PSI - Issue 21

S. Sohrab Heidari Shabestari et al. / Procedia Structural Integrity 21 (2019) 154–165 S. Sohrab Heidari Shabestari et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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4

2.1. Calculation of Forman model Constants In order to calculate fatigue lifes , ΔK for every crack length should be calculated analytically. In this study, Bowie (1956) method is applied as a reference. For a DTC geometry under tensile loading, Equations 1 and 2 are used to calculate the ΔK in each loading cycle. = σ√πc β (1) β = 0.5 (3.0 − r+ c c ) (1.0 + 1.243 (1.0 − r+ c c ) 3 ) ∗ F W (2) where is the finite width correction factor given by: = √sec ( ) sec ( ( + ) ) (3) Since the load ratio R is zero, ΔK is calculated as in Equation 4. Forman model (Equation 5) is used to fit the fatigue data for life prediction in the study. Forman constants are obtained by plotting log-log scale of ∆K versus / (Kc − ∆K) by fitting the experimental data into Equation 5. Log-log plot of ∆K versus da/dN (Kc − ∆K) for each specimen is depicted in Figure 2 . A linear fit of the data, gives the Forman constants as shown in Equation 6 and 7. Table 1 gives the Forman constants for each specimen and also averaged constants used in the rest of this study. ∆ = ( ) − ( = 0) (4) d d N a = C∆K m Kc−∆K (5) ( − ∆ ) = . ∆ (6) Log ( ( − ∆ )) = ( ) + (∆ ) (7) 

-3.05 -3 -2.95 -2.9 -2.85 -2.8 -2.75 -2.7 -2.65

Average Linear Fit y = 3.9412x - 9.4158 R² = 0.9926

Specimen#1 Specimen#2 Specimen#3 Average

1.62 da/dN(Kc - delta K)

1.64

1.66

1.68

1.70

Linear (Specimen#1) Linear (Specimen#2) Linear (Specimen#3) Linear (Average)

Delta K (MN/m^3/2)

Specimen#3 Linear Fit y = 3.6312x - 8.8985 R² = 0.935

Specimen#2 Linear Fit y = 4.1854x - 9.8241 R² = 0.977

Specimen#1 Linear Fit y = 4.0071x - 9.5248 R² = 0.9564

Figure 2. Linear Fit of the Experimental Data on LOG-LOG Scale