Predicting times to low strain for a 1CrMoV rotor steel using a 6-θ projection technique

The projection method of creep analysis is known to produce the poorest predictions of creep properties at low strains. This paper applies a recently suggested modification of the concept to 1CrMoV rotor steel where long term data exists to enable an assessment of this modification to be made. The modification takes the form of two additional terms that allow the initial stages of any creep curve to be modelled more accurately. The paper shows that the resulting 6- approach produces predictions of long-term failure times and minimum creep rates that are as good as those obtained using the traditional 4- approach. Unlike the 4- approach, the 6- approach is also shown to be capable of accurately predicting times to very low strains (0.05% and 0.1%) at stress levels as low as 77 MPa (well below the lowest stress of 230 MPa used in the theta analysis). For times to 1.0% strain or more the 4- and 6- techniques give similar short and long-term predictions.     

The θ projection method and small creep strain interpolations in a commercial Titanium alloy

The paper describes the early and final uniaxial creep behaviour of a Titanium alloy used for manufacturing intermediate power compressor disks and blades. Tests were conducted at the operating temperature (773 K) for such components and for rupture lives up to 3600 hours. Creep curves were fitted using either the conventional 4 model or the recently developed 6 equation. Parameters allowing the interpolation of times to small strains were produced and their accuracy checked against experimental values using distributions found to be most supported by the data. At strains above 0.75% both methods yielded zero mean interpolation errors. At strains above 0.27% and below 0.75% the 4 equation produced systematic errors in interpolation but the 6 function gave errors which were not statistically different from zero. For strains below 0.27% both techniques produced systematic interpolation errors but the 6 interpolations were always significantly better than their 4 counterparts. Both the 6 and 4 techniques produced systematic errors when predicting the failure time using interpolated rupture strains. Unlike the 4 function, the 6 equation produced unbiased predictions of the minimum creep rate and so produced failure time interpolations from the Monkman–Grant relation that were indistinguishable from zero.     

Adhesion to skin

The failure energy of an adhesive bond can be factorized into two terms, one of which is a dimensionless loss function and the other, the true interfacial bonding energy, ₀. Experimental techniques have been developed to effect a separation of these two terms and thus measure ₀, but they are unsuitable for the pressure-sensitive adhesives used in surgical tapes and dressings. This is because these adhesives flow readily under load. This paper describes an extrapolation technique by which this problem can be resolved. Adhesive peel data are extrapolated both to zero peel velocity and zero load, to give a true threshold value for peeling energy which is independent of temperature. Values of ₀ are given for a natural-rubber based adhesive and substrates of glass and human skinin vivo. For glass ₀ = 28J m^–2 and for normal skin ₀ 14J m-2.     

Near surface flaw detection by ultrasonic critical angle imaging

Acoustic critical angle measurements usually involve broad beam or global isonification of a water-solid interface. In order to obtain local interface data, it is convenient to use a focused acoustic source with lens axis at incident angle and point-receiver at specular reflection angle . By scanning this combination at various critical angles (=_crit), interface waves are generated locally near the lens focus. These waves penetrate the solid to a depth of approximately one shear wavelength _T and are modulated by discontinuities such as flaws, inclusions, and debonds that may be present there. A radiated longitudinal wave in water accompanies these modulated interface waves and carries information on subsurface flaws to the point-detector along the direction of a specularly reflected wave. By scanning the focus-receiver combination along the interface, the receiver output may be used to form images of local subsurface detail. We show that in anisotropic materials, such as crystals, there are generally two different _crit where a radiating interface wave provides subsurface information. We also discuss special problems associated with the use of a focused acoustic source including nonlinear effects (generation of harmonics) in the water.     

Polymer solutions confined in slit-like pores with attractive walls: An off-lattice Monte Carlo study of static properties and chain dynamics

Summary Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density , chain length N, and strength of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > , being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T < ) were considered. It is shown that phase separation in a polymer-rich and polymer-poor solution in the slit competes with polymer adsorption at the walls. A qualitative connection to the wetting behavior of semi-infinite polymer solutions is drawn. The acceptance rate for monomer motions was studied for various conditions, and profiles of monomer mobility across the slit were recorded. Also, average chain relaxation times were extracted from the time dependence of mean-square displacements. Although with increasing density the chain radii (at T > ) show a crossover from two-dimensional excluded volume behavior (R_g N² with = 3/4) to ideal random walk behavior ( = 1/2), the relaxation times show effective exponents Z_eff ( N^{Z eff}) that clearly deviate from the Rouse prediction in concentrated confined solutions.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

Grain growth in the two-phase Al-Cu alloys

Grain and phase growth in the two-phase Al-Cu alloys containing 6, 11, 1 7, 24 and 33 wt % Cu were investigated by annealing at 535 °C for 0.5–100 h. The grain and phase sizes of the phase are seen to be larger than that of the phase. The size of phase decreases whereas the size of phase increases with increasing copper content in the alloy. As such, the phase- and grain-size distributions are broader than the phase- and grain-size distributions, but the size range depends on annealing time and alloy composition. The grain sizes of the ,d , and ,d , phases can be related to the volume fraction of the phase,f , according to the equationd = 0.497d /f .     

