A modified thickness criterion for fracture toughness testing

A modified criterion is developed on an empirical basis for the minimum thickness $\text{B}{}_{\min }$ of a plane strain fracture toughness test specimen: $\text{B}{}_{\mathrm{<mtext>min</mtext>}}\text{= 400}\text{K}{}_{\mathrm{Ic}}{}^2\text{Eδ}{}_{\mathrm{Y}}$ where $\text{K}{}_{\mathrm{Ic}}$ is the plane strain fracture toughness, $\text{E}$ is the Young's modulus and δ_Y is the yield stress of the material. The modified criterion is tested alongside the ASTM thickness criterion against published data on the variation of $\text{K}{}_{\mathrm{c}}$ with thickness, and shows significantly the better agreement with observed values of $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$ for a wide range of materials.An attempt has been made to rationalise this criterion. The expression is considered to take into account two major factors which determine $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$, the attainment of plane strain in the specimen interior ahead of the crack tip, and the role of microstructure in determining how far the quasi-plane strain fracture (square fracture) extends beyond the region of true plane strain.     

A high resolution dilatometer for in situ studies of the electrointercalation of layered materials

A dilatometer with an estimated resolution of ?25 nm is described which allows a continuous recording of the crystal expansion during electrointercalation of layered materials. We report on two examples: the galvanostatic intercalation of $\text{HSO}{}_4{}^{\mathrm{?}}\text{H}{}_2\text{SO}{}_4$ into graphite and $\text{K}{}^{\mathrm{+}}\text{H}{}_2\text{O}$ into 2HTaS₂. In the graphite system, the dilatometer record confirms the pronounced staging phenomenon, whereas for TaS₂ no higher than a second stage shows up. For both systems, the overall behaviour of the crystal expansion during intercalation suggests that no coherent intercalation front exists. In the case of TaS₂ with a rather high stacking fault density in situ dilatometry turns out to be ideally suited for the investigation of the intercalation mechanism.     

Characterization of wurtzite type boron nitride synthesized by shock compression

Graphite-like boron nitride was shock-compressed up to 550 kbar. The X-ray diffraction pattern of the recovered specimen identified the wurtzite structure whose hexagonal cell dimensions were $\text{a}{}_0\text{= 2.553±0.003}\text{A}\text{?}$, $\text{c}{}_0\text{= 4.228±0.004}\text{A}\text{?}$. No trace of zinc blende form was found. The conversion rate was related to the crystallization of the starting material. The density of the wurtzite type boron nitride was proved to be smaller by about 1 % than that of zinc blende type boron nitride synthesized under static compression.     

Pyroelectric and electrooptic effects in LiInS2 and LiInSe2

The electrooptic (r_ij and pyroelectric ($\text{dP}{}_{\mathrm{s}}\text{dT}$) coefficients of two new chalcogenides LiInS₂ and LiInSe₂ have been determined. The same linear relationship between $\text{dP}{}_{\mathrm{s}}\text{dT}$ and r₃₃, based on the anharmonic oscillator model, which has been found to hold for a wide variety of oxides also holds for these materials.     

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.     

Flux-pinning by superconductor-normal boundaries

It is shown that flux-pinning by Nb₃Sn-Cu interfaces in in-situ superconducting composites can lead to a pinning function of the form $\text{F}{}_{\mathrm{p}}\text{∝ b}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1 ? b)}{}^2$, as is found experimentally.     

Fatigue crack propagation behaviour of rotor and wheel materials used in steam turbines

The fatigue crack propagation characteristics of several rotor and wheel materials that are commonly used in rotating components of steam turbines were investigated. Particular emphasis was placed on the behaviour at near-threshold growth rates, ie below 10^?5 mm/cycle, approaching the fatigue-crack propagation threshold, $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The lifetimes of the cracks of interest lie mostly in this region, and it is also the region where few data are available.The effects of load ratio on the fatigue crack growth rates were examined, as well as the tensile, Charpy V-notch and fracture toughness properties of the rotor and wheel materials. The relationship between fatigue crack propagation behaviour and fractographic features was examined. Fatigue crack growth rate data, $\text{da/d}\text{N}$ vs stress intesity range $\text{ΔK}$, were fitted with a four parameter Weibull survivorship function. This curve fitting can be used for life estimation and establishment of $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The results show that load ratio and microstructure play a role in determining the fatigue crack threshold and fatigue crack growth behaviour.     

