Microstructural characterization of as-cast high-nitrogen Fe-15Cr-15Ni alloys

A base composition of Fe-15Cr-15Ni was melted in a hot-isostatic-pressure furnace under nitrogen pressures from 0.1–150 MPa (1–1500 atm) to produce materials with nitrogen concentrations from 0.04–3.6 wt%. Microstructural characterization of the as-cast materials was completed using optical microscopy, X-ray diffraction, scanning electron microscopy, and transmission electron microscopy techniques. The phases present in the materials were austenite, nitrides (Cr₂N and CrN), and martensite. All of the materials solidified with primary austenite dendrites. Dendritic solidification of CrN occurred in interdendritic regions of the austenite in alloys containing between 0.6 and 1.9 wt % N. Cellular precipitation of Cr₂N occurred in alloys with intermediate nitrogen concentrations (0.6 and 1.0 wt %). The orientation relationship between the Cr₂N and austenite, expressed as {1 1 1}y{0 0 0 1}Cr₂N and 1 1 0 –1 1 0 0Cr₂N, was confirmed. Precipitates of CrN with both lamellar and disc morphologies formed in the austenite. Both had a cube-cube orientation relationship with the austenite. Only about 10% of the 3.6 wt% N material solidified as primary austenite. The remainder of the material solidified as a eutectic according to the reaction L +CrN. All of the austenite in the eutectic region subsequently transformed to martensite. Increasing volume fractions of martensite formed with increasing bulk nitrogen concentrations in the materials due to alloy depletion of austenite caused by nitride formation.     

Theory of thermohyperelasticity for near-incompressible elastomers

Summary Elastomers are often used in hot and confining environments in which thermomechanical properties are important. It appears that published constitutive models for elastomers are mostly limited to isothermal conditions. In this study, athermohyperelastic constitutive model for near-incompressible elastomers is formulated in terms of the Helmholtz free energy density . Shear and volume aspects of the deformation are decoupled. Thermomechanical coupling occurs mostly as thermal expansion. Criteria for thermodynamic stability are derived in compact form. As illustration, a particular expression for is presented which represents the thermomechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. It is used to analyze several adiabatic problems in a rubber rod.List of symbols A _i matrices appearing inD - c _e, _e, c _e specific heat at constant strain - C Cauchy strain tensor - C _R reduced Cauchy strain tensor - C ₁,C ₂ coefficients of Mooney-Rivlin model - c vectorial counterpart ofC: VEC (C) - c ₂ vectorial counterpart ofC ²: VEC (C ²) - D isothermal tangent stiffness matrix - e vectorial counterpart of : VEC () - deviatoric Lagrangian strain tensor - e _R reduced deviatoric Lagrangian strain tensor - e volume strain - e _T reduced volume strain - f thermal expansion function,=[1+(T–T ₀)/3]^–1 - F, F _T deformation gradient tensor - F _R reduced deformation gradient tensor - H Hessian matrix for the Gibbs free energy density - H related toH - I ₁,I ₂,I ₃ invariants ofC - I _1R,I _2R,I _3R invariants ofC _R - I, I ₉ identity matrix - i vectorial counterpart ofI: VEC (I) - J determinant ofF - J _R determinant ofF _R - J _T determinant ofF _T - J ₁,J ₂ invariants of /J _{R 2} ³ - J _1R,J _2R invariants of _R /R _J ^2/3 - k thermal conductivity coefficient - K ₁,K ₂,K ₃ invariants of /J ^2/3 - K _1R,K _2R,K _3R invariants ofe _R/J^2/3 - p hydrostatic pressure - s vectorial counterpart of stress : VEC () - s isotropic stress - T (absolute) temperature - T ₀ reference temperature - conventional (isothermal) strain energy density (per unit volume) - volumetric thermal expansion coefficient - thermal expansion vector - strain, Lagrangian strain - entropy density - isothermal bulk modulus - Lagrange multiplier - _i extension ratio - shear modulus - stability coefficient - mass density - stress, 2nd Piola-Kirchhoff stress - _i principal stress - Cauchy stress - _d deviatoric Cauchy stress - , _{M C T 0} Helmholtz free energy density - _i /I _i - _ij ²/I _i I _j - Gibbs free energy density - (.) variational operator - VEC (.) vectorization operator - operator for Kronecker product     

Spatial structure of the superconducting phase in heavy-fermion systems and anomalies in the excitation spectrum

A degenerate superconducting phase in a metal with strong spin-orbital coupling may have a domain structure at low temperatures. The domain walls (of width =v_F/₀) carry a finite density of states N(0)mk _f/² per unit volume, which in turn results in the presence of a linear term T in the electronic specific heatC _e (T). With the help of the Atiyah-Singer theorem, this can be proved for a wide class of domain structures.     

