Theorems of zaremba type for thermoelastic solid

It was shown in [2] that any solution of the equation of coupled dynamic thermoelasticity (a) $\text{[(?}{}^2\text{??}{}_{\mathrm{t}}{}^2\text{)(?}{}^2\text{??}{}_{\mathrm{t}}\text{)?∈?}{}_{\mathrm{t}}\text{?}{}^2\text{]phi = 0, (?}{}_{\mathrm{t}}\text{= ?/?t)}$, subject to homogeneous initial conditions admits the representation $\text{phi = phi}{}_1\text{+ phi}{}_2$, where (b) $\text{(?}{}^2\text{??}{}_{\mathrm{t}}{}^2\text{?∈?}{}_{\mathrm{t}}\text{?∈?∈K 1)phi}{}_1\text{= 0}$, and (c) $\text{?}{}^2\text{??}{}_{\mathrm{t}}\text{+∈+teK (s)phi}{}_2\text{= 0}$. Here $\text{K = K(t, epsi)}$ is a given function and ¹ denotes the operation of convolution with respect to time $\text{t}$. In the present paper three uniqueness theorems associated with (a), (b) and (c) are given, and a domain of influence theorem for (b) is established. Next, these theorems are used to show that there exist such couplings between the external mechanical and thermal fields applied to the boundary of a thermoelastic solid that inside the body the temperature is either of a wave type or of a diffusive type, but not of both types.     

The elastic field around an elliptical crack in an anisotropic medium under an applied stress of polynomial forms

A general form is presented for the stress disturbance caused by an elliptical crack in an anisotropic medium under an arbitrary stress field in the form of polynomials. Somigliana's dislocation method is employed for analysis as Willis [4] did, but a different integral process is taken. The results are expressed in the integral forms defined on the subspace of the surface of a unit sphere. The following theorem is proved: If the displacement discontinuity of the elliptical Somigliana's dislocation has the form where is a homogeneous polynomial of degree $\text{N}$ in the coordinates $\text{x′}{}_1$ and $\text{x′}{}_2$ and $\text{a}{}_1$ and $\text{a}{}_2$ are the semi-axes of the elliptical Somigliana's dislocation, the stresses on the plane of the Somigliana's dislocation are inhomogeneous polynomials in the coordinates, whose terms are of degree $\text{N, (N ? 2}$), $\text{(N ? 4),4.}$     

Distribution coefficients in (YSmLuCa)3(FeGe)5O12 film growth

The composition of bubble garnet films has been analyzed by Inductively Coupled Plasma Emission Spectroscopy (ICP) to determine the distribution coefficients for different growth conditions. Under typical growth conditions, the distribution coefficients, k, of each element are as follows: k^Y = 2.15, k^Sm = 1.56, k^Lu = 1.32, k^Ca = 0.45, k^Fe = 0.98, k^Ge = 1.10. As the supercooling temperature (growth rate) increases, k^Ca, which is the smallest and deviates most from 1.0, changes in the direction approaching 1.0. For charge compensation, k^Ge also increases, consequently, k^Fe must decrease. Also k^Y, which is the largest, $\text{k}{}^{\mathrm{Sm}}\text{k}{}^{\mathrm{Y}}$ and $\text{k}{}^{\mathrm{Lu}}\text{k}{}^{\mathrm{Y}}$ change in the direction approaching 1.0. On the other hand, as the melt parameter R₁ (≡ $\text{Fe}{}_2\text{O}{}_3\text{Σ}\text{Ln}{}_2\text{O}{}_3$) increases, k^Fe decreases, and k^Y, k^Sm and k^Lu increase, whereas $\text{k}{}^{\mathrm{Sm}}\text{k}{}^{\mathrm{Y}}$ and $\text{k}{}^{\mathrm{Lu}}\text{k}{}^{\mathrm{Y}}$ remain constant at 0.73 and 0.61, respectively.     

