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Prediction of necking for two aluminum alloys under non-proportional loading by using an FE-based approach

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Abstract

Forming Limit Diagrams (FLDs) were found numerically for sheets under non-proportional loading by means of an FE-based Marciniak–Kuczynski (M-K) analysis. The material model used in the analysis includes two instability criteria; a non-local criterion to detect incipient localized necking and a through-thickness shear instability criterion. The objective was to study whether the effects of pre-straining on the FLD could be predicted by the chosen modeling approach, and compare the results from the two instability criteria. The results with the two criteria were different, but both criteria were able to capture the strong strain-path dependence of the FLDs as the governing phenomenon is plastic instability.

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Abbreviations

NLIC:

Non-local instability criterion

TTSIC:

Through-thickness shear instability criterion

RD:

Rolling direction

TD:

Transverse direction

WTM:

Weak texture model

ɛ x , ɛ y :

Logarithmic strains in the rolling and transverse direction

ɛ, ɛ e, ɛ p :

Strain tensor; total, elastic and plastic

σ :

Stress tensor

f :

Yield function

σ 0 :

Reference yield stress

R :

Strain hardening variable

Q i , C i :

Constants in Voce hardening rule

a, c, h, p, m :

Material constants in Yld89

R :

Strain ratio

\(r_\alpha \) :

Flow stress ratio

\(\sigma _\alpha \) :

Flow stress in α-direction

W p :

Specific plastic work

k :

Coefficient in the power-law hardening equation

n :

Exponent in the power-law hardening equation

n el :

number of elements in patch

t :

Thickness

CoV(t)σ t, t 0 :

Coefficient of variation, standard deviation and mean value of the thickness

\(\Delta \varepsilon _z^\Omega \) :

Non-local value of increment in thickness strain

τ :

Shear stress

σ 1, σ 2, σ 3 :

Principal stresses

φ :

Inclination of the localization band in the shear instability criterion

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Acknowledgements

The present work was carried out with financial support from the Faculty of Engineering Science and Technology, Norwegian University of Science and Technology (NTNU), the Research Council of Norway, Renault, Fondation Franco-Norvégienne, and Hydro Aluminium Structures.

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Authors and Affiliations

  1. Structural Impact Laboratory (SIMLab), Centre for Research-based Innovation, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway

    A. Reyes & O. S. Hopperstad

  2. SINTEF Materials and Chemistry, 7465, Trondheim, Norway

    T. Berstad & O.-G. Lademo

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  1. A. Reyes
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  2. O. S. Hopperstad
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  3. T. Berstad
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  4. O.-G. Lademo
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Correspondence to A. Reyes.

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Reyes, A., Hopperstad, O.S., Berstad, T. et al. Prediction of necking for two aluminum alloys under non-proportional loading by using an FE-based approach. Int J Mater Form 1, 211–232 (2008). https://doi.org/10.1007/s12289-008-0384-6

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  • DOI: https://doi.org/10.1007/s12289-008-0384-6

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