Abstract
Abstract
Statistical continuum mechanics theory was used to simulate the inelastic stress of polycrystalline materials using two-point statistics. For the experimental part, the Electron beam melting (EBM) technique (Arcam EBM Q10 additive machine) was used to fabricate cylindrical rods of Ti-6Al-4V both in horizontal and vertical directions. Electron backscatter diffraction (EBSD) technique was employed to achieve statistically reliable orientation maps of vertically and horizontally printed samples. In this study, high strain rate compression tests at six different strain rates were performed, and the stress–strain curves were generated. This work is amongst the first attempts to model the microstructure of additively manufactured hexagonal alloys under compressive loadings using the statistical continuum mechanics theory. The model is capable of simulating reasonably large microstructures (statistically representative) with a practical computational cost and accuracy, unlike numerical models that require a high computational cost. It should be noted that in additive manufacturing, due to large grains and high anisotropy, microstructures used in the simulations should be large enough to include sufficient information from the material’s structure. Therefore, using finite element models would be very challenging here. On the other hand, the statistical continuum mechanics theory uses the statistical representation of the material’s characteristics for solving the governing equations with Green’s function that enables this methodology to use more microstructure characteristic information without having a noticeable change to the computational cost. The proposed model in this study uses different microstructure characteristics such as crystal grain orientation, total slip systems, active slip systems, gain morphology, and chemical phases that are obtained from EBSD images for simulating the inelastic mechanical behavior of polycrystalline materials. Although this model simulates polycrystalline materials by considering various crystal and grain information, unlike numerical methods, it doesn’t simulate the grain interactions well and we cannot study local deformation and crack nucleation sites. This model works very well for simulating the overall behavior of material instead of each individual grain and failure analysis. This model has shown a good combination of computational cost and accuracy in which the error between the simulated and experimental strength for vertical and horizontal samples was 6.21% and 8.07%, respectively.