Creep of ceramics

This review analyses a wide range of experimental data on the creep of ceramic materials and reveals many similarities with the creep of metals. It is demonstrated that there are two important differences in the creep behaviour of ceramics: (1) there is an enhanced role of diffusion creep, and (2) in the power-law regime, ceramics divide into two categories with stress exponents of 5 and 3, respectively. It is concluded that the behaviour with an exponent of 5 represents fully ductile behaviour as in f cc metals, whereas the behaviour with an exponent of 3 is due to dislocation climb from Bardeen-Herring sources under conditions where there is either a lack of five independent slip systems or, if five independent slip systems are available, a lack of interpenetration of these systems.     

Friction properties of cork

The friction coefficient, , of cork sliding on another material (glass and steel in most experiments and also cork) was measured for various compressive stresses and sliding velocities. There is a strong effect of stress and a negligible effect of velocity on the friction coefficient. Values of are in the range 0.4 to 1.2. The effect of moisture content of cork was also evaluated. For dry cork (6% moisture content) there is anisotropy of the friction coefficient related to the orientation of the sliding plane of cork, with larger values for sliding in the tangential plane (compression in the radial direction) as compared to sliding in planes perpendicular to this. At larger moisture contents, the anisotropy of decreases. No in-plane of sliding anisotropy was detected. The friction coefficients for sliding on glass and on steel are comparable, but an effect of roughness was detected. The friction coefficients for sliding on glass and on steel are comparable, but an effect of roughness was detected. The friction against cork is large, with close to unity. The interplay between the friction coefficient and the compression properties of cork is discussed. © 1998 Chapman & Hall     

Creep of CoO single crystals

Cobalt monoxide single crystals having a [100] orientation were creep tested in compression over ranges of temperature, stress and oxygen pressure. The creep curves were S-shaped and only the inflection creep rate, ₂, was analysed. In the range of 1000 to 1200° C, 850 to 1700 psi and 10^–3 to 1 atm oxygen, ₂ was given by ₂=A po ₂ ^{0.45 7.1}exp(– Q _c /RT) where Q _c =87±6 kcal/mol at 0.01 atm O ₂ and 100±16 kcal/mol at 1 atm O ₂. Slip occurred on two orthogonal {011} 0¯11 slip systems. The presence of subboundaries was observed by optical and transmission electron microscopy. It is suggested that the creep rate is controlled by oxygen diffusion.     

High temperature creep in a 2-3-4 garnet: Ca3Ga2Ge3O12

High temperature plastic deformation in a single crystal of a 2-3-4 garnet, Ca₃Ga₂Ge₃O₁₂, was investigated. A Czochralski-grown single crystal of Ca₃Ga₂Ge₃O₁₂ was deformed in compression in air along 100 or 110 at temperatures of 1472 to 1573 K (T/T_m = 0.90–0.96). The samples show higher resistance to creep than other 3-3 garnets, namely the flow stress at the strain-rate of 4 × 10^{– 6} s^{– 1} is 200–400 MPa in this temperature range. The TEM observations of dislocation microstructures show little evidence of climb and plastic deformation in this garnet appears to occur exclusively by dislocation glide, using mostly the 1/2111{110} slip systems. Dislocations with b = 100 are frequently observed but they are interpreted as products of dislocation reactions among 1/2111. The single crystal used contained a number of precipitates that grew during annealing and also during deformation. These precipitates act as sources for dislocations but no evidence for their significant effects on creep strength is observed. The normalized flow law of Ca₃Ga₂Ge₃O₁₂ is similar to other 3-3 oxide garnets (e.g., YAG, GGG), but in contrast to 3-3 garnets, the more stable and hence less mobile dislocations have a large edge component.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

High-temperature creep response of a commercial grade siliconized silicon carbide

Creep studies conducted in four-point flexure of a commercial siliconized silicon carbide (Si-SiC, designated as Norton NT230) have been carried out at temperatures of 1300, 1370, and 1410°C in air under selected stress levels. The Si-SiC material investigated contained 90% -SiC, 8% discontinuous free Si, and 2% porosity. In general, the Si-SiC material exhibited very low creep rates (2 to 10×10^–10 s^–1) at temperatures 1370°C under applied stress levels of up to 300 MPa. At 1410°C, the melting point of Si, the Si-SiC material still showed relative low creep rates (0.8 to 3 × 10^–9 s^–1) at stresses below a threshold value of 190 MPa. At stresses >190 MPa the Si-SiC material exhibited high creep rates plus a high stress exponent (n=17) as a result of slow crack growth assisted process that initiated within Si-rich regions. The Si-SiC material, tested at temperature 1370°C and below the threshold of 190 MPa at 1410°C, exhibited a stress exponent of one, suggestive of diffusional creep processes. Scanning electron microscopy observations showed very limited creep cavitation at free Si pockets, suggesting the discontinuous Si phase played no or little role in controlling the creep response of the Si-SiC material when it was tested in the creep-controlled regime.     

