PSI - Issue 19

Ho Sung Kim / Procedia Structural Integrity 19 (2019) 472–481 Author name / Structural Integrity Procedia 00 (2019) 000–000

474

3

� = (� �� ) �� �(���) �� � ��� � �� � ��� − 1� + � or � = |� �� | �� �(���) �� � ��� � �� � ��� − 1� + � . These equations are invertible such that: ��� = �� � �(���)(� � �� � ) (� �� ) �� + 1� �� � � or | ��� | = | �� | � �(���)(� � �� � ) |� �� | �� + 1� �� � �

(3)

(4)

R = -1

N f =0.75 cycle

N f =0.25 cycle

R=χ

N f >0.25 cycle

N f <0.25 cycle

σ uT σ max

σ max = σ uT

σ min = σ uC σ mean =0

σ mean

0

σ min = σ uC

= N f =0.5cycle

�� + | �� | 2

=  ∞ N f =0.5cycle

| �� | σ uT

σ mean σ max = σ uT

σ mean σ max σ min

T-C

C-T

T-T

��

�� 0

C-C

�� − | �� | 2

0

Fig. 1. CFL diagrams for the first cycle CFL lines for �� > | �� | .

T-T or T-C loading

��

D f1(H) and N f1(H)

�� + | �� | 2

R rχ’

R =χ

N f1

D f1(L) and N f1(L)

ΔD f1 /ΔN f

a

R =-1

First cycle CFL line

R rχ

Log dD f /dN f

R r0’

D f2(H) and N f2(H)

R =0

N f2

R =  ∞

R r0

R r∞

R

ΔD f2 /ΔN f

R r∞’

a

Fatigue CFL/ N f 1 line

b

R =1

R r1T

R r0

R

R =1

b

R

R r1T

r1C

��

��

D f2(L) and N f2(L)

0

�� − | �� | 2

N f 2 line

Log σ max

(a) (b) Fig. 2. (a) schematic fatigue CFL lines for fatigue behaviour with various stress ratios for �� > | �� | ; (b) log ( dD f /dN f ) versus log σ max . The term N 0 in each equation is to adjust the initial number of cycles for the first cycle failure point. For example, N 0 =0.5 cycle at σ max = σ uT with R =0. The two parameters ( α and β ) can be numerically determined. 2.2 Characteristics of constant fatigue life (CFL) diagram