Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition

The traditional contour method maps a single component of residual stress by cutting a body carefully in two and measuring the contour of the cut surface. The cut also exposes previously inaccessible regions of the body to residual stress measurement using a variety of other techniques, but the stresses have been changed by the relaxation after cutting. In this paper, it is shown that superposition of stresses measured post-cutting with results from the contour method analysis can determine the original (pre-cut) residual stresses. The general superposition theory using Bueckner’s principle is developed and limitations are discussed. The procedure is experimentally demonstrated by determining the triaxial residual stress state on a cross section plane. The 2024- T351 aluminum alloy test specimen was a disk plastically indented to produce multiaxial residual stresses. After cutting the disk in half, the stresses on the cut surface of one half were determined with X-ray diffraction and with hole drilling on the other half. To determine the original residual stresses, the measured surface stresses were superimposed with the change stress calculated by the contour method. Within uncertainty, the results agreed with neutron diffraction measurements taken on an uncut disk

Stochastic Characterization of Cast Metal Microstructure

The major goal of this work is to provide a means to characterize the final structure of a metal that has solidified from a melt. The thermally controlled solidification of a binary alloy, nucleated at isolated sites, is described by the evolution of a probability distribution function (PDF). The relevant equation required for propagating the PDF is developed with variables for grain size and distance to nearest neighbor. The phenomena of nucleation, growth, and impingement of the grains are discussed, and used as the basis for developing rate equations that evolve the PDF. The complementary equations describing global heat and solute transfer are discussed, and coupled with the microstructure evolution equations for grain growth and PDF evolution. The full set of equations is solved numerically and results are compared with experimental data for the plutonium 1 weight percent gallium system. The three principal results of this work are: (1) The formulation of transient evolution equations for the PDF description of nucleation, growth, and impingement of a distribution of grain sizes and locations; (2) Solution of the equations to give a correlation for final average grain size as a function of material parameters, nucleation site density, and cooling rate; and (3) Solution of the equations for final distribution of grain size as a result of the initial random spatial distribution of nucleation sites

Stochastic Characterization of Cast Metal Microstructure

The major goal of this work is to provide a means to characterize the final structure of a metal that has solidified from a melt. The thermally controlled solidification of a binary alloy, nucleated at isolated sites, is described by the evolution of a probability distribution function (PDF). The relevant equation required for propagating the PDF is developed with variables for grain size and distance to nearest neighbor. The phenomena of nucleation, growth, and impingement of the grains are discussed, and used as the basis for developing rate equations that evolve the PDF. The complementary equations describing global heat and solute transfer are discussed, and coupled with the microstructure evolution equations for grain growth and PDF evolution. The full set of equations is solved numerically and results are compared with experimental data for the plutonium 1 weight percent gallium system. The three principal results of this work are: (1) The formulation of transient evolution equations for the PDF description of nucleation, growth, and impingement of a distribution of grain sizes and locations; (2) Solution of the equations to give a correlation for final average grain size as a function of material parameters, nucleation site density, and cooling rate; and (3) Solution of the equations for final distribution of grain size as a result of the initial random spatial distribution of nucleation sites

Probability Distribution Function Evolution for Binary Alloy Solidification

The thermally controlled solidification of a binary alloy, nucleated at isolated sites, is described by the evolution of a probability distribution function, whose variables include grain size and distance to nearest neighbor, together with descriptors of shape, orientation, and such material properties as orientation of nonisotropic elastic modulus and coefficient of thermal expansion. The relevant Liouville equation is described and coupled with global equations for energy and solute transport. Applications are discussed for problems concerning nucleation and impingement and the consequences for final size and size distribution. The goal of this analysis is to characterize the grain structure of the solidified casting and to enable the description of its probable response to thermal treatment, machining, and the imposition of mechanical insults

Characterization of Cast Metals with Probability Distribution Functions

AbstractCharacterization of microstructure using a probability distribution function (PDF) provides a means for extracting useful information about material properties. In the extension of classical PDF methods developed in our research, material characteristics are evolved by propagating an initial PDF through time, using growth laws derived from consideration of heat flow and species diffusion, constrained by the Gibbs-Thomson law. A model is described here that allows for nucleation, followed by growth of nominally spherical grains according to a stable or unstable growth law. Results are presented for the final average grain size as a function of cooling rate for various nucleation parameters. In particular we show that the model describes linear variation of final grain size with the inverse cube root of cooling rate. Within a subset of casting parameters, the stable-to-unstable manifests itself as a bimodal distribution of final grain size. Calculations with the model are described for the liquid to epsilon phase transition in a plutonium I weight percent gallium alloy.</jats:p