13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Figure 3. Relative error on ( ) 1 22 , 0 r σ θ= for series representations with 5,7 and 9 terms and their associated Padé approximants[ ] 2,2 ,[ ] 3,3 and[ ] 4,4 . Acknowledgements This work was financially supported by French National Research Agency (ANR) under grant project COSINUS MACSIM. References [1] M. L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech, 19 (1952) 526–528. [2] M. L. Williams, On the stress distribution at the base of a stationary crack. J Appl Mech, 24 (1957) 109–114. [3] D.R.J. Owen, A.J. Fawkes, Engineering fracture mechanics: numerical methods and applications, Pineridge Press, Swansea, 1983. [4] B.L. Karihaloo, Q.Z. Xiao, Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Eng Frac Mech, 68 (2001) 1609–1630. [5] G. Hello, M. Ben-Tahar, J.-M. Roelandt, Analytical determination of coefficients in crack-tip stress expansions for a finite crack in an infinite plane medium. Int J Solids Struct, 49 (2012) 556–566. [6] P. Theocaris, C. Spyropoulos, Photoelastic determination of complex stress intensity factors for slant cracks under biaxial loading with higher-order term effects. Acta Mechanica, 48 (1983) 57–70. [7] P. C. Paris, Secondary elastic crack tip stresses which may influence very slow fatigue crack growth. Fatigue Fract Eng Mater Struct, 25 (2002) 791–794. [8] G. Kolosov, On the application of the complex function theory to a plane problem of the mathematical theory of elasticity [in russian], Dorpat University, 1909. [9] N. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity, Noordhoff, Leyden, 1953. [10]H. Westergaard, Bearing pressures and cracks. J Appl Mech, A (1939) 49–53. [11] G. Sih, On the Westergaard method of crack analysis. Int J Fract, 2 (1966) 628–631. [12]H. Tada, P. C. Paris, Irwin G. R., The stress analysis of cracks handbook, ASME, New York,
RkJQdWJsaXNoZXIy MjM0NDE=