Fracture mechanics approach to fatigue crack initiation from deep notches

Fracture mechanics approach is applied to fatigue crack initiation at the tips of deep, blunt notches including those with very small notch-tip radius. The theoretical relations between the stress intensity range ΔK_ρ and the notch-tip radius ρ for a fixed life for crack initiation were derived based on the models of dislocation-dipole accumulation and blocked slip-band. Those are approximated by a simpler equation: $\text{ΔK}{}_{\mathrm{\rho }}\text{ΔK}{}_{\mathrm{o}}\text{= (1 + ρ/ρ0)}\text{1}\text{2}$ where ΔK₀ and ρ0 are material constants which are related to the fatigue strength of smooth specimens Δρ0 as $\text{Δρ0 =}\text{2ΔK}{}_0\text{(πρ0)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The results of experiments done with bluntly notched compact tension specimens of a structural low-carbon steel agree with the above relation between $\text{ΔK}{}_{\mathrm{gr}}\text{ΔK}{}_{\mathrm{o}}$ and ρ/ρ_o. The method to predict ΔK_o, ρ_o and Δρ_o from the fatigue data of cracked and smooth specimens is proposed.     

Refinement of the structure of K2Cr2O7

The parameters for the structure of K₂Cr₂O₇ have been refined from 7511 observed reflections; $\text{a}{}_{\mathrm{o}}\text{= 7.4200(6)}\text{A}\text{?}$, $\text{b}{}_{\mathrm{o}}\text{= 13.399(3)}\text{A}\text{?}$, $\text{c}{}_{\mathrm{o}}\text{= 7.3845(9)}\text{A}\text{?}$, cosα = ?0.1396(2) (α = 98°2'), cosβ = ?0.0154(2) (β = 90°53'), cosγ = ?0.1078(2) (γ = 96°11'). The discrepancy factor R(F_o²) = 0.0702 with a type 2 extinction correction. The average CrO distances are 1.609Å (unshared) and 1.783Å (shared).     

Ordering of interstitial nitrogen and oxygen in vanadium near to V8N and V8O

The ordered structure of the V₈N subnitride was studied by X-rays, electron diffraction and electron microscopy. V₈N exists in two different modifications (α′ and α″). The vanadium sublattice of both phases is pseudo-tetragonal, in reality triclinic, with lattice parameters: $\text{α}{}_{\mathrm{<mtext>o</mtext>}}\text{=}\text{b}{}_{\mathrm{o}}\text{= 3.114}\text{A}\text{?}$, $\text{c}{}_{\mathrm{o}}\text{= 2.994}\text{A}\text{?}$, α_o = β_o = 90.5^o ± 0.1^o, γ_o = 90^o. The proposed unit cell of α′-V₈N has dimensions: a = 2√2 a_o, c = 2c_o and corresponds to V₃₂N₄. Doublets of nitrogen atoms occupy two sets of octahedral cavities whose shortest axes are aligned along the x and y directions of the sublattice in an ordered fashion. The α″-V₈N phase is a periodically twinned modification of the α′-V₈N, the twin plane being of the (001) type. The V₈O suboxide has the same structure as the α″-V₈N, the sublattice parameters being: $\text{a}{}_{\mathrm{o}}\text{=}\text{b}{}_{\mathrm{o}}\text{= 3.11}\text{A}\text{?}$, $\text{c}{}_{\mathrm{o}}\text{= 2.994}\text{A}\text{?}$, α_o = β_o = 90.3^o ± 0.1^o, γ_o = 90^o.     

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.     

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.     

Ellipsometry as a means of mass-thickness determination in the earliest film growth stages

Gold was evaporated onto a fused silica substrate, and the normalized Stokes parameters S₁, S₂ and S₃, which represent the state of polarization of the light reflected from the sample, were determined in situ for films of average thickness less than a few monolayers with an automatic ellipsometer; the film mass m per unit substrate area was measured simultaneously with a torsion microbalance. It was found that $\text{ΔS = {(ΔS}{}_1\text{)}{}^2\text{+ (ΔS}{}_2\text{)}{}^2\text{+ (ΔS}{}_3\text{)}{}^2\text{}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ changes linearly with m for light of wavelength λ well outside the absorption band of the film. For λ = 440 nm the sensitivity is comparable with that of a good torsion microbalance. Thus an automatic ellipsometer can conveniently be employed in the microgravimetry of submonolayer films.     

Polar Langmuir-Blodgett films

An optical and electro-optical technique is described for measuring the orientational order parameters $\text{P}\text{(}\text{cos}{}^{\mathrm{n}}\text{θ)}$ of Langmuir-Blodgett films (where θ is the angle between the long molecular axis and the normal to the film plane and $\text{P}$_n are the Legendre polynomials for n = 1, 2, 3, 4). Using these data the orientational distribution function $\text{F}$ (θ) was constructed.Polar multilayers $\text{(}\text{cos}\text{θ}\text{,}\text{cos}{}^3\text{θ}\text{≠ 0)}$ of the X and Z types were obtained from amphiphilic azony compounds. These layers were shown to have a macroscopic electrical polarization P = 10^-6 C cm^-2 and, as a result, they exhibit pyroelectric and piezoelectric properties as well as the linear electro-optical (Stark) effect.     

