On notch fracture mechanics

Different stress distributions for an elastic behavior are presented as analytical expressions for an ideal crack, a sharp notch and a blunt notch. The elastic plastic distribution at a blunt notch tip is analyzed. The concept of the notch stress intensity factor is deduced from the definition of the effective stress and the effective distance. The impacts of the notch radius and constraint on the critical notch stress intensity factor are presented. The paper ends with the presentation of the crack driving forceJρfor a notch in the elastic case and the impact of the notch radius on the notch fracture toughnessJρ,c. The notch fracture toughnessJρ,cis a measure of the fracture resistance which increases linearly with the notch radius due to the plastic work in the notch plastic zone. If this notch plastic zone does not invade totally the ligament, the notch fracture toughnessJρ,cis constant. This occurs when the notch radius is less than a critical one and there is no need to use the cracked specimen to measure a lower bound of the fracture resistance.