PSI - Issue 58

A. Chiocca et al. / Procedia Structural Integrity 58 (2024) 35–41

39 5

A. Chiocca et al. / Structural Integrity Procedia 00 (2024) 000–000

(a)

100

( i )

∆ γ 2

∆ γ

σ i + 1

2 ( ¯ ω )

π 2 )

n , max ( ±

(c)

τ i + 1

σ i + 1

∆ γ max 2

τ i

σ i

∆ ε

σ i

50

π 2 )

n , max ( ±

+ π 2

F (kN)

0

+ ¯ ω − ¯ ω

σ i

( i + 1)

σ i + 1

∆ ε

− 50

− π 2

Load step n.

σ i

n , max ( ± ¯ ω )

σ i + 1

n , max ( ± ¯ ω )

Coincident eigenvalues

Coincident eigenvalues

Coincident eigenvalues

(b)

(d)

F

2 · 10 − 3

2 · 10 − 3

FS (-)

FS (-)

0

0

Node

1

1

0

0

ψ

ψ

2

2

− 1

− 1

0

θ

0

θ

FS ( θ,ψ )

Infinite critical planes

F

Fig. 3. Loading history (a), specimen (b), Mohr’s circle representation of di ff erent tensors (c) and comparison between the plane scanning method and the e ffi cient methods (d) for a tensile loaded component.

(a)

100 200

∆ γ

2 ( ¯ ω )

∆ γ 2

( i )

(c)

τ i

τ i + 1

σ i + 1

σ i

∆ ε

∆ γ max 2

+ π 2

− 200 − 100 0

σ i + 1

π 2 )

n , max ( ±

σ i

π 2 )

n , max ( ±

M (Nm)

+ ¯ ω − ¯ ω

σ i

σ i + 1

∆ ε

( i + 1)

− π 2

σ i

i + 1 n , max ( ± ¯ ω )

n , max ( ± ¯ ω )

σ

Load step n.

(b)

M

(d)

0 2 4 · 10 − 3

0 2 4 · 10 − 3

FS (-)

FS (-)

Node

2

2

0

0

ψ

ψ

− 2

− 2

0

0

θ

θ

FS ( θ,ψ ) FS closed form ( + ¯ ω )

FS closed form ( − ¯ ω ) Conjugate planes

M

Fig. 4. Loading history (a), specimen (b), Mohr’s circle representation of di ff erent tensors (c) and comparison between the plane scanning method and the e ffi cient methods (d) for a fully reversed torsion loaded component.