Prediction of component life by application of fatigue crack growth knowledge

The concept of fatigue-crack propagation is discussed as it relates to life prediction. Since the use of propagation concepts assumes the presence of a minimum detectable initial flaw size this concept is discussed as it relates to the fatigue process. The relative roles of fatigue-crack initiation and propagation are presented. The acquisition of data is discussed and is then followed by a brief discussion of the variables that influence fatigue-crack propagation. A detailed discussion of the development of fatigue-crack growth ‘laws’ is then presented. These are then generalized to three forms, viz.: $\text{da/dN = C}{}_1\text{(S}{}_{\mathrm{a}}\text{)}$ (1) $\text{da/dN = C}{}_2\text{S(a)}{}^{\mathrm{n}}$ (2) $\text{da/dN = C}{}_3\text{f(K)}{}^{\mathrm{n}}$ (3) Examples of the use of these crack growth ‘laws’ and the knowledge of fracture mechanics then is presented to illustrate the application of fatigue-crack growth concepts to:Predict life; establish greater reliability; select materials: improve design; establish inspection and maintenance intervals.The paper is concluded with a brief discussion of the needs for further knowledge and understanding to aid the science and engineering community in better utilization of engineering materials.     

Crystal chemistry of (Cd,Me)3(PO4)2 solid solutions

A number of solid solutions of $\text{Me}$₃(PO₄)₂ in Cd₃(PO₄)₂ have been prepared and equilibrated at 1070 K ($\text{Me}\text{=}\text{Mg, Mn, Fe, Co, Ni, Cu, Zn, or Ca}$). The respective ($\text{Cd}{}_{\mathrm{<mtext>1?</mtext><mtext>z</mtext>}}\text{Me}{}_{\mathrm{<mtext>z</mtext>}}\text{)}{}_3\text{(}\text{PO}{}_4\text{)}{}_2$ phases are either isotypic with β′-Cd₃(PO₄)₂ or with the mineral graftonite, both with five- and six- (or even seven)-coordinated cations. The monoclinic unit cell dimensions have been accurately determined from Guinier-Hägg photographs, and complete X-ray powder diffraction data are given for β′-Cd₃(PO₄)₂. The cell volumes are strongly correlated to the size and amount of incorporated $\text{Me}$²⁺ cation. The homogeneity regions and structures of the (Cd,$\text{Me}$)₃(PO₄)₂ phases, though, seem rather to be controlled by the $\text{Cd}{}^{\mathrm{2+}}\text{Me}{}^{\mathrm{2+}}$ cation ordering.     

Crack tip closure and environmental crack propagation

Crack propagation rate, da/dN, and crack tip closure stress, σ_cc, in part-through crack fatigue specimens of aluminum alloys are drastically affected by gaseous environments. The present studies indicate that the crack closure reflects the influence of the environment on the plastic deformation at the crack tip, and, therefore, on the crack propagation rates. Postulating that da/dN is mainly determined by $\text{ΔK}{}_{\mathrm{eff}}\text{∝ (σ}{}_{\max }\text{?σ}{}_{\mathrm{cc}}\text{)}$ (instead of $\text{ΔK ∝ (σ}{}_{\max }\text{?σ}{}_{\min }\text{)}$, as is done traditionally) leads to the relationship $\text{da/dN = A(ΔK}{}_{\mathrm{eff}}\text{)}{}^{\mathrm{n}}$ in which $\text{A}$ and $\text{n}$ are virtually independent of the gaseous environment. The exponents are $\text{n ≈ 3.3}$ for Al 7075 T651 and $\text{n ≈ 3.1}$ for Al 2024 T351, respectively.     

Etude par spectrometrie d'absorption infra-rouge des facteurs influencant la transformation ordre-desordre de ferrites γ lacunaires derivant de l'oxydation de spinelles ferreux

The order-disorder phenomenon in defect γ-spinels of type $\text{(Fe}{}_{\mathrm{<mtext>(8?8y)</mtext><mtext>3</mtext>}}{}^{\mathrm{3+}}\text{M}{}_{\mathrm{<mtext>8y</mtext><mtext>3</mtext>}}{}^{\mathrm{3+}}\text{□}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{)O}{}_4{}^{\mathrm{2?}}$ and $\text{Fe}{}_{\mathrm{<mtext>(8?2x)</mtext><mtext>3</mtext>}}{}^{\mathrm{3+}}\text{M}{}_{\mathrm{x}}{}^{\mathrm{2+}}\text{□}{}_{\mathrm{<mtext>(1?x)</mtext><mtext>3</mtext>}}\text{)O}{}_4{}^{\mathrm{2?}}$ with M³⁺ = A1³⁺, Cr³⁺ and M²⁺ = Zn²⁺, Co²⁺, Mn²⁺ obtained from ferrous spinels was investigated using IR spectrometry. These compounds possess a vacancy ordering on octahedral sites for substitution extents of less than 0.30 and no ordering has been observed for substitution extent > 0.40. The ordering process is also influenced by the nature and position of the trivalent or divalent cation, particle size, heating temperature and oxidation time.     

