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Multiscale Experimental Analysis in Plasticity: Linking Dislocation Structures to Continuum Fields

Oztop, Muin S.

Plastic deformation in metals is a complex phenomenon and is result of competition between different complicated mechanisms, and among all, dislocation nucleation and motion are the most dominant ones. Dislocation evolution is known to be a multiscale phenomenon, and has been incorporated to crystal plasticity theories to analyze the size effect in metals for almost a decade ago. Although the theories suffice to predict the size effect in metals, they are largely phenomenological. Here a novel experimental method is developed to resolve the complexity in plastic deformation due to dislocations and to extract new material length scales that can be incorporated to numerical models. A continuum-based quantity: the geometrically necessary dislocation density (GND) that describes the signed part of the overall dislocations is measured on a nickel single crystal sample using recently developed high resolution electron backscatter diffraction (HR-EBSD) over different field of view, 90 μm^2 − 1mm^2 with various step sizes, 50 nm to 2, 500 nm . The net Burgers vector density, which includes the information of the direction of the overall dislocation motion and also quantifies the flux of atoms changing positions due to dislocations, is measured for the first time using continuum methods. A new parameter, β, that is extracted from the net Burger vector density to monitor dislocation activity on crystallographic slip planes is measured. Measurements reveals patterning in GND densities and a distribution of length scales rather than a single length scale as assumed. The length scales, such as dislocation spacing, and dislocation cell sizes are quantified. The linear relationship between dislocation spacing and dislocation cell size is obtained, where the slope of the linear fit varies with different crystallographic slip systems and the number of the active slip systems. The slope ranges between 23-29 for dominantly single slip regions, whereas it ranges between 13-16 for multislip regions, which agrees with the findings from TEM analysis in the literature showing how a continuum based method can be used to obtain same material parameters. The experimental measurements and the assumptions are elaborated in a detailed analysis. The effect of step size in EBSD results is presented, and the information loss with increasing the step size is shown. The uncertainty in GND density from the HR-EBSD measurements is found to be 10^13, which is two order of magnitude less than results from traditional diffraction methods. The effect of dislocation mobility on microstructure evolution has been also investigated, specifically tantalum single crystal specimens tested at 77 K and 293 K. The results unraveled occurrences of different deformation mechanisms: kink shear, and twinning at low temperatures. Interactions between dislocations and twin formations are observed and striking microstructure differences are examined. The dislocations density measurement results on tantalum are unique in the experimental sense and data can be used to extract length scale information. The experimental observations have been exploited to build the foundations of a numerical model. The effect of microstructure evolution on mechanical response has been investigated numerically based upon experimental observations. One of the main outcome of the experimental analysis -the variation of GND densities in cell walls- has been incorporated into a strain gradient plasticity framework. The proposed model is demonstrated with constrained shear and pure bending problems. The results presented show patterning in the GND density profile depending on the prescribed initial variation of the saturation value of GND densities and also change in overall mechanical response depending on the complexity of the prescribed profile.

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More About This Work

Academic Units
Mechanical Engineering
Thesis Advisors
Kysar, Jeffrey W.
Degree
Ph.D., Columbia University
Published Here
June 28, 2013
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