Stability of the perovskite phase LaBO3 (B = V,Cr, Mn,Fe, Co,Ni) in reducing atmosphere I. Experimental results

The chemical stability of perovskites LaBO₃ where B = V, Cr, Mn, Fe, Co, Ni was studied by thermogravimetry at 1000°C in gas mixtures of $\text{CO}{}_2\text{H}{}_2$, $\text{O}{}_2\text{CO}{}_2$ and $\text{O}{}_2\text{Ar}$ at 1 bar.The stability limits of the perovskite phases expressed in terms of -log Po₂★ (Po₂★ = critical oxygen partial pressure in bar) were for LaCrO₃ and LaVO₃ (greater than 21.1), LaFeO₃ (16.95), LaMnO₃ (15.05), LaCoO₃ (7.0) and for LaNiO₃ (～0.6). The changes in standard enthalpy ΔH° and entropy ΔS° of the following reactions were obtained.$\text{LaVO}{}_4\text{=}\text{LaVO}{}_3\text{+}\text{1}\text{20}{}_2\text{δ=328}\text{kJ}\text{mol}\text{°=135}\text{J}\text{mol·deg.}$,$\text{LaMnO}{}_3\text{=}\text{1}\text{2}\text{La}{}_2\text{O}{}_3\text{+}\text{MnO}$     

The electrical properties of vacuum deposited tellurium films

A study has been made of the electrical properties of tellurium films deposited onto two different substrate materials, 7059 alkali free glass and single crystal potassium bromide. The films were always p-type with crystallographic defects resulting in the formation of additional acceptor centres. The carrier mobility was found to be dependent on temperature through an equation of the form $\text{μ}{}_{\mathrm{<mtext>H</mtext>}}\text{= μ}{}_0\text{exp}\text{(}\text{?E}\text{kT)}$, which is typical of polycrystalline films, where the effects of grain boundaries predominate. The value of μ₀ was found to vary linearly with crystallite size for specimens with a comparable carrier concentration. Crystalline defects, within the grains, were also found to be significant in determining the value of the carrier mobility. At no time was there any evidence to suggest that surface scattering was significant in tellurium films.     

Low cycle fatigue behaviour of dual-phase steel with different volume fractions of martensite

Completely reversed low cycle fatigue tests were carried out at a constant strain rate of 10^?2s^?1 on 3 mm thick sheet specimens of a dual-phase steel treated to give 1.5 to 28% martensite without changing the carbon content. Hysteresis loop shape, stress/strain response and plastic strain energy as a function of applied cycles are analysed for different microstructures. Strain/life and plastic strain energy per cycle ($\text{Δ}\text{W}\text{?}{}_{\mathrm{<mtext>p</mtext>}}$)/life (2N_f) plots are discussed in terms of microstructure. It is shown that during cycling the shape of the hysteresis loop continuously changes at lower volume fractions of martensite whereas it remains more or less constant for microstructures with a higher percentage of martensite. A Coffin-Manson type of plot between log ($\text{Δ}\text{W}\text{?}{}_{\mathrm{<mtext>p</mtext>}}$) and log (2N_f) is found to be applicable to test results of dual-phase steel with a wide range of martensite contents and is thus more versatile than the plot between log (Δ?_p/2) and log (2N_f) for predicting the fatigue life.     

Fracture toughness characterization of several aluminum alloys in semi-brittle fracture

A method has recently been developed for determining a nonlinear fracture toughness parameter defined by the relation $\text{G}\text{?}{}_{\mathrm{c}}\text{=}\text{C}\text{?}\text{G}{}_{\mathrm{c}}$ where G_c is the critical elastic strain energy rate as defined by Irwin. The $\text{C}\text{?}$ term is a function of the nonlinearity of the load-displacement test record and has been evaluated using the three parameter Ramberg-Osgood approach, although other curve fitting techniques could be applied as well. The method is quite straightforward and is applicable to plane stress, plane strain and mixed mode testing although only plane stress conditions are considered in this paper. For the case of a linear load-displacement record $\text{C}\text{?}\text{→ 1}$ and $\text{G}\text{?}{}_{\mathrm{c}}$ reduces to the linear elastic result.The toughness parameter $\text{G}\text{?}{}_{\mathrm{c}}$ has been evaluated for a number of high strength aluminum alloys and compared with published G_c values for these materials. The tests were conducted on center-cracked sheets of 2014-T6, 2024-T81, 7075-T6 and 7475-T61 aluminum alloys under conditions of varying specimen geometry and displacement gage length. It was found that the values of $\text{G}\text{?}{}_{\mathrm{c}}$ obtained from displacement readings with a gage length of 2 in. generally agreed with published values of $\text{G}{}_{\mathrm{c}}\text{=}\text{K}{}_{\mathrm{c}}{}^2\text{E}$. The $\text{G}\text{?}{}_{\mathrm{c}}$ values were found to vary inversely with gage length and a/w ratios. The variation in values for $\text{G}\text{?}{}_{\mathrm{c}}$ is of the same order of magnitude as the scatter in published values for G_c. However, $\text{G}\text{?}{}_{\mathrm{c}}$ appears to be less sensitive than G_c to changes in a/w.     

