If this process is limited to the elastic domainof the material, the strain and stretching will return to theoriginal length, as the profile leaves the stand. On the otherhand, if the stress in the edge has exceeded the yield pointbetween two bending steps, a permanent strain is induced inthe material. This leads to problems like waviness, twist orother unwanted deformations of the profile. Based on exper-imental results available in the open literature (Kiuchi, 1973),our simulation is performed. The reliability of the simulationis judged through a comparison with experimental results onthe distribution of longitudinal strains.Attention is also paid to the identification of forming prob-lems likely to happen. In this regard, one of the importantissues is springback. Being the shape discrepancy between thefully loaded (sheet and tools in full contacts) and unloadedconfigurations (removal of forming tools), springback occursafter the formed part exits the roll-forming stations. Highstrength steels have amore pronounced springback thanmildsteels, since high strength materials are less ductile. Given aconfiguration of forming stations and the geometry of formingprofiles, the total number of bends, the sequence of bendingangles, the bend radius of the exit section and the condition ofentrance, the material properties have a direct impact on thedeformation and hence on the formability of the sheets. Thespringback trend in connection with different yield strengthsand work-hardening capacity will also be numerically inves-tigated.Finally, the computation time of a 3D analysis should besignificantly reduced to react more efficiently on complexindustrial demands. A study of the product related set-up offinite element analysis strategies such as friction at sheet-roll interfaces, rotation speed of rolls is necessary in order toreduce the computational effort, improve the robustness andconsolidate the accuracy of the simulation.2. Modelling and simulation of aroll-forming line2.1. Experimental set-up descriptionLet us consider the roll-forming process of a U-profile, whichwas experimentally studied by Damm (1989) and numericallymodelled elsewhere Heislitz et al. (1996) and Hong et al. (2001).The forming line is composed of 3 stations, and the bendingsequence is 30◦,60◦, and 90◦ (Fig. 1). The sheet has an initialthickness of 4mm and a width of 236mm. The mechanical behaviour of the sheet material used inthe experiment can be described by the Swift’s isotropic strainhardening law as also used in Heislitz et al. (1996): v = K(ε0 + εp)nwhere  v is the flow stress; εp the plastic strain; K = 617.2MPathe hardening coefficient, ε0 = 0.001292 the offset strain andn = 0.143 is the hardening exponent. The Young’smodulus andthe Poisson’s ratio are respectively E = 210GPa and   = 0.3. Thiscorresponds to an initial yield stress of 238MPa and a maxi-mum elastic strain; i.e. before entering the plastic domain ofabout 0.11%.2.2. Numerical simulationFrom the observation on the development of longitudinalstrains during the experiment extracted from Hong et al.(2001), the inter-stand distance is 585mm in our simulation.A sheet 1200mm long has been analysed in our model.The in-house finite element code Metafor (Ponthot, 1995)has been used for all simulations. The elastic–plastic consti-tutive law has been integrated according to Ponthot (2002).In order to better capture the bending behaviour, 8-nodesenhanced assumed strain (EAS) elements as described in Buiet al. (2001) have been used.Due to the symmetry, only a half of the structure has beenmodelled (Fig. 2). The mesh consists of 4560 (240×19×1) ele-ments. Mesh refinement has been made in the folding zone,where an important amount of plastic flow is expected. Thedie rolls have been supposed to be perfectly rigid and theircircular geometry has been exactly taken into account (nodiscretization of the rigid tools).The contact condition between the sheet and the rolls isenforced by the penalty method and a sufficiently high valueof penalty parameter, i.e.   = 1.E5N/mmis adopted. In order toadvance the sheet into the roll-forming direction, a displace-ment is imposed along the plane of symmetry of the sheet.A Coulomb friction model with a coefficient of friction  = 0.2,as suggested by Hong et al. (2001), is assumed at the interfacebetween the sheet and the rolls.2.3. Results and discussionsThe development of longitudinal strains measured along astreamline 1.5mm away from the strip edge (see Fig. 2)isrecorded for the sake of comparison. For all the stations,our simulation is generally in a fairly good agreement withthe experiment (Fig. 3). 冷弯成形过程的数值模拟英文文献和中文翻译(2):http://www.youerw.com/fanyi/lunwen_54806.html