PSI - Issue 5

G. Lesiuk et al. / Procedia Structural Integrity 5 (2017) 904–911

905

Lesiuk et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

During the fatigue process, the area of a special interest is the stage of stable crack propagation from the initial length a ini (i.e. from the moment of detection with the help of suitable defectoscopy methods) up to a critical length a cr where the crack propagates with a velocity close to a sound propagation velocity in a given material. The kinetics of fatigue crack growth is most often characterized by the semi-empirical laws in general form = ( , , , , , , … ) , (1) where: Y – geometric constraints,  – stress state, a – crack length, R – stress ratio,  – microstructural parameters,  – environment factors. From the engineering point of view, the problem is dealing with the determination of the period of a pre-critical crack propagation. A lifetime for the cyclic loaded component can be written in the generalized form = ∫ ( , , , , , ,… ) (2) The solutions simplicity of the (2) depends strongly from the mathematical representation of the function (1). In several physically determined theoretical models the solutions of (2) can be problematic. As an example we can take the exact solution of the fatigue crack growth based on energy considerations Szata (2002): where:  – dimensionless constant,  plf – cyclic yield strength,  zw – external stress range, S * - critical crack (defect) area, S 0 – initial crack (defect) area, R – stress ratio. Of course, we can propose some simplification based on equivalent surface methods (ESM) presented by Szata (2002), Szata and Lesiuk (2009) or using equivalent flaw approach Correira (2016). However, in engineering practice for proper model formulation and parameters estimation, the kinetic fatigue fracture diagrams (KFFD) are constructed. The main way (a classic one) of describing the fatigue fracture kinetics is the force approach proposed by Paris (1963), based on experimental data has the exponential form in relation to stress range  and  K , as it has been well known as a Paris’ law (1963): = (∆ ) , (4) where: C and m are experimentally determined factors,  K represents the range of stress intensity factor. However, the number of factors (like R -ratio) strongly influenced the FCGR description. This is schematically shown in Fig. 1. In this case we can use Paris’ law with proper adjustment of C - constants for each R or use another formulas involved R -ratio effect, like Paris-Forman equation presented by Forman et al. (1967) = (∆ ) (1− ) −∆ (5) or Walker (1970) equation: = [ (1− ∆ ) ] . (6) In (5) K c represents critical value of stress intensity factor (under plane strain conditions - K IC ), C , m ,   are experimentally determined constants. In literature exists hundreds of FCGR formulas, in many papers Rozumek 4 0 * 2 1 0 * S S    2 1 1 2 2  plf zw (1 ) R ln 2 1 1 16.051                S S N g , (3)