Prediction of threshold and ultra-low fatigue crack growth rates

A model was derived to predict the true threshold value for fatigue crack growth in the absence of crack closure. The model, based only on the tensile and cyclic properties of the material, was successfully verified against a set of experimental data on medium and high strength steels and one aluminium alloy. Good agreement with experimental results was also obtained for Region I of the $\text{d}\text{a/}\text{d}\text{N vs ΔK}$ curve using a fatigue crack growth rate equation based on the same model.Fatigue crack growth data obtained from the medium strength steel CK45 in the normalized state and two heat-treated conditions were analysed. Good data correlation was shown using a previously developed normalizing parameter, $\text{φ = (ΔK}{}^2\text{?ΔK}{}^2{}_{\mathrm{<mtext>th</mtext>}}\text{)/(K}{}^2{}_{\mathrm{<mtext>c</mtext>}}\text{?K}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{)}$, in the entire range of fatigue crack growth rates and for stress ratios ranging from 0.1 to 0.8.     

Some formulas for the crack opening stress level

Crack growth data for 2024-T3 sheet material were analysed with different formulas for $\text{ΔK}{}_{\mathrm{eff}}$ as a function fo the stress ratio $\text{R}$. The data covered $\text{R}$ values from ?1.0 to 0.54. A good correlation was obtained for $\text{ΔK}{}_{\mathrm{eff}}$/$\text{ΔK}$ = 0.55 + 0.33$\text{R}$ + 0.12$\text{R}{}^2$ The relation between log $\text{d}\text{a/}\text{d}\text{n}$ and log $\text{ΔK}{}_{\mathrm{eff}}$ was non-linear for high crack rates (> 1 μm/c).     

Preparation and properties of LiTaO3-based solid solutions with cation vacancies

It has been found that nonstoichiometric solid solutions $\text{(}\text{Li}{}_{\mathrm{<mtext>1?</mtext><mtext>x</mtext>}}\text{M}{}^{\mathrm{2+}}{}_{\mathrm{<mtext>x</mtext><mtext>2</mtext>}}\text{□}{}_{\mathrm{<mtext>x</mtext><mtext>2</mtext>}}\text{)}\text{TaO}\text{3}$ with M=Zn, Ni, Mg and Ca exist over wide ranges. In the case of the Zn-system, especially, a LiTaO₃ structure was still stable even at x=0.5, where 25% of the Li sites are vacant. A new series of solid solutions shows ferroelectric properties. The Curie temperature is closely related with the axial ratio c/a of the hexagonal cell.     

Copper doped zinc oxide Y2BaZnO5: ERS and optical investigation

In copper doped Y₂BaZnO₅ oxides, copper exhibits a distorted square pyramidal coordination which is consistant with the values of g and A tensors obtained from O band ERS spectrum for a sample containing about 1 % Cu. Three values for g and A are observed, g₁ = 2.049₅, g₂ = 2.051₅, g₃ = 2.275, $\text{¦}\text{A}{}_1\text{¦ = 13 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$, $\text{¦}\text{A}{}_2\text{¦ = 10 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$ and $\text{¦}\text{A}{}_3\text{¦ = 147.5 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$. Since $\text{g}{}_1\text{?}\text{g}{}_2$ an approximate C_4v point symmetry can be assumed for copper. The electronic spectrum shows three bands at 11700, 14500 and 20500 cm^?1 which can be assigned to the transitions A₁ → B₁, B₂ → B₁ and E → B₁ respectively. The orbital reduction parameters are calculated and the bonding covalency is discussed.     

