Skip to main content
SpringerLink
Log in

Calculation of Stress Intensity Factors – An Interface Crack

  • Chapter
  • First Online:
Interface Fracture and Delaminations in Composite Materials

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSSTME))

  • 983 Accesses

Abstract

In this chapter, aspects of the finite element method for obtaining the displacement field of a body containing an interface crack are described. Square-root singular, quarter-point elements in two and three dimensions will be presented. Once the displacement field is found three methods are suggested for computing stress intensity factors; they include the displacement extrapolation (DE) method, the conservative interaction energy integral or M-integral, and the Virtual Crack Closure Technique (VCCT). The stress intensity factors are then employed to obtain the interface energy release rate and two phase angles.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Agrawal A, Karlsson AM (2006) Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique. Int J Fract 141:75–98

    Article  MATH  Google Scholar 

  2. Banks-Sills L (1991) Application of the finite element method to linear elastic fracture mechanics. Appl Mech Rev 44:447–461

    Article  Google Scholar 

  3. Banks-Sills L (2010) Update - application of the finite element method to linear elastic fracture mechanics. Appl Mech Rev 63:020803-1–020803-17

    Article  Google Scholar 

  4. Banks-Sills L, Bortman Y (1984) Reappraisal of the quarter-point quadrilateral element in linear elastic fracture mechanics. Int J Fract 25:169–180

    Article  Google Scholar 

  5. Banks-Sills L, Dolev O (2004) The conservative \(M\)-integral for thermal-elastic problems. Int J Fract 125:149–170

    Article  MATH  Google Scholar 

  6. Banks-Sills L, Farkash E (2016) A note on the virtual crack closure technique for an interface crack. Int J Fract 201:171–180

    Article  Google Scholar 

  7. Banks-Sills L, Sherman D (1989) On quarter-point three-dimensional finite elements in linear elastic fracture mechanics. Int J Fract 41:177–196

    Article  Google Scholar 

  8. Banks-Sills L, Sherman D (1992) On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. Int J Fract 53:1–20

    Google Scholar 

  9. Banks-Sills L, Travitzky N, Ashkenazi D, Eliasi R (1999) A methodology for measuring interface fracture toughness of composite materials. Int J Fract 99:143–161

    Article  Google Scholar 

  10. Banks-Sills L, Freed Y, Eliasi R, Fourman V (2006) Fracture toughness of the \(+45^{\circ }/-45^{\circ }\) interface of a laminate composite. Int J Fract 141:195–210

    Article  Google Scholar 

  11. Barsoum RS (1974) Application of quadratic isoparametric finite elements in linear fracture mechanics. Int J Fract 10:603–605

    Article  Google Scholar 

  12. Barsoum RS (1976) On the use of isoparametric finite elements in linear fracture mechanics. Int J Num Methods Eng 10:25–37

    Article  MATH  Google Scholar 

  13. Beuth JL (1996) Separation of crack extension modes in orthotropic delamination models. Int J Fract 77:305–321

    Article  Google Scholar 

  14. Bjerkén C, Persson C (2001) A numerical method for calculating stress intensity factors for interface cracks in bimaterials. Eng Fract Mech 68:235–246

    Article  Google Scholar 

  15. Chan SK, Tuba IS, Wilson WK (1970) On the finite element method in linear elastic fracture mechanics. Eng Fract Mech 2:1–17

    Article  Google Scholar 

  16. Chen FHK, Shield RT (1977) Conservative laws in elasticity of J-integral type. Z Angew Math Phys 28:1–22

    Article  MathSciNet  MATH  Google Scholar 

  17. Dattaguru B, Venkatesha KS, Ramamurthy TS, Buchholz FG (1994) Finite element estimates of strain energy release rate components at the tip on an interface crack under mode I loading. Eng Fract Mech 49:451–463

    Article  Google Scholar 

  18. Deng X (1993) General crack-tip fields for stationary and steadily growing interface cracks in anisotropic bimaterials. J Appl Mech 60:183–196

