A note on the resistance to brittle fracture in various ceramic materials

The square of the ratio of the abraded bending strength, _d, to the unabraded bending strength, , is proposed as a measure of the resistance to crack propagation in ceramic materials. Data for various porcelains, glass-ceramics, and glasses showed that _d is essentially constant and that (_d/)² decreased rapidly with increase of the unabraded strength.     

The dielectric behaviour of single-crystal MgO,Fe/MgO and Cr/MgO

The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10^–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as ⁿ withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms.     

On the measurement and physical meaning of the cleavage fracture stress in steel

Elastic-plastic two-dimensional (2D) and three-dimensional (3D) finite element models (FEM) are used to analyze the stress distributions ahead of notches of four-point bending (4PB) and three-point bending (3PB) specimens with various sizes of a C-Mn steel. By accurately measuring the location of the cleavage initiation sites, the local cleavage fracture stress _f and the macroscopic cleavage fracture stress _F is accurately measured. The _f and _F measured by 2D FEM are higher than that by 3D FEM. _f values are lower than the _F, and the _f values could be predicted by _f=(0.8––1.0)_F. With increasing specimen sizes (W,B and a) and specimen widths (B) and changing loading methods (4PB and 3PB), the fracture load P _f changes considerably, but the _F and _f remain nearly constant. The stable lower boundary _F and _f values could be obtained by using notched specimens with sizes larger than the Griffiths–Owen specimen. The local cleavage fracture stress _f could be accurately used in the analysis of fracture micromechanism, and to characterize intrinsic toughness of steel. The macroscopic cleavage fracture stress _F is suggested to be a potential engineering parameter which can be used to assess fracture toughness of steel and to design engineering structure.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Evaluation of the true activation enthalpy of superplastic flow including a threshold stress

A new method is suggested for the evaluation of the true activation enthalpy for alloys where the strain rate of the superplastic flow varies with a power of an effective stress _e = -_o, where and _o are the applied stress and a threshold stress, respectively. Some earlier results concerning superplastic AlMgZnCu alloys containing chromium and in which a strongly temperature-dependent threshold stress can be revealed, are reanalysed. The results are in good agreement with the previous ones. It has been shown further that for the alloys investigated the true activation energy increases with increasing chromium content.     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

Coarsening of δ′ (Al3Li) and composite precipitates in an Al-2.5% Li-0.15% Zr alloy

The early stage coarsening behaviour of (Al₃Li) precipitates and composite precipitates, consisting of (Al₃Zr) core enveloped by a shell, in an Al-2.5% Li-0.15% Zr alloy has been studied at 443, 473 and 503 K by conventional transmission electron microscopy using superlattice dark-field images. Coarsening kinetics of precipitates was found to exhibit considerable deviation from the t ^1/3 law corresponding to diffusion control at 473 and 503 K. This deviation may be explained either by the operation of a surface-reaction controlled coarsening mechanism represented by t ^1/2 law, or by the presence of a slower precoarsening stage preceding diffusion-controlled coarsening. The particle-size distributions of precipitates were not in accordance with either the earlier theoretical predictions or the normal distribution. They were symmetrical or slightly skewed to the left, and particle sizes twice the average were observed. The coarsening kinetics of composite precipitates, was found to be rather different from that of ; a diffusion model which yields t ^1/n law with n changing from 1/4 to 1/6 as the coarsening progresses, was predicted. The composite precipitates have exhibited quite a narrow and rather symmetrical size distribution.     

Stress relaxation in hot-drawn low density polyethylene

The tensile stress relaxation behaviour of hot-drawn low density polyethylene, (LDPE), has been investigated at room temperature at various draw ratios. The drawing was performed at 85° C. The main result was an increase in relaxation rate in the draw direction, especially at low draw ratios when compared to the relaxation behaviour of the isotropic material. This is attributed to a lowering of the internal stress. The position of the relaxation curves along the log time axis was also changed as a result of the drawing, corresponding to a shift to shorter times. The activation volume, , varied with the initial effective stress ₀ ^* according to ₀ ^* 10kT, where ₀ ^* =₀ — _i, is the difference between the applied initial stress, ₀, and the internal stress _i. This result supports earlier findings relating to similarities in the stress relaxation behaviour of different solids.     

