TPT January 2007

If the comparative strain for the entire forming process is summed up, the result is a measure of the strain history of a certain node. This can be taken as a qualitative measure of work hardening on this node 4 . Figure 12 shows the pattern of work hardening (TEPS) over the circumference in the final state of the formed tube (red curve). This pattern is very similar to that for wall thickness in the final state of the tube (blue curve).

› Figure 9 : Pattern of wall thickness versus circumference as a function of pass number

The tool set for this purpose was designed in Copra RF and the entire initial forming simulated. The simulated pattern of the wall thickness of the coil versus circumference as a function of the pass number is shown in the above diagram (figure 9). Three extreme values of wall thickness appear. They are in the region of the plane of symmetry (Max 1), in the region of the strip edge (Max 3) and at approximately 90°. In this diagram, it is evident that all three extremes are formed in stands 16 and 17. These are fin passes, which apply heavy compression to the metal strip. Calculation of work hardening The value of total equivalent plastic strain (TEPS) is used to calculate work hardening. This value is the sum of the comparative logarithmic plastic strain values over the entire forming process, and consequently exhibits a monotonically increasing pattern.

‹ Figure 12 : Pattern of wall thickness (blue curve) and work hardening (red curve) over circumference; final state of tube

The patterns of wall thickness distribution and TEPS, each in the final state of the tube, both exhibit maxima at approximately 92° and 180°. The wall thickness shows a further maximum at 14°, which may not be so conspicuous for TEPS but is nevertheless recognisable. From this it can be concluded that zones of high work hardening may be expected in the ready profile (tube) at approximately 15°, 90° and on the strip edge (180°) 4 . An element in the refined region in stand 17, where the wall shows the largest increase in thickness (fin pass), exhibits the following stress condition (figure 13):

inside

› Figure 10 : Total equivalent plastic strain (TEPS) values at the entry to the first fin pass. A huge amount of calibration and forming work is being applied

outside

fi Figure 11 : Total equivalent plastic strain as a measure of work hardening

› Figure 13 : Increase in wall thickness at 90°

Longitudinal Strain total plastic strain component: logarithmic plastic strain value in one direction real strain: cannot indicate work hardening history of material Example:

Work Hardening total equivalent plastic strain: comparative logarithmic plastic strain value scalar value! Strain values are added unsigned Example:

The comparative stresses are calculated as follows:

б v _tresca_inside = | -430 N/mm 2 – 82 N/mm 2 | = 512N/mm 2

and б v _tresca_outside = | -126N/mm 2 – 215N/mm 2 | = 341N/mm 2 Both comparative stresses exceed the yield point. The wall can be expected to thin on the outside, but the inside will thicken. The value of the strain on the inside exceeds that on the outside, so here the wall will thicken overall. These findings are confirmed by practical observations.

z

tpsc 33 = 0

teps = 0

t=0

t=0

tpsc 33 = -0,3

teps = 0,3

t=1

t=1

tpsc 33 = 0

teps = 0,6

t=2

t=2

117

J ANUARY /F EBRUARY 2007