Modified Kitagawa Diagram and Transition from Crack Nucleation to Crack Propagation

Abstract

Kitagawa-Takahashi diagram combines the endurance limit of a smooth specimen and the crack propagation threshold in a fracture mechanics specimen into single diagram thus providing the connection between the stress or strain-life and damage tolerance approaches. The diagram is modified by considering that (a) fatigue requires two independent load-parameters for unambiguous description, (b) long crack growth behavior defines the material resistance under constant stress amplitudes along with the associated R-ratio effects, (c) remote applied stresses and localized plasticity-effects can be combined to provide the total mechanical force opposing the material resistance leading to crack initiation, growth and failure describable in the diagram, (d) localized plasticity contributes to internal stresses that either augment or retard the remote stresses, and finally (e) the magnitude and gradient of these internal stresses determine the condition for propagation and/or non-propagation of the incipient cracks that form either at pre-existing stress concentrations or in situ formed stress concentrations due to localized plasticity. Localized plasticity forms the basis for the additional crack tip driving forces in either accelerating or decelerating crack growth kinetics thereby providing conditions for either crack arrest with resulting non-propagating cracks or for continuous uninterrupted crack growth. Internal stresses are generated during fatigue damage in the form of dislocation pile-ups, intrusions and extrusions. The analysis shows that critical magnitude and gradient of the internal stresses are required for an incipient crack to grow continuously, failing which crack arrest can occur. The methodology is based on separating the mechanically introduced crack tip driving forces vs the material resistance; the later can be extracted from long-crack growth data under constant amplitudes. Analysis of incipient short cracks growing under the elastic-plastic notch tip stress fields are analyzed systematically for various elastic stress concentrations, K t, and notch-tip radii, ρ. A general formulation is developed based on the calculations that can be incorporated into the unified life predication model that is being developed.