Convection in a shallow laterally heated cavity with conducting boundaries

Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R _c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R _c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.     

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.     

Strength improvement of cemented carbides by hot isostatic pressing (HIP)

HIP treatment after sintering increases the strength of the investigated cemented carbide alloy by a factor of two whereas hardness, fracture toughness, and work of fracture remain unchanged. HIP does not affect the microstructural parameters of the carbide skeleton and the binder phase, but the residual pores are eliminated entirely. Failure of both the as-sintered and post-densified material occurs by a pure Griffith mechanism. The strength-flaw size relationship is established experimentally and is shown to obey exactly Griffith's basic strength equation. The strength is controlled by the largest microstructural defects, i.e. pores in the as-sintered material, and coarse WC grains and inclusions in the HIP-treated specimens.Nomenclature a size of the fracture initiating flaw - a _th theoretical flaw size - b sample thickness - c length of the pre-crack - C contiguity of the carbide phase - D _WC mean carbide grain size - E Young's modulus - F fracture surface - G _IC critical energy release rate - h sample height - H _V Vicker's hardness - K _IC critical stress intensity factor - l span length - l _Co mean Co layer thickness - m Weibull parameter - P load - r _p1 radius of the plastic zone - R crack resistance - S probability of failure - U fracture energy - X relative crack length - Y K-calibration - _F specific work of fracture - _I specific energy for fracture initiation - spread of grain size distribution - compliance of the pre-cracked specimen - ₀ compliance of the uncracked specimen - v Poisson's ratio - fracture stress - ₀ maximum stress - _B bend strength - _Y Yield strength - _eff maximum local stress     

Statistical analysis of the Hertzian fracture of pyrex glass using the Weibull distribution function

Hertzian fracture tests were carried out on specimens of ground-and-polished Pyrex glass using polished Pyrex glass balls of 6 and 8 mm diameter. The results were analysed according to the theory of flaw statistics originally proposed by Weibull. The Weibull parameters m and ₀ were found to be independent of ball size; _u however decreased with increase in ball size. The parameters _u,₀ and m obtained from the Hertzian tests differed from those obtained from a four-point bend test. The predicted mean fracture stress and the mean fracture location for Hertzian fracture using the derived Weibull parameters agreed reasonably well with the experimental values.     

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.     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

Fracture behavior of stitched warp-knit fabric composites

Pilot studies are conducted to characterize the macroscopic fracture resistance behavior using linear elastic fracture mechanics and attempt to quantify the fracture parameters in which may govern the fracture and failure patterns of stitched warp-knit fabric composites. Methods based on the J-integral method and Betti's reciprocal theorem in extracting the fracture parameters, critical stress intensity factors, T-stress, and the second term of _y(r,0) near the crack tip prior to fracture initiation are formulated. Two fracture criteria, [_c,r _c] and [_c,r _c] are attempted to characterize the failure initiation for the fiber-dominated failure mode and self-similar crack extension in a given thickness of the laminate. Based on linear elastic fracture mechanics principle, these criteria are transformed into crack-driving forces [K _Q,T] and [K _Q,g ₃₂]. The two-parameter fracture criteria, [K _Q,T] and [K _Q,g ₃₂] provide a good correlation for the CCT and SENT specimens, but not for the high constraint CT specimens. With the limited experimental data, the results tend to show that the large tensile T-stress and large magnitude of negative g ₃₂ may inhibit the crack extension in the same crack plane and promote crack kinking.     

Application of the Griffith criterion to fracture of boron fibres

Tensile tests were performed on boron fibres and the resulting fracture stresses _f recorded. The fracture surfaces were investigated by SEM, with emphasis on the type of flaw nucleating the fracture. It was found that pre-existing, so-called proximate voids, in the boron mantle near the core-mantle interface, have transverse irregularities, large enough to create stress concentrations. The radial extensions, 2c, of fracture initiating proximate voids in mirror zones were measured from the micrographs. The obtained 2c _f relation was found to be in good agreement with the Griffith criterion for brittle fracture. In addition, the experimental log 2c-log _f plot gives some information on the value of the surface energy,, of boron.     

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.     

Effect of shot peening on the fatigue and fracture behaviour of two titanium alloys

The fatigue and fracture behaviour of two titanium alloys, the near-alpha IMI-685 and alpha-beta IMI-318, were studied in the machined and polished (MP) as well as the machined, polished and shot (glass-bead) peened (MPS) conditions. Glass-bead peening reduced the room-temperature as well as the high-temperature (450°C) fatigue life of alloy IMI-685 at high stress amplitudes, _a, approaching the proof stress, _ps, of the material (LCF region). When the applied stress amplitude (0–770 MPa, HCF region) was comparable to the peen-induced peak longitudinal residual stress, _LP, i.e. (_LP/a)=0.92, an improvement in the room-temperature fatigue life of IMI-685 was observed. When the (_LP/a) ratio was less than this value, decreases in the fatigue life were seen. The room-temperature fatigue behaviour of IMI-318 at high stress amplitudes was similar to that of IMI-685. The decrease in the fatigue life of this alloy, at a stress amplitude (770 MPa) where improvement was observed for IMI-685, could be attributed to the higher relaxation of peen-induced residual stresses in IMI-318 compared with IMI-685. Glass-bead peening improved the hightemperature (450°C) fatigue life of IMI-685 at a low stress amplitude (465 MPa; (_a/PS)=0.87). The crack-initiation sites in the MP and the MPS conditions were at the surface for both the alloys. However, fracture in the surface layers of the alloys appeared more brittle in the peened (MPS) rather than in the unpeened (MP) condition.     

