DOI: https://doi.org/10.20535/2521-1943.2018.2.124761

Application of the internal and external Williams functions to plane elasticity problem for A Mode I crack

E. Yakovleva, A. Oryniak, І. Orynyak

Abstract


The main idea of this research is in applying Williams functions to calculate stress intensity factors (SIF) in case of 2D elastic bodies with cracks. Firstly, we employ the concept of Williams functions converging on infinity which can be used along with
traditional functions to analyse infinite bodies and to study partially loaded crack boundaries. We show the convergence of SIF for the case of a strip and for the bodies with circular boundary depending on the number of Williams functions and on the number of
intervals on the boundary in case of numerical integration. Secondly, we complement the standard set of equations with the global equilibrium conditions of the elastic body to improve the accuracy of the calculation. We compared the computed stress with the one
defined on the boundary.


Keywords


Crack; stress intensity factor; inner and outer Williams function; convergence; Eri functions; static plane body

References


Williams, M. L., Pasadena, C. (1957), “On the Stress Distribution at the Base of a Stationary Crack”, J. Appl. Mech., 24, N 1, pp. 109 – 114.

Hellan, K. (1984), Introduction to Fracture Mechanics, McGraw-Hill, New York.

Williams, M. L. (1961), “The Bending Stress Distribution at the Base of a Stationary Crack” Journal of Applied Mechanics, March.

Malíková, L. and Seitl, S. (2017), “Application of the Williams Expansion near a Bi-Material Interface”, Key Engineering Materials, Vol. 754, pp. 206-209, https://doi.org/10.4028/www.scientific.net/KEM.754.206

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Bouledroua, O., Meliani, M. H., Pluvinage, G. (2016), “A review of T-stress calculation methods in fracture mechanics” Nature & Technologie. A Sciences fondamentales et Engineering, N1. V5. Juin.

Gross, B., Srawley, J. E. W. F., Brown, Jr, (1964), “Stress-Intensity Factor for a Single – Edge – Notch Tension Specimen by Boundary Collocation of a Stress Function” National Aeronautics and Spase Administration, Washington, D.C.

Wilson, W. K., Clark W. G., Jr, and Wessel, E. T. (1966), Engineering Methods for the Design and Selection of Materials Against Fracture, Final Technical Report, Contract DA-30-069-AMC-602(T) June 1966. Available through Defense Documentation Center, Cameron Station, Alexandria, Va., #AD 801005.

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Chiang, C.R. (1989), “A numerical method for solving elastic fracture problems”, Computers & Stmcrures Vol. 32, No. 5, pp. 1195-l 197

Gao, Pei-Qing (1985), “Stress intensity factors for a rectangular plate with a point-loaded edge crack by a boundary collocation procedure, and an investigation into the convergence of the solutions”, Engineering Fracture Mechanics Vol. 22, N 2, pp. 295-305.

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GOST Style Citations


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