PSI - Issue 7

F. Fomin et al. / Procedia Structural Integrity 7 (2017) 415–422 Fedor Fomin and Nikolai Kashaev / Structural Integrity Procedia 00 (2017) 000–000

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the crack origin site varied in the 50 - 100 µm range. Since these values are almost two orders of magnitude larger than the average thickness of the martensitic plate in the FZ, the behaviour of such cracks, in principle, can be described by a continuum fracture mechanics framework, with special attention paid to the crack driving force parameter. After crack initiation, which is normally assumed to be negligible in the presence of sharp defects or inclusions, an internal crack propagates until it reaches the surface. Taking into account the typical depth of the crack nucleation site, we can conclude that the internal cracks are at most 500 - 700 µm long. The simplest approach to estimate the number of cycles for internal crack propagation is based on traditional linear elastic fracture mechanics (LEFM); however, realization of this concept encountered difficulties because the SIF range at the early stages of crack growth was lower than the threshold value, as shown in Fig. 3(b). This discrepancy can be explained by the propagation of the so-called short cracks. It was shown by many researchers that short fatigue cracks propagate faster than long cracks at the same applied SIF range; moreover, they can grow at stress intensities lower than the fatigue threshold (Anderson, 2005; Zerbst et al., 2016). Depending on the main mechanism leading to their faster growth, the short cracks can be categorized into microstructurally, mechanically, physically, and chemically short cracks (Ritchie and Peters, 2001). The approach used in the present work focuses on physically short cracks that are already significantly larger than the microstructural dimension; however, their growth rate is still increased due to the reduced crack closure effect. The basic idea behind this approach is that the crack closure phenomenon shows transient behaviour and gradually builds up until it reaches a constant value for long cracks. The evolution of crack closure is reflected by the reduced threshold values for short cracks and is usually expressed by the cyclic R-curve (Tanaka and Akiniwa, 1988) shown in Fig. 4.

Fig. 4. Schematic illustration of the cyclic R-curve. In general, the overall threshold ∆ K th ( a ) can be subdivided into an intrinsic part, ∆ K th,eff , which is material specific, and a crack length-dependent extrinsic part, ∆ K th,op , reflecting the gradual build-up of crack closure. In the present model, a simplified approach for constructing the cyclic R-curve, proposed by Zerbst and Madia (2015) is used. The cyclic R-curve is approximated by the following equation:

* a a a   a a

(2)

( ) K a K K a K        ( )

,

, th eff

, th op

, th LC

th

*   

0

where ∆ a = a - a i is the crack extension, a i is the initial crack length, and a 0 is the El Haddad parameter (El Haddad et al., 1979). The parameter a * has to be chosen such that the condition ∆ K th (0) = ∆ K th,eff is fulfilled. The El Haddad parameter is obtained from the Kitagawa-Takahashi (KT) diagram according to

2

, th LC         e K

(3)

1

,

a

 

0

Y  

where ∆ σ e is the fatigue limit of the smooth specimen (plain fatigue limit). The boundary correction function Y in Equation (3) was chosen for small surface semi-elliptical cracks ( Y = 0.728) because the cracks nucleate at the surface in smooth specimens. It is important to note that a 0 obtained by Equation (3) was assumed to be valid also for internal cracks investigated in this research. Thus, to construct the simplified cyclic R-curve, three experimentally determined