The Size-dependence of Plane Strain Fracture Toughness: A Mechanistic Analysis by Enforcing Constant Crack Tip Fracture Stress and Scaling Laws

Abstract

Experimental measurements of plane strain fracture toughness, made using single-edge-notched-bend (SENB) specimens, show strong crack (or ligament) size and specimen size effects on toughness. The fracture toughness varies strongly with crack size even at relatively small crack sizes, where linear-elastic conditions (LEFM) are applicable. Experimental data on brittle and relatively ductile materials show such behaviors. This study focuses on exploring why the crack size and the specimen size (width) influence the plane strain fracture toughness so strongly and provides a mechanistic explanation based on the change in elastic strain energy stored in the net-section due to the crack. A net-section based analysis of elastic deformation of the ligament, with the enforcement of constant of crack tip fracture stress at all crack lengths, shows that fracture toughness indeed should vary with crack size and specimen width. It is shown that in most materials, fracture occurs at constant crack tip fracture stress that is nearly equal to the tensile strength. Extensive evaluation using data from a diverse set of materials demonstrates the validity of this approach. In exceptional cases, fractures still occurred at constant crack tip stresses at all crack and specimen sizes, although these stresses are significantly lower than the tensile strength. The net-section stress analysis leads to expressions to predict the fracture toughness variation with crack/specimen size, facilitating the scaling of fracture toughness from small or laboratory specimens to large structures, with constant crack tip fracture stress enforced as the fracture criterion.