Issue 31

J.A.F.O. Correia et alii, Frattura ed Integrità Strutturale, 31 (2015) 80-96; DOI: 10.3221/IGF-ESIS.31.07 81 in a very simple form: the power function. It has been rather documented in the literature the Paris’s law limitations [4]: i) it only models stable fatigue crack propagation behaviour (propagation regime II) and ii) does not account for stress ratio effects. Many alternative fatigue crack propagation relations have been proposed to overcome the limitations of the Paris’s law and also to deal with variable amplitude loading. Nevertheless, the Paris’s law still has been intensively used to model fatigue crack growth under constant amplitude loading due to its attractive simplicity. The number of parameters involved in the more comprehensive fatigue crack propagation models may increase significantly which makes their evaluation a costly task and very often discouraging engineers of their application. Fatigue crack growth testing is costly and alternative less expensive approaches to derive fatigue crack growth data are consequently welcome. Local strain-based approaches [5-8] were originally proposed to model fatigue crack initiation on notched components [9]. A link between the local strain-based approaches to fatigue and the Fracture Mechanics based fatigue crack propagation models has been proposed by some authors [1, 10-14]. Glinka [13] was one of the first researchers to use the local strain approaches to model fatigue crack propagation. The original idea of Glinka was later followed and developed by his collaborators, such as Noroozi et al. [1, 10-11], using crack tip residual stress concepts to explain stress ratio effects as well as loading interaction effects on fatigue crack growth rates. Peeker and Niemi [12], based on the original idea of Glinka, made also independent contributions, using crack closure concepts to explain stress R-ratio and load interaction effects. In general, elastoplastic stress analysis at the crack tip vicinity has been performed using analytical approaches, however numerical approaches based on finite element analysis were followed by Hurley and Evans [14]. The underlying concept behind the proposed local approaches for fatigue crack propagation modelling consists of assuming fatigue crack propagation as a process of continuous failure of consecutive representative material elements (continuous re-initializations). Such a kind of approaches has been demonstrated to correlate fatigue crack propagation data from several sources, including the stress ratio effects [1, 10-14]. The crack tip stress-strain fields are computed using elastoplastic analysis, which are applied together a fatigue damage law to predict the failure of the representative material elements. The simplified method of Neuber [15] or Moftakhar et al. [16] may be used to compute the elastoplastic stress field at the crack tip vicinity using the elastic stress distribution given by the Fracture Mechanics [1, 16-17]. This paper proposes an assessment and extension of the model proposed by Noroozi et al. [1, 10-11] to predict the fatigue crack propagation rates, based on local strain approach to fatigue. This model has been denoted as UniGrow model and classified as a residual stress based crack propagation model [18]. The model is applied in this paper to derive probabilistic fatigue crack propagation da/dN-ΔK fields for the S355 structural mild steel, for distinct stress R -ratios ( p - da/dN-ΔK-R ). Results are compared with available experimental fatigue crack propagation data from testing of compact tension specimens [19]. A central parameter in the UniGrow model is the material representative element size, ρ* , which is tuned in this research by means of a trial and error procedure. The elastoplastic stresses at the vicinity of the crack tip are computed using both simplified formulae and elastoplastic finite element analyses for comparison purposes. The deterministic strain-life damage relation adopted in the original UniGrow model is replaced by a probabilistic counterpart. The probabilistic model as proposed by Castillo and Fernández-Canteli [20] for the strain-life field, based on Weibull distribution, was generalized in order to incorporate a damage parameter definition able to account for mean stress effects. In particular, the Smith-Watson-Topper damage parameter was selected resulting the p-SWT-N which was applied to derive the probabilistic crack propagation fields. T HEORETICAL BACKGROUND n this section, an overview of the UniGrow model that has been proposed to predict the fatigue crack growth by means of a local approach to fatigue, is presented. Also, a recently proposed probabilistic strain-life model is introduced. An extension/generalization of the probabilistic strain-life approach, to account for mean stress effects, is proposed which will be applied latter, in this chapter, in conjunction with the UniGrow model to predict probabilistic fatigue crack propagation data. Overview of the deterministic UniGrow model The UniGrow model as proposed by Noroozi et al. [1] is supported on the following assumptions: - The material is composed of elementary particles of a finite dimension ρ* also called material representative elements, below which material cannot be regarded as a continuum, Fig. 1.a); - The fatigue crack tip is considered equivalent to a notch with a radius equal to ρ* , Fig. 1.b). I