A method of predicting macroscopic yield strength of polycrystalline metals subjected to plastic forming by micro–macro de-coupling scheme

We introduce a method of predicting the macroscopic yield strength of polycrystalline metals subjected to plastic forming, which hinges on the reliability of the micro–macro decoupling scheme for solving the corresponding two-scale boundary value problem. A polycrystalline aggregate composed of several crystal grains is adopted as a periodic microstructure, namely unit cell, and is regarded as a numerical specimen for numerical material tests (NMTs) based on the homogenization theory. The NMTs are conducted to identify the material parameters of the assumed approximate macroscopic constitutive model and followed by the de-coupled macro-scale analysis to simulate the macro-scale forming process. We then conduct the de-coupled micro-scale analysis by applying the resulting macroscopic deformation histories to the microstructures associated with the macroscopic points of interest in order to obtain the numerical specimens after plastic forming. Finally, the NMTs are conducted on the prepared specimens to evaluate the macroscopic post-forming yield strengths. We validate the proposed method by taking the three-step forming process as an example of macroscopic plastic forming. The validation of the method is made in comparison with the results with those obtained by the equivalent two-scale analysis with the coupling scheme. To demonstrate the capability and promise of the proposed method for practical applications, we also present an numerical example of the rolling process that causes the texture development in crystal grains.