13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- experimentally and theoretically. The power laws originally established by Paris [2] (and presently referred to as the Paris law) reflect the automodel (self-similar) nature of development of fatigue cracks. This law is related to a nonlinear character of damage development in the vicinity of the crack tip (called the “process zone” [2]): ( )m A K dN dl = Δ , (1) where A and m are the experimentally determined constants. For a broad class of materials and wide range of crack propagation velocities under multicycle fatigue conditions, the exponent is typically close to m = 2–4. The universal nature of the Paris law was interpreted [3] based on the self-similar laws of damage development and fracture focus formation in the form of “dissipative structures” representing ensembles of defects localized on the spectrum of spatial scales. The formation of these structures reveals a critical character of the transition from dispersed to macroscopic fracture as manifested by the structural-scaling transitions [4]. According to these notions, the propagation of cracks is related to establishing a long-range correlation interaction in multiscale ensembles of dissipative structures. This interaction which can be characterized by a certain correlation scale, above which the interaction proceeds to a scale that determines the subsequent increment in the length of the propagating crack (size of the “process zone”). This assumption concerning the critical conditions for the aforementioned transition was used in interpretation of the experimental data so as to explain the self-similar scenario of fatigue crack propagation in a steel sample under conditions of gigacycle loading. 2. Experimental conditions and materials The samples (Fig. 1) of R4 high-strength steel (with a room-temperature fatigue limit of 600 MPa for 106 cycles at 10 Hz) were tested under fatigue loading conditions with symmetric tension–compression cycling at 20 kHz (gigacycle loading regime) on an original setup [5]. The testing machine consisted of the following main parts: (i) generator, which converted 50 Hz oscillations into an ultrasonic electric sinusoidal signal with a frequency of 20 kHz; (ii) piezoelectric transducer, which generated longitudinal ultrasonic waves and produced mechanical action at a frequency of 20 kHz; and (iii) ultrasonic waveguide, which increased the amplitude of mechanical stresses in the (working) central part of the sample. Figure 1. Schematic diagram and characteristic dimensions of the initial sample (in millimeters) At the initial stage, a fatigue crack with a length of ~1.5 mm was nucleated, the subsequent growth
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