    Article  MATH  Google Scholar 

  19. Farkash E, Banks-Sills L (2017) Virtual crack closure technique for an interface crack between two transversely isotropic materials. Int J Fract 205:189–202

    Article  Google Scholar 

  20. Freed Y, Banks-Sills L (2005) A through interface crack between a \({\pm 45^{\circ }}\) transversely isotropic pair of materials. Int J Fract 133:1–41

    Article  MATH  Google Scholar 

  21. Fung YC (1965) Foundations of solid mechanics. Prentice Hall, New Jersey, pp 354–355

    Google Scholar 

  22. Gosz M, Dolbow J, Moran B (1998) Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks. Int J Solids Struct 35:1763–1783

    Article  MATH  Google Scholar 

  23. Hemanth D, Shivakumar Aradhya KS, Rama Murthy TS, Govinda Raju N (2005) Strain energy release rates for an interface crack in orthotropic media - a finite element investigation. Eng Fract Mech 72:759–772

    Article  Google Scholar 

  24. Henshell RD, Shaw KG (1975) Crack tip finite elements are unnecessary. Int J Num Methods Eng 9:495–507

    Article  MATH  Google Scholar 

  25. Irwin GR (1958) Fracture. In: Flügge S (ed) Encyclopedia of physics, vol IV. Springer, Germany, pp 551–590

    Google Scholar 

  26. Krueger R (2004) Virtual crack closure technique: history, approach, and applications. Appl Mech Rev 57:109–143

    Article  Google Scholar 

  27. Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21:405–421

    Article  Google Scholar 

  28. Mantic̆ V, París F, (2004) Relation between SIF and ERR base measures of fracture mode mixity in interface cracks. Int J Fract 130:557–569

    Google Scholar 

  29. Moran B, Shih CF (1987) Crack tip and associated domain integrals from momentum and energy balance. Eng Fract Mech 27:615–642

    Article  Google Scholar 

  30. Oneida EK, van der Meulen MCH, Ingraffea AR (2015) Methods for calculating \(G\), \(G_{I}\) and \(G_{I\!I}\) to simulate crack growth in 2D, multiple-material structures. Eng Fract Mech 140:106–126

    Article  Google Scholar 

  31. Raju IS (1987) Calculation of strain-energy release rates with higher order and singular finite elements. Eng Fract Mech 28:251–274

    Article  Google Scholar 

  32. Raju IS, Crews JH Jr, Aminpour MA (1988) Convergence of strain energy release rate components for edge-delaminated composite laminates. Eng Fract Mech 30:383–396

    Article  Google Scholar 

  33. Rybicki EF, Kanninen MF (1977) A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 9:931–938

    Article  Google Scholar 

  34. Shih CF, Moran B, Nakamura T (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int J Fract 30:79–102

    Google Scholar 

  35. Sun CT, Jih CJ (1987) On strain energy release rates for interfacial cracks in bi-material media. Eng Fract Mech 28:13–20

    Article  Google Scholar 

  36. Sun CT, Qian W (1997) The use of finite extension strain energy release rates in fracture of interfacial cracks. Int J Solids Struct 34:2595–2609

    Article  MATH  Google Scholar 

  37. Toya M (1992) On mode I and mode II energy release rates of an interface crack. Int J Fract 56:345–352

    Article  Google Scholar 

  38. Wilson WK, Yu I-W (1979) The use of the \(J\)-integral in thermal stress crack problems. Int J Fract 15:377–387

    Google Scholar 

  39. Yau JF, Wang SS (1984) An analysis of interface cracks between dissimilar isotropic materials using conservation integrals in elasticity. Eng Fract Mech 20:423–432

    Article  Google Scholar 

  40. Yau JF, Wang SS, Corten HT (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47:335–341

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel

    Leslie Banks-Sills

Authors
  1. Leslie Banks-Sills
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leslie Banks-Sills .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 The Author(s)

About this chapter

Cite this chapter

Banks-Sills, L. (2018). Calculation of Stress Intensity Factors – An Interface Crack. In: Interface Fracture and Delaminations in Composite Materials. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-60327-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60327-8_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60326-1

  • Online ISBN: 978-3-319-60327-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation