The geometry and deformation functions in ductile fracture mechanics and methodologies

The recent evaluation of the material fracture toughness parameter J is based on load separation. Load separation is the assumption that the load can be represented as a multiplication of two separate functions: a crack geometry function and a material deformation function. Until recently, the main experimental basis for such assumption was the approximate agreement between the experimental results of the single specimen J form and the energy rate interpretation of J for blunt notched bending geometries. However, load separation has also been implied in precracked specimen test records in order to develop the R-curve analysis for bending geometries. In this study, the assumption of load separation was examined in the test records of specimens with different crack sizes, geometries, constraints, and materials, for both stationary and growing crack cases. The study proved that load separation is a dominant criterion in material ductile fracture behavior that exists in both bending and tension geometries. Also, it illustrated the material basis for such criterion. In addition, the study developed a generalized form for the geometry function as a power law function. Also, the deformation function for the different test records was constructed. Moreover, the study proposed an approach to develop a unified deformation function that is independent of constraint and displacement measurement. A new reliable method for the evaluation of the η-factor was proposed. The η-factor is the multiplication factor in the single specimen J form. This method avoids most of the approximation errors in other methods. The study proved that the geometry and deformation functions maintain their form as the crack grows far beyond the J-controlled crack growth limit, which validates using J analysis for growing cracks in different geometries. Through the experimental development of the geometry and deformation functions, an advanced ductile fracture methodology was established that could provide accurate predictions of the fracture behavior of defective materials and structures.