Development of solidification microstructures in a fibre reinforced alloy

The solidification behaviour of a fibre reinforced Al-6 wt% Cu alloy, containing 30 vol% of 3 m diameter, semi-continuous, aligned alumina fibres has been studied. Results are presented to show the influence of fibres on the microstructural development of and microsegregation in the matrix during freezing. The effect of total solidification time, _t, on solidification behaviour was examined for 1<_t<520 S. By using interrupted solidification experiments microstructural development was studied in detail. It was found that -Al begins to grow within interfibre regions, and grows towards the Al₂O₃ fibres, avoiding them where possible. Consequently fibres are located in the last regions to solidify. When _t>10 s the final microstructure is non-dendritic, and CuAl₂ is located predominantly at the fibre-matrix interface. When _t 1 s it was observed that the final microstructure is dendritic with a periodic segregation pattern, and the CuAl₂ is more dispersed. The matrix composition becomes more uniform, and the minimum matrix composition rises as _t increases. The growth and microsegregation are analysed and discussed using simple semi-analytical models. The implications are that fibres significantly influence solidification behaviour if _f/_s<1, where _f is the average interfibre spacing and _s the secondary dendrite arm spacing which would develop in the unreinforced alloy.     

Effect of crack shape,inclination angle,and friction coefficient in crack surface contact problems

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle =15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for =45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for =15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K _II, K _III are calculated with varying the crack shape b/a, inclination crack angle , and crack face friction coefficient . The calculations show that the present method is useful for the analysis for =15–30 deg with high accuracy. It is seen that the K _II-values when b/a0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K _II values under Hertzian contact load, the results of =15 deg are smaller than the ones of =45 deg by 23–34%. Regarding the amplitude of (K _{II max}–K _{II min}), the results of =15 deg are smaller than the ones of =45 deg by 4–24%. With increasing the value of friction coefficient for crack faces the value of K _II decreases significantly. When the crack is short and the inclination angle is small, the value of friction coefficient f for Hertzian contact load largely affect the K _II value.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(). We do this usign simple models forN() and a realistically shapedN() taken from recent band structure work for Nb₃Sn. It turns out that peak structure inN() near _F may lead to gross errors in the derived Eliashberg function ²F() when the energy dependence ofN() is omitted in the inversion procedure. For Nb₃Sn, this leads to a 40% overestimate of when ²F() is evaluated via the standard McMillan program.     

Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source

Summary In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.

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Wärmespannungen in einer dünnen Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle

Zusammenfassung In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.

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Nomenclature r, polar coordinates - T temperature rise - ² ratio of conductivities - ² thermal diffusivity in -direction - J _n Bessel function ofn-th order - t time - p introduced in equation (2) - h heat transfer coefficient - a radius of circular disc - f(r, ) temperature distribution at initial state - r ₀, ₀ a point on the disc - T ₀ strength of point heat source - Dirac delta function - F stress function in two dimensions - ₁, ₂ coefficient of thermal expansion - a ₁₁,a ₁₂,a ₂₂,a ₆₆ elastic constants With 9 Figures     

Numerical method for solving heat-conduction problems for two-dimensional bodies of complex shape

A finite-difference scheme is described for a curvilinear orthogonal net which permits the use of a single algorithm for calculating bodies of various shapes.Notation x, y independent variables - u, v orthogonal coordinates - F(w)=F(u + iv) function of a complex variable - g(u,v)= F(w)/w Jacobian of transformation from (u,v) to (x,y) - thermal conductivity - c volumetric heat capacity - Q heat release per unit volume - T temperature - f value of temperature on boundary of region - time - L, L₁, L₂ differential operators - (u,v) solution of differential problem in canonical region - ^j, ₁ ^j , ₂ ^j , t^J, t ₁ ^j , t ₂ ^j network functions in canonical region - ^j, t^*j solutions of difference problems using rectangular and orthogonal nets respectively - {u_i, v_k} rectangular net in canonical region G - {x_i,k, y_i, k} orthogonal net in given region G^* - u_i, v_k dimensions of cell of rectangular net - u_i,v _i,k dimensions of cell of orthogonal net - h, maximum dimension of cell for rectangular and orthogonal nets respectively - ₁, ₂, difference operators for rectangular and orthogonal nets - A, B, C, D, A^*, B^*, C^*, D^* coefficients of difference scheme for rectangular net - D, Ã, B coefficients of difference scheme for orthogonal net Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 503–509, March, 1981.     

