This paper examines the crack size effect of homogenization and microstructure on the materials. It is proposed that the size of the microstructure should not only affect the mean response of the material, which would correspond to the conventional deterministic concept of material size effect, but should also affect its whole probabilistic structure. As an example, a non-stationary stochastic tensor field is characterized as an equivalent continuum model of a solid medium with a random distribution of micro-cracks. The crack size dependence of the variance and covariance functions of the tensor field is verified and fitted to a proposed functional form. Once the correlation structure is determined, the corresponding stochastic field can be synthesized and standard computational algorithms can then be used to predict the behavior of the material.

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