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The crack growth can be expressed as:, where is the crack length and is the crack growth rate. Assuming that the crack length in a fatigue crack growth test obeys a Gaussian distribution, the crack growth rate distribution obeys a lognormal distribution. If the crack length in a fatigue crack growth test obeys a Gaussian distribution, the crack growth rate obeys a lognormal distribution. Considering the crack growth rate variation of the fatigue crack growth test specimen, the crack length in the fatigue crack growth test is obtained in the following way. Before the fatigue crack growth test, the crack length is assumed to be, where is the crack length. When the crack length is 0 mm, the crack length in the fatigue crack growth test is assumed to be, and is the crack growth rate ( in this study). When the crack length is, the crack growth rate is 2 ( in this study). When the crack length is, the crack growth rate is 3 ( in this study). Therefore, based on these assumptions, the crack length in a fatigue crack growth test is calculated as, where is the crack growth rate. It is assumed that the crack growth rate obeys a lognormal distribution. This assumption is supported by the fact that the crack growth rate in a fatigue crack growth test varies from specimen to specimen. If the crack growth rate obeys a lognormal distribution, the crack length obeys a lognormal distribution. Therefore, the crack growth rate in a fatigue crack growth test is calculated as, where and are the mean and standard deviation, respectively. When the crack length in a fatigue crack growth test is, the crack growth rate is 2 ( in this study). If the crack length in a fatigue crack growth test is, the crack growth rate is 3 ( in this study).
The crack length in a fatigue crack growth test is calculated in the following way. When the crack length in a fatigue crack growth test is, the crack length in the fatigue crack growth test obeys a lognormal distribution, and thus, the crack growth rate obeys a lognormal distribution. Therefore, the crack length in a fatigue crack growth test obeys a lognormal distribution. The crack length in a fatigue crack growth test is calculated using the following equations. When the crack length in a fatigue crack growth test is, the crack length in the fatigue crack growth test obeys a lognormal distribution, and the crack growth rate obeys a lognormal distribution.
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