Near tip fields for a stationary mode III crack between a linear elastic and an elastic power law hardening material

The asymptotic stress field near the tip of an antiplane crack lying along a planar bimaterial interface between an elastic and an elastic power law hardening material is analysed. Deformation plasticity theory is assumed in the analysis. We show that the shear stress field near the tip is of the form% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaDaaaleaacaWGPbaabaGaeyySaelaaOGaaeiiaiab% gYJi+jaabccacaWGYbWaaWbaaSqabeaadaWcgaqaaiabgkHiTiaaig% daaeaacaGGOaGaamOBaiabgUcaRiaaigdacaGGPaaaaaaakiaabcca% caWGubWaa0baaSqaaiaaicdadaWgaaadbaGaeyySaelabeaaaSqaai% aacIcacaWGPbGaaiykaaaakiaabccacaGGOaGaeqiUdeNaaiykaiaa% bccacqGHRaWkcaqGGaGaamOCamaaCaaaleqabaGaamiDamaaBaaame% aacaaIXaaabeaaliabgkHiTiaaigdaaaGccaqGGaGaamivamaaDaaa% leaacaaIXaWaaSbaaWqaaiabgglaXcqabaaaleaacaGGOaGaamyAai% aacMcaaaGccaqGGaGaaiikaiabeI7aXjaacMcacaqGGaGaey4kaSIa% aeiiaiabl+UimjaabccacqGHRaWkcaqGGaGaamOCamaaCaaaleqaba% GaamiDamaaBaaameaacaWGRbaabeaaliabgkHiTiaaigdaaaGccaqG% GaGaamivamaaDaaaleaacaWGRbWaaSbaaWqaaiabgglaXcqabaaale% aacaGGOaGaamyAaiaacMcaaaGccaqGGaGaaiikaiabeI7aXjaacMca% caqGGaGaey4kaSIaaeiiaiabl+Uimbaa!809A!\[\tau _i^ \pm {\text{ }} \sim {\text{ }}r^{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} {(n + 1)}}} \right. \kern-\nulldelimiterspace} {(n + 1)}}} {\text{ }}T_{0_ \pm }^{(i)} {\text{ }}(\theta ){\text{ }} + {\text{ }}r^{t_1 - 1} {\text{ }}T_{1_ \pm }^{(i)} {\text{ }}(\theta ){\text{ }} + {\text{ }} \cdots {\text{ }} + {\text{ }}r^{t_k - 1} {\text{ }}T_{k_ \pm }^{(i)} {\text{ }}(\theta ){\text{ }} + {\text{ }} \cdots \]for. Here r is the radial distance from the crack tip, is the angle measured from the interface, n is the hardening exponent, and + and — indicate the plastic and elastic regions respectively. The exponents t _k are uniquely determined by n, and for k1,t _k+1> t _k , t ₁. For kM, where M is the largest positive integer for which (n(M+1)-M)/(n+1) < 0.5 (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaakaaabaGaamOBamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaa% iodacaaI0aGaamOBaiabgUcaRiaaigdaaSqabaaaaa!431D!\[\sqrt {n^2 + 34n + 1} \] + 1 + n – 1)/(n + 1),t _k = (n(k + 1) – k)/(n + 1). The corresponding angular functions % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadsfadaqhaaWcbaGaam4AamaaBaaameaacqGHXcqSaeqaaaWc% baGaaiikaiaadMgacaGGPaaaaOGaaiikaiabeI7aXjaacMcaaaa!45AB!\[T_{k_ \pm }^{(i)} (\theta )\] are determined by the J-integral and material parameters and can be obtained completely from the asymptotic analysis. Some of the terms of stresses with kM may be singular. For k>M, t _k can be obtained numerically, and the corresponding % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadsfadaqhaaWcbaGaam4AamaaBaaameaacqGHXcqSaeqaaaWc% baGaaiikaiaadMgacaGGPaaaaOGaaiikaiabeI7aXjaacMcaaaa!45AB!\[T_{k_ \pm }^{(i)} (\theta )\] can be obtained completely or within multiplicative constants. All the terms of stresses with k>M vanish as r , when r0, where >0, for all 1<n<. It is important to note that although the individual terms of the stress expansion is variable separable, the resultant stress field is non-separable. The values of t ₁,...,t ₅ for 1<n20 and the first three terms of stresses for various values of n and material parameters are computed explicitly in the paper. Our analysis shows that, in the series solution for stresses in the plastic domain, the effect of the linear elastic material appears in the second or higher order terms depending on the value of n. In spite of this effect of elasticity on the higher order terms, the region of dominance of the HRR field in the plastic zone % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadkhadaahaaWcbeqaaiabgkHiTmaalyaabaGaaiikaiaaigda% aeaacaWGUbGaey4kaSIaaGymaiaacMcaaaaaaOGaamivamaaDaaale% aacaaIWaWaaSbaaWqaaiabgUcaRaqabaaaleaacaGGOaGaamyAaiaa% cMcaaaGccaGGOaGaeqiUdeNaaiykaaaa!4B3E!\[r^{ - {{(1} \mathord{\left/ {\vphantom {{(1} {n + 1)}}} \right. \kern-\nulldelimiterspace} {n + 1)}}} T_{0_ + }^{(i)} (\theta )\] may be significantly reduced compared to the corresponding region of dominance when the crack is in a homogeneous elastic power law hardening material.     

