Bending of pipe, tube, or extruded shapes involves practices and theories of the simple supported beam, the cantilever beam, and many of the problems of forming and deep drawing. Although the theories may become quite complete, the concept of tension stresses in the outside of the bend and compression of the inside surface is common to all bending, regardless of the method.
Bending produces a physical deformation of the material and since the flow of metal occurs in the plastic range, there is a permanent change in shape. Thinning of the outer wall of a bent tube or other hollow section and corresponding thickening of the inner wall of the bent tube are noticeable effects of plastic flow.
The plastic flow of metal introduces complex interrelated changes in structure, and its range is so critical and so limited that greatest care is necessary to preserve adequate physical characteristics in the material. The forming of metals is complicated in that different materials have unlike value of yield and ultimate strength and these are again changed by heat-treatment.
These facts make evident the need for accurate and strong, correctly designed equipment for forming. The tool must control the flow of material throughout the critical period. During work within the limited plastic range, a jerky start or uneven pull during bending may cause overstressing of material to the point of fracture.
ADVERTISEMENTS:
Another interesting occurrence which is universal on all, whether of hollow or of solid section, is the displacement of the neutral axis. This phenomenon is best shown by hollow section, as in Fig. 6.31. It is easy to prove mathematically that the location of the neutral axis of any cross section of a homogeneous material coincides with the centre of gravity of that cross section.
The examination of the cross section of a bent tube will reveal that the inside wall has become thicker and the outside wall thinner. Thus, the centre of gravity of the section has moved, with the redistribution of the weight, toward the inside of bend, and with it has moved the neutral axis.
This fact becomes important in determining the bendability of a thin-walled hollow section, since the relocation of the neutral axis means that the outside wall stretches more than the inside wall compresses. With reference to Fig. 6.32, the neutral axis CC is properly shown inside the bent material’s physical centre line.
ADVERTISEMENTS:
Measurement shows that the difference between the arcs AA and CC is greater than that between CC and BB, hence the ductility of the metal must be sufficient to provide the maximum stretch. In practice, the movement of the neutral axis varies from 5 per cent of the material width or diameter, for heavy sections bent to large radii, to approximately 25 per cent, for very light sections bent to very small radii.
Total stretch (difference between AA and CC) is not evenly distributed throughout the length AA. Actually, there is little stretch near the beginning and end of the bend; hence there must be more in middle section. An average of many tests shows this increased stretch to be 30 per cent greater than the calculated average elongation.
Many times, undue concern is felt about the thinning of the outside wall in cold bending. This thinning effect does not necessarily weaken the structure as bent, for it is an established fact that cold working is used extensively to harden and strengthen metals.
ADVERTISEMENTS:
Within practical limits, the stretched and work-hardened outside of a hollow section resulting from cold bending will have greater strength than the same material before bending. Of course, this effect will not persist if annealing is necessary after bending.
The graphs of Fig. 6.33 are the results of actual tests made op short radius bends, where the stretch of the outside wall is considerably more than average. It may be noted that curve 4 (per cent change in strength) shows a 30 to 35 per cent increase in strength in the outside wall after bending, although the wall was thinned 25 per cent. To substantiate further the work-hardening effect, bursting tests have been made, with the resulting failure being in the tangent outside the bend area.
