Abstract
The industrial demand for products with better quality and lower production costs have encouraged the widespread application of the finite element analysis (FEA) in the development and optimization of sheet metal forming processes. To ensure that the FEA solutions are reliable and robust it is important to take into account the uncertainties that inevitably arise in a real industrial environment. In this context, a numerical study on the influence of the material and process uncertainty in the stamping results of a square cup is presented. In this analysis, it is assumed uncertainty in the elasticity properties, hardening law parameters, anisotropy coefficients, blank thickness, friction coefficient and in the blank holder force. The effect of the uncertainty in these input parameters is evaluated in the punch force, equivalent plastic strain, thickness and cup geometry. Firstly, quasi-Monte Carlo method was used to evaluate the variability in the simulation outputs, considering the uncertainty of the input parameters. This analysis shows that the geometry is the output most sensitive to the uncertainty of the input parameters. Afterwards, a variance-based sensitivity analysis was carried out to identify the input parameters that most influence the output variability. It was concluded that the hardening law parameters and the anisotropy coefficients have the most influence in the stamping results variability of a square cup.
Highlights
Sheet metal forming processes are among the most common and important metal working operations associated with the automotive, aeronautics and metalworking industries
We present the main results of the sensitivity analysis for the maximum values of the forming results, PFmax, εpmax, TCmax and GCmax
A numerical study was performed to evaluate the influence of material and process uncertainty in the variability of the square cup forming results
Summary
Sheet metal forming processes are among the most common and important metal working operations associated with the automotive, aeronautics and metalworking industries. Li [2] stated that these uncertainties have a significant influence in the quality of the formed component, leading to unreliable and non-robust solutions, and to the eventual rejection of the component For these reasons, the stochastic modelling and uncertainties quantification of sheet metal forming processes are of current industrial interest. A quasi-Monte Carlo method and a variance-based sensitivity analysis (Sobol’s indices [12]), will be used to numerically evaluate the influence of the uncertainties associated with 11 input parameters (elasticity properties, hardening law parameters, anisotropy coefficients, blank thickness, friction coefficient and the blank holder force) in the stamping results variability of a square cup [13]. This work intends to fill the lack of research studies associated with the variability of the square cup benchmark, which is one of the most used test cases [7, 14,15,16,17]
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