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In the present work, experimental techniques for evaluating the deformation and the redundant work factor in the axisymmetric drawing of ferritic AISI 420 stainless steel bars were investigated. Six operation conditions, involving two reductions of area and three die semi-angles, were employed in the study. Regarding the redundant deformation analysis, the visioplasticity technique was considered as the most adequate procedure for estimating the average deformation in drawing. In this case, an increasing relationship between the redundant deformation factor and the parameter D was obtained. On the other hand, the stress-strain curves superposition technique led to redundant deformation factor values almost insensitive to variations of the parameter D and below unity, a phenomenon which was associated with strain path effects. Concerning the redundant work factor study, the experimental results were lower than those obtained through a theoretical approach and, in some conditions, below unity. This was also attributed to strain path effects.KEY WORDS: drawing; average strain; visioplasticity; redundant deformation factor; redundant work factor. 63© 2008 ISIJ ones, employing a previously obtained relationship between hardness and strain. This approach, however, is not evaluated in this work and, therefore, no details are given in the text. For more information see Refs. 4), 6), 9).The visioplasticity, also called incremental grid method, 8,9) was originally proposed by Thomsen,11) based on the establishment of a velocity vector field on the meridian plane of the metal, followed by the calculation of the complete distribution of strain rate, strain and stress. The process is carried out by placing a grid pattern in the internal plane surfaces of sectioned samples. As plastic deformation is conducted, the rate of distortion of the grid lines is evaluated, and subsequent analysis is performed employing equilibrium and plasticity equations. Therefore, contrasting with the stress-strain curves superposition and the hardness profile methods, the results obtained in visioplasticity are non-dependent of the measurement of the mechanical properties of the metal after the processing. In addition to providing detailed information concerning the forming operation, this technique may act as a kind of calibration procedure, whose results would be used for checking the accuracy of solutions obtained through other investigative methods. 14,15) On the other hand, even though the visioplasticity has been considered as the experimental procedure leading to the most realistic solutions to various processes, 11) the time consuming calculations and the requirement of smoothing procedures for treating the experimental data seem to have restrained the use of the method, seldom employed in recent investigations concerning metal forming operations. 12) In the case of axisymmetric drawing, as far as the present authors know, the analyses have been performed only for few materials and process parameters, 8,9) with no reference to the calculat...

The cold axisymmetric drawing of metals leads to effective strains that increase from the centerline to the surface of the material cross section. This strain heterogeneity depends on the die semi-angle and reduction in area related through a “Δ” parameter. The average strain in the product is evaluated through a redundant deformation coefficient, “ϕ,” which has a minimum value of unity and rises as Δ is increased. Anomalous experimental results for this relationship (ϕ values below unity and insensitive to variations in Δ) have been reported for the AISI 420 stainless steel. Strain path affects the work hardening of metals during sheet forming, where some materials harden more and others less than under pure tension, for the same strain path. The present paper analyses the possibility that a similar dependence of the work hardening on the strain path, during the axisymmetric drawing of AISI 420 stainless steel causes the anomalous ϕ versus Δ relationship. The strain path followed along various material streamlines in axisymmetric drawing involves the superposition of a radially varying reversed shear strain on a basic radial compression/longitudinal tension pattern. A new method was developed for the determination of the effective stress versus effective strain curves of the material along three material streamlines, located close to the material surface, along its centerline and following a midcourse between these two flow lines. A relationship between the local microhardness of the material and its flow stress was established and visioplasticity was employed for the determination of local strains in the deformation region. Data were obtained for six situations resulting from the combinations of two reductions of area (8% and 20%) and three die semi-angles (3 deg, 8 deg, and 15 deg). The various strain paths followed in axisymmetric drawing of AISI 420 stainless steel led to effective stress versus effective strain curves tending to be often lower than that obtained in pure tension. The degree of lowering seems to depend on the reduction in area and die semi-angle. The effect of strain path on the work hardening during axisymmetric drawing causes the anomalous experimental results for the ϕ versus Δ relationship of the AISI 420 stainless steel. The present paper seems to be the first report in literature covering such effects under cold bulk forming conditions.

ResumoEste artigo apresenta o SALF, um software nacional desenvolvido para simular o processo de laminação a frio de chapas através do método dos elementos finitos. O programa utiliza a formulação implícita/rígido-plástica em suas análises. Simulações retiradas da literatura foram realizadas com o software, sendo os materiais simulados alumínio e aço, com espessuras de 3,0 mm e 1,0 mm, reduções de 5% e 30% e atrito de 0,06 a 0,15. Os resultados do SALF ficaram bem próximos dos resultados descritos na literatura. Desta forma, a partir de agora, as siderúrgicas nacionais têm uma ferramenta nacional para simular o processo de laminação a frio, a qual pode auxiliar na melhoria de seus processos e produtos. Palavras-chave: Laminação a frio de chapas; Método dos elementos finitos; Formulação implícita e rígido-plástica. SALF PROGRAM AS TOOL TO ANALYZE COLD FLAT ROLLING PROCESS AbstractThe article presents SALF program, a national software developed to simulate the cold rolling metal sheet process by the finite element method. The program uses the implicit and rigid-plastic approaches to perform numerical analyses. Simulations from the literature were performed using the program on materials such as steel and aluminum, with thicknesses of 1.0 mm and 3.0 mm, reductions of 5% and 30%, and friction coefficients of 0.1 and 0.3. There was a strong approximation between the program results and those described in the simulations chosen from the literature. However, starting now domestic steel industries may use a national program to simulate the cold flat rolling process to improve their processes and products.