PSI - Issue 14

Nikolay A.Makhutov et al. / Procedia Structural Integrity 14 (2019) 199–206 N.Makhutov et al./Procedia Structural Integrity 00 (2018) 000 – 000

202 4

K K

max     max / / k n k n





max k Y    .

for

(3)





Besides, in the plastic region local stress concentration factor K σ decreases with respect to K t and local strain concentration factor K ε increases as well (fig.2). For power law approximation of the stress-strain curve the following relation between maximum local stress and strain can be written:

E



 



max    k Y

for

(4)

k

k

max

max

m

max (     / ) k Y k Y max

max    k Y

for

.

(5)

Similar expressions can be written for nominal stresses and strains that describe the cases of nominally elastic and plastic behavior of the structural component:

E   

  

(6) (7)

for

n

n

n

Y

( / ) m

n Y n Y     

  

for

.

n

Y

The rearrangement of equations (5) and (7) gives the expression between K σ and K ε .

m

m n        Y

Y    

n Y    , max

Y    .

for

(8)

K K  

n

The concepts of pseudoelastic (fictitious) stress σ e-f and strain ε e-f fields are used in notch mechanics. They are calculated using methods of linear elasticity theory in the assumption that material at the notch zone deforms elastically when maximum local stresses accede to yield strength value:

K





t n 

e f 

n Y    .

(9)

, for

K





t n 

e f 

Similar concepts of pseudoplastic (fictitious) stresses σ p-f and strain ε p-f may also be introduced for approximation of notch stresses and strains when nominally plastic behavior according equation (7) is assumed:

K





t n 

p f 

n Y    .

,

for

(10)

K





t n 

p f 

Approximate analytical methods for assessment of stress-strain response in the notch zone are based on the following two types of equations: 1) Constitutive laws that relate maximum local stresses and strains in the stress concentration zone in the plastic region. For the case of monotonic loading a Ramberg-Osgud relation might be used:   1/ max max max m k k k E K      . (11) 2) Postulated expression (mapping, transformation) Φ that relates the values of elastic pseudo stresses and strains ( σ e-f ; ε e-f ) that are calculated by elasticity theory in the assumption that material in the notch zone is deformed