Publications

Quantifying uncertainty from material inhomogeneity

Battaile, Corbett C.; Brewer, Luke N.; Emery, John M.; Boyce, Brad B.

Most engineering materials are inherently inhomogeneous in their processing, internal structure, properties, and performance. Their properties are therefore statistical rather than deterministic. These inhomogeneities manifest across multiple length and time scales, leading to variabilities, i.e. statistical distributions, that are necessary to accurately describe each stage in the process-structure-properties hierarchy, and are ultimately the primary source of uncertainty in performance of the material and component. When localized events are responsible for component failure, or when component dimensions are on the order of microstructural features, this uncertainty is particularly important. For ultra-high reliability applications, the uncertainty is compounded by a lack of data describing the extremely rare events. Hands-on testing alone cannot supply sufficient data for this purpose. To date, there is no robust or coherent method to quantify this uncertainty so that it can be used in a predictive manner at the component length scale. The research presented in this report begins to address this lack of capability through a systematic study of the effects of microstructure on the strain concentration at a hole. To achieve the strain concentration, small circular holes (approximately 100 {micro}m in diameter) were machined into brass tensile specimens using a femto-second laser. The brass was annealed at 450 C, 600 C, and 800 C to produce three hole-to-grain size ratios of approximately 7, 1, and 1/7. Electron backscatter diffraction experiments were used to guide the construction of digital microstructures for finite element simulations of uniaxial tension. Digital image correlation experiments were used to qualitatively validate the numerical simulations. The simulations were performed iteratively to generate statistics describing the distribution of plastic strain at the hole in varying microstructural environments. In both the experiments and simulations, the deformation behavior was found to depend strongly on the character of the nearby microstructure.