Прогнозування напрацювання авіаційних панельних конструкцій при випадковій швидкості зростання втомних тріщин

The stochastic nature of fatigue crack growth rates must be considered when predicting the cyclic service life of aircraft fuselage skin structures. This study proposes a modelling approach based on the Paris power-law relationship. Analysis of empirical data from various literature sources demonstrates that a linear inverse correlation exists between the Paris law coefficients C and m for a wide range of structural aluminium alloys, wherein log C decreases as m increases. Based on this dependence, we propose a modified fatigue crack growth model that uses only one governing parameter: the exponent m. This contrasts with the conventional Paris equation, which uses two governing parameters. The crack propagation behavior is represented as random by treating m as a random variable. Numerical simulations were performed for crack growth in sheet structures under the assumption of a uniformly distributed random exponent m, and the operating stress range was calculated using actual fuselage geometry. The resulting predictions define the structural life until the critical crack length is reached, corresponding to the material’s fracture toughness. The minimum service life across all random realizations of m within the specified range provides a conservative and practical prediction metric. A parametric numerical study was carried out for multiple stress ranges to account for variable loading conditions. The shortest predicted life to critical crack growth was determined for each case, assuming a constant initial half-crack length of 0.003 m. The relationship between the minimum residual life and applied stress range exhibits a linear trend in semi-logarithmic coordinates, with a correlation coefficient equal to one.