The quantitative application of Fermi-Dirac functions to two- and three-dimensional systems

Expressions for the various physical parameters of the ideal Fermi-Dirac gas in two dimensions are derived and compared to the corresponding three-dimensional expressions. These derivations show that the Fermi-Dirac functions most applicable to the two-dimensional problem are F ₀(), F ₁(), and F₀(). Analogous to the work of McDougall and Stoner in three dimensions, these functions and parameters derived from them are tabulated over the range of the argument, –420. The physical applications of the tabulated 2D and 3D functions to ³He monolayer and bulk liquid ³He nuclear magnetic susceptibilities, respectively, are considered. Calculational procedures of fitting data to theoretical parameters and criteria for judging the quality of fit of data to both two- and three-dimensional Fermi-Dirac values are discussed.This work was performed under the auspicious of the U.S. Department of energy, Office of Solar Application. Work also supported in part by the National Science Foundation and a Navy Equipment Lone Contract.     

Single-fibre polymer composites

We have used Raman spectroscopy to measure the axial stress distribution along a fibre during a quasi-static single fibre pull-out test. The stress distribution at the debonding front during the progress of debonding gives the maximum interfacial shear strength _s directly. In addition, the stress distribution along the fibre after debonding can be used to evaluate the interfacial normal stress and the frictional coefficient. For the plasma treated high modulus polyethylene (PE) fibres used here, _s is found to be 28 MPa by this method, while the apparent mean interfacial shear strength _a obtained from the regular single fibre pull-out test varies from 3 to 15 MPa with the fibre embedded length I _e. Stress distributions derived from the shear-lag theory fit the experimental data for fully bonded fibres well, giving values for the shear-lag constant K and the stress transfer length 1/ [1]. According to the shear-lag theory, _s = l _eacoth(l _e). If can be found for a given system from Raman spectroscopy, _s can be evaluated from the pull-out test using this equation.The regular pull-out tests, corrected for residual stress and interfacial friction, give the same _s but not the same or pull-out load as the slower Raman test. The shear-lag constant K can be expressed as a function of the matrix shear modulus and geometric terms. One of these terms is the effective interfacial radius, r _e, the radius at which the strain in the matrix equals the average matrix strain. Raman measurements indicate that r _e is small, only four times the fibre radius. This result is supported by polarizing optical microscopy. The model of Greszczuk [2], which assumes a uniform shear within an effective interaction thickness b _i, gives a similar result. We find that b _i = 20 m, about twice the fibre radius. Using the pull-out test data, as for other fibre composites, b _i and r _e predicted by shear-lag theories do not agree with the results of microscopy to this extent. In these cases _s is much larger than the yield strength of the matrix and as neither treatment considers plastic deformation of the matrix agreement should not be expected.     

Comparison of the long-term strength of α- and α + β- titanium alloys under a layer of chlorides in the temperature range 200–380°C

Conclusions Chlorides have no effect up to a temperature of 300°C on the-Ti alloys studied, but the strength characteristics of the+-Ti alloys fall by 10% (on the basis of 2000 h). In the range 300–380°C the long-term strength under a layer of chlorides on a basis of 2000 h decreases by 2.5 times in the+-Ti alloys, but only by 20—30% in the-alloys. Under the influence of the prolonged action of chlorides (up to 2000 h), the+-Ti alloys suffer corrosion cracking at a lower stress level than do the-alloys. The deformation capacity of the-alloys falls by 2–4 times in the same temperature range, while in the + —alloys it falls practically to zero. A decrease in thickness of the specimen from 5 to 1.5 mm leads to a reduction in the long-term strength limit based on 2000 h by 1.3–1.4 times. A significant size-scale effect appears in- and+-Ti alloys which have a room-temperature yield point of not less than 70 kg/mm². The extent of the fall in long-term strength and deformation capacity with reduction in the thickness of the specimen is somewhat greater in+ —Ti alloys than in-alloys.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 11, No. 5, pp. 67–70, September–October, 1975.     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of a single-crystal Heusler structure Cu41Mn20Al39 alloy