Frequency-Dependent Bulk Viscosity in One- And Two-Component Near-Critical Fluids

We assume isomorphism between near-critical fluids and Ising spin systems to calculate the critical anomaly of transport coefficients. As an example we present a very simple and general expression for the frequency-dependent bulk viscosity *() in one- and two-component fluids near the critical point. It reads is a universal complex function, c is the zero-frequency sound velocity, c _c is its critical value, and is the order parameter relaxation rate. We also examine macroscopic adiabatic relaxations of pressure, temperature, and density after stepwise changes of pressure or density. Such measurements give information on the time correlation function of the diagonal part of the stress, which relaxes anomalously slowly near the critical point.     

Phase relations in the system Cu-La-O and thermodynamic properties of CuLaO2 and CuLa2O4

Phase relations in the system Cu-La-O at 1200 K have been determined by equilibrating samples of different average composition at 1200 K, and phase analysis of quenched samples using optical microscopy, XRD, SEM and EDX. The equilibration experiments were conducted in evacuated ampoules, and under flowing inert gas and pure oxygen. There is only one stable binary oxide La₂O₃ along the binary La-O, and two oxides Cu₂O and CuO along the binary Cu-O. The Cu-La alloys were found to be in equilibrium with La₂O₃. Two ternary oxides CuLaO₂ and CuLa₂O₄₊ were found to be stable. The value of varies from close to zero at the dissociation partial pressure of oxygen to 0.12 at 0.1 MPa. The ternary oxide CuLaO₂, with copper in monovalent state, coexisted with Cu, Cu₂O, La₂O₃, and/or CuLa₂O₄₊ in different phase fields. The compound CuLa₂O₄₊, with copper in divalent state, equilibrated with Cu₂O, CuO, CuLaO₂, La₂O₃, and/or O₂ gas under different conditions at 1200 K. Thermodynamic properties of the ternary oxides were determined using three solid-state cells based on yttria-stabilized zirconia as the electrolyte in the temperature range from 875 K to 1250 K. The cells essentially measure the oxygen chemical potential in the three-phase fields, Cu + La₂O₃ + CuLaO₂, Cu₂O + CuLaO₂ + CuLa₂O₄ and La₂O₃ + CuLaO₂ + CuLa₂O₄. Although measurements on two cells were sufficient for deriving thermodynamic properties of the two ternary oxides, the third cell was used for independent verification of the derived data. The Gibbs energy of formation of the ternary oxides from their component binary oxides can be represented as a function of temperature by the equations:

Energy considerations in fatigue crack propagation

The concept of Griffith fracture theory was extended to fatigue crack propagation problems by defining the Gibbs free energy of solids under cyclic loading.As a result, the rate of fatigue crack propagation, dc/dN, was obtained as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbqfgBHr% xAU9gimLMBVrxEWvgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvA% Tv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9% vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea% 0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabe% aadaabauaaaOqaamaalaaabaGaciizaiaadogaaeaaciGGKbGaamOt% aaaacqGH9aqpcaGGOaGaaGOmaiaac6cacaaIZaGaciiEaiaaigdaca% aIWaWaaWbaaSqabeaacaGGTaGaaGOmaaaakiaacMcadaWcaaqaaiab% eQ7aRjaacIcacqGHuoarcaWGlbGaaiykamaaCaaaleqabaGaaGinaa% aaaOqaaiabeY7aTjabeo8aZnaaCaaaleqabaGaaGOmaaaaiqGakiaa% -vfaaaaaaa!547A!\[\frac{{\operatorname{d} c}}{{\operatorname{d} N}} = (2.3\operatorname{x} 10^{ - 2} )\frac{{\kappa (\Delta K)^4 }}{{\mu \sigma ^2 U}}\] where is a proportionality constant (01), K is the stress intensity amplitude, is the shear modulus, is an appropriate strength parameter for fatigue failure of the alloy and U is the energy to make a unit fatigue surface.

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Résumé Le concept de la théorie de rupture de Griffith a été étendu aux problèmes de propagation des fissures de fatigue en définissant l'énergie libre de Gibbs pour les solides soumis à sollicitations cyclique.Le résultat de cette approche est la détermination de la vitesse de propagation d'une fissure de fatigue dc/dN par la formule suivante: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbqfgBHr% xAU9gimLMBVrxEWvgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvA% Tv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9% vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea% 0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabe% aadaabauaaaOqaamaalaaabaGaciizaiaadogaaeaaciGGKbGaamOt% aaaacqGH9aqpcaGGOaGaaGOmaiaac6cacaaIZaGaciiEaiaaigdaca% aIWaWaaWbaaSqabeaacaGGTaGaaGOmaaaakiaacMcadaWcaaqaaiab% eQ7aRjaacIcacqGHuoarcaWGlbGaaiykamaaCaaaleqabaGaaGinaa% aaaOqaaiabeY7aTjabeo8aZnaaCaaaleqabaGaaGOmaaaaiqGakiaa% -vfaaaaaaa!547A!\[\frac{{\operatorname{d} c}}{{\operatorname{d} N}} = (2.3\operatorname{x} 10^{ - 2} )\frac{{\kappa (\Delta K)^4 }}{{\mu \sigma ^2 U}}\] où est une constante de proportionnalité, K est l'amplitude de l'intensité de contrainte, est le module de cisaillement, est un paramètre de résistance approprié à la rupture par fatigue de l'alliage considéré, et U est l'énergie nécessaire à la création d'une surface de fatigue unitaire.

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This research was supported by the Air Force Office of Scientific Research, Grant No. AF-AFOSR-76-2892A, and partially supported under the NSF-MRL program through the Materials Research Center of Northwestern University (Grant DMR 76-80847).     

Anharmonic effects in ultrasonic propagation near the lambda transition of 4He

Anharmonic effects are studied by measuring the temperature dependence of second harmonics of a 10-MHz ultrasonic wave generated near the transition of pressurized liquid ⁴He. The anharmonic coupling coefficient C between the fundamental wave and the second harmonic is found to diverge as % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSipIOZaaq% WaaeaaieaacaWF0baacaGLhWUaayjcSdWaaWbaaSqabeaaieqacaGF% TaGaa4hiaGqadKqaGkaa9fdaaaacbiGccaaFBbGaaeiDaiaa+1daca% aFOaGaaeivaiaa+9cacaqGubWaaSbaaSqaaGGadiab7T7aSbqabaGc% caaFPaacciGaeONeI0IaaWxmaiaa81faaaa!4911!\[ \sim \left| t \right|^{ - 1} [{\rm{t}} = ({\rm{T}}/{\rm{T}}_\lambda ) - 1]\] near . A phenomenological relation is developed expressing C in terms of known relevant thermodynamic quantities. This relation accounts well for the experimental results.This research was supported in part by the National Science Foundation under Grant DMR77-12249 and through the Materials Research Laboratory of Brown University.     

