PSI - Issue 7

Mirco D. Chapetti / Procedia Structural Integrity 7 (2017) 229–234 Mirco D. Chapetti / Structural Integrity Procedia 00 (2017) 000–000

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3

The material threshold as a function of crack length is then defined as:

[

( ] k a d )

(

)

dR (5) Fig. 2 plots schematically the threshold for crack propagation given by expression (5) as a function of the square root of the crack length. thR dR th e − − − K K K K ∆ = ∆ + ∆ − ∆ 1

Crack Propagation

Chapetti (2003)

Threshold, ∆ K th

∆ K CR

∆ K thR

Crack Initiation

∆ K dR

√ �

Crack Length,

Crack Initiation Mode II

Short crack propagation. Mode I

Fig. 2. Threshold for fatigue crack propagation as a function of a 1/2 , defined according to expression (5).

K A B H d V dR π ∆ = + As we can appreciate in Fig. 2, expressions (1) and (5) allows a clear definition of the transition between the crack initiation and propagation stages. The initiation stage can be defined by the number of cycle to create a crack of length d . The threshold for fatigue crack propagation can be then analyzed from a = d by using the threshold given by the expression (5), that needs the fatigue limit, the threshold for long cracks and the microstructural dimension. 2. Estimation of the intrinsic fatigue limit In those cases where the plain fatigue limit is not available, the following general expression is proposed in order to estimate ∆ K dR that uses the Vickers hardness H V and the microstructural dimension d : (6) Where A and B are non-dimensional material constants, H V is in Kg/mm 2 , d in µ m, and ∆ K dR in MPa m 1/2 . Fig. 3 shows schematically the microstructural threshold given by expression (6) as a function of ( π d ) 1/2 . The parameter A represents the lower bound for the microstructural threshold, as the microstructural dimension d tends to zero. On the other hand, B defines the slope of the liner influence of the hardness.