Microstructure and Property-Based Statistically Equivalent Representative Volume Elements for Polycrystalline Ni-Based Superalloys Containing Annealing Twins
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This paper has three major objectives related to the development of computational micromechanics models of Ni-based superalloys, containing a large number of annealing twins. The first is the development of a robust methodology for generating 3D statistically equivalent virtual polycrystalline microstructures (3D-SEVPM) of Ni-based superalloys. Starting from electron backscattered diffraction (EBSD) images of sections, the method develops distributions and correlation functions of various morphological and crystallographic parameters. To incorporate twins in the parent grain microstructure, the joint probability of the number of twins and parent grain size, and the conditional probability distributions of twin thickness and twin distance are determined. Subsequently, a method is devised for inserting twins following the distribution functions. The overall methodology is validated by successfully comparing various statistics of the virtual microstructures with 3D EBSD data. The second objective is to establish the microstructure-based statistically equivalent representative volume element or M-SERVE that corresponds to the minimum SERVE size at which the statistics of any morphological or crystallographic feature converge to that of the experimental data. The Kolmogorov–Smirnov (KS) test is conducted to assess the convergence of the M-SERVE size. The final objective is to estimate the property-based statistically equivalent RVE or P-SERVE, defined as the smallest SERVE, which should be analyzed to predict effective material properties. The crystal plasticity finite-element model is used to simulate SERVEs, from which the overall material response is computed. Convergence plots of material properties including the yield strength and hardening rate are used to assess the P-SERVE. A smaller P-SERVE compared to the M-SERVE indicates that the characteristic features of twins implemented in determining the M-SERVE are more stringent than those for determining material properties.
This study has been supported through a grant No. FA9550-12-1-0445 to the Center of Excellence on Integrated Materials Modeling (CEIMM) at Johns Hopkins University awarded by the AFOSR/RSL Computational Mathematics Program (Manager Dr. A. Sayir) and AFRL/RX (Monitors Dr. C. Woodward and C. Przybyla). This sponsorship is gratefully acknowledged. Computing support by the Homewood High Performance Compute Cluster (HHPC) and Maryland Advanced Research Computing Center (MARCC) is gratefully acknowledged. The authors gratefully acknowledge the contributions of Dr. C. Torbet to the instrumentation and experimental methodologies.
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