Study on the behavior of elastic-plastic fracture under mixed I+II mode loading in aluminum alloy Ly12-J-integral analysis

The elastic-plastic fracture behavior of aluminum alloy Ly12 under mixed I+II mode loading was studied by finite element method and fracture test. A mixed mode elastic-plastic fracture criterion of J-integral was proposed by using the J-resistance curve, and the maximum fracture effective plastic strain _p max of different mixed ratios at crack tip were also calculated. The results show that(1) the initiation J-integral values of different mixed ratios have the equation

On strength scaling of composites with long aligned fibres

Strength measurements of a specially made composite material are reported. The material consisted of an epoxy matrix and the reinforcement of one layer of well aligned and equally spaced glass fibers. For a certain range of fiber spacing , matrix initiation strength _c, under uniaxial tension, and were related as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZTGaam% 4yaOWaaOaaaeaacqaH7oaBaeqaaiabgIKi7UGaae4saaaa!3E6C!\[\sigma c\sqrt \lambda \approx {\text{K}}\]. Dimensional analysis indicated that the constant was proportional to the matrix fracture toughness. Using reported data on matrix initiation strength of a borosilicate glass-SiC composite under bending, a similar relation was suggested between _c and the maximum fiber spacing, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZTGaam% 4yaOWaaOaaaeaacqaH7oaBjeaycaqGTbGaaeyyaiaabIhaaOqabaGa% eyisISlaaa!40D6!\[\sigma c\sqrt {\lambda {\text{max}}} \approx\]. The latter relationship was also applicable to hardened cement paste with the largest void on the fracture surface as the appropriate length scale. The results outlined in this paper suggest that, for a range of fiber spacing, matrix initiation strength is dictated by a Griffith type flaw proportional to the fiber spacing (uniform case) or the largest fiber spacing (non-uniform case).     

Thermal conductivity and quantum diffusion in solid H2

The thermal conductivity of solid H₂ and the NMR absorption signal of isolated o-H₂ were measured simultaneously along isotherms 0.07<T<1.5 K as a function of time after a rapid cooldown from 2 K. The o-H₂ concentration ranged from 3.4% to 0.4%, and the pressure was 90 atm. During the measurements, clustering of o-H₂ particles occurred as seen from the changes both of the NMR signal amplitude and of with time t. The difference ^–1 = ^–1 ()– ^–1(0) between the thermal resistivity ^–1 (t=0) just after cool down and in equilibrium, ^–1 (), was found to change sign near 0.23 K, and this result is discussed with respect to previous experiments. The equilibrium resistivity attributed to the o-H₂ impurities, , is derived and is compared with previous determinations and with predictions. An analysis of the equilibration process for ^–1 and for the NMR signal amplitude is presented. It shows that the characteristic times are of comparable but not equal magnitude. Comparison of the derived from NMR data atP=90 and 0 atm favors resonant ortho-para conversion over quantum tunneling as the leading mechanism for quantum diffusion.     

‘When can we apply LEFM principles to elastic softening materials?’

The paper focusses on the determination of R, the size of the fully developed softening zone associated with a semi-infinite crack in a remotely loaded infinite elastic softening solid. R is a characteristic length for a material, and is important in that if R is less than an appropriate characteristic dimension of a structure, then LEFM principles can be used to describe the structure's failure. With p _c and _c being respectively the maximum stress and displacement within the softening zone, then provided the softening is not particularly pronounced, i.e. the area under the stress (p)-displacement (v) curve is % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaacaaeaacq% GH+aGpaiaawoWaaiaabccacaqGWaGaaeOlaiaabkdacaqG1aGaamiC% aSGaam4yaOGaeqiTdq2ccaWGJbaaaa!3FB5!\[\widetilde > {\text{ 0}}{\text{.25}}pc\delta c\], it is shown that R 0.4E _0c/P _c and R is relatively insensitive to the precise p-v softening behaviour (E ₀ = E/(1 – v ²) where E is Young's modulus and is Poisson's ratio. However, when the area under the curve is % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaacaaeaacq% GH8aapaiaawoWaaiaabccacaqGWaGaaeOlaiaabkdacaqG1aGaamiC% aSGaam4yaOGaeqiTdq2ccaWGJbaaaa!3FB1!\[\widetilde < {\text{ 0}}{\text{.25}}pc\delta c\], then R increases above this 0.4E _0c/P _c value. For this case, and provided most of the area under the p-v curve is not associated with the tail in the softening law, a more appropriate expression for R is R 0.1E ₀ ² / ₀ ² /K ² , with K ² /E ₀ being the area under the p-v curve and K being the stress intensity associated with the full development of a softening zone.     

