Constraint Effect in Brittle Fracture

Abstract

Variation of apparent fracture toughness under predominantly (elastic) brittle fracture is investigated. Williams' asymptotic series solutions, including higher order terms, are used to characterize the crack tip stress and strain fields for various specimen geometries. Using a fracturing stress or a strain as the material property, it is demonstrated that a fracture event can be quantified by two mechanics parameters, K and A3 for stress-controlled fracture or K and T for strain-controlled fracture. A set of test data that covers a wide range of T and A3 is used to demonstrate the proposed fracture assessment procedure. Constraint-related issues such as size, crack depth, and biaxial stress effect are investigated. The material's failure locus is discussed relative to the ASTM recommended specimen geometries. It is shown that the ASTM in-plane size requirements place a finite-size window on the complete material failure locus. Since real structures may possess constraint levels either higher or lower than the ASTM standard test specimens, structures may fracture at an applied K either higher or lower than KIC. It is demonstrated that KIC determined according to ASTM E 399 and based on a linear elastic solution is not conservative when used to predict the fracture of specimens with low-constraint geometries. This trend is opposite to the corresponding constraint effect in cleavage fracture when the crack tip deformation at fracture is characterized by large-scale yielding.