A 3-dimensional experimental and numerical analysis of the T* E integral in aluminum fracture specimens

Abstract

The T*epsilon integral, an elastic-plastic toughness parameter which is based on the incremental theory of plasticity, has been calculated experimentally and numerically in two-dimensional (2-D) metallic specimens. These established methods for 2-D characterization of the T*epsilon integral are used to expand this relatively new elastic-plastic toughness parameter to 3-D elastic-plastic fracture problems. This is a necessary step toward completely validating T*epsilon integral as an elastic-plastic toughness parameter capable of characterizing unloading and crack propagation. Since the T*epsilon parameter was originally derived to overcome inherent shortcomings involved with the use of creep fracture toughness parameters such as the C* integral, its use in creep fracture is also briefly reviewed.The early foundation that has been set for the T* epsilon integral is further expanded in this dissertation as a viable alternative to the J-integral for use as a toughness characterizing parameter in the presence of a 3-D flaw. Since the J-integral is based on the deformation theory of plasticity, it lacks the capacity for characterizing a growing flaw that will inevitably include unloading and extensive plasticity. Further, the J-integral is calculated along a constant sized contour that moves with the crack tip, meaning it is a measure of only the energy release rate at the crack tip. The T* epsilon integral approach attempts to overcome these drawbacks by utilizing incremental (flow) plasticity and a growing integration contour to capture the material behavior at the advancing crack tip as well as behind. A 2024-T351, aluminum alloy, which is considered a ductile material, is used for proof of concept in this study. The research includes experimental work for validation of, and application to, a numerical model in a generation phase approach for a toughness-characterization curve. Issues including near field integration contour size, method of calculation, and comparison between near, and far field J-integral and T*epsilon are discussed. An extensive numerical study including the calculation of the T*epsilon contour integral via the equivalent domain integral (EDI) method is performed to meet this end.A numerical model is built incorporating tunneling behavior observed in experimental work. The behavior in a case of extreme tunneling is relatively unknown so attempts are made wherever possible to compare to baseline behavior of established parameters. Comparisons are made between T* epsilon calculated along an idealized straight crack front, deformation theory J-integral along an idealized straight crack front, incremental J-integral calculated in the extreme tunneling case, and T*epsilon calculated using nodal displacements and the deformation theory of plasticity on a truncated contour. The T*epsilon integral is observed to behave similarly in a qualitative sense to the CTOA for the case of extreme tunneling and as the mid-plane of the specimen is approached. The T*epsilon calculated on the surface of the specimen with experimentally obtained surface displacements is found to compare quantitatively with near surface, numerically obtained, T*epsilon values.