Further Monte Carlo studies of the rotation-libration transition in solid H2 under pressure

The pressure-induced transition in solid para-H₂ from free rotation of molecules to libration around the three-fold axes of the fcc structure is calculated using a completely anisotropic interaction potential of the form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOvamaaBa% aaleaacaqGPbGaaeOAaaqabaGccqGH9aqpdaaeqaqaaiaaboeaaSqa% aiaab2gaaeqaniabggHiLdGcdaWgaaWcbaGaaeyBaaqabaGccaGGOa% GaaeOCamaaBaaaleaacaqGPbGaaeOAaaqabaGccaGGPaGaaeywamaa% BaaaleaacaqGYaGaaeyBaaqabaGccaGGOaGaeuyQdC1aaSbaaSqaai% aabMgaaeqaaOGaaiykaiaabMfadaWgaaWcbaGaaeOmaiaab2cacaqG% TbaabeaakiaacIcacqqHPoWvdaWgaaWcbaGaaeOAaaqabaGccaGGPa% aaaa!5132!\[{\text{V}}_{{\text{ij}}} = \sum\nolimits_{\text{m}} {\text{C}} _{\text{m}} ({\text{r}}_{{\text{ij}}} ){\text{Y}}_{{\text{2m}}} (\Omega _{\text{i}} ){\text{Y}}_{{\text{2 - m}}} (\Omega _{\text{j}} )\] including quadrupole-quadrupole and repulsive valence interactions. The rotational part of the Hamiltonian is assumed to be operating on a Jastrow-type wave function, including two variational parameters. The variational integrals are evaluated by a Monte Carlo procedure. The orientational order parameter in the low-density region increases very gradually with increasing density, until a sharp jump (indicating first-order) is observed at the transition density corresponding to R/R ₀ = 0.5775, where R ₀ is the nearest neighbor distance at zero pressure. This is 60% higher than the density obtained in previous work.     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures     

Comparison of the Electronic Structures of La2CuO4, Sr2CuO2Cl2, and Sr2CuO2F2

First-principles cluster calculations are reported of the local electronic structure of the three compounds: La₂CuO₄, Sr₂CuO₂Cl₂, and Sr₂CuO₂F₂. The copper and the planar oxygen 2p atomic orbitals exhibit a similar degree of covalency. The out-of-plane orbitals, however, are quite different with the atomic orbital lowered significantly in energy for chlorine and fluorine apical positions.     

Surface and grain-boundary energies of cubic zirconia

Using the multiphase equilibration technique for the measurement of contact angles, the surface and grain-boundary energies of polycrystalline cubic ZrO₂ in the temperature range of 1173 to 1523 K were determined. The temperature coefficients of the linear temperature function obtained, are expressed as $$\frac{{{\text{d}}\gamma }}{{{\text{d}}T}}({\text{ZrO}}_{\text{2}} ){\text{ }} = {\text{ }} - 0.431{\text{ }} \times {\text{ }}10^{ - 3} {\text{ }} \pm {\text{ }}0.004{\text{ }} \times {\text{ }}10^{ - 3} {\text{ Jm}}^{ - {\text{2}}} {\text{ K}}^{ - {\text{1}}} $$ and $$\frac{{{\text{d}}\gamma }}{{{\text{d}}T}}({\text{ZrO}}_{\text{2}} - {\text{ZrO}}_{\text{2}} ){\text{ }} = {\text{ }} - 0.392{\text{ }} \times {\text{ }}10^{ - 3} {\text{ }} \pm {\text{ }}0.126{\text{ }} \times {\text{ }}10^{ - 3} {\text{ Jm}}^{ - {\text{2}}} {\text{ K}}^{ - {\text{1}}} $$ respectively. The surface fracture energy obtained with a Vickers microhardness indenter at room temperature is found to be γ _F=3.1 J m^?2.     

