Statistical Analysis of Unidirectional Multicracking of Coatings by a Two-Dimensional Poisson Point Process

Abstract

The statistical aspect of the unidirectional multiple cracking of coatings is studied in the theoretical case in which cracks form independently from each other. The analysis is presented in the specific situation of the "multiple-cracking test," in which cracks result from an external uniaxial straining. The unidirectional multiple cracking is described through a two-dimensional Poisson point process. The two random variables are independent and play a similar role. The random variable related to the crack geometrical position is uniform (cracks forming independently) in the specimen length, whereas the random variable associated to the strain at which a crack forms is distributed according to a physical quantity that characterizes the material brittleness. In practice, the intercrack distance distribution constitutes the main quantity in the mechanical test. A good agreement with experiment is exemplified by a real case.