Ph.D. Thesis Defense by Valerie P. Bennett
Friday, July 23, 1999

(Dr. David McDowell, advisor)

"A Microscale Study of Small Crack Propagation in Multiaxial Fatigue"

Abstract

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.