Determination of Local Flexibility Coefficients of a Functionally Graded Shaft with Breathing Crack

Stress intensity factors (SIFs) play a fundamental role in the calculation of local flexibility coefficients (LFCs) in a cracked structure. Many researchers have calculated SIFs in a cracked beam or rotor made of homogeneous materials, but for functionally graded (FG) materials is scarce. The radially graded FG shaft consists of aluminum oxide (Al₂O₃) as ceramic constituent and stainless steel (SS) is as metal constituent and properties of material are computed following power law gradation under thermal gradient. LFCs of a spinning FG shaft with breathing crack behavior are determined analytically with the help of Castigliano’s theorem and energy principal of Paris. A MATLAB code is developed and validated with the literatures results. The effects of crack size and orientation, gradient index, and thermal gradient are examined on the direct and cross-couple LFCs. Numerical results show that magnitudes of LFCs increase with an increase in orientations of crack, maximum, while crack is completely open and then decrease with an increase in the orientations of crack. In addition, the magnitudes of LFCs increase while crack size, gradient indices, and thermal gradients also increase.