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.     

Dependence of the crystallization rate of vacuum-deposited amorphous antimony films on the film thickness

The crystallization rate of vacuum-deposited amorphous antimony (a-Sb) films was investigated as a function of the film thickness d. Experimental plots of the observed growth rate v against d^-1 for systems such as Sb/glass and Sb/Ge show that the relationship between v and d^-1 are convex towards the origin. Such a feature is well interpreted by a model in which

$\text{v=}\text{1}\text{d}\text{∫}\text{d}\text{0}\text{u}\text{d}\text{z}$

where u is the actual growth rate of the crystallite in the a-Sb film and z the distance from the film surface adjacent to the substrate. The quantity u is assumed to vary as follows: u = αzⁿ + u_s when 0 ? z ? d_s0, u = u_i when d_s0 ? z ? d ? d_v0 and u = β(d ? z)ⁿ + u_v, when d ? d_v0 ? z ? d where $\text{α =}\text{(u}{}_{\mathrm{i}}\text{? u}{}_{\mathrm{<mtext>s</mtext>}}\text{)}\text{d}{}_{\mathrm{<mtext>s</mtext><mtext>0</mtext>}}{}^{\mathrm{n}}$, $\text{β =}\text{(u}{}_{\mathrm{i}}\text{? u}{}_{\mathrm{<mtext>v</mtext>}}\text{)}\text{d}{}_{\mathrm{<mtext>v</mtext><mtext>0</mtext>}}{}^{\mathrm{n}}$, d_s0 and d_v0 are thickness of surface regions near the substrate and the vacuum respectively, u_i is the growth rate inside the film, u_s and u_v are the rates at surfaces adjacent to the substrate and the vacuum respectively and n an adjustable numerical parameter. As a typical example, for the Sb/Ge system at 30°C, u_i, u_s and u_v are estimated to be 139 μm s^-1, 25.4 μm s^-1 and 0.2 μm s^-1 respectively and d_s0 and d_v0 to be 133 Å and 143 Å respectively with n = 3.     

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.     

Effect of loading history on stress corrosion cracking in high strength steel

The effect of preloading on crack nucleation time was examined with compact tension specimens having various notch radius in 0.1N-H²SO⁴ aqueous solution for 200°C tempered AISI 4340 steel. Crack nucleation time t_n increases by preloading for a given apparent stress intensity factor K_p2. The curve K_?2 vs. t_n deviates upward from the curve for the non preloading case. A linear relationship between the crack nucleation time and parameter is seen in semi-log diagram, where is taken as the value at t_n=α due to preloading. The apparent threshold stress intensity factor increases with K_?2 which is the apparent stress intensity factor of preloading. A detached crack is nucleated at some distance from the notch root and extends in a form of circle. This distance increases with increasing K_?2. The effect of load reduction during crack growth was examined. When the K-value was reduced from K₁ to K₂, an incubation time was observed before the crack started growing under the K₂-value. The incubation time t_m tends to increase with increasing ΔK = K₁-K₂. The threshold stress intensity factor was also found to increase for high load reduction.In order to explain these experimental results, a new dislocation model is proposed on the basis of stress induced diffusion of hydrogen in high stress region ahead of the notch root or a crack. This model suggests that the change in the crack nucleation time and the increase of the incubation time due to preloading or load reduction are caused by reducing the hydrostatic pressure and by spreading the hydrogen saturated region which requires more time for the hydrogen accumulation due to preloading or load reduction. The theory predicts the experimentally observed relations between and t_n and between log t_in and ΔK.     

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.     

Crystal structure and fluorescence lifetime of a laser material NdNa5(WO4)4

The structure of NdNa₅(WO₄)₄, determined by single-crystal x-ray analysis, is tetragonal with space group I 4₁/a and cell parameters $\text{a}\text{= 11.559(2)}\text{A}\text{?}$, $\text{b}\text{= 11.453(2)}\text{A}\text{?}$, z = 4. A full-matrix, least-squares refinement gives R = 0.077. The W atoms and the Nd atoms occupy isolated tetrahedra and dodecahedra, respectively. These polyhedra are connected by the Na atoms, which are located at two different sites, tetrahedral and octahedral. The fluorescence lifetime of the ${}^4\text{F}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{→}{}^4\text{I}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ transition of Nd⁺³ is reported for the system La_1?xNd_xNa₅(WO₄)₄. The lifetime of NdNa₅(WO₄)₄ is 85 ± 5 μsec, which is comparable to NdP₅O₁₄. Concentration quenching is considerably reduced in both host structures, which we conclude is due to the isolation of the rare-earth polyhedra.     

