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Inferring Post-Necking Strain Hardening Behavior of Sheets by a Combination of Continuous Bending Under Tension Testing and Finite Element Modeling

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Abstract

This paper presents a combined experimental and simulation approach to identify post-necking hardening behavior of ductile sheet metal. The method is based on matching a measured load-displacement curve from a continuous bending under tension (CBT) test with the curve simulated using the finite element method (FEM), while adjusting an input flow stress curve into the FEM. The CBT test depletes ductility uniformly throughout the gauge section of a tested sheet, and thus, stretches the sheet far beyond the point of maximum uniform strain in a simple tension (ST) test. Having the extended load-displacement curve, the calibrated flow stress curve is extrapolated beyond the point of necking. The method is used to identify the post-necking hardening behavior of an aluminum alloy, AA6022-T4, and two dual-phase (DP) steels, DP 980 and DP 1180. One measured load-displacement curve is used for the identification of a flow stress curve per material, and then the flow stress curve is used to simulate two additional measured load-displacement curves per material for verification. The predictions demonstrate the utility of the developed CBT-FEM methodology for inferring the post-necking strain hardening behavior of sheets. Furthermore, the results for AA6022-T4 are compared with the hydraulic bulge test data. Unlike the hydraulic bulge test, the CBT-FEM method can predict increasing as well as decreasing anisotropic hardening rate in the post-necking regime. The latter is associated with probing stage IV hardening. The proposed methodology along with the results and these key advantages are presented and discussed in this paper.

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Acknowledgements

Authors are grateful for financial support to the U.S. National Science Foundation under the CAREER grant no. CMMI-1650641.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of New Hampshire, 33 Academic Way, Kingsbury Hall, W119, Durham, NH, 03824, USA

    C.M. Poulin, T.J. Barrett & M. Knezevic

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  1. C.M. Poulin
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  2. T.J. Barrett
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  3. M. Knezevic
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Correspondence to M. Knezevic.

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Appendix

Appendix

The extrapolated portion of the curve representing the post necking behavior is adjusted using an optimization procedure, while the portion of the curve measured in ST remains the same. The procedure explored here for the extrapolation starts with a consideration of two curves selected to represent the solution space, a perfect plasticity curve as the lower bound and a curve based on the final slope of the measured stress-strain curve as the upper bound (Fig. 10(a) for AA6022-T4 and (c) for DP 980). Figure 10(b) and (d) show the predicted load vs displacement corresponding to the upper and lower bound extrapolated stress-strain curves. As expected, these calculations over-predict and under-predict the load-displacement behavior of the materials indicating that the extrapolated curve for the materials are in between. Next, a set of curves in between the upper and lower bound curves is selected to simulate the resulting load vs displacement. Based on the comparison between the calculated and measured load vs displacement, the extrapolated stress-strain curve can be roughly estimated. After several subsequent trials, the procedure arrives at an accurate extrapolated curve capturing the measured load vs displacement.

Fig. 10
figure 10

A perfect plasticity curve as the lower bound and a curve based on the final slope of the measured stress-strain curve as the upper bound along with the fitted extrapolated curve for (a) AA6022-T4 and (c) for DP 980. Comparison of the measured and predicted load vs displacement based on the upper and lower bound extrapolated stress-strain curves for (b) AA6022-T4 and (d) DP 980. The onset of the extrapolation is indicated in (b) and (d)

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Poulin, C., Barrett, T. & Knezevic, M. Inferring Post-Necking Strain Hardening Behavior of Sheets by a Combination of Continuous Bending Under Tension Testing and Finite Element Modeling. Exp Mech 60, 459–473 (2020). https://doi.org/10.1007/s11340-019-00577-1

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