Issue34

N.R. Gates et alii, Frattura ed Integrità Strutturale, 34 (2015) 27-41; DOI: 10.3221/IGF-ESIS.34.03 28 situations where a damage tolerant design philosophy has been employed. Crack growth mechanisms and their influence on crack growth rate have been researched extensively over the years for uniaxial loadings and mode I crack extension. Most of these studies, however, utilize specimens which promote ideal crack growth conditions. In practical applications, where components are often subjected to complex multiaxial loading histories, these ideal conditions usually don’t exist. Instead, naturally initiated fatigue cracks can grow in a complex and mixed-mode manner which is not easy to predict or quantify. One of the complexities involved in mixed-mode crack growth is predicting crack path by determining in what direction a crack will grow throughout different stages of its development [1]. For example, cracks initiated naturally at a mechanical notch tend to nucleate and grow a short distance, usually comparable to the length of a few grains, on planes of maximum shear, but almost always turn so that long crack growth occurs on planes of maximum tensile stress [2–5]. In this case, well established mode I crack extension models can be employed to predict growth rates for a given loading history. On the other hand, long cracks in un-notched (smooth) specimens have been shown to propagate on maximum shear planes, maximum tensile planes, or a combination of both. The preferred growth plane has been shown to depend on material, nominally applied loading, and/or loading magnitude [6]. In general, cracks in the low cycle fatigue regime tend to grow on maximum shear planes while cracks at longer lives tend to transition into mode I growth [7–11]. One explanation offered for the discrepancy between crack growth in smooth and notched specimens is that a fundamental difference in crack growth mechanism exists. In the smooth specimens, the uniformly stressed gage section allows for a large number of microcracks to develop and form “crack networks” across the specimen surface. The growth of these cracks is driven primarily by far field stresses and plasticity of the gage section. Each small crack can grow to a different length and at a different rate due to microstructural variations, shielding, and other interaction with adjacent cracks in the network. These cracks grow individually and remain relatively small until near fracture where they coalesce to form a failure crack which retains the same orientation of the individual cracks. Shamsaei and Fatemi [12] observed that the development of microcrack networks in smooth specimens is more prominent in the low cycle fatigue regime due to increased plasticity in the gage section activating more slip systems. This observation agrees with the higher tendency for macroscopic shear-mode crack growth in this regime. They also observed a larger number of microcracks initiating in more ductile behaving materials, as opposed to higher strength materials, for solid cylindrical specimens, as opposed to tubular specimens, and for in-phase axial-torsion loadings, as opposed to 90° out-of-phase loadings. For the notched specimens, in contrast to the smooth, only a small number of dominant cracks nucleate at the location(s) of maximum stress around the notch, typically on the maximum shear plane. With the absence of microcrack networks, unable to develop in the lower stressed material surrounding the notch, the cracks quickly turn into the mode I direction and grow independently, driven by the stress and plasticity fields at the crack tip. Therefore, cracks initiated from notches generally grow in a continuous manner and lack the retardation or acceleration effects observed for the smooth specimens due to crack interaction. This is also the case for cracks growing in smooth specimens tested at lower stress amplitudes. As early as the 1950s, Marco and Starkey [13] noted a difference between these two types of crack growth mechanisms and termed the growth of long cracks through microcrack coalescence a type R crack system, whereas crack growth dominated by the propagation of a single crack was termed a type S crack system. Knowing by which mechanisms and on which planes a crack will grow is essential to performing accurate crack growth analysis. There are many parameters that can influence mixed-mode crack growth behavior, some of which include loading magnitude and R ratio, loading sequence, material strength, and crack closure [14]. To account for these effects, several prediction models or correlation parameters for both mixed-mode growth direction and growth rate have been proposed. For example, the maximum tangential stress criterion [15] has been found to give close predictions of the experimentally observed crack growth path [3], and equivalent stress intensity factor parameters, such as that proposed by Tanaka [16] can satisfactorily correlate the experimental growth rate data [4]. However, these models are most effective in the absence of crack coalescence and cannot account for differences in crack path for such cases. For example, the maximum tangential stress criterion would predict a mode II crack initiated under pure torsion loading to immediately branch at an angle of 70.5° to the crack growth direction and grow in mode I regardless of the applied loading magnitude [8, 17]. This prediction is not in agreement with the shear-mode crack growth observed in many smooth specimens from initiation up until fracture. Owing to the complexity of the task, little research is available on models which attempt to quantify when or if cracks will grow by type R mechanisms, type S mechanisms, or whether or not these two mechanisms are even responsible for the differences in smooth and notched specimen crack paths. To simplify this problem for the following discussion, it will be assumed that naturally occurring fatigue cracks always tend to initiate on planes of maximum shear stress. This is an assumption backed by both the physics of fatigue crack initiation and by large amounts of experimental evidence [12].

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