Studies on crack growth rate under high temperature creep,fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter aeffσg

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor $\text{K}{}_{\mathrm{I}}\text{= α}\text{aσ}{}_{\mathrm{g}}$, where a is the equivalent crack length as the sum of the initial notch length a₀ and the actual crack length $\text{a}{}^1$, that is, $\text{a = a}{}_0\text{+ a}{}^1$. On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of $\text{aσ}{}_{\mathrm{g}}\text{?(σ}{}_{\mathrm{g}}$), where a is the cycloidal notch length, σ_g is the gross section stress and $\text{?(σ}{}_{\mathrm{g}}$) is a function of σ_g. Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a_eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}\text{, σ}{}_{\mathrm{g}}$ and temperature.In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a_eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}$ with gross section stresses and temperatures as parameters, respectively.     

Interactions of Cr2+ with the F− ligands in CdF2:Cr2+

Superhyperfine structure s.h.f.s. resulting from the Cr²⁺ - F^? interaction was studied in Cr²⁺ doped CdF₂ crystals. The s.h.f.s. observed can be described with by the following spin-Hamiltonian

$\text{H}\text{=}\text{g}{}_{\mathrm{eff}}\text{β}\text{HS}{}_{\mathrm{z}}\text{+ST}{}_{\mathrm{i}}\text{I+ST}{}_{\mathrm{j}}\text{I}$

The constants calculated are $\text{T}{}_{\mathrm{i\perp }}\text{≈}\text{T}{}_{\mathrm{i}}\text{= 50}\text{MHz}$$\text{T}{}_{\mathrm{j\perp }}\text{≈}\text{T}{}_{\mathrm{j}}\text{= 5}\text{MHz}$. The measurements were made with an ESR spectrometer at X band at 4.2 OK.     

New phase with K2NiF4 structure in the LaLiFeO system

The existence has been proved, for the first time, in the LaLiFeO system of the phase (La_1.75Li_.25) (Fe_.5Li_.5)O_4?x with tetragonal symmetry ($\text{a}{}_{\mathrm{o}}\text{=3.765±0.001}\text{A}\text{?}$; $\text{c}{}_{\mathrm{o}}\text{=12.918±0.01}\text{A}\text{?}$; $\text{c}{}_{\mathrm{o}}\text{a}{}_{\mathrm{o}}\text{=3.43}$) and K₂NiF₄-type structure.This phase gives probably the first example of lithium distribution in both A and B sites of A₂BO₄-type mixed oxides. The high $\text{c}{}_{\mathrm{o}}\text{a}{}_{\mathrm{o}}$ ratio suggests a strong elongation of FeO₆ octahedra induced by a high spin Fe(IV) d⁴ configuration. The results of structural studies and of Mössbauer analysis, confirming the above conclusions, are reported.     

ESR evidence for the existence of rutile-type,nonstoichiometric vanadium antimonate

A nonstoichiometric vanadium antimonate has been synthesized from a high temperature solid state reaction of V₂O₅ and Sb₂O₃. Powder-X-ray diffraction data of this phase could be indexed on a tetragonal basis with $\text{a}\text{= 4.60}\text{A}\text{?}$, $\text{c}\text{= 3.02}\text{A}\text{?}$. The phase exhibits a well resolved hyperfine ESR spectrum at 298 K due to V(4+)(3d′) ions interacting with ${}^{51}\text{V}\text{(}\text{I}\text{=}\text{7}\text{2}\text{)}$, thus establishing its identity as a rutile type phase postulated earlier. The ESR parameters are $\text{g}{}_{\mathrm{}}\text{= 1.933±0.002}$, g_⊥ = 1.984±0.002, $\text{A}{}_{\mathrm{}}\text{= 193±3}\text{G}$, A_⊥ = 75±3G. Present results are discussed in relation to ESR of V(4+) in other rutile-type hosts.     

Nature de la fluorescence de l'europium divalent dans les fluorures

The levels of the ${}^6\text{P}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ (4f⁷) and 4f⁶5d¹ states of europium (+II) have been determined from fluorescence spectra in a series of fluorides M_xB_yF_z (M = alkaline-earth element, B = Li, Be, Mg, Y, Si). As in BaY₂F₈, SrSiF₆ and BaSiF₆, the ${}^6\text{P}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ level lies even at room temperature far below the 4f⁶5d¹ band, only the f → f emission is observed. The influence of the choice of the alkaline-earth and the B cations and of the coordination of europium on the relative positions of the energy levels is discussed.     

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.     

Une modelisation du comportement magnetique d'un compose de l'iridium pentavalent: LaLi12Ir12O3

A new interpretation is proposed for the magnetic properties of perovskite-type iridium (+V) oxide $\text{LaLi}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{Ir}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{O}{}_3$. In its unusual +5 oxidation state iridium has a t⁴_2ge⁰_g configuration. The magnetic susceptibility has been calculated assuming cubic symmetry of the crystal field and a Coulomb repulsion of the same order of magnitude than spin-orbit coupling. Fitting of the experimental data leads to a single spin-orbit constant $\text{ζ ? 3470}\text{cm}{}^{\mathrm{?1}}$ close to that of previously investigated Ir(+V) compounds.