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1. Introduction
Numerical analysis of forming processes has been a popular computational tool for new product development and industrial design. Various finite element software are commercially available and often used by metallurgical companies for bulk metal forming processes. The majority of that software is based on either static implicit method or dynamic explicit method.
In flat rolling, the product’s conditions (e.g. stress state, temperature profile, geometry, friction, etc.) are very often difficult to measure in each step of the process. Process parameters greatly influence the final product quality; therefore, they have to be very carefully studied. Understanding the nature, advantages and disadvantages of each algorithm is essential to ensure the accuracy, efficiency and robustness of the numerical simulation in the flat rolling process.
The static implicit method has been shown to work well for quasi-static metal forming processes as reported by many researchers (Gelin et al., 1995; Sun et al., 2000; Yang et al., 1995). Implicit algorithms allow working with larger time step size, as a set of equations must be solved repeatedly until a convergence criterion is satisfied for each time increment achieving higher accuracy. However, it is not favored by problems dominated by highly discontinuous non-linearities such as rapidly changing contact conditions, frictional sliding, local instabilities and non-linear time-dependent materials. A complex model leads to larger memory requirements and to a higher CPU cost, resulting in significantly increased computational time. Convergence difficulties may arise to such an extent that very small time increments and more iterations per increment are required, and in many cases a solution is difficult to obtain whatsoever (Van den Boogaard et al., 1998; Kacou and Parsons, 1993; Mahnken, 1995; Jefferson and Thomas, 1997; Ferencz and Hughes, 1998; Demarco and Dvorkin, 2001; Mocellin et al., 2001; Pauskar et al., 2004; Prior, 1994).
For these problems to be overcome, the dynamic explicit techniques were introduced. In the explicit method, the diagonal mass matrix is used to solve the equations of motion with so small time step that a stable solution is ensured (Prior, 1994; Mattiasson et al., 1991; Mercer et al., 1995). Unlike the implicit solution, the time increment is only influenced by element size and material properties and not by complex contact...