Using fractal void analysis in predicting mode I stress intensity factors and crack paths for single void systems in uniaxial compression

While porosity is known to control the compressive strength of brittle materials, fracture mechanics has not been used to elucidate this interaction. A primary limitation is the complexity of the analysis of mode I cracks emanating from void surfaces in continua loaded in compression. Fractal void analysis (FVA) has recently been proposed as a means by which robust, quick K I estimates for cracks of length a cr emanating from voids subject to distant uniaxial compression can be calculated. While FVA predictions in single-void infinite continua are encouraging, applying FVA to multi-void systems remains premature. This numerical study examines three aspects of FVA critical to its broader application: FVA K I (a cr ) predictions for cracks initiating from locations other than boundary tensile stress maxima; FVA crack path prediction quality; and effects of continuum boundaries on FVA predictions. Continua containing one circular void of radius a are considered. Key conclusions regarding FVA include: Accurate crack path predictions; dependence of K I (a cr ) estimates on angular crack initiation position relative to the nearest local void boundary tensile stress maximum; and consistency of K I (a cr ) estimates at a cr /a = 0.05 among considered void edge distances. Results suggest immediate applicability towards the analysis of initial cracking loads in multi-void two-dimensional continua • Fractal void analysis (FVA) accurately predicts crack paths in infinite continua. • FVA KI accuracy depends on angle between crack root and void local tension maximum. • Continuum boundary proximity can cause increasing KI for some crack length ranges. • FVA KI accuracy for short crack lengths constant for considered continuum sizes.