Effect of multiple strain-anneal cycles on the 1000° C creep behaviour of γ/γ′-α

An investigation of the influence of multiple strain-anneal cycles on the 1000° C creep behaviour of the directionally solidified eutectic alloy /- has been undertaken. Cycles consisted of swageing at room temperature or 900° C by about 5 to 10% per pass followed by annealing at 900° C, and were repeated to total strains of approximately 10, 30 and 50%. Transmission electron microscopy (TEM) of strain-annealed materials revealed that three-dimensional dislocation networks were introduced into the matrix, but very little work remained in the fibres. Constant-velocity creep testing indicated that all thermomechanical processing schedules improved the creep strength for strain rates 2 x 10^–6sec^–1; however only strain-annealing with a total of 13% work at room temperature (RT13) improved the behaviour at strain rates 2 x 10^–7sec^–1. The advantage of RT13 processing over as-grown materials at lower strain rates was confirmed by constant-load creep testing. It was also shown that 900° C annealing slightly improves the 1000° C creep properties in comparison to as-grown alloys. TEM of crept materials indicated that the active creep mechanism had been changed from dislocation pile-ups at fibres in as-grown alloys to dislocations being stopped by sub-boundaries in the matrix for RT13.     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

Hall-Effect study of YNi2B2C superconductor

Hall-effect and critical magnetic fields H_c2(T) have been studied for YNi₂B₂C (prepared using high pressure technique) at H130 kOe and 1.6T300K. The normal state Hall coefficient R_H was found to be negative (R_H=–1.43.10^–11 cm/Oe at T=4.2 K and H=130 kOe) and slightly growing in absolute value with increase of temperature. The dependence of the Hall voltage on magnetic field in the mixed superconducting state shows no sign reversal as was observed earlier for some high-T_c systems. The values of ¦H_c2/ T¦and H_c2(0) are found to be 4.8 kOe/K and 47 kOe respectively.     

The role of Coble creep and interface control in superplastic Sn-Pb alloys

The creep behaviour of superplastic Sn-2 wt% Pb and Sn-38.1 wt % Pb is investigated at temperatures between 298 and 403 K and for grain sizes between 2.5 and 260m. In Sn-2 wt% Pb with grain sizes larger than 50 m, diffusion-controlled Coble creep is found and it is experimentally shown that this type of creep is inhibited in smallgrained specimens. Measurements covering low stresses ( 0.1 MPa) and strain rates ( 10^–10 sec^–1) rule out any explanation which relies on a threshold stress for plastic deformation. The observations are explained by a model in which, at low stresses or small grain sizes, Coble creep is rate-limited not by diffusion of vacancies but by the rate of emission and absorption at the curved dislocations in the grain boundaries which are the ultimate sources and sinks of vacancies.     

Equal-channel angular pressing of an Al-6061 metal matrix composite

An Al-6061 metal matrix composite, reinforced with 10 vol % Al₂O₃ particulates, was subjected to equal-channel angular (ECA) pressing at room temperature to a total strain of 5. It is shown that the intense plastic straining introduced by ECA pressing reduces the grain size from 35 m to 1 m and this leads to an increase in the microhardness measured at room temperature. Inspection revealed some limit cracking of the larger Al₂O₃ particulates as a consequence of the ECA pressing. Tensile testing after ECA pressing gave a maximum ductility of 235% at a temperature of 853 K when testing at strain rates from 10^–4 to 10^–3 s^–1. It is suggested that high strain rate superplasticity is not achieved in this material after ECA pressing due to the presence of relatively large Al₂O₃ particulates.     

On strong Dickson pseudoprimes

It is known that the Lucas sequenceV _n(,c)=aⁿ + bⁿ,a, b being the roots ofx ² – x + c=0 equals the Dickson polynomial .^n–2i Lidl, Müller and Oswald recently defined a number b to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [itg_n(b, c)b modn for all b. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined.     

Predicting times to low strain for a 1CrMoV rotor steel using a 6-θ projection technique

The projection method of creep analysis is known to produce the poorest predictions of creep properties at low strains. This paper applies a recently suggested modification of the concept to 1CrMoV rotor steel where long term data exists to enable an assessment of this modification to be made. The modification takes the form of two additional terms that allow the initial stages of any creep curve to be modelled more accurately. The paper shows that the resulting 6- approach produces predictions of long-term failure times and minimum creep rates that are as good as those obtained using the traditional 4- approach. Unlike the 4- approach, the 6- approach is also shown to be capable of accurately predicting times to very low strains (0.05% and 0.1%) at stress levels as low as 77 MPa (well below the lowest stress of 230 MPa used in the theta analysis). For times to 1.0% strain or more the 4- and 6- techniques give similar short and long-term predictions.     