Third-order bounds on the effective bulk and shear modulus of a dispersion of fully penetrable spheres

We evaluate the third-order Beran-Molyneux bounds on the effective bulk modulus K_e and the third-order McCoy bounds on the effective shear modulus $\text{μ}{}_{\mathrm{e}}$ of a model of a two-phase composite in which one of the phases consists of spherical inclusions (or voids), with bulk and shear moduli, K₂ and $\text{μ}{}_2$, respectively, and volume fraction $\text{φ}{}_2$, dispersed randomly throughout a matrix phase, with bulk and shear moduli, K₁ and $\text{μ}{}_1$, respectively, and volume fraction $\text{φ}{}_1$. We tabulate the two fundamental microstructural parameters I₁ and L₁ required to evaluate the bounds, which depend upon the three-point matrix probability function of the model, for the aforementioned fully-penetrablesphere model. We compare the third-order bounds on K_e and $\text{μ}{}_{\mathrm{e}}$ to the second-order bounds due to Hashin and Shtrikman and to Walpole. We find that the third-order bounds for our model are always more restrictive than the corresponding second-order bounds. When the moduli of the phases differ by an order of magnitude, the third-order bounds are sharp enough to provide quantitatively useful estimates of K_e and $\text{μ}{}_{\mathrm{e}}$ for all $\text{φ}{}_2$. The third-order bounds are very restrictive at low $\text{φ}{}_2$ values (e.g., $\text{φ}{}_2\text{= 0.1}$) where they remain useful for cases in which the moduli of the phases differ by two orders of magnitude. Experimental values of $\text{μ}{}_{\mathrm{e}}$ measured by Corson for a tungstenlead composite are found to lie within the McCoy bounds for our model, with the lower bound giving a good estimate of the data.     

Growth of Ca3Fe2Ge3O12 and Ca3Fe(Al,Cr) Ge3O12 garnets in molten bismuth germanate glasses

Additions of Fe₂O₃ to CaO·Bi₂O₃·2 GeO₂ cause Ca₃Fe₂Ge₃O₁₂ garnets to precipitate from the resultant melt at 1250°C. Garnets with the composition Ca₃Fe(Al, Cr) Ge₃O₁₂ are also precipitated by adding either $\text{Al}{}_2\text{O}{}_3\text{Fe}{}_2\text{O}{}_3$ or $\text{Cr}{}_2\text{O}{}_3\text{Fe}{}_2\text{O}{}_3$ mixtures. The well-formed crystals range from several to 100 μm in size and are obtained in 50 to 70% yields at $\text{Fe}\text{Bi}\text{= 0.4}$. Additions of Fe₂O₃ (up to $\text{Fe}\text{Bi}\text{= 1.0}$) to compositions containing ZnO, CdO, SrO, and BaO yield only dark glasses. The physical properties of these glasses suggest that Fe(III), in contrast to AL(III) & Ga(III), prefers octahedral coordination.     

Luminescence of some oxygen-octahedric ferroelectrics exposed to an electron beam

Spectral and temperature dependence of cathodo luminescence (CL) was studied in oxygen-octahedric ferroelectrics Ba_XSr_1-XNb₂O₆, $\text{PbMg}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{Nb}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{O}{}_3$, LiNbO₃, SrTiO₃, Ba₂NaNb₅O₁₅, and PLZT-ceramics. CL in these materials is of admixture type. In the region of ferroelectric phase transition (PT) of Ba_XSr_1-XNb₂O₆ and $\text{PbMg}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{Nb}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{O}{}_3$ an anomaly in CL is observed. Redistribution of recombination flows between the centers of radiative and non-radiative recombinations in PT region due to variation of dielectric constant is proposed to account for this phenomenon.     

Thermal expansion — An empirical correlation

The average thermal expansion coefficient (α_L) of a large variety of cubic and close-packed materials is shown to depend upon the coincidence of preferred orbital extension and site symmetry as well as melting point (Mp in °C). The product $\text{α}{}_{\mathrm{<mtext>L</mtext>}}\text{M}{}_{\mathrm{<mtext>p</mtext>}}\text{? 0.016}$ tends to hold for close-packed structures and $\text{α}{}_{\mathrm{<mtext>L</mtext>}}\text{M}{}_{\mathrm{<mtext>p</mtext>}}\text{? 0.027}$ for rectilinear arrays. Deviations occur when orbital extension tends to sp³ symmetry for an ion in an octahedral site or the site symmetry is reduced to tetrahedral or planar.     

