This thesis examines the crack-front response during sustained ductile tearing in structural metals at quasi-static rates using high resolution finite element computations. At load levels approaching the steady-growth regime, well-established computational methods that model material damage break down numerically as vanishingly small load increments produce increasingly large amounts of crack extension. The computational model adopted here determines the deformation history of a steadily advancing crack directly without the need for a priori (transient) analysis that considers blunting of the pre-existing stationary crack and subsequent growth through the associated initial plastic zone. Crack extension occurs at the remotely applied, fixed loading without the need for a local growth criteria. This numerical scheme utilizes a streamline integration technique to determine the elastic-plastic fields, generalized from a two-dimensional to a fully three-dimensional setting and implemented within mixed Matlab/C++/F-90 based software. Modifications of the conventional finite element formulation lead to an efficient procedure -- readily parallelized -- and determine the invariant near-front fields, representative of steady-state growth, on a fixed mesh in a boundary-layer framework. In the small-scale yielding regime, the crack front does not sense the existence of remote boundaries, and computational results retain a strong transferability among various geometric configurations where near-front, plastic deformation remains entirely enclosed by the surrounding linear-elastic material. The global stress intensity factor (KI) and imposed T-stress fully specify displacement constraints along the far-field boundary, and in a three-dimensional setting, the panel thickness reflects the only natural length scale.
The initial studies in this work consider steady crack advance within the small-scale yielding context under plane-strain conditions and mode I loading. These analyses focus on steady crack growth within a hydrogen-charged material to explore primary features of the streamline integration methodology while providing new results relevant to hydrogen embrittlement at engineering scales. Ductile crack propagation occurs through a homogeneous, high solubility material characteristic of niobium and through a steel weld in the presence of hydrogen. The constitutive model includes the influence of hydrogen on elastic-plastic regimes of material response at the continuum level, \emph{e.g.} hydrogen-induced material softening, based on the hydrogen-enhanced, localized plasticity (HELP) mechanism, and reflects the amount of hydrogen in the material under stress and the intensity of hydrogen-induced softening in the material. Achievements using this two-dimensional framework encouraged further extensions of the research to a fully three-dimensional setting.
Subsequent work, and the focal point of this thesis, develops a finite element formulation to investigate key features of the elastic-plastic fields near a steadily advancing crack under three-dimensional, small-scale yielding conditions. The computational model represents a structurally thin component constructed of a material (e.g. Al and Ti alloys) with flow stress and fracture toughness properties that together limit the size of the in-plane plastic zone during steady growth to no more than several multiples of the plate thickness. These studies consider a straight crack front advancing under local and global mode-I loading in a moderately hardening material. The nonsingular T-stress provides a first-order estimate of geometry and loading mode (e.g. tension vs. bending) effects on elastic-plastic, crack front fields. The T-stress has a marked effect on measured crack-growth resistance curves (J-da) -- trends most computational models confirm using a two-dimensional setting. In the first computations of this type to be modeled, the 3D numerical results here demonstrate similarity scaling of the crack front response -- stresses, strains, and displacements -- in terms of two non-dimensional loading parameters. These fields serve as input to key engineering failure models for brittle and ductile crack growth and provide estimates of the apparent fracture toughness linked to changes of the material flow response, geometry, and applied loading. For the first time in the scientific literature, these studies document 3D analyses of steady-state crack growth and represent a key advance in computational analyses of crack extension
