Bounds on fatigue damage: relation to microstructure dependent crack growth: I. Constant amplitude cyclic damage

The paper attempts to account for the complex micro-processes at a crack tip through a phenomenological model of damage accumulation based on macro damage curves. With the S-N curve as a basis, bounds are established that bracket the mean cyclic damage in reversed constant amplitude cycling. Proceeding from single slip and opening mode damage curves, two-mode damage curves are derived that reflect the micro process of crack tip advance by the presence on a macro scale of both damage modes in each cycle. Discrete microstructure barriers are identified that help divide the fatigue process on a macro scale into three stages, the analogues of the three creep stages under constant stress whereby the microstructure short crack (MSC), physically small crack (PSC) and macro crack regimes correspond to the `primary', `steady' and `tertiary' creep macro stages. The fatigue process is found to consist at each cyclic load level of a macro slip stage followed by an opening mode stage with an abrupt damage rate change at the transition, in line with experimental evidence (Socie, 1993). The barriers divide the entire region behind the S-N curve into distinct cyclic strain (stress) domains dominated on a macro scale by the opening mode in regions nearest the fatigue limit and by the slip mode in the uppermost region while an intermediate region is dominated by both. In the region nearest the fatigue limit the opening mode dominates virtually from first load reversal, in line with a view (Miller, 1985, 1987) that relates damage to surface imperfections. Macro damage accumulation involving a discontinuous damage rate transition is treated on the basis of discrete barriers while a continuous spectrum of barriers is introduced in an attempt to reflect the crack tip process on a macro scale. A theoretical model of microstructure resistance is introduced that describes crack arrest by the barriers and leads to a distinct set of macro-damage bounds in the interval between barriers, hence in each region of the S-N curve. The entire range of fatigue lifetimes below and above the fatigue limit is examined showing that only the slip mode carries over to the region below the fatigue limit resulting in non-propagating damage. Assuming that macro damage can be defined as a ratio of crack lengths, two scales are introduced that lead to bounds on mean crack length: a macro scale connecting two disparate levels of the fatigue process defines a macro volume element enclosing a sufficiently large number of grains to be representative of the actual medium as a whole and a micro scale of grain size order with a corresponding role. Bounds on mean crack growth rate are found to reduce in the limit of long cracks to the known Paris rate relation. Two distinct sets of bounds on mean damage and damage rate are found: one for unloading from a high to low cyclic strain another for loading from a low to high strain (stress), congruent with the distinct loading/unloading paths in a hysteresis loop. A simple test method is proposed to locate the fatigue limit indirectly. The model is applied to cumulative damage analysis in part II where residual lifetime mean and variance in two-stage fatigue cycling are predicted.