PSI - Issue 65

A.N. Romanov / Procedia Structural Integrity 65 (2024) 200–208 A.N. Romanov / Structural Integrity Procedia 00 (2024) 000–000

202

3

each cycle separately in accordance with the deformation-kinetic Romanov’s (2007, 2020, 2021, 2022) criterion can be defined as follows in the form:

p 2

 

 0 N

 0 N

(1)





dN

dN







st 2



st

and, in the extreme case,

2 p

 

N

N

(2)





f

f

dN

dN

1





0 

0 

2 st



st

For the whole range of fatigue failure (low-cycle and multi-cycle fatigue), when the damaging effect from elastic deformation becomes significant, and in multi-cycle fatigue the damage is defined in the form:

st 2   

 0 N

 0 N

(3)





p ep

dN

dN









st

at breakdown

2 st   

N

N

(4)





f

f

p ep

dN

dN

1





0 

0 



st

With representation of the damaging role of elastic deformation, Eqs. (3) and (4) can be written in the form:

p 2

 

st 2    p e

 0 N

 0 N

N

(5)





dN

dN

dN







 

st 2



0

st

and at fracture

2 p

N

N

N

 

2 st    p e





f

f

f

(6)

dN

dN

dN

1



 



0 

0 

2 st



0

st

where ε р is plastic deformation in the half-cycle of stretching, ε ер is elastic-plastic deformation, ε е is elastic deformation equal to, and ε е = σ а / Е , ε st is deformation of a single static fracture corresponding to the true strength limit (resistance to tear-off) at the moment of loss of plastic deformation stability (Fig.1a), N is the current number of loading cycles, N f - number of cycles before fracture (formation and development of a crack to the limit value or loss of plastic deformation stability). Fig. 1, a shows the diagram of the static deformation of steel 22k at 2700C under conditional (curve 1) and true (curve 2) stresses. As shown in Fig. 1,a, the limit state (loss of plastic deformation stability) as a result of exhaustion of the bearing capacity (reaching the true strength limit) of the material is at the moment of brittle breakaway (Fig. 1,b). The ultimate deformation at this ε st = 29% (Fig.1,a). In Eq. (1) through (6), the design strain ε st corresponds to the deformation at the level of the true tensile strength (Fig. 1,a). The first term in Eqs. (5) and (6) defines damage from reversible plastic deformation (reversal of deformation occurs in a compression half-cycle), the second term refers to unilateral accumulation, and the third term reflects the damaging role of elastic deformation.