Quantifying uncertainty from material inhomogeneity.

Abstract

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 µm in diameter) were machined into brass tensile specimens using a femto-second laser. The brass was annealed at 450 ℃, 600 ℃, and 800 ℃ 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.3 Acknowledgment

The Morphology of Tensile Failure in Tantalum

“…[23] The design of the load frame permits tilting the loadframe by up to 70 deg, allowing ready access for in situ EBSD experiments. The 2 kN force capacity of the load frame facilitates testing of relatively large tensile bars, such as those shown in Figure 3, and the displacement range of >8 mm permits testing to engineering strains of>100 pct with active LVDT sensing of actuator displacement.…”

Fatigue reliability assessment of turbine discs under multi‐source uncertainties

“…However, its failure usually exhibits a stochastic behavior due to variations from material properties, geometries, and loading spectra. In addition, for most engineering materials, material inhomogeneity exists in their processing, internal structure, properties, and performance and often manifests across multiple length (from the microstructure scale to the component and part scale) and time scales (over time as the material ages) and leads to variabilities . In order to reach an acceptable level of probability of component failure, these multiple variations or spreads or scatter should be fully quantified and controlled when developing or utilizing a lifing procedure for fatigue design and/or subsequent life prediction.…”

Multi-scale Modeling of Plasticity in Tantalum.

“…Tensile tests were conducted in a custom-built in situ load frame, Figure 21 Supra 55VP field emission SEM. The tensile stage was specifically designed and built at Sandia National Laboratories to be used for in situ EBSD experiments [16,25]. The load frame uses a linear variable differential transformer (LVDT) to measure displacement, and a custom-built, strain-gage-based transducer to measure applied load.…”