International Journal of Fracture

, Volume 211, Issue 1–2, pp 217–235 | Cite as

A state-based peridynamic model for quantitative fracture analysis

Original Paper
  • 305 Downloads

Abstract

A new state-based peridynamic model is proposed to quantitatively analyze fracture behavior (crack initiation and propagation) of materials. In this model, the general relationship of the critical stretch and the critical energy release rate is for the first time obtained for the state-based peridynamic model of linear elastic brittle materials, and the released energy density is defined to quantitatively track the energy released during crack propagation. The three-dimensional (3D) and two-dimensional (2D) (for both plane stress and plane strain) cases are all considered. As illustrations, the compact tension and double cantilever beam tests are analyzed using the proposed model, which is capable of successfully capturing fracture behaviors (e.g., crack path and concentration of strain energy density) of the considered fracture tests. The characteristic parameters (i.e., critical load, critical energy release rate, etc.) are calculated and compared with available experimental and numerical data in the literature to demonstrate validity of the proposed model.

Keywords

Peridynamics State-based model Critical stretch Bond failure 

Notes

Acknowledgements

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

References

  1. ASTM D-5528-01 (2001) Standard test method for mode I interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites. Annual book of ASTM standards, vol 15.03. American Society for Testing and Materials, West Conshohocken, PAGoogle Scholar
  2. ASTM E-399-12 (2013) Standard test method for linear elastic plane strain fracture toughness \(\text{K}_{{\rm IC}}\) of metallic materials. Annual book of ASTM standards, vol 03.01. American Society for Testing and Materials, West Conshohocken, PAGoogle Scholar
  3. Baydoun M, Fries TP (2012) Crack propagation criteria in three dimensions using the XFEM and an explicit-implicit crack description. Int J Fract 178:51–70CrossRefGoogle Scholar
  4. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–620CrossRefGoogle Scholar
  5. 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
  6. Bobaru F, Yang M, Alves LF, Silling SA, Askari E, Xu J (2009) Convergence, adaptive refinement, and scaling in 1D peridynamics. Int J Numer Meth Eng 77(6):852–877CrossRefGoogle Scholar
  7. Foster JT, Silling SA, Chen W (2011) An energy based failure criterion for use with peridynamic states. Int J Multiscale Comput Eng 9:675–687CrossRefGoogle Scholar
  8. Gerstle W, Sau N, Silling S (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237:1250–1258CrossRefGoogle Scholar
  9. Ghajari M, Iannucci L, Curtis P (2014) A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media. Comput Methods Appl Mech Eng 276:431–452CrossRefGoogle Scholar
  10. Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78:1156–1168CrossRefGoogle Scholar
  11. Hairer E, Lubich C, Wanner G (2003) Geometric numerical integration illustrated by the Störnier-Ver let method. Acta Numer 12:399–450CrossRefGoogle Scholar
  12. 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
  13. Hu YL, De Carvalho NV, Madenci E (2015) Peridynamic modeling of delamination growth in composite laminates. Compos Struct 132:610–620CrossRefGoogle Scholar
  14. 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
  15. Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, New YorkCrossRefGoogle Scholar
  16. Neale BK (1978) An investigation into the effect of thickness on the fracture behaviour of compact tension specimens. Int J Fract 14:203–212Google Scholar
  17. Silling SA (2010) Linearized theory of peridynamic states. J Elast 99:85–111CrossRefGoogle Scholar
  18. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209CrossRefGoogle Scholar
  19. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–1535CrossRefGoogle Scholar
  20. Silling SA, EptonM WO, Xu J, Askari E (2007) Peridynamic states and constititive modeling. J Elast 88:151–184CrossRefGoogle Scholar
  21. Sun CT, Jin Z-H (2013) Fracture mechanics. Academic Press, WalthamGoogle Scholar
  22. Xu J, Askari A, Weckner O, Razi H, Silling SA (2007) Damage and failure analysis of composite laminates under biaxial loads. In: 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, HI, AIAA2007-2315Google Scholar
  23. Zhang G, Le Q, Loghin A et al (2016) Validation of a peridynamic model for fatigue cracking. Eng Fract Mech 162:76–94CrossRefGoogle Scholar
  24. Zhang H, Qiao P (2018) An extended state-based peridynamic model for damage growth prediction of bimaterial structures under thermomechanical loading. Eng Fract Mech 189:81–97CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Ocean Engineering, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, 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