Issue 75

R. Ince et alii, Fracture and Structural Integrity, 75 (20YY) 435-462; DOI: 10.3221/IGF-ESIS.75.30

for each a 0 / d and s / d . According to this, stress distributions along the notch line (  xx ) were determined. Subsequently, the FPZ depths (  a c ) in front of the notch were determined at  Nc /  xx =1. Consequently, the value of  a c was determined as 3.92±0.86 mm. For the statistical comparison of both approaches, by considering the above-mentioned numerical analysis, a total of 8 fracture toughness values ( ref K Ic ) were computed based on Eqn. (1) using the values of a c = a 0 +3.92 mm ( a 0 =5, 10, 15, and 20 mm) and corresponding to the mean values of  Nc for s / d = 0.3 and 0.35. In response, a total of 19 fracture toughness values ( s un K Ic K Ic  ) determined according to the compliance method were utilized for statistical comparison. The t-test based on Eqn. (29) is valid for paired comparisons. If the number of data to be compared is different, the following relation is used for the t-test:

1 2   

(31)



t calc









2

2

1    n  1 2   2 1 2 n n



n

1

1 1 1 2 n n 

1

2

0.7

s/D

0.6

d i

d i

Method SNDB1 SNDB2 SNDB3 SNDB4

Compliance Peak Load

Compliance Peak Load

-0.012 -0.100 -0.009 0.003

0.434 0.386 0.557 0.632

0.485 0.504 0.585 0.628

-0.052 -0.118 -0.029 0.003

0.500 0.361 0.580 0.619

0.512 0.461 0.589 0.616

Descriptive Statistics

n

4

4

0.515 0.114

0.545 0.071

-0.030 0.048

0.502 0.112

0.551 0.067

-0.049 0.051





95% Confidence Interval for Mean

[0.334, 0.696] [0.324, 0.680]

[0.432, 0.658] [0.444, 0.658]

Normality Check

Shapiro-Wilk ( p )

0.608

0.761

0.516

0.596

Result

Normal

Normal

Normal

Normal

Hypothesis Testing

t calc

1.24 ( p >0.05)

1.89 ( p >0.05)

t 3,0.025 Result

2.35

2.35

t calc = 1.24 < t 3, 0.025 =2.35

t calc = 1.89 < t 3, 0.025 = 2.35

F calc

2.58 ( p >0.05)

2.77 ( p >0.05)

F 0.05,3,3 Result

9.28

9.28

F calc = 2.58 < F 0.05, 3, 3 =9.28

F calc = 2.77 < F 0.05, 3, 3 = 9.28

Effect Size (Hedges' g ) Achieved Power (1-  )

0.08 (Negligible )

0.10 (Negligible)

0.056 0.054 There is not a significant difference between initiation fracture toughness. Table 5: Statistical comparison based on t -test and F -test for ini Ic K in this study

Here, n 1 and n 2 are the numbers of data in samples. Details of the second statistical comparison conducted are summarized in Tab. 6. Prior to applying the comparison formulas, the normality of the datasets was verified via the Shapiro-Wilk test. Despite the unbalanced sample sizes ( n 1 =19 vs. n 2 =8), the data followed a normal distribution ( p > 0.05), validating the

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