Propagation of a Dugdale crack at the edge of a half plane

1. Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions. Appl. Math. Ser. 55, 785 (1964)

   MATH  Google Scholar 

2. Bowie, O., Tracy, P.: On the solution of the dugdale model. Eng. Fract. Mech. 10, 249–256 (1978)

   Article  Google Scholar 

3. Erdogan, F., Gupta, G.D., Cook, T.: Numerical solution of singular integral equation. In: Sih, G.C. (ed.) Methods of Analysis and Solutions of Crack Problems, pp. 368–425. Noordhoff International Publishing, Leyden (1973)

   Chapter  Google Scholar 

4. Eshkuvatov, Z., Nik Long, N., Abdulkawi, M.: Approximate solution of singular integral equations of the first kind with Cauchy kernel. Appl. Math. Lett. 22, 651–657 (2009)

   Article  MathSciNet  MATH  Google Scholar 

5. Ferdjani, H., Abdelmoula, R., Marigo, J.J.: Insensitivity to small defects of the rupture of materials governed by the Dugdale model. Contin. Mech. Thermodyn. 19, 191–210 (2007)

   Article  ADS  MathSciNet  MATH  Google Scholar 

6. Ferdjani, H., Marigo, J.J.: Application of the Dugdale model to a mixed mode loading of a semi infinite cracked structure. Eur. J. Mech. A Solids 53, 1–9 (2015)

   Article  ADS  MathSciNet  Google Scholar 

7. Francfort, G.A., Marigo, J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319–1342 (1998)

   Article  ADS  MathSciNet  MATH  Google Scholar 

8. Howard, I., Otter, N.: On the elastic–plastic deformation of a sheet containing an edge crack. J. Mec. Phys. Solids 23, 139–149 (1975)

   Article  ADS  MATH  Google Scholar 

9. Ioakimidis, N.I.: The numerical solution of crack problems in plane elasticity in the case of loading discontinuities. Eng. Fract. Mech. 13, 709–716 (1980)

   Article  Google Scholar 

10. Jaubert, A., Marigo, J.J.: Justification of Paris-type fatigue laws from cohesive model via variational approach. Contin. Mech. Thermodyn. 1–2(18), 23–45 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

11. Kaya, A.C.: Applications of integral equations with strong singularities in fracture mechanics. Ph.D. thesis, Lehigh University (1984)

12. Koiter, W.: Rectangular tensile sheet with symmetrical edge cracks. J. Appl. Mech. 87(32), 237 (1965)

    Article  Google Scholar 

13. Koiter, W.T.: On the flexural rigidity of a beam weakened by transverse saw-cuts. In: Proc. Kon. Ned. Ak. Wet., pp. 354–374. Amsterdam (1956)

14. Marigo, J.J., Truskinovsky, L.: Initiation and propagation of fracture in the models of Griffith and Barenblatt. Contin. Mech. Thermodyn. 4(16), 391–409 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

15. Petroski, H.: Dugdale plastic zone sizes for edge cracks. Int. J. Fract. 15(3), 217–230 (1979)

    Google Scholar 

16. Tada, H., Paris, P.C., Irwin, G.: The Stress Analysis of Cracks Handbook. Del Research Corporation, Hellertown, Pennsylvania (1973)

    Google Scholar 

17. Wu, X.F., Dzenis, Y.: Closed-form solution for the size of plastic zone in an edge-cracked strip. Int. J. Eng. Sci. 40, 1751–1759 (2002)

    Article  Google Scholar 

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