(Dr. David McDowell, advisor)
"A Microscale Study of Small Crack Propagation in Multiaxial Fatigue"
The problem of properly assessing the small crack regime is one of the primary limiting factors in estimating the remaining life in components under HCF conditions. Since small cracks may account for 50-90% of the total life of the component (for Nf = 1 mm), characterizing this regime is crucial. With many of the factors that affect small crack behavior such as the role of the free surface, microstructural barriers and inhomogeneities, crack closure, and grain boundary blockage, developing and Ďall-inclusive' small crack model is indeed a challenge. This work is an effort to shed light on some of these first order effects which influence small crack growth. A crystal plasticity micromechanical model embedded within a finite element context was used to assess these factors. This method allows for the assessment of heterogeneity effects caused by plasticity within individual grains and the interactions among these grains. Using crystal plasticity concepts to assess fatigue damage as well as small crack fatigue behavior is an innovative approach.
Two types of analyses were performed. First, a random, initially isotropic ensemble of grains were subjected to a range of constant strain amplitudes to explore the amplitude and stress-state dependencies of the development of heterogeneous deformation within the microstructure and its effect on the behavior of an uncracked polycrystal. To study this, the distribution of three candidate fatigue initiation parameters (normalized cyclic microplasticity, Mohr-Coulomb, and Fatemi-Socie) were analyzed for loading cases of cyclic tension-compression, cyclic shear, and combined loading to determine which one correlates more closely with the density and distribution of microcracks found experimentally. The Fatemi-Socie parameter produced distributions which were indicative of the nature of the accumulation of the cyclic microplasticity as found experimentally. This parameter also provides information regarding the planes on which damage will occur and the normal stress acting on that plane. Both elastic and elastic-plastic shakedown limits were qualitatively determined, where the elastic shakedown limit also corresponded with the smooth specimen fatigue limit for cyclic tension-compression. It was also found that there was an accentuation of the maximum of the plastic shear strain amplitude on a slip system above the average plastic shear strain for the aggregate for both cyclic tension-compression and cyclic shear.
Secondly, CTSD and CTOD were determined as a function of stress state,
amplitude and crack length ratio (a/d). Understanding the nature
of the crack tip mode-mixity is an essential link in the development of
driving force parameters for small cracks. Mode-mixity and nonproportional
CTSD and CTOD is reflected sooner for cyclic tension-compression as compared
to the cyclic shear case. This nonproportionality is primarily evidenced
at higher strain amplitudes for small a/d and at smaller strain amplitudes
for large a/d and is a manifestation of many factors: (i) reversed
plasticity which translates to restricted motion at the crack tip, (ii)
microstructural heterogeneity, and (iii) multislip ahead of the crack tip.
Such complex phasing and ratchetting behavior have not come to light in
previous computational studies based on homogeneous elasto-plasticity.
This nonsymmetric development of cyclic microplasticity on the crack faces
may also contribute to the transition of the crack from Stage I to Stage
II because of a local imbalance of cyclic microplasticity. The development
of crack closure was also evident. From evaluating | CTSD/CTOD |,
DCTSD/DCTOD, and the DCTD as a function of stress state and amplitude,
two key observations were made: (i) the opening displacements dominate
the behavior for both loading cases for small a/d ratios (a/d = 0.25 and
0.5) and (ii) the DCTD has consistently higher values for cyclic tension-compression
as compared to cyclic shear. These studies point to some of the deficiencies
in understanding small crack behavior such as (i) surface measurements
of CTSD and CTOD may be very misleading and unrepresentative of crack tip
phenomena, (ii) sliding and opening displacements ratchet at the crack
tip in a manner which appears to maximize the CTD and decrease closure
effects, and (iii) plasticity-induced closure need not occur first at the
crack even for initially planar cracks, (iv) the DCTD has consistently
higher values for cyclic tension-compression as compared to cyclic shear,
and (v) there is a linear relationship between a critical plane driving
force parameter and the DCTD (under nominally elastic conditions) with
higher overall slopes for the cyclic tension-compression case.