A study of the Bailey-Orowan equation of creep

A new method was developed to study the Bailey-Orowan equation of creep, _c=r/h, where _c is the creep rate,r is the recovery rate andh is the work-hardening coefficient. The method was to vary the strain rate,, around the creep rate, _c, and to measure the corresponding stress rate,. In a plot of stress rate against strain rate, a straight line was obtained. The slope of the straight line was equal toh, and the intersection of the straight line with the stress axis was equal to –r, as in the equation=–r+h. The creep test under a constant stress is a special case of this equation when the stress rate,, is zero. The above measurement was carried out within a very small stress variation, less than 1% of the total stress, so that the values ofr andh were not disturbed. The creep test was performed on Type 316 stainless steel. The creep rate was shown to be equal to the ratior/h, but the value ofh was approximately equal to Young's modulus at the testing temperature, rather than, as is commonly believed, to the work-hardening coefficient.     

Investigation of the creep and micropolar creep of various materials under static and dynamic loads

Creep is investigated under a uniform stress state with allowance for the micropolar creep of the following materials: lignostone (T=293°K), steel ON2M (T=773° K), and an AIMgSi aluminum alloy (T= 293° K) understate and cyclic tension, i.e., atA = ^a/^m = 0, 0.25, and 0.5. It is established that for lignostone, the microstrains I₁₁ are two orders lower than 2₁₂ in torsion, and the values of 2l₁₂ are only a half order lower than ₁₁ in tension. The creep strain of lignostone is described using nonlinear theory of viscoelasticity. For alloys and metals under static creep, the value of I_ij is two or three orders lower than _ij A qualitative change in microipolar creep occurs in the case of dynamic loading: whenA = 0.5,the ratio of values of fatigue creep rate 21₁₂/₁₂ = 0.2.A subject investigated in 1990 with funding provided by the Ministry of National Education.Translated from Problemy Prochnosti, No. 12, pp. 18–23, December, 1993.     

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.     

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     

Combined effects of thin-section size, grain size and cavities on the high temperature creep fracture properties of a nickel-base superalloy

The creep fracture characteristics of a conventionally cast (CC) MAR-M 002 superalloy, controlled by the grain-boundary diffusion mechanism, have been investigated at various specimen section-sizes D, and grain sizes, d. It is observed that the creep rupture strain (or ductility, R, is controlled by the D2/(nGl) ratio, where nG is the number of grains per cross-section of specimen and l is the half-cavity spacing, at the creep conditions (900° C/ 300MPa). A rapid improvement in creep rupture life can be made by reducing the (dC/d)/D ratio [ or, equivalently, the (dCnG)/D2 ratio] below a critical value ( 100×10-8 10m-1), where dC is the cavity size. The thin-section size dependent creep rupture life, tR/D, and creep rupture strain, R/D, are explained on the basis of grain boundary sliding (GBS) and creep crack growth (CCG) behaviour of the alloy. R/D and tR/D can be improved by reducing the GBS rate. A large improvement in tR/D can be achieved by reducing the GBS and CCG rates below the critical values of these rates by reducing the crack size through increasing the grain size above a critical value. (Above a critical grain size value the crack size becomes so small that, as a result, a large increment of tR is achieved.)     

The dielectric properties of alumina substrates for microelectronic packaging

The dielectric characterization of alumina substrate materials used in high-performance microelectronic packaging is described. These materials included both pure and impure polycrystalline substrates and, as a reference standard, pure and chromium-doped single crystals of alumina. For each material the permittivity () and dielectric loss () has been measured over a frequency range of 0.5 kHz to 10 MHz, at room temperature, and correlated with the structure and composition as determined by supplementary techniques. At room temperature the pure substrates show the frequency independence of both and , characteristic of pure single-crystal material. The permittivity (= 10.1) agrees closely with the average of the anisotropic values for the single crystal but the dielectric loss is an order of magnitude higher than in the single crystal, giving tan 1.5 × 10^–3. The impure substrates compared with the pure, show a small increase in and a marked, frequency-dependent increase in dielectric loss. Measurements have also been made in both the high- and low-temperature ranges (i.e. 20 to 600 ° C and 77 to 293 K, respectively) in order to establish the variation of permittivity with temperature and frequency. At temperatures below 200 °C the temperature coefficient of permittivity, [( –1)( + 2)]^–1 (/T) _p is about 9 × 10^–6 K^–1 for the pure materials but this increases rapidly with impurity addition.     

