Spatial autocorrelation of fiber fracture in ceramic composites: Theory and simulations

Abstract This study investigates spatial autocorrelation of fiber fracture in ceramic matrix composites, with a focus on statistical characterization of fracture surfaces. While conventional micromechanical models assume global load sharing, experimental evidence increasingly supports the presence of local load sharing (LLS), leading to clustering of fiber breaks. To better understand spatial autocorrelation under LLS conditions, this work applies three geostatistical techniques: Global Geary's C statistic, semivariograms, and Local Geary's C statistic. Simulated fracture surfaces with prescribed levels of spatial autocorrelation are used to evaluate the effectiveness and limitations of each method. Results show that Global Geary's C effectively detects autocorrelation across a range of fiber counts and autocorrelation lengths, even in only partially correlated surfaces. Semivariograms provide insight into the range and strength of correlation but are sensitive to composite size and sample variability. Local Geary's C enables identification of spatially localized clusters of autocorrelated breaks, although interpretation requires careful thresholding. The study establishes guidelines for applying these techniques and demonstrates their utility in diagnosing spatial fracture patterns. The resulting tools pave the way for more detailed analysis of real fracture surfaces, with implications for understanding failure mechanisms and guiding micromechanical modeling.