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Computation and modeling applied to ceramic materials Failure modeling One of the important aspects of using ceramic materials in structural applications is dealing with the statistical nature of brittle failure. Ensuring reliability under operating stresses is particularly critical. Steve Freiman discussed work at NIST6 to develop a new statistical approach to predict safe operating lifetimes for ceramics. Researchers need to calculate such a lifetime and to determine uncertainty in the lower limit of the calculation. A statistical approach is needed, because nondestructive techniques cannot distinguish critical flaws in a ceramic part. Although proof testing is used to eliminate lower strength parts, such procedures are costly and difficult to apply accurately. Freiman explained that most uncertainty determinations of brittle failure currently are conducted using a twoparameter Weibull expression,7 but this approach is unduly conservative and may not best fit data. In most cases, a threeparameter Weibull equation provides a better fit to experimental data, but other mathematical expressions also can be used to fit data. Possible growth of flaws due to environmentally enhanced crack growth also can be accounted for in the calculations given the proper series of test procedures. Freiman proposed a three-step approach to determining mechanical reliability. Step 1: Fit an expression to test data, e.g., using three-parameter Weibull, and establish minimum initial strength and standard deviation. Step 2: Determine uncertainty in the lower limit to initial strength of the universe of components, using appropriate statistical software. Step 3: Combine measurement uncertainties associated with determining values for various measurement parameters in calculating probability-of-failure, if the existence of environmentally enhanced crack growth has been determined. Atomistic modeling Chandler Becker (NIST) presented a snapshot of some materials modeling efforts at NIST, particularly focused on atomic-scale simulations of ceramic materials. These efforts include combined computational and experimental efforts to study defect structures in graphene (Cockayne) and elucidate structures in gas sorption materials (Wong-Ng). NIST researchers also use high-throughputdensity functional methods to screen appropriate substrates for growth and functionalization of 2-D materials. Density functional theory (DFT) and cluster expansion methods examine the effect of vibrational entropy in DFT-based phase diagram calculations. These effects can be particularly large for NaCl–KCl composites. Additional NIST efforts focus on documenting limits of various methods. Specifically, these efforts assess and document uncertainties in DFT calculations that result from various approximations, including the effect of basis set expansion and exchange correlation functional in silicon, aluminum, carbon, and zirconium. A demonstration was conducted of how choices related to surface location (and thus cross-sectional area) of nanowires in molecular simulations affected the calculated axial Young's modulus and, specifically, how the determination of cross-sectional area can alter calculated diameter dependence of this property. This analysis might be useful in understanding the origins of various calculated and observed size effects in these systems. Tim Mueller (Johns Hopkins University) addressed the availability of data needed to conduct computational studies. He noted several available web sites to acquire such data, including the Electronic Structure Project,8 The Materials Project,9 and AFLOWLIB.10 He demonstrated how analysis of material data sets can effectively facilitate discovery of promising new materials. Noam Bernstein (NRL) discussed use of DFT to calculate properties of a material. He used the example of lithium-ion batteries to demonstrate effectiveness of DFT in searching for new materials. However, he also stated that DFT is computationally expensive to use. Government sponsored computation and modeling R&D Ken Lipkowitz (ONR) discussed computer-aided materials design activities focused on power and energy applications. ONR’s program objectives encompass discovery of new materials and improvement of materials. Thrusts include new mathematical procedures, high-throughput screening, informatics, and multiscale simulation. The “materials fingerprint” concept (similar to that used in the pharmaceutical industry) to identify new materials with similar characteristics and functions to established materials is another path for materials design. Lipkowitz also cited the AFLOWLIB as a resource. Lynnette Madsen (NSF) reported that computation and modeling is spread across the foundation. Ceramic proposals that are solely experimental or that have a computational component and an experimental component often are reviewed in the Ceramics Program within the Division of Materials Research (DMR). Within the Ceramics Program, about 150 projects are active at any given time. About one-third have two or more investigators, and many of these (35%–40%) have a computational/theory expert as part of the project. On the other hand, purely computational/theory scientific projects are considered within the Condensed Matter and Materials Theory Program (in DMR). The Division of Mathematical Sciences (DMS), which is within the Directorate for Mathematical and Physical Science (MPS), supports research that develops and explores properties and applications of mathematical structures. DMS researchers are encouraged to develop collaborations in a range of areas (manufacturing, clean energy, etc.) through its innovation incubator program.11 Proposals dealing with application of fundamental science to design and development of new devices and engineering systems are reviewed in the Engineering Directorate. The Computer and Information Science and Engineering (CISE) Directorate’s goals include advanced infrastructure and computing. Small team projects (in the $0.5M to $1.5M range) are reviewed in the competition titled Designing Materials to Revolutionize and Engineer our Future, which is NSF’s response to MGI and cuts across three directorates (MPS, ENG, and CISE). 38 www.ceramics.org | American Ceramic Society Bulletin, Vol. 95, No. 3


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