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As a remedy, the use of a lowwork-hardened material, which has less accumulated plasticstrains and is characterised by a larger value of the work-hardening exponent n, may help to reduce this straightnessdeviation while the yield limit ofmaterial remains unchanged(Fig. 11). This is achieved by a reduction of permanent plas-tic strains produced in the edge zone especially after the laststation (Fig. 12).The material actually used in the experiment has a lowinitial yield limit of 238MPa. Suppose that the hardening prop-erties remain unchanged, and let us consider the use of ahigher initial yield limit of 600MPa; i.e. a high-strength mate-rial. Since high-yield materials produce more elastic strainscompared to low-yieldmaterials for a given total bending, theamount of springback is expected to be more important. Thisis in agreementwith our numerical prediction (Fig. 13).We alsonotice that, for high-strength steels, the value of maximumyield strength can be considerably higher than the nominalspecified minimum, and it can fluctuate from coil to coil oreven within a coil from the beginning to the end. The pre-diction of springback is hence more challenging. Finally, theamplitude of edge waviness induced by a high yield materialappears to be more important (Fig. 14).3.2. Inter-stand distancesPractical experiments ofmaterial forming hint that geometri-cal conditions have some significant impact on the formingprocess. For example, the thicker the material is, the lessspringback there is. Also, a larger bending radius leads to amore important compression and stretching area. This alsoincreases the springback. Such universal guides appear to bealso applicable for cold-roll-forming.In the following, our attention is particularly paid to inves-tigate the impact of inter-stand distances, which is a specificfeature of cold-roll-forming. An increase of inter-distancesbetween stations leads to a longer distance between the firstand the last stations in the roll-forming line.More progressivedeformation is allowed to develop in the sheet flange. As aresult, a higher recovery of strain is obtained and permanentplastic strain created at edge can thus be reduced (Fig. 15).However, the springback remains unchanged (Fig. 16).lengths.
3.3. Roll-sheet frictionRather than a forming action, friction at tool-sheet interfacesappears in the present process to be mainly used to trans-mit the driving power from the rotating rolls to the sheet.The numerical simulation turns out to support this argument,since the prediction of forming trajectory remains mostlyidentical for both cases with ( = 0.2) and without friction( =0) (Fig. 17).A recent numerical study of (Sheu, 2004) also shows thatthe effect of friction is found to be insignificant on the angledeviation of the U channel product; i.e. on the springbackangle. Moreover, reasonable numerical predictions on lon-gitudinal strains can still be achieved, while the friction isFig. 17 – Insignificant influence of friction on the formationof profile. completely neglected in the simulation as previously per-formed by Heislitz et al. (1996).From this result, if the attention is mainly paid to studythe formation of profiles rather than to estimate the powerrequirement for the roll-forming machine, friction can bedropped out for the sake of saving computational time.Besides, we also mention that an exact measurement of fric-tion coefficient between sheet and rolls is not a trivial task.3.4. Roll velocitySince the strip speed is rather moderate (for example0.0833m/s in the present experiment) in most cold-roll-forming operations, the proportion of kinetic energy is ratherinsignificant with respect to the total energy, which is mainlydominated by the strip bending. This gives a justification towhich the whole forming process can be considered as quasi-static and why it has been adopted so in the above numericalanalysis.Towards a more realistic simulation, let us perform adynamic analysis, using a Chung-Hulbert scheme (Chung andHulbert, 1993) as a time marching algorithm and where theadvancement of sheet is carried out through the rotation ofrolls. A friction coefficient of 0.2 is assumed at the sheet-rollinterface and an angular rotation, which leads to a strip speedabout 0.1m/s is imposed at the rolls. Under this condition,it is the friction force at sheet-roll interfaces that forces theadvance of the metal sheet in the roll-forming direction inthis dynamic analysis. In contrast, the sheet advancementwasobtained through an imposed displacement at the plane ofsymmetry of the sheet in the above static analysis.Numerical experiments show that there is almost no dif-ference between static and dynamic predictions (Fig. 18). Inthis regard, different velocity boundary conditions have beenalso tested in the work of Heislitz et al. (1996) such as (i)constant velocity at the sheet front end (ii) constant veloc-ity at sheet-roll interface. The predictions were quite close.Ultimately,