Abstract
The evolution of the macroscopically observed yield surface has been the subject of many studies due to its significant effect on the numerical simulation of metal forming processes. Although macroscopic models exist that aim to define this evolution accurate data for calibration as well as validation of these models are difficult to obtain. One common approach is to use crystal plasticity simulations for analyzing the mesoscopic behavior followed by a homogenization scheme for gathering the aggregate behavior. In this study a similar approach is followed the difference being the choice of the crystal plasticity and homogenization methods. A rate-independent crystal plasticity framework where all slip system activities are solved implicitly using a backward Euler approach in combination with an interior point method for constrained optimization is used for single crystal behavior. The aggregate behavior is obtained using a self-consistent analytical homogenization scheme. The results of the homogenization scheme are compared against full-field crystal plasticity finite element simulations. The determination of the yield surface is done by considering the macroscopic behavior where the strain rate direction and magnitude changes over a threshold during stress-based loading.
Highlights
For metal forming simulations one of the important goals is to predict failure which in sheets mostly occur due to localized necking
The behavior of the material usually depends on its plastic deformation history where strain path changes and the Bauschinger effect have a strong influence on the subsequent yield behavior
A Self-Consistent Mean-Field homogenization algorithm is implemented where the individual behavior of each phase is modeled using a rate-independent crystal plasticity algorithm. This Crystal plasticity-based modeling (CP) algorithm allows definition of a clear elasticplastic transition and an elastic domain which is essential in determining the yield behavior of a polycrystal aggregate
Summary
For metal forming simulations one of the important goals is to predict failure which in sheets mostly occur due to localized necking. It is known that the accuracy of the prediction of localized neck strongly depends on the ability of the yield function in representing the material behavior correctly. The aim of the current work is to provide an understanding on these dependencies using a multi-scale modeling approach known as the Mean-field homogenization framework. Crystal plasticity-based modeling (CP) of the plastic deformation of metals has been the subject of many studies since it gives a direct relation between the microstructure and the observed macroscopic properties [1,2,3] which allows prediction of the yield locus as well as localization. The CP implementation is based on a rate-independent approach [6,7]
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