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Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation

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Abstract

Local strain data obtained throughout the entire weld region encompassing both the weld nugget and heat affected zones (HAZs) are processed using two methodologies, uniform stress and virtual fields, to estimate specific heterogeneous material properties throughout the weld zone. Results indicate that (a) the heterogeneous stress–strain behavior obtained by using a relatively simple virtual fields model offers a theoretically sound approach for modeling stress–strain behavior in heterogeneous materials, (b) the local stress–strain results obtained using both a uniform stress assumption and a simplified uniaxial virtual fields model are in good agreement for strains ɛ xx < 0.025, (c) the weld nugget region has a higher hardening coefficient, higher initial yield stress and a higher hardening exponent, consistent with the fact that the steel weld is overmatched and (d) for ɛ xx > 0.025, strain localization occurs in the HAZ region of the specimen, resulting in necking and structural effects that complicate the extraction of local stress strain behavior using either of the relatively simple models.

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Notes

  1. Similar results were obtained with both weld specimens. Hence, results are only reported for one of the experiments.

  2. The translation stage is used to move the camera parallel to the specimen surface to center the region of interest in the field of view during the applied loading process.

  3. To minimize out-of-plane motion effects, the camera is placed approximately 1.5 m from the specimen surface.

  4. In this work, N = 5, where N is the number of displacement data points in each direction. Thus, each 5 × 5 displacement sub-array is selected by moving over one subset spacing (five pixels in this work) and selecting a new data set centered about the new mid-point. Since N = 5, the process gives a spatial resolution of 25 × 25 pixels for the strain estimates.

  5. In-plane bending is more likely in welded specimens undergoing elastic-plastic response because the material response generally is asymmetric relative to the loading axis.

  6. Increasing the number of measurements (N and M) improves parameter estimation. When using DIC, each data point corresponds to a correlation subset. Though overlapping subsets will increase data density, limited additional information is obtained when performing the matching process in this manner. Overlapping subsets will tend to smooth out local variations and transitions.

  7. The decision regarding weld zone separation was based on a combination of (a) etching of weld cross-sections to clearly delineate differences in microstructure and (b) previous experimental evidence that showed marked differences in strain levels within specific weld zone regions. Though more (less) weld zones could be defined, the choice used in this study is believed to be appropriate for the application.

  8. The strain field shown is based on 250 × 75 values obtained from the measured displacement field at each time.

  9. Pre-smoothing is not used since the least squares solution process defined in equation (13) will perform the smoothing process when estimating the material properties.

  10. The cost function defined in equation (18) is minimized in 3,800 iterations with the Nelder–Mead approach. Convergence requires 90 min on a PC that uses a 1.4 GHz Pentium M processor.

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Acknowledgements

The authors gratefully acknowledge the support of (a) the Army Research Office and Dr. Bruce Lamattina through W911NF-06-1-0216, (b) Dr. Stephen Smith and NASA Langley under Grant NASA-NRA-NNX07AB46A and (c) General Motors and Dr. Pablo Zavattieri through both contractual support ND0144200 and an unrestricted gift 002259249. The technical assistance provided by Prof. Xiaomin Deng in the Department of Mechanical Engineering at the University of South Carolina and Dr. Hubert Schreier and Correlated Solutions Incorporated for supporting this effort through modifications to their software, VIC-2D, for our use is deeply appreciated.

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Author notes

  1. S. Avril (SEM Member)

    Present address: Departement of Health Science and Engineering, Ecole Nationale Supérieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023, Saint-Etienne Cedex 2, France

Authors and Affiliations

  1. Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA

    M. A. Sutton (SEM Member) & J. H. Yan

  2. Ecole Nationale Supérieure d’Arts et Métiers, Rue Saint Dominique, BP508, 51006, Châlons en Champagne, France

    S. Avril (SEM Member) & F. Pierron (SEM Member)

  3. Department of Civil and Environmental Engineering, University of Alberta, 3-016 Markin/CNRL Natural Resources Engineering Facility, Edmonton, Alberta, T6G 2W2, Canada

    S. M. Adeeb

Authors
  1. M. A. Sutton
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  2. J. H. Yan
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  4. F. Pierron
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Correspondence to M. A. Sutton.

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Sutton, M.A., Yan, J.H., Avril, S. et al. Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation. Exp Mech 48, 451–464 (2008). https://doi.org/10.1007/s11340-008-9132-6

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