This is in contrast with the numeri-cal results from Hong et al. (2001), where a good agreementbetween the simulation and the experiment was found in sta-tion 1, whereas there were increasing errors in stations 2 and3.Notice that the present simulation has been performedwith a full 3D finite elementmodel (8-node EAS brick elementsBui et al. (2001)),whereas the computation strategy adopted byHong et al. (2001) was rather a combination of 2D–3D analysis.Moreover, the material behaviour has been described by anelastic–plastic model in our simulation, while a rigid-plasticmodel was employed in the study of Hong et al. (2001).As we may observe, the longitudinal strain at first standquickly rises and then it reaches a peak before the particlepasses the roll axis (located at position 487mm). Afterwards,the longitudinal strain goes down due to springback—a phe-nomenon that cannot be correctly simulated by a rigid-plasticmodel. Before reaching the plastic yield, themaximumelasticstrain of the material is around 0.11%. Since the longitudi-nal strain in the sheet is clearly above this elastic limit, theFig. 3 – Development of longitudinal strain at a distance1.5mm away from the strip edge. occurrence of plastic longitudinal strain at the strip edge isinevitable (Fig. 4). Indeed, the existence of a permanent defor-mation (around±0.5%) after being fully formed is numericallydetected (Fig. 3). Once it has been plastically deformed, itis more difficult to compress the thin metal edge back to astraight section without buckling. This inevitably leads to awavy edge as it can be detected from the simulation (Fig. 5).Let us consider the vertical displacement of a point located1.5mmfromthe edgewhen itmoves fromthe first station (30◦)to the second station (60◦). The verticalmovement of this pointgives an idea about the forming action (Fig. 6). The numericalprediction is quite close to the experimental data extractedfrom Hong et al. (2001).Roughly speaking, the bending action takes place in alocalised region that plays the roles of a plastic hinge andthe flange “rotates” about this zone. The change of directionof a line segment on the flange in comparison with the hor-izontal plan represents the forming angle. The latter is notalways increasing during the roll-form process as our numer-ical results show (Fig. 7).As a result, an amount of springback is recorded after thebending action is completed in the third roll set (90◦). It isthe residual elastic zone in the middle of the sheet section that allows the sheet to recover, at least partially, from thedeformed shape.Actually, the deformed flange is however not quite “flat” asit is detected fromthe simulation (Fig. 8), which exhibits somecurvature along the vertical wall. Such a deformed geometryis rather close to the experimental observation Heislitz et al.(1996). As one might observe, the number of passes in this case israther limited. Hence, too much forming is done per stand fora given final geometry. Under this condition, practical experi-ences hint that end flare—the outward turn of the front endcan occur. The simulation is in agreement with this experi-ment (Figs. 4 and 9).Finally, bow or the deviation froma straight line in the ver-tical direction is also detected from the simulation. Precisely,the deviation can be either across the panel width – cross bow,or along the length of the panel – longitudinal bow. Since thesheet thickness is rather important (4mm), crossbow remainsrather moderate. In contrast, some significant amount of lon-gitudinal bow is detected (Fig. 10). 3. Parametric studiesAs one might observe, parameters, which may have someinfluence on the roll-forming process are multiple. Nonlinearnumerical simulation and 3Dmodelling tools can thus be veryuseful to give a better insight of this complicated technologi-cal process. In the following, our attention is particularly paidto the elastic–plastic properties of the formed material, thehorizontal distance between stations, the friction at roll-sheetinterface and the rotation speed of the rolls.3.1. Material propertiesAsmentioned above, waviness is formed due to the importantplastic deformation at the edges. 冷弯成形过程的数值模拟英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_54806.html