Concentration quenching of Tb3+ luminescence in LaOBr and Gd2O2S phosphors

The concentration quenching of trivalent terbium ${}^5\text{D}{}_{\mathrm{3,4}}\text{→}{}^7\text{F}{}_{\mathrm{J}}$ emissions from UV-excited (La, Tb) OBr and (Gd, Tb)₂O₂S phosphors was studied. The activation concentration x was varied from 5·10^?5 to 0.2 for (La_1?xTb_x) OBr and from 10^?3 to 0.1 for (Gd_1?xTb_x)₂O₂S. ${}^5\text{D}{}_3\text{→}{}^7\text{F}{}_{\mathrm{J}}$ emissions (blue) were observed to quench first and the Tb³⁺ concentration giving rise to maximum intensity was 0.003 in (La, Tb) OBr and between 0.005 and 0.01 in (Gd, Tb)₂O₂S. The optimum concentration for ${}^5\text{D}{}_4\text{→}{}^7\text{F}{}_{\mathrm{J}}$ (green) emissions was 0.05 in (La, Tb) OBr and 0.03 in (Gd, Tb)₂O₂S. Dipole-dipole and dipole-quadrupole interactions are possible mechanisms for the quenching of emissions from the ⁵D₃ and ⁵D₄ levels.A method for determining the Tb³⁺ concentration in these phosphors, based on the intensity ratios of the ${}^5\text{D}{}_3\text{→}{}^7\text{F}{}_{\mathrm{J}}$ and ${}^5\text{D}{}_4\text{→}{}^7\text{F}{}_{\mathrm{J}}$ transitions, is also presented.     

The overall sink strength of an inhomogeneous lossy medium. Part I: self-consistent estimates

Steady-state diffusion in a medium containing a continuous distribution of sinks is considered. The medium comprises a matrix, with sink strength $\text{k}{}_2{}^2$, which contains a random array of identical spherical inclusions, with sink strength $\text{k}{}_1{}^2$. On a macroscopic scale, the medium appears homogeneous, with uniform sink strength $\text{k}\text{?}{}^2$. This work is devoted to the estimation of the overall sink strength $\text{k}\text{?}{}^2$, in terms of $\text{k}{}_1{}^2\text{, k}{}_2{}^2$ and the statistics of the distribution of the inclusions. Part I discusses three distinct schemes of self-consistent type. One is based upon a simple embedding procedure and makes no explicit allowance for spatial correlations. The other two make use, in different ways, of the quasicristalline approximation (QCA). Part II develops variational principles which yield bounds for $\text{k}\text{?}{}^2$. The self-consistent estimates are interpreted relative to the variational formulation and explicit numerical results are presented.     

Rate law versus oxygen pressure in spinel oxidation to γ lacunar spinels

In the controlled oxidation of spinels (Fe²⁺Fe³⁺_2?xM³⁺_x)O^2?₄ (M³⁺=Al³⁺, Cr³⁺ ; 0 < x < 2) and (Fe²⁺Al³⁺_2?xCr³⁺_x)O^2?₄ to the metastable phases γ(Fe³⁺_1?yM³⁺_y)₂O^2?₃ and $\text{γ(}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{Al}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext><mtext>?</mtext><mtext>y</mtext>}}\text{Cr}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>y</mtext>}}\text{O}{}^{\mathrm{2?}}{}_{\mathrm{3?}}\text{(0 <}\text{y}\text{<}\text{2}\text{3}\text{)}$, over the temperature range 200–450°C, the rate law is usually v = k Pⁿ_(O2) with $\text{n}\text{=}\text{1}\text{2}$. This law is well interpreted if we consider a total association vacancy-positive charge. However, for low oxidation extents a (a < 0.3) the law written as is in better agreement with a partial association of defects. For a total dissociation of defects exponent n of the pressure law is always smaller.     

Carburization and decarburization kinetics of iron in CH4 — H2 mixtures between 1000 – 1100 °C

In this study the rate constants of the methane decomposition reaction on iron surfaces were determined in the 1000–1100°C temperature range, by grav? metric methods. Earlier works showed that the reaction velocity was given by The results indicate that the constant values vary from 2.72 × 10^?6 to $\text{16.74 × 10}{}^{\mathrm{?6}}\text{mol C/cm}{}^2\text{/sec/atm}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for k and 2.61 × 10^?8 to $\text{8.62 × 10}{}^{\mathrm{?8}}\text{mol C/cm}{}^2\text{/sec/atm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ for k′ between 1000 and 1100°C.     

Un nouveau conducteur protonique [H(H2O)n]12Sb12O36 (n ⩽ 1)

Single crystals of K₁₄Sb₁₂O₃₆F₂ undergo rapid ion exchange in 9N sulfuric acid to produce “hydronium” compound (H(H₂O)_n)₁₂Sb₁₂O₃₆ (n ? 1). Between 30 and 140°C this phase undergoes a partial and reversible dehydratation in which approximately 85 % of its “H₃O⁺” content is converted to H⁺.The structures of hydrated and dehydrated phases have been refined by full-matrix least squares, respectively to factor R = 0.030 and 0.047. The conductivity of $\text{(H(H}{}_2\text{O)}{}_{\mathrm{<mtext>n</mtext>}}\text{)}{}_{12}\text{Sb}{}_{12}\text{O}{}_{36}\text{(σ}{}_{20}\text{? 1O}{}^7\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$) increases in an Arrhenius relationship with an activation energy of 8.8 kcal.mole^?1, the dehydrated compound (H(H₂O)_0.33)₁₂Sb₁₂O₃₆ has a much lower conductivity but the same activation energy.     

