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A semi-analytical solution method for problems of cohesive fracture and some of its applications

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Abstract

Cohesive zone models are extensively used for the failure load estimates for structure elements with cracks. This paper focuses on some features of the models associated with the failure load and size of the cohesive zone predictions. For simplicity, considered is a mode I crack in an infinite plane under symmetrical tensile stresses. A traction–separation law is prescribed in the crack process zone. It is assumed by the problem statement that the crack faces close smoothly. This requirement is satisfied numerically by a formulation of the modified boundary conditions. The critical state of a plate with a cohesive crack is analyzed using singular integral equations. A numerical procedure is proposed to solve the obtained systems of integral equations and inequalities. The presented solution is in agreement with other published results for some limiting cases. Thus, an effective methodology is devised to solve crack mechanics problems within the framework of a cohesive zone model. Using this methodology, some problems are solved to illustrate the (i) influence of shape parameters of traction–separation law on the failure load, (ii) ability to account for contact stress for contacting crack faces, (iii) influence of getting rid of stress finiteness condition in the problem statement.

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References

  • Aissaoui N, Matallah M (2017) Numerical and analytical investigation of the size-dependency of the FPZ length in concrete. Int J Fract 205(2):127–138

    Article  Google Scholar 

  • Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. In: Dryden HL, von Kármán Th, Kuerti G, van den Dungen FH, Howarth L (eds) Advances in applied mechanics, vol 7. Elsevier, pp 55–129

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

    Article  Google Scholar 

  • Erdogan F, Gupta GD, Cook TS (1973) Numerical solution of singular integral equations. In: Sih GC (ed) Methods of analysis and solutions of crack problems. Springer, Dordrecht, pp 368–425

    Chapter  Google Scholar 

  • Gross D, Seelig T (2011) Fracture mechanics. Springer, Berlin

    Book  Google Scholar 

  • Hillerborg A, Modéer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6(6):773–781

    Article  Google Scholar 

  • Hui CY, Ruina A, Long R, Jagota A (2011) Cohesive zone models and fracture. J Adhes 87(1):1–52

    Article  Google Scholar 

  • Kaminsky AA, Selivanov MF, Chornoivan YO (2014) Determination of the safe crack length and cohesive traction distribution using the model of a crack with prefacture zone. Dopov Nac Akad Nauk Ukr 11:58–64

    Article  Google Scholar 

  • Leonov M, Panasyuk V (1959) Growth of the smallest cracks in solids. Prikl Mech 5(4):391–401

    Google Scholar 

  • Murthy ARC, Palani GS, Iyer NR (2009) State-of-the-art review on fracture analysis of concrete structural components. Sadhana 34(2):345–367

    Article  Google Scholar 

  • Park K, Paulino GH (2013) Cohesive zone models: a critical review of traction–separation relationships across fracture surfaces. Appl Mech Rev 64(6):060802–060802-20

    Article  Google Scholar 

  • Selivanov MF, Chornoivan YO (2017) Comparison of the crack opening displacement determination algorithms for a cohesive crack. Dopov Nac Akad Nauk Ukr 7:29–36

    Article  Google Scholar 

  • Stang H, Olesen JF, Poulsen PN, Dick-Nielsen L (2007) On the application of cohesive crack modeling in cementitious materials. Mater Struct 40(4):365–374

    Article  Google Scholar 

  • Turon A, Dávila CG, Camanho PP, Costa J (2007) An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng Fract Mech 74(10):1665–1682

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences, Nesterov st., 3, Kyiv, 03057, Ukraine

    M. F. Selivanov & Y. O. Chornoivan

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  1. M. F. Selivanov
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  2. Y. O. Chornoivan
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Correspondence to Y. O. Chornoivan.

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Selivanov, M.F., Chornoivan, Y.O. A semi-analytical solution method for problems of cohesive fracture and some of its applications. Int J Fract 212, 113–121 (2018). https://doi.org/10.1007/s10704-018-0295-6

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  • DOI: https://doi.org/10.1007/s10704-018-0295-6

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