On some applications and properties of the random transects

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Abstract
A Monte Carlo model employing random transects is proposed to determine the distribution of properties of duplex materials. The model allows determination of the probability that the value of a specified property will be smaller than the average of the smallest values in several sets of measurements. The probability is determined without prior knowledge of the actual variation of the property as a function of the intercept from the second microstructural constituent. Some limitations of Poisson's formula to describe the fraction covered by overlapping objects are also discussed and a more general equation is proposed. An important property of the random transects is derived, concerning all systematic point-counting methods for determining the volume fraction of a selected constituent. It is established that for a duplex-phase microstructure without anisotropy, the correlation between the sampling results of the grid nodes does not depend on the amount of the second phase or on the size of the aggregates it forms. The only controlling parameter is the size of the largest grain from the second phase which would have been formed if no impingement existed during its growth.