PSI - Issue 60

Md Rakim et al. / Procedia Structural Integrity 60 (2024) 298–310

303

6

Md Rakim et al. / Structural Integrity Procedia 00 (2023) 000 – 000

2000

1800

1500

1600

1200

1200

Model

Allometric1 y = a*x^b

Model

Allometric1 y = a*x^b

Equation

Equation

Plot

J-Integral

Plot

J-Integral

a b

396.69043 ± 1.51 1.03723 ± 0.0055

a b

640.87935 ± 11.213 0.66487 ± 0.02924

900

Reduced Chi-Sqr R-Square (COD)

554.92481

Reduced Chi-Sqr R-Square (COD)

825.51369

0.99279 0.99277

0.98564 0.9842

Adj. R-Square

800

Adj. R-Square

600

1.5 mm Exclusive Line 0.2 mm Offset Line 0.15 mm Exclusive Line Blunting line

1.5 mm Exclusive Line 0.2 mm Offset Line 0.15 mm Exclusive Line Blunting line

J-Integral (MPa.mm)

400 J-Integral (MPa.mm)

300

0

0

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Crack Growth (mm)

Crack Growth (mm)

Fig.7: J-R curve at 27 °C with the as-received condition for forged material

Fig.8: J-R curve at 750 °C with 5000 hours ageing condition for forged material

From the Experimental Load-LLD and crack growth data J- Δa curve has been prepared based upon the following formulations. For computing J -integral concerning crack growth ( Δa ), the most effective way is to divide J into two components i.e., elastic ( ) and plastic ( ) as shown in the following equations as per ASTM E 1820-13. = + (3) where, the elastic component of J is considered for elastic stress intensity factor K , ‘ ν’ denotes Poisson’s ratio also E denotes Young’s modulus as shown in the following equation as per ASTM E 1820-13. = 2 (1− 2 ) (4) For the side grooved specimen, the stress intensity factor has been calculated from the following equation, where ‘ B ’ denotes gross thickness and ‘ B N ’ denotes net thickness as per ASTM E 1820-13. = √ ( / ) (5) According to ASTM E1820-13 standard, the plastic part of J can be calculated from plastic region ( A pl ) situated in the load-displacement curve as shown in the following equation, where ‘ η ’ is a dimensionless constant and ‘ b 0 ’ denotes the initial uncrack ligament length as per ASTM E 1820-13. = 0 , ℎ = 2+ 0.522 0 (6) After determining the J- Δa curve, considering a slope of , two exclusion lines have been drawn at different crack extensions of 0.15 mm and 1.5 mm respectively. Where denotes effective yield strength that is assessed by considering the mean value of yield and ultimate strength in a material. According to the ASTM E1820-13 standard, the value of ‘ M’ is 2. As J-R trends are numerous points, this requires regression to obtain the intersection point with the offset line. The regression is a power law in the form of = 1 ( ) 2 (7) where 1 and 2 are constants coefficient and exponent respectively for regressions and are not based on