Metal Forming and the Finite-Element Method

Abstract

The application of computer-aided design and manufacturing techniques is becoming essential in modern metal-forming technology. Thus process modeling for the determination of deformation mechanics has been a major concern in research . In light of these developments, the finite element method--a technique by which an object is decomposed into pieces and treated as isolated, interacting sections--has steadily assumed increased importance. This volume addresses advances in modern metal-forming technology, computer-aided design and engineering, and the finite element method.

Finite element modeling of thermal and mechanical stresses in work-rolls of warm strip rolling process

“…In the above equation, k is the shear yield stress of the strip material, and a is a positive constant of the order 10 −3 –10 −4 , according to Kobayashi et al 24 It should be noted that the sticking friction coefficient in this work was taken to be 0.45, 7 which was shown to be a rather reasonable value in high-temperature rolling operations. 1…”

“…A plane-strain FE model was used to evaluate the mechanical response of the strip in the deformation zone, assuming a rigid visco-plastic material behavior for the rolled strip. The velocity distribution within the deformation zone can be computed based on the following minimization 24…”

“…where σ ¯ and true ε ¯ . are flow stress and equivalent strain rate, respectively; ε · v is the volumetric strain rate; F i is the traction force; v i is the nodal velocity vector; V and S represent volume and interface boundary of the deforming body, respectively; and K is an arbitrary large positive number known as the penalty constant. 24 Note that the flow stress of the material in the deformation zone was obtained using a simple “power-law” equation as…”

Finite-element modeling of thermal aspects in high speed cold strip rolling

“…Note that v r in this equation is the relative surface velocity between the work-roll and the strip, while the frictional stress, τ , is calculated as 30…”

“…Sticking friction coefficient, m fric , was determined using the mathematical models provided by McConnell and Lenard, 31 described in detail in the following section; a is a positive constant of the order of 10 −3 –10 −4 . 30…”