Parameter estimation and its influence on layered metal–composite–metal plates simulation

Abstract

Laminates made of metal—glass fiber-reinforced polymers—metal layers require material parameters for each constitutive model of the constituents. First, although parameter identification for metallic materials has been frequently discussed, the stepwise identification of material parameters in terms of uncertainties of previously determined parameters is investigated by the concept of error propagation. Second, the calibration of a model of orthotropy describing the large deformation behavior of the glass fiber-reinforced kernel layer is a challenging process, especially against the background of a reliable determination of the parameters. The main problem is related to the lack of available experiments. This issue is embedded in the concept of local identifiability. Thus, the article provides experiments to determine the parameters of both the steel as well as the glass fiber-reinforced polymers. Particularly for the latter issue, $$\mu $$ μ -CT data is chosen to provide a representative volume element, where all deformation modes can be investigated. In this sense, a concept to determine all material parameters in a locally unique and reliable manner is studied. A linear error propagation concept provides the uncertainty of the resulting material parameters of the whole parameter set for the homogenized material. The entire parameter identification process is discussed thoroughly, and validation examples such as bending and deep drawing in metal forming processes, are provided to estimate the prediction accuracy. In this respect, the uncertainties found by parameter identification are applied to the prediction of finite element simulations of layered metal–composite–metal forming processes and error propagation is used to estimate the uncertainties of the simulations. In this contribution, we restrict ourselves to experiments at room temperature.

Uncertainty estimation using Gaussian error propagation in metal forming process simulation

“…1c shows the model response. In the subsequent and final step, all data (axial and lateral) of the MSR and the rate-dependent tensile tests are utilized to identify the viscosity parameter η and its uncertainty ∆η concerned by fixing the viscosity exponent r = 1 (due to the strong correlation between the parameters η and r, see discussion in [3] for details). The identified material parameters of the steel material along with its uncertainties are summarized in Tab.…”

“…which have to be determined by experiments. In [3] the entire process of parameter identification is discussed, where Tab. 2 shows the result of the parameter identification and its uncertainties.…”

“…The main goal in [3] was to quantify the uncertainty of the material parameters by the identification procedure and to estimate the uncertainty in finite element simulations, which was demonstrated at a stretch forming process. The uncertainty in the parameter identification is based on two reasons, first, the estimated confidence interval of the calibrated parameterswhich is a subset of all parameters to be determined -and, second, the error propagation for quantities which are calculated on the basis of the uncertain parameters determined before.…”

“…First, a thermo-mechanically consistent finite strain viscoplasticity model representing the steel material at room temperature is chosen, whereas the composite layer is modeled with orthotropic hyperelasticity. In [3] the procedure to identify the material parameters is discussed in detail. Here, the constitutive model for steel is changed, where a slightly modified model of [12] is applied.…”

“…Thus, the calibration step has briefly to be recapped. The calibration of GF-PA6 -shown in [3] -is performed by computations at a representative volume element, where the microstructure of the woven fabric is reconstructed using µ-CT images. There, the individual components, i.e.…”