PSI - Issue 23

Sergiy Kotrechko et al. / Procedia Structural Integrity 23 (2019) 413–418 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

415

3

where c e is the critical value of equivalent strain, corresponding to the maximum CN density; a and b are the coefficients; max e is the maximum strain in approximation dependence (for ferritic steels typically 0 02 c .  e ; 13 3 1 498 10 m    . a ; 13 3 0 124 10 m    . b ); 0 3 0 5 . . max   e .       y     1 c 0 exp (3)  and c  are the coefficients which determined by a calibration procedure (typical values can reach : 0 01 0 04 . .   MPа 1  ;   13 3 c 1 8 10 m      ); Y  is the thermal component of shear stress:   C C T C T e  ln . exp 3 2 1 Y 0 5    (4)

1

1 3 0 000415 K   . C .



  . C

0 0068 K

1033 1  C MPа;

e  is the plastic strain rate; for ferrite steels typically:

;

2

th  is the minimum stress of cleavage fracture. The crack nuclei have microscopic sizes, so,

The threshold stress

they become unstable under the action of tensile microstresses . According to Kotrechko (2013):

11 1 3 c   I min

  

(5)

th

where min c  is the stress corresponding to crack nucleus instability of maximum length, which is most favourably oriented relatively to the direction of normal stresses; 11  I is the coefficient of variation of tensile microstresses 11  (for iron and ferritic steels under tension 0 13 11 .   I ); the coefficient «3» before 11  I means that th  is determined with a probability of 0.997. The idea of experimental determination of the threshold stress magnitude is based on the use of a statistical scale effect for the cleavage stress. This effect manifests itself the tendency of the cleavage stress value f  to approach the level of threshold stress with increasing specimen volume (Fig. 1). The relatively high density of the crack nuclei formed in the iron and structural steels ( 13 10  m -3 ) gives rise to the fact that starting from rather small volumes (  500 mm 3 ) the value of f  slightly (up to 20%) exceeds the threshold level th  . For experimental determination of th  , this enables utilisation of the minimum of the cleavage fracture stress (brittle strength) MC R of standard specimens at uniaxial tension within the temperature range of the ductile to-brittle transition (Fig. 2). Unfortunately, ductile-to-brittle transition range for typical structural steels lies below the nitrogen boiling point (-196 °C ). This means some methodological difficulties at experimental determination of MC R . In this meaning, a method for determining the value of brittle strength, MC R , was developed for structural steels by testing cylindrical specimens with an circumferential notch. The parameters of the notched specimen were experimentally ascertained (the maximum diameter is 8 mm, minimum - 5.2 mm, notch root radius - 2 mm), at which the nominal fracture stress for this particular specimen geometry at 2% average strain in the minimal cross-section is equal to MC R with an accuracy of  4%. Figure 1. Scale effect at cleavage fracture of iron: MC R is the brittle strength, th  is the threshold stress: circles designate the computer simulation findings 0,01 1 100 10000 1000000 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0  th Critical fracture stress,  f / R MC (-) Volume, V ( mm 3 ) R MC V 0 - volume of standard tensile specimen