Full-Field vs. Homogenization Methods to Predict Microstructure–Property Relations for Polycrystalline Materials

In this chapter, we review two recently proposed methodologies, based on crystal plasticity, for the prediction of microstructure–property relations in polycrystalline aggregates. The first, known as the second-order viscoplastic self-consistent (SC) method, is a mean-field theory, while the second, known as the fast Fourier transform (FFT)-based formulation, is a full-field method. The main equations and assumptions underlying both formulations are presented, using a unified notation and pointing out their similarities and differences. Concerning mean-field SC homogenization theories for the prediction of mechanical behavior of nonlinear viscoplastic polycrystals, we carry out detailed comparisons of the different linearization assumptions that can be found in the literature. Then, after validating the FFT-based full-field formulation by comparison with available analytical results, the effective behavior of model material systems predicted by means of different SC approaches are compared with ensemble averages of full-field solutions. These comparisons show that the predictions obtained by means of the second-order SC approach– which incorporates statistical information at grain level beyond first-order, through the second moments of the local field fluctuations inside the constituent grains– are in better agreement with the FFT-based full-field solutions. This is especially true in the cases of highly heterogeneous materials due to strong nonlinearity or single-crystal anisotropy. The second-order SC approach is next applied to the prediction of texture evolution of polycrystalline ice deformed in compression, a case that illustrates the flexibility of this formulation to handle problems involving materials with highly anisotropic local properties. Finally, a full three-dimensional implementation, the FFT-based formulation, is applied to study subgrain texture evolution in copper deformed in tension, with direct input and validation from orientation images. Measurements and simulations agree in that grains with initial orientation near<110>tend to develop higher misorientations. This behavior can be explained in terms of attraction toward the two stable orientations and grain interaction. Only models like the FFT-based formulation that account explicitly for interaction between individual grains are able to capture these effects.