PSI - Issue 28

NikolayA. Makhutov et al. / Procedia Structural Integrity 28 (2020) 1347–1359 N.Makhutov, D.Reznikov / Structural Integrity Procedia 00 (2020) 000–000

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4. Assessment of the limit states in the notch zone As soon as the state of stresses and strains of the notched component subjected to high-speed low-temperature loading has been assessed, it is necessary to compare it with the limit state. If the strain based fracture criterion is applied, then the value of the equivalent strain at fracture e eq f under high-speed low-temperature loading should be estimated. Available experimental data (Makhutov, 1981; Makhutov, 2008; Makhutov, Matvienko, Romanov, 2018; Makhutov and Reznikov, 2018; Makhtov and Reznikov 2019a; Makhutov and Reznikov, 2019b; Yu and Jeong, 2010; Bao and Wierzbicki, 2004) allow us to conclude that the value depends on stress triaxiality: 0 eq f f e c D e e   , (28) where D ec is the plasticity reduction factor that characterizes the reduction of fracture strain when a the multiaxial stress state at the notch root occurs (D ec ≤1), e f0 is fracture strain under uniaxial tension. Stress triaxiality η is defined as the ratio of the hydrostatic pressure (or the mean stress) to the von Mises equivalent stress η= σ m /σ eqH .

1

;

(29)

0 f y e e e  0 f

ln

e



0

f

1





f



  2            2  2 1  2  2 3 3  c c c c  



2

triax eq f uniax eq f

e



1

1

1

(30)

eq c

e c D k 

k

k

k











D

D

D

D

1

e

I

 



 

2

3

m

c

c

c

2

3

c

c

triax eq f e and

uniax eq f e are equivalent strains at fracture for the cases of

where k D is the characteristic of the material,

uniaxial and triaxial states of stresses. Fig. 3 presents the results experiments (carried out on flat specimens and vessels) and calculations according to equations (30) various second principal stress 2  .

Fig. 3. Dependence of the plasticity reduction factor on the value of the second principal stress 1 - mean values; 2 - boundaries of scatter Then the value of the fracture strain in the notch zone may be estimated with accounting for the effects of the increase in the resistance to plastic strains I c and stress triaxiality D ec ,:

D I

(31)

e

e 

e c

maxo

o

f

f

c