PSI - Issue 7

Mirco D. Chapetti / Procedia Structural Integrity 7 (2017) 229–234

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Mirco D. Chapetti/ Structural Integrity Procedia 00 (2017) 000–000

d K Y dR σ ∆ = ∆ 1. Introduction The intrinsic fatigue limit or endurance of the material is one of the most important and needed parameters in many applications for fatigue design. For low and medium strength metals, the fatigue limit corresponds roughly to the static strength or hardness. Besides, it is well known that this fatigue limit can be defined by the ability of the strongest microstructural barrier ( i.e. grain boundary) to arrest a micro-crack. Fig. 1 shows this concept in a Kitagawa-Takahashi diagram (1976) that plots the threshold stress range ∆σ th as a function of crack length, after Miller (1993). This experimental evidence allows to define a minimum intrinsic resistance to micro-crack propagation (microstructural threshold, ∆ K dR ) for a given load ratio R, by using the plain (intrinsic) fatigue limit, ∆σ eR , and the distance from the surface d of the strongest microstructural barrier, as it was proposed by Chapetti (2003) as follows: (1) Where Y is the geometrical correction factor, and d is the microstructure dimension that define the position of the strongest barrier (for example, average grain size, lath spacing, phase size, etc). In most cases the nucleated microstructural short surface cracks are semicircular ( Y = 0.65). From the microstructural threshold ∆ K dR , a resistance curve can be defined as a transition to the fatigue threshold for long cracks, ∆ K thR , as it is shown in Fig. 1. Chapetti (2003) proposed that the crack propagation threshold is also composed by an “extrinsic” component ∆ K C , a function of crack length, in addition to the microstructural threshold. Once this component has fully developed, it reaches a maximum value (for long cracks), ∆ K CR , which is constant for a given material and R-ratio, and it is defined as: (2) The development of ∆ K C as a function of crack length (for a > d ) can be modeled with an exponential function of the form: (3) Where a is the crack length and k is a material and R -ratio dependent constant that defines the shape for the ∆ K C curve and can be estimated as (see Chapetti (2003) for more details about this model): (4) Log. Threshold Stress , ∆σ th ∆ K thR ∆ K dR ∆σ eR Log. Crack Length , a d L 0 l Long Crack Regime Short Crack Regime eR π dR thR CR K K K ∆ = ∆ − ∆ [ ] CR K ∆ k a d − − ) ( C e K ∆ = − 1 k d = Fig. 1. Kitagawa-Takahashi type diagram showing the threshold for fatigue crack propagation.

thR dR K K K

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