Issue 48

A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59 613 Figure 2 : Surface semi-elliptical, corner quarter-elliptical, and internal elliptical cracks [10]. There are authors that claim that, for fatigue life estimation purposes, it can be assumed that surface cracks immediately transform into through-cracks as their depth a reaches the thickness t at the back surface of the cracked component [11]. An example to justify this simplification in the FCG transition is presented by Grandt et al. [12-13]. They studied a crack that grew on a double-T cross-section beam under bending. Theirs initially 2D quarter-elliptical crack propagated two- dimensionally through the lower corner of the section until it almost penetrated the inner rear face of the section at 60,923 cycles. Then, the crack increased rapidly and cut the entire leg in only 80 more cycles. Hence, the 2D to 1D transition cycles could be neglected based on a supposed “catch up effect” [12], assuming the crack front at the back surface experiences a much higher SIF (and so a much faster FCG rate) than at the front surface, tending to straighten its profile. However, this approach creates a discontinuity in the calculated SIF values, often causing the crack growth prediction to be excessively conservative, because such a simplification can behave like if it was an overload that causes subsequent FCG delays in most numerical FGC prediction codes, see e.g. [10, 14]. Moreover, other experimental results reveal that quasi-elliptical surface 2D flaws may not immediately transform into through-cracks. Fawaz e.g. studied the shape of fatigue crack fronts that started from a hole in Al 2024-T3 Alclad thin plates with thickness t  1.6mm, loaded under combined tension and bending [15]. He found that his cracks essentially retained their elliptical shape as they gradually grew into through-cracks. Even though this detailed experiment indicates a need for it, no closed-form SIF-solution is available for through-cracks with such oblique fronts. Some approximations have been suggested based on the boundary element method [8], however they do not account for the component width effect, a major limitation on practical applications. A simplified model for the 2D-1D crack front transition was proposed by Johnson a long time ago [16]. According to him, after the crack depth reaches the specimen thickness t , the crack can be assumed to keep its elliptical shape in the transition zone. Johnson used an adaptation of the surface (2D) stress intensity factor (SIF) expressions described by Hall et al. [17] to model the surface crack transition. However, Johnson’s original approach may be inaccurate, since it uses overly simplified the SIF expressions for surface cracks, without considering the effect of the specimen width 2 w and the variation of the front surface effect (assumed constant and equal to 1.1). In addition, it does not guarantee continuity of the SIF expression K I ( c ) in the width direction between the transitioning period and the 1D crack growth regimen. This problem is particularly deceiving when FCG retardation models are considered in fatigue life calculations. If the considered SIF equation calculates a smaller value for the through crack than for the transitional range, the retardation model may consider the larger SIF as an overload, delaying its subsequent 1D growth. Therefore, when considering load interaction models, Johnson’s approach may predict FCG retardation even under constant amplitude loading, resulting in non-conservative fatigue life predictions.