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ABSTRACT
The calibration of material data to properly describe the stress response of a specific material under various loading conditions in finite element analysis (FEA) is still a challenging task. Not only that new steel grades or aluminum alloys are investigated by the material manufacturers to enhance certain characteristics of their product such as stiffness, strength, or maximum strain to failure, but also FEA software tools add new physically or non-physically motivated material models to their libraries, allowing users to improve the predictability of their process- or structural analysis with these new materials. Since depending on the model size various element lengths are utilized, it is often necessary to repeat the calibration process several times, e.g. for 0.5 mm – 10.0 mm meshes, in order to properly capture mesh size dependent damage and failure parameters.
Experimental test campaigns for material characterization are nowadays often accompanied by measurements of the displacement field of the specimen. Quite commonly, the GOM/ARAMIS optical measurement system is used for this purpose. Prior to the test, a randomized speckle pattern is sprayed onto the specimen, allowing the underlying image processing software to create triangulated facets which are used internally to calculate strain fields. Previous publications (Ilg et. al. 2019) have investigated how these locally varying strain fields can be used to improve accuracy of the parameter identification process comparing measured and simulated stress-strain responses during the optimization. Since a larger area of the specimen is used as optimization target instead of only comparing to the force response, this method is called Full-Field Calibration (FFC). Another method utilizing measured strain fields based on the Principal of Virtual Work is the so-called Virtual Fields Method (VFM) proposed by Grédiac et. al. 2006. Within a selected area of interest, virtual fields are created, allowing to establish scalar equations which together with a selected constitutive model help to obtain the unknown material parameters. Marth et. al. 2016 proposed a piecewise modelling technique, identifying the integration path for force calculation from the last measured state prior to specimen failure. Yield stress vs. effective plastic strain curves can then be derived “piecewise” based on the deformation gradient at each experimental time step and an underlying constitutive equation.
Within this work, we investigate the possibility to combine finite element data mapping with material calibration. Therefore, we transfer the displacement field measured with the GOM/ARAMIS system onto finite element meshes with different element sizes as nodal boundary condition. This allows us to simulate the behavior of the specimen as realistic as possible for several mesh sizes while deriving material parameters through an optimization process. This contribution is split into two parts: the first dealing with the theoretical background and implementation of the image processing and finite element data mapping into the software Envyo®, the second with the parameter identification using LS-OPT®, LS-DYNA®, and a modified test specimen, which provides a broader range of various stress states than the currently used standardized tensile specimen (Ilg et. al. 2023).
LITERATURE
Ilg, C./A. Haufe/K. Witowski/D. Koch/M. Liewald (2019): Parameter Identification using Full-Field calibration (FFC), 38th International Deep-Drawing Research Group Conference, Enschede, NL.
Grédica, M./F. Pierron/S. Avril/E. Toussaint (2006): The virtual fields method for extracting constitutive parameters from full-field measurements: a review, in: Strain: an International Journal for Experimental Mechanics, Vol. 42., pp. 233-253.
Marth, S./H. Häggblad/M. Oldenburg/R. Östlund (2016): Post necking characterisation of sheet metal materials using full field measurement, in: Journal of Materials Processing Technology, Vol. 238, pp. 315-324.
Ilg, C./C. Liebold/A. Haufe/M. Liewald (2023): Displacement based simulation and material calibration based on Digital image correlation PART II – Application, 42nd International Deep-Drawing Research Group Conference, Luleå, SWE.
Keywords: Material Calibration; DIC; Optimization, Displacement Field Mapping