PSI - Issue 38

Martin Killmann et al. / Procedia Structural Integrity 38 (2022) 212–219 Author name / Structural Integrity Procedia 00 (2021) 000 – 000

216

5

The highest influence on the bending effect induced by the gaps is expected by the angle α , since it changes the lever distance to the critical areas. The distances a and b do not have any effect, as long as contact between die and reinforcement is prevented during all of the process. β and γ only influence the length of the transition between the gap and the prestressed area. While this is not critical for the overall stress state, too small values of γ might lead to high contact pressures at the transition. For the reasons given above, the stress state will be analysed depending on the angle α and the contact pressure on the outside with regard to the angle γ . As the interference fit between die and reinforcement should influence the effectiveness of gaps, the analysis will be conducted for interferences of 3‰ an d 9‰. While these values are among the lowest and highest interferences used in praxis , interferences of 9‰ are only possible with the use of expensive special tools such as strip-wound reinforcements. One gap is inserted at each critical area. This means, that there is a gap located both at the upper and the lower end of the major axis for the elliptical geometry. The other geometry has four gaps in total, one per functional element. The stress state depending on the angle α is analysed regarding both the highest compressive prestresses and the tensile stresses induced due to the bending effect. The critical stress state at the end of the process is also analysed for both geometries and interference fits and compared to the values of the reference variants without gaps. The results are summarized in Fig. 5. It should be noted, that the angle α describes only half of the gap as seen in Fig. 4. The total gap angle would be given by 2 α .

Max. compressive stress Prestress

Max. tensile stress Process end critical area

Max. tensile stress Prestress

-2500 -2000 -1500 -1000 MPa 0 -5000 -4500 -4000 MPa -3000 0

1000 1500 MPa 2500

1000 1500 MPa 2500

3‰ 9 ‰

σ t

0 500

0 500

-2500 -2000 -1500 -1000 MPa 0

1000 1500 MPa 2500

σ t

0 500

15 20 25 ° 35

15 20 25 ° 35

15 20 25 ° 35

α

α

α

Angle α

α

Elliptical

5

Functional elements

β γ a b

7,5

Prestress Process end

0.2 mm 0.1 mm

Reference w/o gaps

Fig. 5: Stress state depending on the gap angle α

For dies without gaps, the stress state in the critical area varies between a compressive prestress and tensile stresses or residual compressive stresses at process end depending on the interference fits. Gaps aim to increase the prestress in order to achieve lower tensile stresses at process end. This is achieved by gap angles between α = 20° and α = 30°