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic-stiffness tensor components Cu and the adiabatic bulk modulus, BS, of a ferromagnetic Heusler structure Cu41Mn20Al39 at % alloy single crystal as functions of temperature in the range 14–300 K and hydrostatic pressure up to 0.2 GPa at room temperature. At 295 K the elastic stiffnesses are: C11=133 GPa, C44=92 GPa, C (=(C11–C12)/2)=17 GPa, C12=99 GPa, CL(=C11+C44–C)=205 GPa, and BS (=C11–4C/3)=106 GPa. Cu41Mn20Al39 is a comparatively soft material elastically because its elastic properties are influenced strongly by magnetoelastic effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to obtain the hydrostatic-pressure derivatives of the elastic – stiffness tensor components. At 295 K (C11/P)P=0, (C44/P)P=0, (C/P)P=0, (C12/P)P=0, (CL/P)P=0, and (BS/P)P=0 are 5.0±0.1, 3.0±0.1, 1.0±0.2, 3.0±0.3, 7.7±0.4 and 3.7±0.4, respectively. Application of hydrostatic pressure does not induce acoustic-mode softening: the pressure derivatives (CIJ/P)P=0 and (BS/P)P=0 and the acoustic-mode Grüneisen parameters are positive. An interesting feature of the non-linear acoustic behaviour of this alloy is that the value obtained for (C/P)P=0, associated with the softer shear mode propagated along the [1 1 0] direction and polarized along the [1 1 0] direction, is small in comparison with those of the other shear and longitudinal modes. The Grüneisen parameter of this mode, and hence its vibrational anharmonicity, is much larger than those of the other long-wavelength acoustic phonon modes. © 1998 Kluwer Academic Publishers     

Fracture toughness and hardness of zinc sulphide as a function of grain size

The erosion properties of brittle materials depend upon plastic deformation and crack generation at an impact or indented site. Vickers indentations have been used to investigate the plastic processes and crack systems in chemical vapour deposited zinc sulphide of different grain sizes. The hardness,H, and the local fracture toughnessK _c, are dependent upon the grain size of the material. For small grain size material (<50 m) the Vickers hardness was found to increase with decreasing grain size in accord with the Petch mechanism, i.e.H=H ₀ +kd ^–1/2 wherek andH ₀ are constants andd is the grain diameter. A maximum hardness of ca. 4 GPa has been observed for material with an average 0.5 m grain diameter. In large grain size material, hardness anisotropy within the grains causes significant experimental scatter in the hardness measurements because the plastic impression formed by the indenter (load 10 N and 100 N) is smaller than the grain diameter. The values ofK _c obtained using an indentation technique show that for grain sizes less than 8 mK _c decreases with decreasing grain size. For materials with a grain size in the range 500 m to 8 m, well developed median cracks were not observed, however, the radius of the fracture zone was measured in order to estimate an effectiveK _c. The effectiveK _c was found to increase approximately linearly with the reciprocal root of the grain size. Consideration of the models for elastic/plastic impact and micromechanics of crack nucleation in conjuction with the variation ofK _c andH, indicate that zinc sulphide with a mean grain size of 8 m will give the optimum solid particle and rain erosion resistance.     

The role of starting powder size on the compressive response of stand-alone plasma-sprayed alumina coatings

Cylindrical stand-alone tubes of plasma-sprayed alumina were tested in uniaxial compression at room temperature, using strain gages to monitor axial strains. The effect of lamella size on the mechanical response was investigated by employing different starting powders to fabricate samples. The average powder sizes investigated included 9 m, 19 m and 32 m alumina; the resulting effective lamella diameters were 10 m, 28 m, and 55 m, respectively. Similar stress-strain hysteresis was observed on unloading in all tubes, independent of lamella size. A strong correlation between the failure stress and the cumulative strain at failure was also observed for tubes fabricated from the three powders. For samples with approximately constant densities, tubes plasma sprayed with the 9 m powder exhibited greater moduli than tubes sprayed from either 19 or 32 m powders. This difference was attributed to the greater percentage of unmelted -Al₂O₃ in the coating.     

Conventional Electronic Structure of MgB2 and ZrB2: LDA vs. de Haas-v. Alphen & ARPES Data

We compare full potential LDA band calculations of the Fermi surfaces areas and band masses of MgB₂ and ZrB₂ previously reported and new dHvA data. Discrepancies in areas in MgB₂ can be removed by a small shift of bands relative to bands. Comparison of effective masses lead to orbit averaged el-ph coupling constants =1.3 and =0.5, whereas for ZrB₂ only weak el-ph coupling with <0.3 is found. The ARPES data can be also well described by the LDA showing the presence of surface states.