PSI - Issue 68

Xiangnan Pan et al. / Procedia Structural Integrity 68 (2025) 1038–1044 X. Pan et al. / Structural Integrity Procedia 00 (2025) 000–000

1041

4

Fig. 1. Defect distributions (a,b) and microstructures (c,d) for an AMed Ti-6Al-4V without (a,c) and with (b,d) HIP.

3. One-cycle, high-cycle and very-high-cycle fatigue 3.1. Quantifications of quasi-static tensile curves

Tensile failure can be considered as one-cycle fatigue (OCF) at stress ratio R = 1 with stress amplitude σ a = 0 and mean stress σ m = σ u , i.e. the maximum stress σ max is equal to the UTS of the material tested (Pan and Hong, 2024c). The displacement, deformation, strain, stress and their interrelationships are the main topics of solid mechanics and have been well studied (Fung, 1965). We assume that the fatigue failure obeys the energy Eq. (1),

(1)

!

" # & ' (       = + $ " # % " # & ' ( & ' ( " "

" # & ' ('  

%

"

"

!

+

+

>

!

!

!

!

!

where σ m and σ a are the independent variables, N f is the failure cycle,

is the maximum energy the material can

! ! "

accommodate under this external load, E 1 , E 2 and are the input energies under the 1

st , 2 nd and N f

th cycles. While N f

"

! !

= 1, i.e. the tensile failure or OCF, Eq. (1) is rewritten as Eq. (2).

(2)

!

" ! # $%&

# $%& !

!

!

=

! "

According to the curve of engineering stress versus strain, Eq. (2) can be reformulated as Eq. (3),

!

" !

" "

$

$

$

#

!

! ! % &$'

% '() # ! ! # ! ! ! # # + = % '() % '()

!

=

(3)

$

$

!

!