PSI - Issue 22

N. Makhutov et al. / Procedia Structural Integrity 22 (2019) 93–101 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

94 2

Nomenclature E – elasticity modulus F – correction function in generalized Neuber rule

K ε – strain concentration factor K σ – stress concentration factor K t – theoretical (elastic) stress concentration factor m – strain hardening exponent ε f – fracture strain ε lp – limited plastic strain ε n – nominal strain ε max – maxim local strain at the notch root ε e-f – pseudoelastic (fictitious) strains at the notch root ε p -f – pseudoplastic (fictitious plastic) strains at the notch root ε Y – yield strain

σ max – maxim local stress at the notch root (maximum notch stress) σ e -f – pseudoelastic (fictitious elastic) stresses at the notch root σ p -f – pseudoplastic (fictitious plastic) stresses at the notch root σ n – nominal stress σ n norm – nominal stress due to normal loading σ n extr – nominal stress due to extreme loading σ Y – yield stress Φ – transformation that maps pseudoelastic or pseudoplastic states to actual stress-strain states at the notch zone

Φ N – Neuber transformation Φ M – Makhutov transformation

Until material at the notch root remains elastic, theoretical stress concentration factor K t relates nominal stresses σ n and strains ε n to the maximum local values of stresses σ max and strains ε max at the notch root (Bannantine et al, 1990;. Manson and Halford, 2006):

,

K





t n 

max

(1)

.

K





t n 

max

Values of K t for a variety of notched components are readily available and particularly useful for brittle materials in order to predict the peak stresses. For increasing nominal stresses K t remains constant until yielding begins. For ductile materials, the local region of high stress is relieved as yielding occurs and the maximum stress is no longer equal to K t multiplied by the nominal stress. Upon yielding, local stresses and local strains are no longer linearly dependent. A power law approximation of strain hardening can be used to describe stress-strain relationship in plastic region:

max max m K    ,

(2)

where K and m are material constants. After yielding occurs, local values of stresses and strains are no longer related to the nominal values by K t . In plastic region nominal and local values of stresses and strains are related in terms of stress and strain concentration factors:

K







max

n



max Y   

(3)

for

.

K





n 

max

