PSI - Issue 12

Massimiliano Avalle et al. / Procedia Structural Integrity 12 (2018) 130–144 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

141

12

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

2500

1000 Average axial force, F a (N) 1500 2000

Average axial force, F a (N)

0.15 0.3 0.45 0.6

500

0

0

0.5

1

1.5

2

0

0.5

1

1.5

2

Tube thickness, t (mm)

Tube thickness, t (mm)

(b)

(a)

Fig. 8. Effect of the tube thickness on the expansion of the cupronickel tubes: a) numerical results obtained with four different values of the friction coefficient f ; b) experimental results.

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

t / dᵢ =0.02 t / dᵢ =0.04 t / dᵢ =0.06 t / dᵢ =0.08 t / dᵢ =0.1

i / dᵢ =0.02 i / dᵢ =0.04 i / dᵢ =0.06 i / dᵢ =0.08 i / dᵢ =0.1

Normalized axial expansion force

Normalized axial expansion force

0

0.02 0.04 0.06 0.08 0.1

0

0.02 0.04 0.06 0.08 0.1 Interference/diameter ratio, i / dᵢ

Thickness/diameter ratio, t / dᵢ

(a)

(b)

Fig. 9. Effect on the normalized axial expansion force: (a) of the thickness over the internal diameter ratio ( t / d i ), and (b) of the interference over the internal diameter ratio ( i / d i ).

It appears that both the normalized parameters have an almost linear influence on the normalized force. It can be not obvious that the effect of the interference does not decrease to zero when the interference itself decreases down to zero or near zero. But it should be noted that the force computed by Eq. (6) corresponds to a fully yielded section where a certain interference is required to bring the whole material to plastic flow. An estimate of the minimum interference able to fully yield the section can be obtained with the following expression:

         E S y

  

d i

  

(7)

  1 1 1

i