Spectres vibrationnels,transitions electroniques et structures a courtes distances dans les verres: Sulfures de terres rares - sulfure de gallium

Absorption spectra of chalcogenide glasses of general formula Ln₂S₃-1,8 Ga₂S₃ (Ln = La⁺³, Ce⁺³, Pr⁺³, Nd⁺³, Gd⁺³ were investigated continously from far infrared to ultra-violet region. Raman spectra were recorded in the 5cm^?1–600 cm^?1 range. Vibrational spectra of glasses have been compared to those of polycrystalline compounds $\text{Ln}{}_{\mathrm{<mtext>10</mtext><mtext>3</mtext>}}\text{Ga}{}_6\text{S}{}_{14}$ (Ln = La⁺³, Ce⁺³) and $\text{Ln}{}_6\text{Ga}{}_{\mathrm{<mtext>10</mtext><mtext>3</mtext>}}\text{S}{}_{14}\text{(}\text{Ln = La}{}^{\mathrm{+3}}\text{to Gd}{}^{\mathrm{+3}}\text{)}$.From the observed spectra it could be concluded that the short distance order around gallium atom is strongly modified in going from crystalline to glassy state.Electronic transitions of Ce⁺³, Pr⁺³ and Nd⁺³ ions have been also identified in the visible region and in the mid infrared absorption spectra.     

Development of the AASHTO fracture-toughness requirements for bridge steels

This paper describes the effects of temperature and strain rate on the fracture-toughness behavior of bridge steels. The test results showed the existence of a fracture-toughness transition that is an inherent material property rather than a behavior caused only by a change in the stress state. The effect of a slow loading rate, compared with impact loading rates, is to shift the fracture-toughness transition to lower temperatures. The magnitude of the temperature shift between stow loading ($\text{?≈ 10}{}^{\mathrm{?5}}\text{sec}{}^{\mathrm{?1}}$)and impact loading ($\text{/.? ≈ 10 sec}{}^{\mathrm{?1}}$) decreased with increased yield strength of the steel. The fracture-toughness behavior of bridge steels under strain rates that are encountered in actual bridge ($\text{/.? t~ 10}{}^{\mathrm{?3}}\text{sec}{}^{\mathrm{?1}}$) is closer to slow loading than to impact loading.Relationships are presented among fracture-toughness values determined by testing fracture-mechanics-type specimens, Charpy $\text{V-}\text{notch}$ (CVN) specimens, and nil-ductility-transition (NDT) specimens. Moreover, procedures are presented for using CVN impact-test results to predict $\text{K}{}_{\mathrm{IC}}$ values at slow or at moderate loading rates such as occur in actual bridges. The predicted $\text{K}{}_{\mathrm{IC}}$ values are shown to be close to those experimentally determined by testing $\text{K}{}_{\mathrm{IC}}$ specimens at various strain rates.The test results were used to develop fracture-toughness requirements for bridge steels. These toughness requirements have been approved by the Federal Highway Administration (FHWA) and by the American Association of State Highway and Transportation Officials (AASHTO) and are mandatory requirements on all Federal-aid highway programs in the United States.     

Properties of bone at low temperatures and its potential as cryostat support material

The ultimate compressive strength, $\text{σ}{}_{\mathrm{<mtext>f</mtext>}}$, Young's modulus, E, and the integrated thermal conductivity k_T1–T2, of bone have been measured between 20 and 80 K. The two figures of merit indicating the quality for transmission of forces to low temperature apparatus are determined as $\text{σ}{}_{\mathrm{<mtext>f</mtext>}}\text{/}\text{k}{}_{\mathrm{4–77}}\text{= 42.5 ± 4 Ms m}{}^{\mathrm{?2}}$, and E/k_4–77 = 3.5 ± 0.2 Gs m^?2. According to these figures bone is comparable or superior to the best glass-fibre composites. Some observations on creep strength are added.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.