Ageing characteristics of Al-2.5% Li rapidly solidified alloy

The present work was performed on an Al–2.5 wt% Li alloy produced by melt spinning. The ribbons were aged in the temperature range 180 to 310° C for times between 1 min and 120h. The kinetics of coarsening of (Al₃Li) and (AlLi) phase particles were investigated using transmission electron microscopy and hardness measurements. The results show that coarsening of (Al₃Li) follows a simple linear relation with the cube root of Me, whereas coarsening of (AlLi) does not follow the same trend. We believe that the (AlLi) phase nucleates at the (Al₃Li)/matrix interface and grows by the dissolution of the nearby (Al₃Li) particles. The mechanical properties of the powder metallurgy alloy show that a large volume fraction of PFZ contributes to the alloy ductility, 11 %, in the aged condition. Also, the yield strength is greatly improved due to refinement effects enhanced by rapid solidification.     

Low endurance fatigue in metals and polymers

The fatigue behaviour of commercially pure aluminium and of nylon under sequentially varying strain amplitudes is compared with a damage law of the type suggested by Miner. Aluminium obeys such a law for both cyclic and uniaxial prestrains but the behaviour of nylon is significantly affected by microcracking, which produces a marked effect of loading sequence.Appendix N Number of strain cycles at a given time - N _f Value of N at failure - True tensile stress - True stress range for a strain cycled specimen - _h Value of at half the life of the specimen - True tensile strain - Total true strain range - _p True plastic strain range (= the breadth of the hysteresis loop at = 0) - _d True diametral strain range - E Young's modulus - Linear strain hardening rate when tested at a particular value of _p - D Damage due to cycling - D _p Damage due to prestrain - _p Prestrain. C, K, K₁, , are constants     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

Electronic and ionic conduction in some simple lithium salts

The electrical conductivity () and thermoelectric power (S) of solidified melt samples of Li₂MoO₄, Li₂WO₄ and Li₂SO₄ are presented in the temperature range 415 K to melting point of each compound. The ratio of ionic to electronic contribution to has been obtained with the help of a time-dependence study of d.c. electrical conductivity. It has been shown that in Li₂MoO₄ electronic contribution to remains high up to its melting point (about 8% just below the melting point) and it shows no superionic phase. However, in Li₂WO₄ and Li₂SO₄ a superionic phase is obtained in which the ionic contribution to is more than 99.99%. However, in normal ionic (or) phase it is small and decreases with decreasing temperature. Separate temperature variations of ionic ( _i) and electronic ( _e) conductivities are presented and the conduction mechanisms are discussed. It is shown that ionic conduction in the-phase is dominated by Schottky-type defects.     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

Angular dependence of the resistive transitions in superconducting films in a magnetic field

The resistive transitions aboveH _c on Al films with the thicknessd<(0) have been measured as a function of the angle between the film surface and the magnetic field, where (0) is the coherence length at 0 K. An observed broadness in the transitions is considered to be due to fluctuations aboveH _c and is compared with Aoi's theories taking into account the Aslamazov—Larkin (AL) contribution only, or both the AL and an anomalous (Maki) contribution. At all angles the observed electrical conductivity due to fluctuations ' is larger than the theoretical predictions based on the AL contribution alone. Except for angles near =0, the observed ' can be explained by adding the anomalous contribution to that of AL.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