Effects of rate,temperature and absorption of organic solvents on the fracture of plain and glass-filled polystyrene

The rate/temperature dependent fracture behaviour of plain and glass-filled polystyrene has been investigated over the crack speed (a) range of 10^–6 to 10^–2 m sec^–1 and in the temperature (T) range of 296 to 363 K. TheK _c (a, T) relationships obtained, whereK _c is the stress intensity factor at fracture, are shown to follow those given by the Williams/Marshall relaxation crack growth model and the toughness-biased rate theory. Crack propagation in both materials is shown to be controlled by a-relaxation molecular process associated with crazing. Crack instabilities observed in plain polystyrene are analysed successfully in terms of isothermal-adiabatic transitions at the crack tip. Fracture initiation experiments are also conducted in which the effects of organic liquids on the fracture resistances of both plain/glass-filled polystyrene have been determined. Good correlations betweenK _i ² (K _i being the crack initiation stress intensity factor) and _s, solvent solubility parameter, of various liquid environments have been obtained, which give a minimumK _i ² value at _{s p}, where _p is the solubility parameter of the polymer. For a given temperature, liquid environment and crack speed, the glass-filled polystyrene is shown to possess greater resistances to crack propagation than plain polystyrene.     

A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for 4n ² where n is integer. This implies that the instability area which is emanating from =4n ² in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands     

Retention of a metastable bcc ε-Pu solid solution: ε-Pu(Ti)

A metastable -Pu (bcc) solid solution has been retained to room temperature by rapid quenching of Pu-rich Pu-Ti alloys from the liquid state. Until now, -Pu solid solutions were limited to high temperatures and had not been successfully quenched to room temperature without transformation. The apparatus used to quench the specimens was a modified gun-type splat-cooling unit, capable of producing extremely high cooling rates of from 10⁶ to 10⁸ ° C sec^–1. -Pu(Ti) was retained in the composition region from 20 to more than 45 at.% Ti, and extrapolation of the lattice parameter/composition curve yielded a value of a ₀ = 3.53₀ Å for -Pu at 20° C. This modification differs from the -Pu modification derived by extrapolating from high temperature to 20° C by a small valence increase of 0.1. Metastable -Pu (Ti) (fcc) solid solutions were also quenched-in with alloys containing lesser amounts of Ti, and evidence was found to indicate that the was probably a product of -Pu(Ti) solid-state decomposition.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Prolonged laser ablation effects of YBCO ceramic targets during thin film deposition: Influence of processing parameters

Cumulative laser irradiation during high-Tc superconducting thin film pulsed laser deposition (PLD) may have a detrimental effect on film characteristics. Initial decrease of deposition rate and gradual shift of the center of the deposited material spot towards the incoming laser beam were registered on cold glass substrates. Their absorbance was used for evaluation of the film thickness distribution over the substrate area. At the initial stage, two components of the spot could be distinguished along its short axis: central (cosⁿ , n1) and peripherial (cos ), while with cumulative irradiation the thickness followed an overall cos^m (m相似文献   

Methodology for the determination of the interfacial properties of brittle matrix composites

The interfacial properties of a glass-ceramic matrix composite (SiC/CAS) were determined from single-fibre push-out tests using the interfacial test system. The coefficient of friction, , the residual clamping stress, _c, and fibre axial residual stress, _z , were extracted by fitting the experimental stress versus fibre-end displacement curves using the models of Hsueh, and Kerans and Parthasarathy. Using Hsueh's model, the intrinsic interfacial frictional stress (=_c) was found to be 11.1±3.2 MPa, whereas by using Kerans-Parthasarathy's model it was found to be 8.2±1.5 MPa. Comparisons between these models are included, together with a discussion of data analysis techniques.Nomenclature _z Axial fibre residual stress (Pa) - ^* Effective clamping stress (Pa) - _c Residual clamping stress (Pa) - _p Poisson's effect-induced clamping stress (Pa) - _d ⁰ Debond stress in the absence of residual stresses (Pa) - _d Experimental debond stress (Pa) - Compressive applied stress (Pa) - Interfacial shear stress (Pa) - u Fibre-end displacement (m) - h Debond length (m) - r Fibre radius (m) - E _f Fibre Young's modulus (Pa) - E _m Matrix Young's modulus (Pa) - v _f Fibre Poisson's ratio (dimensionless) - v _m Matrix Poisson's ratio (dimensionless) - f Fibre volume fraction (dimensionless) - k Parameter (dimensionless) - D Parameter (dimensionless) - Interfacial coefficient of friction (dimensionless) - G _i Interface toughness (J m^–2) - C _m Load-train compliance (m N^–1)     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues