Skip to main content
Log in

Characteristic scaling equations for softening interactions between beams

  • Special Invited Article Celebrating IJF at 50
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

A reduced order analytical model for peeling of elastic thin films and interface fracture is presented by treating the thin film as a finite length beam with interface interactions accounted for by cohesive zone modeling. The results obtained are shown to be in excellent agreement with finite element simulations and experimental data. Scaling analysis and equations for steady state load and crack length are derived that clearly summarize their parametric dependence.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Anderson TL (2005) Fracture mechanics: fundamentals and applications, 3rd edn. Taylor & Francis, Boca Raton, FL

  • Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7(1):55–129

  • Blaysat B, Hoefnagels JP, Lubineau G, Alfano M, Geers MGD (2015) Interface debonding characterization by image correlation integrated with double cantilever beam kinematics. Int J Solids Struct 55:79–91

    Article  Google Scholar 

  • Chow CL, Woo CW, Sykes JL (1979) On the determination and application of cod to epoxy-bonded aluminium joints. J Strain Anal Eng Des 14(2):37–42

    Article  Google Scholar 

  • Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8(2):100–104

    Article  Google Scholar 

  • Feraren P, Jensen HM (2004) Cohesive zone modelling of interface fracture near flaws in adhesive joints. Eng Fract Mech 71(15):2125–2142

    Article  Google Scholar 

  • Gialamas P, Vlker B, Collino RR, Begley MR, McMeeking RM (2014) Peeling of an elastic membrane tape adhered to a substrate by a uniform cohesive traction. Int J Solids Struct 51(18):3003–3011

    Article  Google Scholar 

  • Gowrishankar S, Mei H, Liechti K, Huang R (2012) A comparison of direct and iterative methods for determining traction–separation relations. Int J Fract 177(2):109–128

    Article  Google Scholar 

  • Kanninen M (1973) An augmented double cantilever beam model for studying crack propagation and arrest. Int J Fract 9(1):83–92

    Google Scholar 

  • Li S, Wang J, Thouless MD (2004) The effects of shear on delamination in layered materials. J Mech Phys Solids 52(1):193–214

    Article  Google Scholar 

  • Li S, Thouless MD, Waas AM, Schroeder JA, Zavattieri PD (2005) Use of mode-I cohesive-zone models to describe the fracture of an adhesively-bonded polymer-matrix composite. Compos Sci Technol 65(2):281–293

    Article  Google Scholar 

  • Li S, Thouless MD, Waas AM, Schroeder JA, Zavattieri PD (2006) Mixed-mode cohesive-zone models for fracture of an adhesively bonded polymermatrix composite. Eng Fract Mech 73(1):64–78

    Article  Google Scholar 

  • Mohammed I, Liechti KM (2000) Cohesive zone modeling of crack nucleation at bimaterial corners. J Mech Phys Solids 48(4):735–764

    Article  Google Scholar 

  • Na SR, Sarceno DA, Liechti KM (2016) Ultra long-range interactions between silicon surfaces. Int J Solids Struct. 80:168–180

  • Parmigiani JP, Thouless MD (2007) The effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries. Eng Fract Mech 74(17):2675–2699

    Article  Google Scholar 

  • Parvin M, Knauss WG (1990) Damage induced constitutive response of a thermoplastic related to composites and adhesive bonding. Int J Fract 42(1):57–72

    Article  Google Scholar 

  • Prandtl L (1933) Ein gedankenmodell fr den zerreivorgang sprder krper. ZAMM J Appl Math Mech 13(2):129–133

    Article  Google Scholar 

  • Prandtl L, Knauss WG (2011) A thought model for the fracture of brittle solids. Int J Fract 171(2):105–109

    Article  Google Scholar 

  • Stigh U (1988) Damage and crack growth analysis of the double cantilever beam specimen. Int J Fract 37(1):R13–R18

    Article  Google Scholar 

  • Thouless MD, Yang QD (2008) A parametric study of the peel test. Int J Adhes Adhes 28(45):176–184

    Article  Google Scholar 

  • Ungsuwarungsri T, Knauss WG (1987) The role of damage-softened material behavior in the fracture of composites and adhesives. Int J Fract 35(3):221–241

    Article  Google Scholar 

  • Wei Y, Hutchinson J (1998) Interface strength, work of adhesion and plasticity in the peel test. Int J Fract 93(1–4):315–333

    Article  Google Scholar 

  • Williams JG (1989) End corrections for orthotropic DCB specimens. Compos Sci Technol 35(4):367–376

  • Williams JG, Hadavinia H (2002) Analytical solutions for cohesive zone models. J Mech Phys Solids 50(4):809–825

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge financial support from the National Science Foundation Nanosystems Engineering Research Center on Nanomanufacturing Systems for Mobile Computing and Mobile Energy Technologies (NASCENT)—NSF EEC Grant No. 1160494.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kenneth M. Liechti.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jain, S., Na, S.R., Liechti, K.M. et al. Characteristic scaling equations for softening interactions between beams. Int J Fract 201, 1–9 (2016). https://doi.org/10.1007/s10704-016-0106-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-016-0106-x

Keywords

Navigation