What is the physical meaning of effective stress intensity factor?

The effective stress intensity factor (K_eff) quantifies the intensity of stress at the tip of a crack in a material, accounting for the influence of external loads and internal material properties. It effectively captures the combined effects of applied stress and the material's inherent resistance to crack propagation. K_eff is crucial in fracture mechanics, as it helps predict crack growth and failure in structures under various loading conditions. Ultimately, it provides insights into the integrity and reliability of materials in engineering applications.