9:689–706CrossRefGoogle Scholar
  40. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209CrossRefGoogle Scholar
  41. Silling SA (2017) Stability of peridynamic correspondence material models and their particle discretizations. Comput Methods Appl Mech Eng 322:42–57CrossRefGoogle Scholar
  42. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–1535CrossRefGoogle Scholar
  43. Silling SA, Lehoucq RB (2010) Peridynamic theory of solid mechanics. Adv Appl Mech 44:73–168CrossRefGoogle Scholar
  44. Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88:151–184CrossRefGoogle Scholar
  45. Silling SA, Weckner O, Askari E, Bobaru F (2010) Crack nucleation in a peridynamic solid. Int J Fract 162:219–227CrossRefGoogle Scholar
  46. Tupek MR, Rimoli JJ, Radovitzky R (2013) An approach for incorporating classical continuum damage models in state-based peridynamics. Comput Methods Appl Mech Eng 263:20–26CrossRefGoogle Scholar
  47. Vu-Khanh T (1987) Crack-arrest study in mode II delamination in composites. Polym Compos 8:331–341CrossRefGoogle Scholar
  48. Wang JL, Qiao PZ (2006) Fracture analysis of shear deformable bi-material interface. J Eng Mech 132(3):306–316CrossRefGoogle Scholar
  49. Wang H, Vu-Khanh T (1996) Use of end-loaded-split (ELS) test to study stable fracture behaviour of composites under mode II loading. Compos Struct 36:71–79CrossRefGoogle Scholar
  50. Wang Y, Zhou X, Wang Y, Shou Y (2018) A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids. Int J Solids Struct 134:89–115CrossRefGoogle Scholar
  51. Warren TL, Silling SA, Askari A, Weckner O, Epton MA, Xu J (2009) A non-ordinary state-based peridynamic method to model solid material deformation and fracture. Int J Solids Struct 46:1186–1195CrossRefGoogle Scholar
  52. Xu Z, Zhang G, Chen Z, Bobaru F (2018) Elastic vortices and thermally-driven cracks in brittle materials with peridynamics. Int J Fract 209:203–222CrossRefGoogle Scholar
  53. Zhang H, Qiao PZ (2018) A state-based peridynamic model for quantitative fracture analysis. Int J Fract 211:217–235CrossRefGoogle Scholar
  54. Zhou X, Wang Y, Xu X (2016) Numerical simulation of initiation, propagation and coalescence of cracks using the non-ordinary state-based peridynamics. Int J Fract 201:213–234CrossRefGoogle Scholar
  55. Zhu Q, Ni T (2017) Peridynamic formulations enriched with bond rotation effects. Int J Eng Sci 121:118–129CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  2. 2.Department of Civil and Environmental EngineeringWashington State UniversityPullmanUSA

Personalised recommendations