characterized by exponential distribution curves and the stage of accelerated growth due to void coalescence which is described by the power - law function. a b Figure 1. The cumulative number - size distributions of thermal fatigue microcracks in steel Х6CrNi181 plotted using initial data [3] on microcrack growth at various numbers of cycles N: 2500 (curve 1), 4500 (2), 6500 (3), 11000 (4), 15000 (5). The curve 6 was obtained by normalizing the curves 1 - 3 with respect to the coordinates of their knee points. Solids lines in (b) correspond to the exponential (1-3) and power law (4, 5) relations We assume that both the initial stages may obey the hypothesis of self-similarity, even though the characters of the laws describing these two stages of damage accumulation are different. It is important to note that the exponents in the exponential functions characterizing the first stage decrease with increasing a number of cycles. 2.2. Distributions of microcracks by their length at static loading Similar results were obtained by means of analyzing the multiple fracture patterns in plastic zone of notched specimens from low carbon steel [5, 6]. The cumulative length - frequency distributions of microcracks in the plastic zones are shown in Fig. 2, which allows us to observe evolution of the distribution curves over different loading stages. It shows that as the tensile load increases, the change in these curves is similar to the change observed in thermal fatigue. a b c Figure 2. The cumulative distributions of microcracks in notched specimens from low carbon steel at different tension stages (a, b) (the specimen thickness is 6 mm): (а) – δ =2.8, P/Pgy =1,7; (b) –δ = 5.2, P/Pgy = 2.1, and dependencies (c) of the b - and c - values in the power-law and exponential cumulative numberlength distributions of microcracks on the displacement of specimens (1) 16 and (2) 4 mm thick [4]
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