*2.2. Principal Forming Zone*

Depending on the partial heating temperature of the profile, a deviation of the forming zone position from the counter roll position is possible. The forming zone is at the position the bending moment in the profile first surpasses a threshold bending moment. At room temperature (*T* = *T*RT), the flow stress for forming is higher than in the heated case (*T*heat) (Figure 4a). The flow stress results in a threshold bending moment that is necessary to achieve a bending radius of *r*<sup>m</sup> (Figure 4b). One area of the profile is at room temperature (*T*RT) while the other is at heated temperature (*T*heat) for the partially heated profile. As the bending moment is an integral behavior demonstrated over the cross-section geometry, the threshold moment is decreased for a partially heated profile compared to a profile that is at room temperature. This results in the formation taking place at the counter roll position for the room temperature case. Partial heating for this process does not take place directly under the counter roll, but at a position *x* = *l*heat due to technical limitations. As the threshold bending moment is decreased between *x* = *l*heat and *x* = *l*cool, plasticity would not necessarily start at the counter roll. If the threshold moment for the heated area is reached, plasticity starts in the heated zone (*x* = *l*heat). The position at which plasticity starts *x = l*<sup>p</sup> is consequently either the position of the counter roll *(l*<sup>p</sup> = 0) or the position of the heated area (*l*<sup>p</sup> = *l*heat). The position of the forming zone is dependent on the amount of flow stress reduction and the position of the heated area.

**Figure 4.** (**a**) Resulting flow stress *k*<sup>f</sup> to bend a profile to the desired radius *r*m, (**b**) necessary bending moment to reach the desired radius and actual profile bending moment for room temperature (*M*b (*T*RT)) and partial heated case (*M*b (*T*h)).
