A COMPARISON OF ASYMPTOTIC AND NUMERICAL ROLLING MODELS FOR QUASI-3-DIMENSIONAL PROBLEMS

This study compares two quasi-three-dimensional steady-state rolling m odels. The validity of both models assumes that the ratio of strip hal f-thickness to contact length is small. Thickness to length ratios les s than 0.3 are acceptable, and sometimes the models work well beyond t his limit. One model is a finite element calculation which uses one la yer of elements through the strip half-thickness. The other is an asym ptotic approach which includes both first- and second-order terms. For this study, both models use the relative slip friction model at the r oll/sheet interface and a hyperbolic sine constitutive relationship be tween stress and strain rate. An important feature of the solution is that it is very sensitive to the spread. Small changes in spread often lead to significant changes in stresses. The predicted spreads are al ways small and their magnitudes are typical of those found in practice . However, the spreads found by the models do not always agree. Result s show that when the entry and exit forces for the two models coincide , the stress distributions in the roll bite are in good agreement,