PSI - Issue 22

Meng-Fei Hao et al. / Procedia Structural Integrity 22 (2019) 78–83 Meng-Fei Hao et al. / Structural Integrity Procedia 00 (2019) 000 – 000

80

3

∆ 2 = √( ∆ 2 ) 2 + 1 3 ( ∆ 2 ) 2 = ∆ 2

(2) Then, the equivalent stress can be modified by introducing a weight function to account for the mean stress effects, Eq. (2) can then be rewritten as: ∆ ′ 2 = √ ( ∆ 2 ) 2 + ( ∆ 2 ) 2 (3) and = (1 − , ′ ) (4) = 1 3 , ′ (5) where ν is the Possion’s ratio , , .is the maximum normal stress in the maximum shear strain plane, which can reflect the effect of mean stress. Under pure tensional loadings, an equivalent strain energy-based damage parameter can be derived by combining the equivalent strain and corrected equivalent stress as follows: ∆ 4 = ∆ 2 ∆ ′ 2 = ′ 2 (2 ) 2 0 + ′ ′ (2 ) 0 + 0 (6) 3 Model validation and comparison Using experimental data of TC4, GH4169, and Al 7050-T7451 alloys [15-17], the proposed model as well as four other models are assessed and verified. Material and mechanical properties of the three alloys are listed in Tables 1 3, respectively. Due to limited data of Al 7050-T7451 alloys, its torsional performance can be obtained from uniaxial properties according to the von Mises' criterion in Eq. (7) [18]. ′ = ′ √3 ; ′ = √3 ′ ; 0 = ; 0 = (7) Table 1 Material properties for TC4 alloy [15]

G (GPa) 43.2 b -0.049 ′ 0.579 942.5

0.25

E (GPa) 108.4

(MPa)

K (MPa) 1054 ′ (MPa) 1031

n 0.0195 ′ 0.0478 0 ′ 0.016

Monotonic Uniaxial ′ Torsional ′

c -0.679

(MPa)

1116.9 (MPa) 716.9 0 -0. 6 ′ 2.24 0 -0.8 0 ′

(MPa)

446.7

Table 2 Material properties for GH4169 alloy at 650 ᵒ C [16]

0.48 c -0.63

G (GPa) 67 b -0.06

K (MPa) 1079.7

E (GPa) 198.5

n 0.06

(MPa)

Monotonic

1083.1

′ (MPa) 1892.3 ′ 1047.1

Uniaxial ′ (MPa) 1815.5 Torsional ′ (MPa)

′ 0.45

0.078

1091.6 0 -0. 7 ′ 4.46 0 -0.77 0 ′ (MPa)

0 ′ 0.099