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Mechanical and damage analysis along a flat-rolled wire cold forming schedule

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Abstract

Numerical simulation is used to study patented high-C steel flat-rolled wire cold forming processes. An elasto-plastic power law, identified from mechanical tests, is used into Forge2005® finite element (FEM) package in order to describe the material behaviour during wire drawing followed by cold rolling. A through-process approach has been favoured, transferring residual wire-drawing stresses and strain into the flat-rolling preform. This mechanical analysis, associated with a triaxiality study, points to dangerous areas where fracture may initiate due to high tensile stresses. Lemaître’s isotropic damage criterion, including crack closure effect, a -1/3 cut-off value of stress triaxiality, and tension/compression damage asymmetry, has been used and has confirmed the previous analysis. A number of non-coalesced voids nucleated on inclusions have been observed in the Scanning Electron Microscopy (SEM), especially in high-deformation zones (“blacksmith’s cross”). Their evolution has been simulated in the FEM model using spherical numerical markers, which deform into oblate or prolate ellipsoids. The deformation-induced morphological evolution of voids observed in the SEM compares well with the geometrical evolution of the markers, which suggests that the morphologies observed do not result from micro-crack propagation, but from material transport of the nucleated voids.

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Abbreviations

x :

Scalar

x ij :

Component of a second order tensor x

\( \mathop{x}\limits^{ \bullet } \) :

Material time derivative of x \( \left( {\mathop{x}\limits^{ \bullet } = dx/dt} \right) \)

x kk :

Trace of x

δ ij :

Kronecker delta, \( {\delta_{{ij}}} = 1\,if\,i = j\,and\,{\delta_{{ij}}} = 0\,if\,i \ne j \)

\( \left\langle x \right\rangle \) :

Macauley bracket, \( \left\langle x \right\rangle = x\,if\,x \geqslant 0\,and\,\left\langle x \right\rangle = 0\,if\,x < 0 \)

\( {\left\langle x \right\rangle^{ + }}or\left\langle x \right\rangle_{{ij}}^{ + } \) :

Positive part in terms of principal component of tensor x

\( {\left\langle x \right\rangle^{ - }}or\left\langle x \right\rangle_{{ij}}^{ - } \) :

Negative part in terms of principal component of tensor x

a :

Behaviour law parameter

E :

Young’s modulus of elasticity

h :

Microdefect closure parameter

K :

Behaviour law parameter

\( \overline m \) :

Friction factor

n :

Strain hardening index in the behaviour law

R :

Current wire radius

R 0 :

Initial wire radius

R a :

Centre Line Average (CLA) roughness

R ν :

Triaxiality function

s :

Unified damage law exponent

S :

Energetic damage law parameter

Tr :

Stress triaxiality

Y :

Energy density release rate

ε eq :

Equivalent strain

\( {\mathop{\varepsilon }\limits^{ \bullet }_{{eq}}} \) :

Equivalent strain rate

\( {\mathop \varepsilon \limits^ \bullet }^{p}_{{ij}} \) :

Plastic strain rate

\( {\mathop \varepsilon \limits^ \bullet }^{p}_{{eq}} \) :

Equivalent plastic strain rate

ν :

Poisson’s ratio of elastic contraction

ρ:

Mass density

σ, σ ij :

Uniaxial and tensorial Cauchy stresses

\( {\tilde{\sigma }_{{ij}}} \) :

Effective stress

σ y :

Tensile yield stress

σ eq :

Equivalent stress

\( {\tilde{\sigma }_{{eq}}} \) :

Effective equivalent stress

σ H :

Hydrostatic stress

τ c :

Shear stress

Ψ*:

Gibbs specific free enthalpy

\( \psi_e^{*} \) :

Elastic specific free enthalpy

Ψ p :

Plastic state potential (Helmholtz free energy)

Ψ T :

Thermal state potential

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Acknowledgments

The Research Centre of ArcelorMittal Gandrange and ArcelorMittal Wire Solutions are both gratefully acknowledged, for financial support as well as for generous access to their production and research facilities.

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Authors and Affiliations

  1. Mines ParisTech, CEMEF - Centre for Material Forming, CNRS UMR 7635, BP 207, 1 Rue C. Daunesse, 06904, Sophia-Antipolis Cedex, France

    Thomas Massé, Yvan Chastel & Pierre Montmitonnet

  2. ArcelorMittal Gandrange, Research and development - Long Carbon Bars & Wires, BP 3, 57360, Amnéville, France

    Christian Bobadilla & Nicolas Persem

  3. ArcelorMittal Wire Solutions, 25 Avenue de Lyon, 01000, Bourg-en-Bresse, France

    Sylvain Foissey

  4. DER/SESI/LE2S, CEA Cadarache, Bât 212 - P27, 13108, St Paul-Lez-Durance Cedex, France

    Thomas Massé

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  1. Thomas Massé
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  2. Yvan Chastel
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  4. Christian Bobadilla
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Correspondence to Thomas Massé.

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Massé, T., Chastel, Y., Montmitonnet, P. et al. Mechanical and damage analysis along a flat-rolled wire cold forming schedule. Int J Mater Form 5, 129–146 (2012). https://doi.org/10.1007/s12289-011-1032-0

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