Calculation of He II flow in tubes

The flow of superfluid helium through a tube with different temperatures at the ends differs considerably from that of a Newtonian fluid. The strong dependence of the thermodynamic properties on temperature, the internal convection mechanism and the structure of superfluid turbulence causes unusual flows. The equations for the flow of He II are integrated using a new one-dimensional, steady state model to study the flow in a tube. A wide range of driving conditions is studied. The temperature and pressure profiles along the tube fall into four classes. A dimensionless parameter called is defined which determines the progression through the four classes of behavior. The deviation of the flow from Newtonian is measured by . Significant maxima of the temperature and pressure can occur between the ends of the tube for large values of . The shapes of the profiles and the mass flux depend primarily on , the geometry and the boundary conditions. Formulas are presented which relate the variables of interest to the boundary conditions. These formulas result from averaging the equations of motion along the tube. A general and unified approach, based on , is presented for analyzing experimental data and designing new experiments. It is shown that the common practice of neglecting the pressure term in the energy equation results in poor prediction for many situations. The occurrence of large maxima of pressure and temperature imply that the interpretation of some of the experimental data of the literature should be reconsidered.     

On a family of quasi-isotropic fiber-reinforced composites

Summary The spectral decomposition of the compliance and the stiffness tensors for a transversely isotropic body (fiber-reinforced composite), and their eigenvalues derived from, define in a simple and efficient way the respective elastic eigenstates of loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components ₁ and ₂, which are shears, with ₂ a simple shear, and ₁ a suprposition of simple and pure shears, and they are associated with distortional components of energy. The remaining two eigenstates, with stress components ₃ and ₄ are the orthogonal supplement to the shear subspace of ₁ and ₂, and consist of an equilateral stressing in the plane of isotropy, superimposed with a prescribed tension or compression along the symmetry axis of the material.In this paper a particular class of transversely isotropic materials is studied, whose mechanical properties are conveniently selected to reduce the two last eigenstate components in such a manner, that the one is identified to contribute only a dilatational type of strain energy, whereas the other a distortional one. In this way the four eigenstates are clearly separated in two distinct groups creating either distortional or dilatational types of strain energy. It was shown that this family of materials behave like the isotropic body, in spite of their differences in the elastic constants along their principal axes of anisotropy.Since with fiber-composites it is possible to arrange their mechanical properties by selecting the appropriate ratios between matrix and inclusions, according to their properties, this possibility of selecting in advance the properties of the composite is feasible. Taking into consideration that quasi-isotropic materials develop the smallest stress concentrations in the structures, the development and selection of such composites with quasi-elastic properties becomes very important.     

Experimental studies of hydrogen on boron nitride: II. NMR studies of orientational ordering of H2

We report the results of NMR studies of thin films of hydrogen adsorbed on hexagonal boron nitride. Orientational ordering is observed below 1 K but the ordering is not complete, and a clear two-component ordering is observed. Molecules are either (i) almost completely ordered with local order parameters = 1 – 3/2Jz ² clustered close to a maximum value of a 0.94 (comparable to the values for long range ordering in bulk samples at high ortho concentrations), and (ii) a large fraction of the molecules that remain nearly disordered with 0.25. The degree of Orientational ordering depends on the number of hydrogen layers and on the ortho-hydrogen concentration, and these studies indicate that ordering occurs principally in the first four layers closest to the substrate, with weaker Orientational ordering in the outer layers near the free surface even at temperatures as low as 210 mK.     

On the creep rupture life prediction

Combined effects of stress, A, and fracture cavitation on the creep rupture life, tR, have been studied in conventionally cast MAR-M 002 alloy tested at 1173 K (900 °C) over a limited range of stress (A = 200–400 MPa). It is predicted that the creep fracture cavity growth is controlled by the coupled power-law creep with the grain-boundary diffusion mechanism. On the basis of this prediction the Edward–Ashby model overestimates the creep rupture life although this model correctly describes the trend in the data. The observation of a linearity between the cavity density, NA, and the product RtR4A indicates that this relationship can be used to predict the creep time, tR, where R is the rupture strain. Furthermore, another empirical method is the creep-fracture parameter, Kf = f(ac)1/2, approach, developed using the modified Griffith–Irwin type of relationship, which can also be used to predict the creep rupture life in the present alloy, where f is the creep fracture stress (or the applied stress, A) and ac the crack (or cavity) size.