Mixed-Mode Fracture Analysis of Standing Brazilian Disk Rotating about Diameter

  • Singh, Swapnil (Indian Institute of Technology, Kerala)
  • Surendra, KVN (Indian Institute of Technology, Kerala)

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Rotating components have always formed an important part of mechanical systems [1]. Center-cracked circular disk rotating about one of its diameters while standing vertically on a smooth base in a gravitational field, is considered for linear elastic fracture analysis. Two types of mechanical body forces: gravitational and centrifugal; act simultaneously on the disk. The effect of diametral rotation was captured recently [2], while the combined influence of gravity and rotation is modeled in the present work. The two-dimensional stress distribution in the corresponding uncracked disk subjected to combined loading is derived within linear elasticity prior to fracture analysis. The closed-form analytical solution is obtained by superposing the classical solution for a standing disk with the recently solved diametrically rotating disk. The center-cracked disk problem is solved for mixed-mode SIFs (Stress intensity factors) for various combinations of crack length (2a) and crack-inclination (α). The simulated cases correspond to a/R = 0.02, 0.03, 0.04, . . . , 0.98, where a is the semi-crack length and R is the disk radius. The two crack tips (A & B) are subjected to different states of stress, as the symmetry about x-axis is lost and due to the presence of ground reaction closer to the tip B., the Mode-I form factors for crack tips A and B are observed against the relative crack length for the combined loading case. As a → R, the two F_I curves exhibit singularities. The normalized mode-I SIF is defined as: FI = KI /σ_0√πa where, σ_0 = ρR (g + (ω^2)R) for the combined loading, ω is constant angular velocity, ρ is material density, and g is the gravitational acceleration. For α̸ = 90◦, non zero mode-II SIFs will be experienced by the tips along with mode-I SIFs, leading to mixed-mode loading. References: [1] Zare, M. and Fakoor, M., 2025. Fracture analysis of a cracked rotating disc under centrifugal loading: M. Zare, M. Fakoor. Acta Mechanica, pp.1-21. [2] Singh, S. and Surendra, K.V.N., Stress intensity factors of Brazilian disc rotating about diameter, Int. J. Adv. Eng. Sci. Appl. Math., 15(4), 187–195, 2023.