Precipitation phenomena in the Mg-31 at% Li-1 at% Al alloy

Precipitation phenomena produced in the -phase (b c c) of the Mg-31 at% Li-1 at%Al alloy subjected to different heat treatments have been studied by sensitive single-crystal X-ray diffraction techniques. The variation of the hardness values of specimens quenched and then aged was also examined. It was confirmed that AlLi is a stable phase at room temperature for the examined Al content; AlLi precipitation is only produced for very slow cooling rates from the -field. Phase reactions for specimens quenched and then aged can be summarized as follows: ++ after ageing at room temperature; + ++ AlLi after ageing at 473 K. A considerable increase of the hardness, which attains its maximum value after about 30 h ageing at room temperature, was observed. Neither the -phase nor the AlLi-phase precipitation can account for the observed hardening process. The presence of the -metastable phase when the hardness reaches its maximum value is verified.     

Preparation of epitaxially grown LaSrCoO3 thin films on SrTiO3(100) substrates by the dipping-pyrolysis process

LaSrCoO₃ thin films were spin-coated onto SrTiO₃(100) substrates by the dipping-pyrolysis process. X-ray diffraction -2 scans and X-ray diffraction scans were used to determine the crystallinity and in-plane alignment behavior of the films. The X-ray diffraction pattern shows the film obtained by annealing at 800°C was highly oriented. The X-ray diffraction pole-figure analysis and reciprocal-space mapping (-2 scans) of the resulting film showed that the film comprising the pseudocubic phase had an epitaxial relationship with the SrTiO₃ substrate.     

Transient thermal stress analysis of multilayered hollow cylinder

Summary This paper deals with the transient response of one-dimensional axisymmetric quasistatic coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal stress distribution in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder with orthotropic material properties.Nomenclature Lame's constant - density - C _v specific heat - k _r ,k radial and circumferential thermal conductivity - _r , linear radial and circumferential thermal expansion coefficient - E _r ,E radial and circumferential Young's modulus - v _r Poisson's ratio - ₀ reference temperature - ,T dimensional and nondimensional temperature - r ^*,r dimensional and nondimensional radial coordinate - ,t dimensional and nondimensional time - _r ^* , _r dimensional and nondimensional radial stress - ^* , dimensional and nondimensional circumferential stress - U, u dimensional and nondimensional radial component of displacement     

On the nucleation ofθ′ and T1 on Al3Zr precipitates in Al-Li-Cu-Zr alloys

Two quaternary Al-Li-Cu-Zr alloys have been investigated using electron microscopy. Ageing at 190° C resulted in the nucleation of precipitates on the Al₃Zr/matrix interface in addition to heterogeneous nucleation on matrix dislocations. In the majority of cases, the broad, coherent face of the plans ms in contact with the Al₃Zr precipitates. Similar evidence showed that nucleation of T₁ precipitates occurred on the Al₃Zr, but to a lesser extent than. Solid-solid nucleation theory has been used to account for the Al₃Zr acting as a nucleation substrate.     

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

On irreducible polynomials of small height over finite fields

It is shown that, for an arbitrary function(x) , for almost all prime numbersp of any interval of the form [N–,N] there exists an irreducible modulop polynomial with coefficients of orderO((p)).     

Creep crack growth in brittle materials

During steady state crack growth by diffusive cavitation at grain boundaries, crack tip fields are relaxed due to the presence of a cavitation zone. In the present analysis, analytic solutions for the actual crack tip stress fields and the crack velocity in the presence of cavitation zone consisting of continuously distributed cavities ahead of the crack tip are derived using the smeared volume concept. Results indicate that the r ^–1/2 singularity is now attenuated to r ^{–1/2 +} (0<<1/2) singularity. The singularity attenuation parameter is a function of the crack velocity and material parameters. The crack growth rate is related to the mode I stress intensity factor K by K ² at relatively high load, K ⁿ at intermediate load, and approaches zero at small load near K _th. Meanwhile, the cavitation zone extends further into the material due to the stress relaxation at the crack tip and the subsequent stress redistribution. Such relaxation effects become very distinct at low crack velocity and low applied load. Key words: Creep crack growth, brittle material, diffusive cavity growth, sintering stress, crack tip stress field.