The plastic zone and growth of fatigue cracks in magnesium MA12 alloy at room and low temperatures

The plastic zone formed at the fatigue crack tip and the fracture topography in MA12 magnesium alloy samples, tested at 293 and 140 K in air and in vacuum, were analysed. It was found that the plastic zone formed in vacuum is characterized by a greater size ($\text{h}$) and degree of plastic strain that in air, and the crack growth rate ($\text{d}\text{l/}\text{d}\text{N}$) is lower. Temperature reduction leads to a decrease in $\text{h}$, while $\text{d}\text{l/}\text{d}\text{N}$ and the fracture mechanism are affected by temperature ambiguously, depending on the alloy microstructure and the $\text{K}{}_{\mathrm{<mtext>max</mtext>}}$ value. It was established that the size of the plastic zone can be described by the equation:

$\text{h=A}\text{(}\text{K}{}_{\max }\text{σ}{}_{\mathrm{0.2ps}}\text{)}{}^2$

where $\text{A}$ is a coefficient dependent on the alloy structural state, environment and test temperature. Evaluation of the cyclic plastic zone size at $\text{K}{}_{\mathrm{<mtext>max</mtext>}}$, corresponding to the transition from a low temperature region to a ‘Paris’ region, showed that this transition occurred when the cyclic plastic zon reached the structural parameter of the material.     

Lithium organic electrolyte cells using the copper chevrel phase as cathode

The copper Chevrel phase, Cu_xMo₆S_8?z (x=0–4, z=0-0.2), was evaluated as the cathodes in lithium organic electrolyte cells. The cells $\text{Li}\text{Cu}{}_{\mathrm{x}}\text{Mo}{}_6\text{S}{}_{\mathrm{<mtext>8?</mtext><mtext>z</mtext>}}$ showed a good discharge performance for the charge transferred range of 0.5 to 3.5 $\text{electron(e)}\text{Cu}{}_{\mathrm{x}}\text{Mo}{}_6\text{S}{}_{\mathrm{<mtext>8?</mtext><mtext>z</mtext>}}$ under a high current density such as 3mA/cm². The charge and discharge cycle tests of the $\text{Li}\text{Cu}{}_2\text{Mo}{}_6\text{S}{}_{\mathrm{7·8}}$ cell indicated a good rechargeability for the range of 0.5 to $\text{2.5}\text{e}\text{Cu}{}_{\mathrm{x}}\text{Mo}{}_6\text{S}{}_{\mathrm{<mtext>8?</mtext><mtext>z</mtext>}}$. The electrode reaction mechanism was discussed with the help of x-ray diffraction analysis of the cathode reaction products.     

Bounds on the effective thermal conductivity of a dispersion of fully penetrable spheres

We evaluate upper and lower bounds on the effective thermal conductivity K_e of a model of two-phase composite materials in which one of the phases consists of spherical inclusions (or voids) of conductivity K₂ and volume fraction φ₂, dispersed randomly throughout a matrix phase of conductivity K₁ and volume fraction φ₁. Our evaluations compare third-order bounds of Beran and of Brown, which utilize the three-point matrix probability function of the model, with bounds of De Vera and Strieder (which apply only to the aforementioned “fully penetrable sphere” model) and of Hashin and Shtrikman. The comparisons are made over extended ranges of values of both φ₂ and $\text{α =}\text{K}{}_2\text{K}{}_1$ and reveal that the best bounds among those we have tested (generally those of Beran) are sharp enough to give quantitatively useful estimates of K_e for $\text{0.1 ≤}\text{K}{}_2\text{K}{}_1\text{≤ 10}$ over a wide range of φ₂ values. They are sharp at high φ₂ values (i.e., φ₂ = 0.9) and very sharp at low φ₂ values (e.g. φ₂ = 0.1) where they remain useful for $\text{K}{}_2\text{K}{}_1\text{≈ 100}$. They are less sharp at intermediate values (e.g. φ₂ = 0.5). As is well known, such results immediately translate into equivalent results for the electrical conductivity, dielectric constant, or magnetic permeability of composites.     

Syntheses and magnetic properties of Eu3B2O6 and Sr3B2O6

Europium orthoborate and strontium orthoborate crystallize in the rhombohedral system with two formula units in a cell of dimensions $\text{a}{}_{\mathrm{R}}\text{=6.697}\text{A}\text{?}$, α_R=85.17° for Eu₃B₂O₆, and $\text{a}{}_{\mathrm{R}}\text{=6.695}\text{A}\text{?}$, α_R=85.00° for Sr₃B₂O₆. The equivalent hexagonal lattice parameters are $\text{a}{}_{\mathrm{H}}\text{=9.069}\text{A}\text{?}$, $\text{c}{}_{\mathrm{H}}\text{=12.542}\text{A}\text{?}$, and $\text{a}{}_{\mathrm{H}}\text{=9.046}\text{A}\text{?}$, $\text{c}{}_{\mathrm{H}}\text{=12.566}\text{A}\text{?}$ respectively. Eu₃B₂O₆ appears to be ferromagnetic below 7.5K.