ON THE ANALYSIS OF LENGTHWISE FRACTURE OF FUNCTIONALLY GRADED ROUND BARS
Victor Iliev Rizov1, Holm Altenbach2
1)University of Architecture, Civil Engineering and Geodesy, Department of Technical Mechanics, Sofia, Bulgaria,
2)Lehrstuhl für Technische Mechanik und Geschäftsführender Leiter Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Deutschland,
The strain energy release rate for lengthwise circular cylindrical cracks in round bars which are functionally graded in radial direction is derived by applying linear elastic fracture mechanics. The solution obtained is valid for a crack located arbitrarily in the radial direction of the bar cross-section. Besides, the modulus of elasticity and the shear modulus can be distributed arbitrarily in the radial direction. The functionally graded bars are loaded by axial forces, bending and torsion moments. The derived solution is applied to analyse the strain energy release rate for a lengthwise crack in a clamped functionally graded bar configuration. The external load of the clamped bar consists of an axial force and a torsion moment applied at the free end of the internal crack arm and a bending moment applied at the free end of the bar. In order to verify the solution, the strain energy release rate in the clamped bar is determined also by considering the balance of energy and by applying the compliance method. The influence of various factors such as crack location in the radial direction, the material gradient and loading conditions on strain energy release rate in the clamped bar configuration are investigated and discussed.
Keywords: functionally graded material, lengthwise fracture, round bar, linear elastic behaviour