A numerically tractable multi-scale model incorporating the effects of large numbers of discrete dislocations will be constructed and compared with novel electron-backscattering diffraction (EBSD)-based characterization to address the long-standing open question: ?Why does the mechanical strength of polycrystalline metals vary with grain size (Hall-Petch Effect)?? The model will avoid arbitrary length scales (strain gradients) and unobserved microstructures (linear pile-ups). Instead, a predictive capability will be constructed and tested. The new modeling and characterization capabilities will enable material design and improve applications, e.g. metal forming, particular for body-centered cubic metals such as steels. The advances will be incorporated in instructional modules at the two participating universities; undergraduate and graduate students will be trained in research practices; EBSD sensitivity will be extended by up to two orders of magnitude; and results will be disseminated widely by peer-reviewed publications, theses, and dissertations.
Non-Technical Summary:
The strength of common structural metals (e.g. steel, copper, aluminum, titanium) varies greatly with the scale of its microstructures. For example, the strength of steel can be increased 10 times by changing the grain size alone. There is no confirmed mechanism or model that predicts this well-known effect quantitatively. In order to facilitate the design and use of better, stronger materials, a predictive multi-scale (micro/macro) model will be constructed and tested using new analytical techniques. Benefits of a fundamental understanding of this important effect will permit production and use of better materials, resulting in a variety of societal advantages such as increased personal and national safety, reduced fuel consumption, and reduction of greenhouse gas emissions.
Metals are composed of small crystals, called "grains." The average size of these grains can vary over a wide range. Large grains can be 1000 times or more larger than small grains. In some metals, the size of the grains has an enormous effect on the strength. Steel is a particular example, with the strength of a fine-grained steel being several times larger than for a coarse-grained one. This relationship, known as the Hall-Petch effect, has been measured and utilized for more than 60 years. Nevertheless, there has never been a fundamental understanding or model that allows realistic prediction of the effect. Past attempts to understand its physical origin relied on unobserved mechanisms or on arbitrary parameters used to "fit" the right magnitude. In the current project, a physical and computer model was developed with no unrealistic assumptions or arbitrary parameters. It was used to predict the grain-size strengthening of steels, in particular pure iron and iron silicon alloys. In its first complete test, the new model predicted the measured magnitude accurately. More detailed work to verify other aspects of the model are underway using new measurement methods developed by collaborative work at the Brigham Young University. An example result mapping the lattice curvature (related to the density of crystal defects) is shown in Figure 1.
