Difference In Elastic Constants Research Articles

Residual-stress determination of concentric layers of cylindrically orthotropic materials

Equations have been obtained for determining residual stresses in the wall of a hollow, axially symmetric body consisting of concentric layers of elastically dissimilar materials, all having cylindrical elastic orthotropy. These equations permit residual normal stresses in the radial, circumferential, and axial directions and residual shear stresses on planes normal to the axis of the body to be calculated from measurements of the strains developed on the inner or outer cylindrical surface of the body as thin layers of stressed material are serially removed from the outer or inner surfaces, respectively. The equations are applied to a parametric study of stresses in an elastically isotropic, two-component body to determine the nature of the differences in stresses between the composite body and a homogeneous body as a function of the difference in elastic constants.

Elastic interaction and stability of misfitting cuboidal inhomogeneities

The elastic interaction energy between several rectangular parallelepipeds and the elastic self-energy of a cuboid are calculated to first order in the difference in elastic constants between the precipitate and matrix. The system is assumed to be elastically isotropic, the precipitates are coherent with the matrix and possess a dilatational misfit. The functionality and magnitude of the interaction energy per precipitate are extremely sensitive to the precipitate morphology and number of precipitates considered. The interaction energy between three or more precipitates cannot be accurately estimated by summing the pairwise interactions. The influence of the interaction energy on the stability of precipitate arrays is discussed.

紙のカール ＩＩ カール近似公式の誘導とその適用性

Approximate formulas for predicting reversible curl behavior have been derived from the lamination theory of curl, which was developed by Carlsson.Paper sheet is considered here as a laminate which consists of “wire” side and “felt” side sheet having equal thickness and different properties. If difference in elastic constants of both sides is small as compared with their average values over the thickness, curvature equation in the lamination theory is systematically approximated, as described in Appendix I. For relatively small orientation angles, the formulas are expressed as eqs.(1) through (3), which include expansion coefficients, orientation angles, moisture (or temperature) changes and thickness as main parameters. The formulas revealed that bending curl is mainly determined by the difference in expansion coefficients of both sides, while twisting curl is strongly dependent on the orientation angle and the degree of anisotropy.The validity of the formulas has been established through numerical comparison with the exact solutions. It was found that the bending curvature can be described even by the first term of the formula for the case of small orientation angles or weak anisotropy. In order to determine applicability of the two-layer model for the case of real sheets, fine paper samples were ground by using a specially designed surface grinder to obtain wire and felt side sheets, and expansion coefficients and orientation angles were determined for each side to predict the curvature components by using the curl formulas. A general agreement has been found between measured and predicted curl changes.

The state and habit of the Fe 16N 2 Precipitate in b.c.c. iron: elastic theory

The linear elastic theory is used to determine the preferred habit of the α 2 Fe 16N 2 precipitate in α iron, assuming that the precipitate is a coherent, tetragonal phase having the form of a thin circular disc, and neglecting both surface tension effects and the difference in elastic constants between the precipitate and the iron matrix. With these approximations the precipitate habit depends on the tetragonality of the transformation strain connecting the matrix and precipitate lattices, the aspect ratio of the disc, and the elastic constants. The preferred habit of Fe 16N 2 in α iron is found to vary with the precipitate aspect ratio ( K). The preferred habit changes continuously from {100} for K <11.35 to an asymptote near {102} for large values of K. The results can explain the common {100} habit of Fe 16N 2, but predict that this habit is unstable when the precipitate aspect ratio is large. The theory is also used to calculate the lattice parameters of the precipitate when it is constrained within α iron. The results agree with experimental data and provide a simple explanation for discrepancies in the reported values of the lattice parameters of Fe 16N 2.

Simulated strength-grain size study using a glass-glass-ceramic composite system

Strength studies have been conducted on composite specimens of a glass and a glass-ceramic. The composite system consists of a glass fillet on the surface of a bar-shaped glass-ceramic. Controlled surface flaws have been introduced into the glass fillet via indentation. Strength has been studied as a function of indent load and the size of the glass fillet. The glass-glass-ceramic composite system is meant to represent a polycrystalline ceramic with duplex microstructure such that the glass fillet simulates a large single crystal. The glass-ceramic on the other hand simulates a fine-grained matrix. Thus, the present study simulates a strength versus grain size relation for a polycrystalline ceramic. The data indicate that in several coarse grained ceramics, an inherent crack arrests within the body after initial propagation prior to catastrophic failure. Microscopic examination coupled with an electric potential method indicated that the initial crack arrests at the glass-glass-ceramic interface. The data also suggests that differences in elastic constants across an interface may have a significant influence on strength.

Calculated stresses in multilayered heteroepitaxial structures

A useful closed-form expression for stresses within individual layers of a multilayer composite has been obtained as a function of position within the layer. Equal and isotropic elastic constants were assumed in the calculation, although the error introduced by this assumption is found to vary by no more than the difference in elastic constants. Unequal elastic constants may be handled via computer solutions. The stresses within heterojunction AlxGa1−xAs/GaAs lasers are calculated as an example of the technique. The addition of Al to the active GaAs region is shown to have a drastic effect upon the active-region stress, changing it from tension to compression. This change of sign in stress is correlated with improvements in operating lifetimes of lasers.

The effect of uniaxial stress on the periodic morphology of coherent gamma prime precipitates in nickel-base superalloy crystals

The periodic morphology of cube shaped, coherent γ ′ [Ni3(Al, Ti)] precipitates in a representative nickel-base superalloy single crystal is shown to be influenced by the application of a 〈100〉 oriented uniaxial stress during annealing at elevated temperature. Furthermore, the stress annealed γ′ morphologies depend on the stress sense. Tensile and compressive stress annealing result in a directional coarsening of precipitates, and then agglomeration to form γ ′ precipitate plates with broad faces aligned perpendicular to the stress axis and precipitate parallelepipeds with long axes parallel to the stress axis, respectively. In explaining the morphological changes that occur during stress annealing, we consider two driving forces: i) a driving force due to changes in the stress-free shape of the specimen, and ii) a driving force due to changes in the effective modulus of the specimen. The first, which depends on a difference in the elastic constants and the lattice parameters of the two phases, is apparently the dominant driving force for the observed morphological changes in a stress annealed superalloy. The second, which depends only on a difference in elastic constants, may be important in alloys with elastically soft, incoherent inclusions such as pores.

Study of Iron Ions in NaCl Using the Mössbauer Effect. II. The Vacancy-Impurity Associated State

Two types of Mossbauer spectra were observed for dilute concentrations of Fe/sup 57/ ions in NaCl. A doublet with a 0.5 mm/sec quadrupole splitting and a 0.5 mm/sec isomer shift relative to stainless steel (80 deg K) is interpreted as the result of either Te/sup 2+/ or Ce/sup 3+/ associated with a positive ion vacancy. A broad unsplit line at --2.07 plus or minus 0.07 mm/sec (80 deg K) is interpreted as the result of Fe/sup +/ substitutionally replacing Na/sup +/. The data are used to make a rough estimate ot the binding energy between positive ion vacancies and cobalt impurities, and the result is consistent with theoretical expectations. A study of the temperature dependence of these two resonances indicates that the ratio of the recoilless emitted gamma rays from the isolated ions compared with the vacancy associated ions is 0.75 plus or minus 0.15 at 80 deg K, 0.24 plus or minus 0.08 at 296 deg K, and 0.16 plus or minus 0.08 at 478 deg K. This huge effect is believed to be due to the difference in elastic constants and mass-symmetry'' contributions to the localized modes, for the two environments. (auth)