Underpinning of a simple blunt flaw fracture initiation relation

With the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture as a basis, the author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a Mode I fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius . The relation gives the critical elastic flaw-tip peak stress _pcr, and has been derived using a two-extremes procedure, whereby the separate, and indeed exact, solutions for small and large s/ values are blended together to give an all-embracing relation that is valid for all s/ values. _pcr is expressed in terms of the process zone material parameters and geometrical parameters but, for a wide range of flaw geometry parameters, _pcr essentially depends on only one geometrical parameter . This paper provides underpinning for the general thrust of the two-extremes procedure by appealing to exact results for the complete spectrum of s/ values from analyses of appropriate Mode III models. Results obtained by applying the two-extremes procedure are shown to be in very good agreement with the exact results.     

Experimental and numerical studies in model composites Part II: Numerical results

A numerical approach using the boundary element method for strength and toughness of a composite with long aligned fibers is reported. The three-dimensional problem is reduced to a two-dimensional one by substituting the rows of fibers with layers of appropriate width and elastic constants. The configuration examined in this work is a compact tension specimen similar to that used in the experimental studies (Part I, [1]). The experimental results on strength and apparent fracture toughness are compared with the numerical results. For the particular geometry and fiber spacing, the numerical simulations are in good agreement with the experimental findings, i.e. the composite's strength _A , scales with the fiber spacing , in the form of _A . Using the numerical formalism a number of different geometries was examined. The simulations suggested that if the external specimen characteristics remain the same and the fiber spacing in the direction of crack advance is changed, then the strength of the composite specimen can be expressed _A . If the fiber spacing varies in both directions simultaneously, for a certain range of , it can be considered that the composite's strength _A , is proportional to _A .     

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.     

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     

Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

Thermal-stress resistance and fracture toughness of two tool ceramics

The thermal-stress resistance and fracture strength behaviour of two oxide ceramics (a hot-pressed pure Al₂O₃ and a composite ceramic NTK-HC2) subjected to severe thermal shocks have been investigated. The damage resistance parameter (K _IC/ _f)² for both ceramics is also determined for a wide range of temperatures (25° to 800° C) and cross-head rates (10^–2 cm min^–1 2.5 m sec^–1). Fracture strength behaviour of these two oxide ceramics is shown to follow Hasselman's model where the instantaneous strength loss at the critical quenching temperature may be calculated using appropriate (K _IC/ _f)² values to give good agreement with experimental results. Repeated shocks show some further degradation in the retained strength for both ceramics so that these materials are susceptible to thermal fatigue. It is found that both materials possess similar resistance to crack initiation (i.e. similar T _c and retained strength after shocking through T _c) but the pure oxide ceramic has higher resistance to crack propagation.     

The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints

Analytical solutions for beam specimens used in fracture-mechanics testing of composites and adhesively-bonded joints typically use a beam on an elastic foundation model which assumes that a non-infinite, linear-elastic stiffness exists for the beam on the elastic foundation in the region ahead of the crack tip. Such an approach therefore assumes an elastic-stiffness model but without the need to assume a critical, limiting value of the stress, _max, for the crack tip region. Hence, they yield a single fracture parameter, namely the fracture energy, G _c. However, the corresponding value of _max that results can, of course, be calculated from knowledge of the value of G _c. On the other hand, fracture models and criteria have been developed which are based on the approach that two parameters exist to describe the fracture process: namely G _c and _max. Here _max is assumed to be a critical, limiting maximum value of the stress in the damage zone ahead of the crack and is often assumed to have some physical significance. A general representation of the two-parameter failure criteria approach is that of the cohesive zone model (CZM). In the present paper, the two-parameter CZM approach has been coupled mainly with finite-element analysis (FEA) methods. The main aims of the present work are to explore whether the value of _max has a unique value for a given problem and whether any physical significance can be ascribed to this parameter. In some instances, both FEA and analytical methods are used to provide a useful crosscheck of the two different approaches and the two different analysis methods.     

Notch-sensitivity of non-linear materials

The relationships between breaking stress, _B, and crack length, a, and between breaking strain, _B, and a have been calculated for materials whose stress-strain behaviour is approximated by =k ⁿ . The results take the form _B (a) ^–m and _B (a) ^–p , where m=n/(n+1) and p=1/(n+1). For n=1 (the linear case), m=p=1/2. For n>1, m>1/2>p and for n<1, m<1/2<p. Tests on butyl, silicone and latex rubbers as model materials confirm the applicability of the theory. The results imply that for biological materials such as skin where n>1, _B drops off very rapidly with increasing defect size, whereas _B is far less dependent on a. These may be appropriate properties for a material where the degree of extension, rather than the peak loads encountered, is critical to its in vivo performance. For materials where n<1, breaking stress is far less sensitive to crack length than fracture strain, which may be more appropriate properties for applications in which applied stress, but not strain, is critical.     

Study of dielectric and electrical properties of mortar in the early hydration period at microwave frequencies

The dielectric constant, , and electrical conductivity, , of mortars with various sand-cement ratios,s/c, were measured for the first 30 h hydration using microwave techniques in the frequency range 8.2–12.4 GHz. The and of the mortars were found to increase linearly with increasing water-solid ratiow/(s + c), but decrease with increasings/c. It was found that as long as thes/c values were the same, the rate of changes in and of the mortars were the same. It appears that thes/c is the key factor controlling the rates of changes in dielectric and electrical parameters of cement hydration in mortar. The relationship between compressive strength and dielectric and electrical properties of mortars was also discussed.     

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.