Issue 43

L.C.H. Ricardo, Frattura ed Integrità Strutturale, 43 (2018) 57-78; DOI: 10.3221/IGF-ESIS.43.04 71 Figure 11: FEM Model of CT specimen.        max max 1 2 P a K f W BW (4.1)            2 max 1 p y K r plane stress (4.2) where: K max = maximum stress intensity factor; P min = minimum applied load; P max = maximum applied load; B = specimen thickness; a = crack length; W = width of the specimen; a/W = ratio of the crack length to the specimen width; f(a/W) = characteristic function of the specimen geometry. Antunes & Rodrigues [72] discuss that numerical analysis of plastic induced crack closing (PICC) based on finite element method (FEM) consists of discretising and modeling the cracked body having elastic–plastic behaviour, applying a cyclic load, extending the crack and measuring the crack closure level. The finite element mesh must be highly refined near the crack front, with micron scale, in order to model the forward and reversed crack tip plastic zones. The forward plastic zone is made up of the material near the crack tip undergoing plastic deformation at the maximum load, therefore it is intimately related to K max . The reversed plastic zone encompasses the material near the crack tip undergoing compressive yielding at the minimum load and is related to ΔK . Commercial FE software packages offer tools to deal with elastic– plastic deformation, crack propagation and contact between crack flanks, and are therefore adequate to model PICC. However, the numerical models have significant simplifications with respect to real fatigue crack propagation, namely: – discrete crack propagations, of the same size as near crack tip elements, which give fatigue crack growth rates significantly higher than real values; – crack propagation is modeled at a constant load when in reality it occurs continuously during the whole load cycle. In numerical simulations, the crack can be incremented at maximum load [73], at minimum load [74,75] or at other positions of the load cycle. Ogura et al. [49] advanced the crack when the crack tip reaction force reached zero during the load cycle. However, none of these approaches truly represents the fatigue process, where, according to slip models of striation formation, crack extension is a progressive process occurring during the entire load cycle. The proposal to increment at minimum load was designed to overcome convergence difficulties caused by propagating the crack at maximum load. This is unrealistic since the crack is not expected to propagate in a compressive stress field. However, several authors [76,77] have already found that the load at which the crack increment occurs does not significantly influence crack closure numerical results. Under constant amplitude loading, crack tip opening load will typically increase monotonically, with increasing crack growth, until a stabilized value is reached. So, it is important to define the minimum crack extension needed to stabilize the opening level. It is usually sufficient to increase the crack ahead of the monotonic plastic zone resulting from the first load cycle [78,79]. The stress level in the crack tip, Fig.12, must to be positive to characterize the crack opening and negative to characterize the crack closure. Antunes & Rodrigues [72] consider as basic criteria to determine the crack opening or closing: the first contact of the crack flank, which corresponds to the contact