PSI - Issue 7

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

233

5

Table 1. Data used for Fig. 4.

H V [Kg/mm 2 ]

∆ K dR eq. (1) [MPa m 1/2 ]

∆ K dR , eq. (7) [MPa m 1/2 ]

d [ µ m]

∆σ eR [MPa]

Steel

Reference

S10C S10C S10C S10C S20C S20C S20C S20C S15C S15C S15C S35C S35C S35C S55C S55C S55C S55C S45C SNC21 SNC21

15.9

470 495 530 350 480 520 490 460 630 680 364 362 330 442 382 388 548 510 388 432 430

445 355 399 347 444 483 470 442 472 437 175 175 273 185 247 252 239 228 213 254 241

2.16 3.12 4.32 3.82 1.98 3.14 3.97 4.75 2.51 3.91 1.92 2.73 4.09 1.44 2.24 3.66 1.41 1.44 2.45 1.22 1.85

2.57 2.72 3.50 3.91 2.41 3.24 3.93 4.51 2.45 2.93 1.71 2.02 3.61 1.46 2.12 2.83 1.47 1.49 2.03 1.55 1.80

Kunio et al (1979)

30 50

“ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “

89.9 12.8 27.4 49.5 80.4

12

24.9

21 43

Kunio et al (1984)

116

8

26 67

5 6

30

6

14

Tokaji et al (1988)

( The threshold ∆ K th for small cracks and defects have been estimated by many researchers using the well know Murakami model that uses the area 1/2 parameter and the Vickers hardness. Murakami and Endo (1994) proposed, based on threshold data for crack growth of specimens containing artificial defects that range from 40 to 500 µ m, the following expression to estimate ∆ K th for surface cracks and R = -1: (8) Where area 1/2 is in µ m. It is preferred here to define the size of the crack by its depths a , and assuming that the surface crack is semicircular, the following relation holds: (9) With expressions (8) and (9) we obtain the following one to estimate ∆ K th as a function of crack length: (10) Let analyze the data reported by Tokaji et al (1988) for a ferritic-pearlitic S45C steel: H V = 241 kg/mm 2 , σ u = 621 MPa (tensile strength), d = 14 µ m and ∆σ eR = 430 MPa for R = -1. Besides, we consider ∆ K thR = 10 MPa m 1/2 , a conservative value for R = -1 for H V and σ u given by Tokaji and Ogawa (see, for instance, Chapetti (2011)). Expression (1) estimates a value of ∆ K dR equal to 1.8 MPa m 1/2 , near the value given by expression (1.85 MPa m 1/2 ). On the other hand, the estimation given by the Murakami model, expression (10), gives 3.1 MPa m 1/2 for a = d , around 68% higher. Fig. 5 shows the threshold curves given by expressions (5) and (10), where we can appreciate the advantage of using expressions (1) and (5) to estimate ∆ K th . Many researchers applied the Murakami model without taking care of the limitation of expression (10) associated to the propagation threshold for long cracks ∆ K thR , which is a material constant for a given stress ratio R, independent of the crack length. If this limitation is not considered, important overestimations for relatively high hardness values and relatively long crack lengths are obtained. ) ( ) 3 1 3 120 3.3 10 area H K ∆ = × V th + − ( ) 3 1 a 3 120 3.56 10 H K ∆ = × V th + − a area 2 π =