Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning

Abstract

The face number, the volume, and the surface area (boundary area) of grains are measured in recrystallized ␣-iron by serial sectioning coupled with quantitative microstructural analysis on twodimensional (2-D) sections. The sampling volume contained approximately 1000 grains whose mean grain size was ϳ15 m. The grain volume distribution decreased monotonously with increasing grain volume, whereas the surface area had a peak around one-half of the average. The distribution of the sphere equivalent radii significantly deviated from the log-normal distribution and distributions predicted from mean field theories. The peak and the mean of the face number distribution were f ϭ 11 and 12.1, respectively. The linear relationship between the face number of a central grain and the mean face number of surrounding grains, known as the Aboav-Weaire law, was observed in three dimensions. The mean radius of f-faced grains was not proportional to the face number (perimeter law in 3-D), but appeared to be related by a curve convex upward.

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

“…Various experimental techniques are available for microstructural characterization [25,26,27,28,29,71,72,73] and their output is sometimes used as input for finite element (FE) analysis [74,75,48,49]. However a complete 3D reconstruction still remains a challenging task.…”

“…(27) and assigning suitable independent values to the constants α and β: this corresponds to relaxing the requirement of existence of a well defined cohesive potential; the traction-separation laws are then directly given by Eqs. (26) and not derived from a given potential. Therefore, in this work, the cohesive traction-separation laws are specified by Eqs.…”

“…Therefore, in this work, the cohesive traction-separation laws are specified by Eqs. (26), where the constants α and β are given independently from each other, but in such a way to ensure the desired G II /G I ratio between mode II and mode I fracture energies: they are not required to fulfill Eq. (27).…”

“…(4), where the energetic contribution from the opening term δu n is distinguished from that coming from the sliding term δu s , for ϕ ∈ [0, π/2]. The traction-separation laws (26) are valid in all the loading cases, i.e. whether the considered pair is in loading, unloading or reloading.…”

“…(6b), the aggregate is able to carry elastically a load until a cohesive process is started at the interface; at this point, since a compressive load is present, the impenetrability is directly enforced in the system, while the tangential components of tractions are given by the corresponding term in Eqs. (26). As the interface damage grows, the load-carrying capability of the system is progressively reduced: at this point, if the model implements a switch between cohesive and friction laws, then the tangential cohesive tractions must go to zero at d * = 1, i.e.…”