The interface microstructure in alumina (FP) fibre/magnesium alloy composite

The objective of this work was to characterize the interfacial reaction zone in the metal matrix composite system-Al₂O₃(FP)/Mg (ZE41A). The composite was fabricated by liquid infiltration method. The reaction zone, a result of the reaction between magnesium in the alloy and the alumina fibres, was analysed for its morphology, chemistry, and crystallographic orientation using transmission electron microscopy. The results of this study showed the reaction zone to be, on average, 100nm wide and composed of MgO. The grains of the reaction zone ranged from less than 10 nm at the fibre/reaction zone interface to greater than 100nm at the matrix/reaction zone interface. It is proposed that the growth of the reaction zone was controlled by a seepage mechanism involving infiltration of liquid magnesium between MgO crystalS. Finally, it was observed that the MgO grains have the following crystallographic orientation relationship with the alumina grains from which they grew:

Three oxidation states and atomic-scale <Emphasis Type="Italic">p–n</Emphasis> junctions in manganese perovskite oxide from hydrothermal systems

Perovskite oxides have provided magical structural models for superconducting and colossal magnetoresistance, and the search for nano-scale and/or atomic-scale devices with particular property by specific preparations in the same systems has been extensively conducted. We present here the three oxidation states of manganese (Mn³⁺, Mn⁴⁺, Mn⁵⁺) in the perovskite oxide, La_0.66Ca_0.29K_0.05MnO₃, which most interestingly shows the rectifying effect as atomic-scale p–n junctions (namely FY-Junctions) of single crystals and films. The family of cubic perovskite oxides were synthesised by the so-called hydrothermal disproportionation reaction of MnO₂ under the condition of strong alkali media. The new concept of the atomic-scale p–n junctions, based on the ideal rectification characteristic of the p–n junctions in the single crystal, basically originates from the structural linkages of [Mn³⁺–O–Mn⁴⁺–O–Mn⁵⁺], where Mn³⁺ and Mn⁵⁺ in octahedral symmetry serve as a donor and an acceptor, respectively, corresponding to the localized Mn⁴⁺ .     

The influence of elastic mismatch on the size of the plastic zone of a crack terminating at a brittle-ductile interface

This paper presents the results of an investigation of the effects of elastic mismatch on the size of the plastic zone at the tip of cracks terminating at a bimaterial interface. Using the Williams technique, an asymptotic solution is obtained for the magnitude of the crack tip stress singularity and for the stress field associated with a semi-infinite crack impinging on an interface. This solution, together with the Von Mises yield criterion, is used to estimate the location of the plastic zone boundary r ₀ for various levels of the elastic mismatch, which are expressed in terms of the Dundurs constants. Results are expressed in terms of the non-dimensional quantity% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa% aaleaacaaIWaaabeaakmaadmaabaWaaSaaaeaacaaIXaaabaWaaOaa% aeaacaaIYaGaeqiWdahaleqaaaaakmaalaaabaGaam4AamaaBaaale% aacaqGjbaabeaaaOqaaiabeo8aZnaaBaaaleaacaaIWaaabeaaaaaa% kiaawUfacaGLDbaadaahaaWcbeqaaiabgkHiTiaaigdacaGGVaGaeq% 4UdWgaaaaa!4832!\[r_0 \left[ {\frac{1}{{\sqrt {2\pi } }}\frac{{k_{\text{I}} }}{{\sigma _0 }}} \right]^{ - 1/\lambda }\]where k _i is the stress intensity factor and ₀ is the yield stress. These results, together with an integral equation solution for k _i , are used to calculate the size of the plastic zone of a crack of length 2a loaded by uniform pressure. It is shown that the location of the boundary of the plastic zone depends strongly on the elastic mismatch.     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Low-temperature electrical resistance of disordered (Fe1−x Ni x )75P16B6Al3 alloys

