Exploiting fractal features to determine fatigue crack growth rates of metallic materials

Abstract

An alternative approach to the classical fracture mechanics equation to quantify the fatigue crack growth rate is proposed and examined. The method exploits the fractal features of the propagating fatigue crack. The reference crack growth response of AISI 410 martensitic stainless steel is established using compact tension C(T) specimens. Fractal analysis of microscopic images along the edge length of the crack establishes the fractal dimensions, dF of the fatigue crack. The box-counting algorithm is developed for the fractal analysis based on optical images of the crack at 100X magnification and the resolution of 1090 pixels/mm. Results show that the crack initially exhibits a Euclidean nature (dF ˜ 1). The fractal dimension increases steadily with increasing crack length in the Paris crack growth rate region with 1.05 < dF < 1.24. The corresponding stress intensity factor range varies between 18 = ?KI = 40 MPavm. The fractal dimension, dF correlates linearly with the normalized stress intensity factor range, [Formula presented] within the Paris crack growth region. This enables the multifractal fatigue crack growth rate equation to be established in terms of the fractal dimension, Paris coefficient and exponent, and fatigue fracture properties of the material. The fatigue crack growth rate of the material could then be determined using the multifractal fatigue crack growth rate model without requiring the geometry factor of the crack.