Yuksel C. Yabansu

Compositionally graded cylinders of Ti–Mn alloys were produced using the Laser Engineered Net Shaping (LENS™) technique, with Mn content varying from 0 to 12 wt.% along the cylinder axis. The cylinders were subjected to different post-build heat treatments to produce a large sample library of α–β microstructures. The microstructures in the sample library were studied using back-scattered electron (BSE) imaging in a scanning electron microscope (SEM), and their mechanical properties were evaluated using spherical indentation stress–strain protocols. These protocols revealed that the microstructures exhibited features with averaged chord lengths in the range of 0.17–1.78 μm, and beta content in the range of 20–83 vol.%. The estimated values of the Young’s moduli and tensile yield strengths from spherical indentation were found to vary in the ranges of 97–130 GPa and 828–1864 MPa, respectively. The combined use of the LENS technique along with the spherical indentation protocols was found to facilitate the rapid exploration of material and process spaces. Analyses of the correlations between the process conditions, several key microstructural features, and the measured material properties were performed via Gaussian process regression (GPR). These data-driven statistical models provided valuable insights into the underlying correlations between these variables.

While phase-field models have been demonstrated to be highly versatile in performing physics-based simulations of a large variety of materials phenomena involving microstructure evolution (e.g. phase transformation, recrystallization, sintering), they are not practical for rapid exploration of the process design space due to their high demand for computational resources. The extraction of reliable and robust reduced-order models from the microstructure evolution datasets produced by such sophisticated physics-based models continues to be an unsolved problem. Recent advances in the fast computation of a comprehensive set of microstructure statistics and their data-driven low-dimensional representations using principal component analyses have resulted in the successful extraction of practically useful reduced-order models connecting the microstructure statistics and the effective properties exhibited by the material. In this paper, we explore for the first time, the viability of these low-dimensional representations of the microstructure statistics for establishing reduced-order models capable of learning the important details of the microstructure evolution predicted by the computationally expensive phase-field models. More specifically, we will explore the viability of applying the Gaussian process autoregressive models used in the fields of statistics and signal processing for problems in microstructure evolution. This will be accomplished using a specific case study dealing with the time evolution of porous microstructures in sintering of polycrystalline ceramics.