Mathematical modeling of plane-strain bending of sheet and plate

Effects of process variables on V-die bending process of steel sheet

Mathematical models for a fast semi-analytica simulation of the air bending process of thin as well as of thick sheets have been developed, implemented, and successfully been tested. In contrast to a large number of available approaches in this field that – for reasons of assuming the neutral fibre to coincide with the central fibre and the sheet thickness to remain constant – are limited to thin sheets, in the present work special attention has been paid to the mathematical description of the shift of individual fibres and the changes of thickness. The adequate modelling of these two effects is essential to ensure that the resulting simulation procedure is applicable in the same way to the bending of thin and, in particular, of thick sheets.The realistic mathematical modelling of the forming process, the accuracy of the results, and the very short computation times permission the simulation system to be used in production-related applications, such as CAPP systems, virtual prototyping environments, and m...

Semi-analytical process modelling and simulation of air bending:

An elasto-plastic incremental finite element computer code based on an updated Lagrangian formulation was developed to simulate the V-die coining bend process of sheet metal under the plane-strain condition. A modified Coulomb’s friction law was introduced to treat the alternation of the sliding–sticking state of friction at the contact interface. The r-minimum method was used to treat the elastic–plastic stress state and to solve contact problems at the tool–metal interface. V-bends of sheet metals are classified according to the number of contact points of the sheet with the bending die, and include air bends, bottoming bends, and coining bends. The former has three contact points with the bending die at the punch top and die shoulders, and there have been many experimental and analytical research works reported on it. The latter two are in contact at a greater number of points. To clarify the bending characteristics, it is necessary to fully understand the process and stress state in the bent part. The experiment was performed to validate the theoretical formulation and to support the development of the computer code. Simulation was performed on the punch load of the coining bend and the bend angle of the bent part after unloading. Calculated sheet geometries and the forming force agree well with the experimental data. The simulation clearly demonstrates the efficiency of the code to simulate V-die coining bend processes that proceed under contact history.

Finite element analysis on the V-die coining bend process of steel metal

The finite element simulation is now widely used in the design of stamping tools. A trial and error procedure has been replaced by a simulation in which defects associated with sheet forming processes are predicted and evaluated. This paper aims to clarify the process conditions of the V-die bending of a sheet metal. It provides a model that predicts not only the correct punch load for bending, but also the precise final shape of the products after unloading. An incremental elastic-plastic finite element computer code, based on an updated Lagrangian formulation, was developed to simulate the V-die bending of sheet metal. In particular, the assumed strain field (ASF) element was used to formulate the stiffness matrix. The r-minimum technique was used to deal with the elastic-plastic state and solve contact problems at the tool-metal interface. A series of experiments were performed to validate the formulation in the theory, leading to the development of the computer codes. The predicted punch load in the finite element model agrees closely with the experimental results. The whole history of deformation and the distribution of stress and strain during the forming process were obtained by carefully considering the moving boundary condition in the finite element method . A unique feature of this V-die bending process is the camber after unloading. The computer code successfully simulates this camber. The simulation was performed to evaluate the effects of the size of the blank on the camber process. The results in this study clearly demonstrate that the computer code efficiently simulated the camber process .

Influence of blank profile on the V-die bending camber process of sheet metal

V-die bending is a non-steady state forming process, in which bending moment varies during forming; stress--strain distribution differs in different cross-sections of a bend. By assuming that an isotropic-hardening von Mises material undergoes plane bending, the moment of internal stresses is expressed as a function of the curvature of the bend, sheet thickness and properties of the material. With the constitutive equations given, one can calculate the configuration of a sheet metal in bending and predict its elastic springback on removing load. The theoretical results have been compared to the experimental data, and good agreement has been found. Materials were: DRQ 1147, DOCOL 220, DOCOL 260, and SIS 2322. Graphs. 10 ref.--AA

Claes Magnusson

Papers

Mathematical modeling of V-die bending process