We present a systematic study, to very low temperatures (<20 mK), of the electrical resistance of an amorphous metallic system, (Fe_1–x Ni _x )₇₅P₁₆B₆Al₃, with x varying from 0 to 1, so as to go from a magnetic to a nonmagnetic state. In all the alloys studied a minimum in the temperature range 8–40 K is observed. The resistance is found to increase as – lnT below T _min, and as +AT ² above it. While T _min appears to have a maximum around x = 0.5, no systematic concentration dependence is found in the variation of the other parameters describing the characteristic features of the resistivity. The experimental data are compared with the predictions from several theories in their low-temperature limits. It is found that the relation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacaqGWbGaeSipIO% JaaeylaiaabYgacaqGUbGaaeikaiaabsfadaahaaWcbeqaaiaabkda% aaGccqGHRaWkcqqHuoardaahaaWcbeqaaiaaikdaaaaaaa!3CA4!\[{\rm{p}} \sim {\rm{ - ln(T}}^{\rm{2}} + \Delta ^2 \] derived from the tunneling model adequately describes the low-temperature resistivity in these alloys.Supported in part by Naturvetenskapliga ForskningsrÅdet.     

Some viscoelastic wave equations

The authors study the problem of existence, uniqueness and asymptotic behavior for t of (weak or strong) solutions of equations in the form% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% abaeqabaGaamyDamaaBaaaleaacaWG0bGaamiDaaqabaGccqGHsisl% cqaH7oaBcqqHuoarcaWG1bWaaSbaaSqaaiaadshaaeqaaOGaeyOeI0% YaaabCaeaacqGHciITcaGGVaGaeyOaIyRaamiEamaaBaaaleaacaWG% Pbaabeaakiabeo8aZnaaBaaaleaacaWGPbaabeaakiaacIcacaWG1b% WaaSbaaSqaaiaadIhadaWgaaadbaGaamyAaaqabaaaleqaaOGaaiyk% aiabgUcaRaWcbaGaamyAaiabg2da9iaaigdaaeaacaWGobaaniabgg% HiLdGccaWGMbGaaiikaiaadwhacaGGSaGaamyDamaaBaaaleaacaWG% 0baabeaakiaacMcacaqGGaGaeyypa0Jaaeiiaiaaicdaaeaaaeaaae% aaaeaacqaH7oaBcaqGGaGaeyyzImRaaeiiaiaaicdacaqGGaGaaiik% aiaadIhacaGGSaGaamiDaiaacMcacqGHiiIZcqGHPoWvcaqGGaGaae% iEaiaabccacaGGOaGaaGimaiaacYcacaWGubGaaiykaaqaaaqaaaqa% aaqaaiabgM6axjaabccacaqG9aGaaeiiaiaabggacaqGGaGaaeizai% aab+gacaqGTbGaaeyyaiaabMgacaqGUbGaaeiiaiaabMgacaqGUbGa% aeiiaiabl2riHoaaCaaaleqabaGaamOBaaaakiaacYcaaaaa!879A!\[\begin{array}{l}u_{tt} - \lambda \Delta u_t - \sum\limits_{i = 1}^N {\partial /\partial x_i \sigma _i (u_{x_i } ) + } f(u,u_t ){\rm{ }} = {\rm{ }}0 \\\\\\\\\lambda {\rm{ }} \ge {\rm{ }}0{\rm{ }}(x,t) \in \Omega {\rm{ x }}(0,T) \\\\\\\\\Omega {\rm{ = a domain in }}^n , \\\end{array}\]with various boundary and initial conditions on u(x, t). The case >0 corresponds to a nonlinear Voigt model (for nonlinear). The case =0, N=1 and f(u, u ₁ )=|u ₁ | sgn u ₁ , 0<<1 with nonhomogeneous boundary conditions corresponds to the motion of a linearly elastic rod in a nonlinearly viscous medium. The method followed is the Galerkin method.

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Résumé En suivant la méthode de Gaberkin, les auteurs ont étudié le problème de l'existence, de l'unicité et du comportement asymptotique lorsque t des solutions des équations d'état des ondes visco-élastiques, pour diverses conditions initiales et aux limites de U (x, t). On analyse les cas auxquels correspondent des valeurs positives (modèle non linéaire de Voigt) ou nulle du paramètre, ce dernier cas étant représentatif du mouvement d'un barreau élastique linéaire dans un milieu visqueux non linéaire, monyennant l'adoption de diverses conditions aux limites.