PSI - Issue 14

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

201

3

2. Key concepts and methods used in notch mechanics 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 σ maxk and ε maxk at the notch root (Bannantine et al, 1990;. Manson and Halford, 2006):

K

,





t n 

k

max

(1)

K

.





t n 

k

max

Fig.2. Relationship between K t , K σ , K ε

Fig.1. Stress strain conversion rules for different strain ranges 1 – Stress-strain curve, 2 – Pseudoelastic states; 3 – Pseudoplastic states; Φ N is a Neuber’s mapping according to (14) Φ M is a Makhutov mapping according to (20); I – range of elastic strains; II – range of limited plastic strains; III – range of extensive plastic strains

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 m   , k K



(2)

k

max

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: