PSI - Issue 7

G. Härkegård / Procedia Structural Integrity 7 (2017) 343–350 F / Structural Integrity Procedia 00 (2017) 000–000

346

4

G. Härkegård 0

0 a a and fatigue limit

A σ σ ∆ ∆ .

Table 2. Power law exponent m and the associated crack size

0 0 1

m

1 6 −

1 4 −

1 3 −

1 2 −

∞

1

2

0 a a

1

2

0

A σ σ ∆ ∆

0.71 =

0.82 =

0.58 =

2

1

1

2

3

3

The power-law curve is tangent to the El Haddad curve, if its ‘constant’ is chosen so that the two curves coincide at the point, where eq. (7) is satisfied. This is demonstrated in Fig. 2, where the ‘Frost’ curve ( ) 1 3 m = − is tangent to the El Haddad curve at 0 2 a a = . Similarly, the ‘Murakami’ curve ( ) 1 6 m = − is tangent to the El Haddad curve at 0 2 a a = . In the following two Sections, predictions by the El Haddad relationship, eq. (1), using the fatigue data of Table 1, will be compared with predictions using models by Frost et al. (1974) and Murakami (2002). 3. Comparison between El Haddad and Frost predictions for specimen with small surface through-crack Frost et al. (1974) made comprehensive experimental investigations of the growth of fatigue cracks, which were typically in the range from a few tenths of a millimetre to several millimetres. For surface through-cracks, the ‘threshold’ for FCG was generally found to be well described by ( ) 1 3 3 F a F 2 2 a a C C a σ σ σ ⋅ = ⇒ ∆ = = . (8)

A σ σ ∆ ∆ and

0 a a yields

Introducing the dimensionless variables

(9)

1 −     3 C a a a =     ∆ ∆     F A 0 0 2 σ σ σ ∆ A

1

3

.

6 0 15 10 m a − = ⋅ .

6 18.4 10 m L − = ⋅ and

1 R = − from Table 1 and

With fatigue data for

1.1215 F = , one obtains

For an alloy steel, and with units MPa and m, Frost et al. (1974) report F 510 C = . Fig. 3 shows a comparison between the predictions due to El Haddad, eq. (3), and Frost, eq. (9). The Frost curve nearly touches the El Haddad curve, and is therefore in good agreement with the corresponding tangent curve in Fig. 2. The Frost predictions of the fatigue limit of a cracked member deviate < 15% from the El Haddad curve in the range 0 a a = 0.5–10, i.e ., over more than one order of magnitude.

Fig. 3. Comparison between El Haddad and Frost predictions for the fatigue limit of Cr steel with a surface trough-crack.