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Research Papers

# The Anomalous Redundant Deformation and Work Hardening of the AISI 420 Stainless Steel During Axisymmetric Drawing

[+] Author and Article Information
C. A. Santos

Department of Mechanical Engineering, Federal University of Pernambuco, Avenida Arquitetura s/n, Cidade Universitária, Recife, Pernambuco 50670-901, Brazilcarlos.asantos3@ufpe.br

E. C. S. Corrêa

Federal Center of Technological Education of Minas Gerais, Avenida Amazonas 5253, Nova Suiça, Belo Horizonte, Minas Gerais 30480-000, Brazilelaine@deii.cefetmg.br

M. T. P. Aguilar

Department of Materials and Construction Engineering, Federal University of Minas Gerais, Rua Espírito Santo 35, Centro Belo Horizonte, Minas Gerais 30160-030, Brazilteresa@.ufmg.br

Technology Center Foundation of Minas Gerais, Avenida José Cândido da Silveira 2000, Belo Horizonte, Minas Gerais 31170-000, Brazilmargareth.spangler@cetec.br

P. R. Cetlin

Department of Metallurgical and Materials Engineering, Federal University of Minas Gerais, Rua Espírito Santo 35, s214 Centro Belo Horizonte, Minas Gerais 30160-030, Brazilpcetlin@demet.ufmg.br

J. Eng. Mater. Technol 132(1), 011011 (Nov 05, 2009) (7 pages) doi:10.1115/1.3184082 History: Received January 21, 2009; Revised April 10, 2009; Published November 05, 2009; Online November 05, 2009

## Abstract

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.

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## Figures

Figure 1

Experimental relationships between ϕ and Δ for the AISI 420 stainless steel measured through visioplasticity or the stress-strain curves superposition techniques (4)

Figure 2

AISI 420 stainless steel optical photomicrographs: (a) before the heat treatment and (b) after the heat treatment

Figure 3

Location of microhardness measurements in the longitudinal sections of (a) specimens after uniform tension or (b) specimens after rupture

Figure 4

Illustration of (a) the various layers considered in the longitudinal sections of the partially drawn samples and (b) of the middle lines and microhardness location points taken in the material layers

Figure 5

Experimentally determined curve relating the ratio C (microhardness/effective stress) to the effective strain +0.08 curve for effective strains above 0.08

Figure 6

Experimentally determined effective stress versus effective strain curves for the pure tension (tensile) and LC, LM, and LE of the drawn material for the following drawing conditions (die semi-angle and reduction in area): (a) 3 deg and 8%, (b) 3 deg and 15%, (c) 8 deg and 8%, (d) 8 deg and 15%, (e) 20 deg and 8%, and (f) 20 deg and 15%

Figure 7

Microhardness values after drawing of the material, at the center, middle and surface layers of the material.

Figure 8

(a) Illustration of the tensile and shear strain components in axisymmetric drawing and (b) evolution of the tensile strain and of the shear strain in a point as it traverses the drawing die

Figure 9

Average cyclic shear values ((γ1+γ2)/2) for the various drawing conditions and for the LC, LM, and LE for each drawing condition

Figure 10

Schematic illustration of the strain components during simultaneous tension and cyclic shear by torsion

Figure 11

Effective stress versus effective strain curves for material submitted to pure torsion or tension with superimposed cyclic torsion of amplitudes 0.05, 0.1, or 0.2 (39)

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