The physical properties of polycrystalline two-phase alloys depend on the properties and the amounts of the constituent phases and on the geometrical arrangement of the grains in the two-phase microstucture. Establishing microstructure-property relationships for two-phase materials requires the correct quantitative characterization of all topological features of the microstructure. Stereology and quantitative metallography provide the means to analyse both real and idealized model microstructures with this respect. The two most important quantitative parameters involved in the formulation of microstructure-property relationships are the contiguity C and the fraction of clusters r which quantify the continuity of the phases and to which extent the phases are present as matrix or as inclusion, respectively. Idealized random model microstructures closely approximating real microstructures are generated and joined with continuum and micromechanical models. The essence of the micromechanical model is the unit cell approach combined with finite element calculations. Properties computed for the unit cell are then representative for the overall microstructure. With this method four important physical properties of a ferritic-austenitic stainless duplex steel are modeled successfully: the magnetic permeability, the diffusion of hydrogen, the thermal expansion behavior and the mechanical properties at elevated temperatures. From these examples the relevance of the parameters C and r is evident. Furthermore, the linear rule of mixture is not appropriate to describe both experimentally obtained properties and the results from the numerical analyses for the respective entity.

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