The Introduction of Crack Opening Stress Modeling into Strain-Life and Small Crack Growth Fatigue Analysis

Abstract

The work in this thesis is concerned with the mechanics of the initiation and growth of small fatigue cracks from notches under service load histories. Fatigue life estimates for components subjected to variable amplitude service loading are usually based on the same constant amplitude strain-life data used for constant amplitude fatigue life predictions. The resulting fatigue life estimates although they are accurate for constant amplitude fatigue, are always non conservative for variable amplitude load histories. Similarly fatigue life predictions based on small crack growth calculations for cracks growing from flaws in notches are non conservative when constant amplitude crack growth data are used. These non conservative predictions have, in both cases, been shown to be due to severe reductions in fatigue crack closure arising from large (overload or underload) cycles in a typical service load history. Smaller load cycles following a large near yield stress overload or underload cycle experience a much lower crack opening stress than that experienced by the same cycles in the reference constant amplitude fatigue tests used to produce design data. This reduced crack opening stress results in the crack remaining open for a larger fraction of the stress-strain cycle and thus an increase in the effective portion of the stress-strain cycle. The effective strain range is increased and the fatigue damage for the small cycles is greater than that calculated resulting in a non conservative fatigue life prediction. Previous work at Waterloo introduced parameters based on effective strain-life fatigue data and effective stress intensity versus crack growth rate data. Fatigue life calculations using these parameters combined with experimentally derived crack opening stress estimates give accurate fatigue life predictions for notched components subjected to variable amplitude service load histories. Information concerning steady state crack closure stresses, effective strain-life data, and effective stress intensity versus small crack growth rate data, are all obtained from relatively simple and inexpensive fatigue tests of smooth specimens in which periodic underloads are inserted into an otherwise constant amplitude load history. The data required to calibrate a variable amplitude fatigue crack closure model however, come from time consuming measurements of the return of crack closure levels for small cracks to a steady state level following an underload (large cracks for which crack closure measurements are easier to make cannot be used because at the high stress levels in notches under service loads a test specimen used would fracture).

For low and moderately high hardness levels in metals crack growth and crack opening stress measurements have been made using a 900x optical microscope for the small crack length at which a test specimen can resist the high stress levels encountered when small cracks grow from notches. For very hard metals the crack sizes may be so small that the measurements must be made using a confocal scanning laser microscope. In this case the specimen must be removed from the test machine for each measurement and the time to acquire data is only practical for an extended research project. The parameters for the crack closure model relating to steady state crack closure levels vary with material cyclic deformation resistance which in turn increases with hardness. One previous investigation found that the steady state crack opening level was lower and the recovery to a steady state crack opening stress level after an underload was more rapid for a hard than for a soft metal. This observation can be explained by the dependence of the crack tip plastic zone size that determines crack tip deformation and closure level on metal hardness and yield strength. Further information regarding this hypothesis has been obtained in this thesis by testing three different steels of varying hardness levels (6 HRC, 35 HRC, and 60 HRC) including a very hard carburized steel having a hardness level (60 HRC) for which no crack opening stress data for small cracks had yet been obtained. This thesis introduced a new test procedure for obtaining data on the return of crack opening stress to a steady state level following an underload. Smooth specimens were tested under load histories with intermittent underload cycles. The frequency of occurrence of the underloads was varied and the changes in fatigue life observed. The changes in damage per block (the block consisted of an underload cycle followed by intermittent small cycles) were used to determine the value of the closure model parameter governing the recovery of the crack opening stress to its steady state level. Concurrent tests were carried out in which the crack opening stress recovery was measured directly on crack growth specimens using optical microscope measurements. These tests on metals ranging in hardness from soft to very hard were used to assess whether the new technique would produce good data for crack opening stress changes after underloads for all hardness levels. The results were also used to correlate crack closure model parameters with mechanical properties. This together with the steady state crack opening stress, effective strain-life data and the effective intensity versus crack growth rate data obtained from smooth specimen tests devised by previous researchers provided all the data required to calibrate the two models proposed in this investigation to perform strain-life and small crack growth fatigue analysis.