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A simple ductile failure model with application to AA5182 aluminium sheet forming

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Abstract

In the present work the recently introduced Joined Ductile Failure (JDF) model has been slightly improved and is applied to sheet forming of an AA5182 aluminium alloy. Despite its simplicity the validation examples documented in the present work reveal that the JDF model is able of accurately predicting the onset as well as the location of ductile failure.

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Acknowledgments

The authors are grateful for the support by the technical staff at Hydro R&D Bonn, in particular to Mr. M. Stellbogen, Mr. A. Hausen and Mr. F. Burgartz who carried out the experimental work. Furthermore, we would like to thank our colleagues for numerous fruitful discussions.

The constructive comments of the unknown reviewers on the original manuscript are gratefully acknowledged.

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Authors and Affiliations

  1. Hydro Aluminium Rolled Products GmbH, Research & Development, Georg-von-Boeselager-Str. 21, 53117, Bonn, Germany

    Holger Aretz, Stefan Keller, Olaf Engler & Henk-Jan Brinkman

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  1. Holger Aretz
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  2. Stefan Keller
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Correspondence to Holger Aretz.

Appendix

Appendix

On stress-based necking criteria

In a theoretical work Hill [30] derived a criterion for the onset of plastic instability in the bulge-test. He assumed a power-law hardening of the form

$$Y_{\mathrm{ref}}(\bar{\varepsilon}) = K \cdot \bar{\varepsilon}^{n} $$
(22)

with \(\bar {\varepsilon } = |\varepsilon _{33}|\), whereby \(\varepsilon _{33}\) denotes the true thickness strain. Hill derived the critical strain \(\bar {\varepsilon }^*\) at maximum pressure, which marks the onset of plastic instability in the bulge-test, as follows [30]:

$$\bar{\varepsilon}^* = \frac{4}{11} \cdot (2n + 1) $$
(23)

One may easily see that even for a non-hardening (i.e. ideal-plastic) material with \(n = 0\) the critical strain is \(\bar {\varepsilon }^* = 4 / 11 \approx 0.36\), which is still a remarkable (but often too optimistic) value. For a non-hardening material the stresses in the sheet can not grow during plastic straining. In this case a stress-based necking criterion predicts necking at \(\bar {\varepsilon }^* = 0\), which is obviously in conflict with Hill’s theory and also with experimental results, see below. However, a necking criterion based on the equivalent plastic strain (as in the present work) provides correct results even in the non-hardening case. This illustrates (i) that these two necking criteria are not equivalent in general and (ii) that stress-based necking criteria are not generally applicable.

It should be mentioned that according to the authors’ experience the results of Hill’s theory for non-hardening metals can be qualitatively reproduced by means of bulge-test experiments using heavily cold-rolled pure as well as low-alloyed aluminium sheets of the AA1xxx and AA8xxx series.

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Aretz, H., Keller, S., Engler, O. et al. A simple ductile failure model with application to AA5182 aluminium sheet forming. Int J Mater Form 7, 289–304 (2014). https://doi.org/10.1007/s12289-013-1127-x

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