Analytical model to calculate the grain size of bulk material based on its electrical resistance

Abstract

The electrical resistivity of a material can provide information on the microstructure. However, this is usually limited to thin layers. In this study, an analytical model is derived that correlates the measured electrical resistance with the average grain size of the material for different grain shapes and orientations. Rolled steel sheets (material: DC04) are microstructurally characterized by X-ray diffraction and optical microscopy. Their electrical resistivity is measured using the four-point probe method. The sheets are utilized to validate the model. An excellent agreement between the model predictions and the experimental data is achieved. By using a calibration, unknown grain sizes can be determined. The model is applicable for materials with monomodal grain-size distributions.