Indications that the yield point at constant strain rate and the inception of tertiary creep are manifestations of the same failure criterion using the universal viscoelastic model

In a preceding publication this author introduced a new universal viscoelastic model to describe a definitive relationship between constant strain rate, creep and stress relaxation analysis for viscoelastic polymeric compounds. Since creep failure criterion for this model had not been addressed in detail in previous publications, selected creep failure criterion for this model were addressed in this study.The first manifestation of the yield stress failure criterion as applied to creep was elucidated at the intersection of the yield stress relaxation curve and the creep stress vs time curve. A second way to apply yield point failure criterion to creep failure was through the identification of a specific creep time associated with the limiting strain to yield, . The creep strain at occurs at the very end of the straight line portion of secondary creep and is also the strain at which tertiary creep appears to be initiated, _itc = .As the strain increases from the inception of tertiary creep, _itc, eventually a strain is reached where a calculation option using this model would require a step back in time to go to the next differential element of strain. Since going back in time is currently impossible, only a huge jump in strain obtained by another calculation option for the next element of time would be realistic. Since this critical creep strain, _CC, is slightly greater than the inception of tertiary creep, if failure did not occur at the inception of tertiary creep then it would almost surely be expected to fail catastrophically at this condition.The near equivalency of the critical creep strain criterion and the yield strain criterion was found to be much more probable the lower the value of efficiency of yield energy dissipation such that 0 < n .4.     

Singularity parametersε andκ for interface cracks in transversely isotropic piezoelectric bimaterials

Two parameters, and (Suo et al., 1992), are of key importance in fracture mechanics of piezoelectric material interfaces. In this paper, it is shown, for any transversely isotropic piezoelectric (TIP) bimaterial, that one of the two parameters and always vanishes but the other one remains non-zero. Physically, it means that the non-oscillating crack-tip generalized stress field singularity exists for some TIP bimaterials (with vanishing ). Consequently, TIP bimaterials can be classified into two classes: one with vanishing performed crack tip generalized stress field oscillating singularity and the other one with vanishing is independent from the oscillating singularity. Some numerical results for and are given too.     

Potential flow past a sinusoidal wall of finite amplitude

Summary The classical regular perturbation problem of plane potential flow past a sinusoidal wall is pursued via series extension. Fifty terms of the series in non-dimensional wall height are produced by computer. Analysis reveals convergence to be limited by a branch point at =±i. The series is recast using an Euler transformation and also summed using Padé approximants to yield accurate answers for higher real values of .     

Dielectric properties of nanostructured nickel oxide

Nanostructured NiO samples having different average particle sizes were prepared and the variations of the real and imaginary components of the complex dielectric function * were studied as a function of the frequency of the applied signal and temperature. The dielectric relaxation mechanism is discussed considering nanostructured NiO as a carrier dominated dielectric with high density of hopping charge carriers. The observed ^{n – 1} dependence of the real and imaginary components of * is discussed in the light of the 'Universal' model of dielectric response. The various contributions to the measured dielectric loss such as the steady state charge transport, delayed readjustment of screening charges and the Debye delays are discussed. It is shown that the temperature dependence of both the real and imaginary components of * are in accordance with the models used for discussing the dielectric relaxation and loss mechanisms. The variation of with average particle size seems to be rather complex depending on a number of parameters associated with the interfacial region which vary with the average particle size.     

Ageing characteristics of cast Zn-Al based alloy (ZnAl7Cu3)

Microstructure and ageing characteristics of a cast Zn-Al based alloy (ZnAl7Cu3) were studied using X-ray diffraction, electron scanning microscopy and back-scattered diffraction techniques. Two stages of phase transformation, i.e., decomposition of zinc rich phase and four phase transformation, + T + , were detected during ageing at 150°C. Electron back-scattered diffraction technique was applied in distinguishing both zinc rich and phases.     

The Possibility of Reproducing the Units of Complex Permittivity at High Frequencies

The results of theoretical investigations of the reproduction of the units of the components of complex permittivity and by a method based on the use of the wave properties of a coaxial line are presented. The errors in reproducing and are analyzed.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

The role of ε-martensite in the impact toughness of an Fe-17Mn alloy

The influence of -martensite on the cryogenic toughness of an Fe-17 wt% Mn alloy was studied in this work. Alloys were tempered at various temperatures in order to systematically increase the volume fraction of -martensite. This was followed by Charpy impact testing conducted at room temperature and at–196°C. The experimental results indicated that although room-temperature toughness was not influenced by the -martensite content, the cryogenic toughness was strongly dependent on the volume fraction of -martensite. In particular, with the exception of the alloys tempered at 400 and 450°C, the impact toughness consistently increased with -martensite content. Microstructural and fractographic evaluations using SEM and TEM suggested that the toughness improvements were attributed to the stress-induced martensite transformation. No microstructural evidence was found which could be ascribed to an effect of -martensite on the low-temperature embrittlement exhibited by Fe-Mn alloys tempered at 400–450°C.     

Dielectric Properties of Melt-Grown Cd1 – xZnxTe Crystals

The real (") and imaginary (") parts of the complex dielectric permittivity of Cd_{1 – x} Zn _x Te (x= 0.1–0.2) crystals are measured as a function of temperature and frequency. The "-vs.-temperature data show a maximum, and " rises rapidly at about the same temperature. This behavior is interpreted in terms of compositional fluctuations, structural defects, and the associated internal electric fields.     

Surface and interior measurements of grain boundary sliding during creep

Measurements of grain boundary sliding have been made on polycrystalline specimens of Magnox AL80, a magnesium-0.78 wt% aluminium alloy, at successive strains during creep at 200° C under a stress of 2800 psi. Three independent methods were used to determine the strain due to sliding ( _gb) at the surface and two to determine _gbin the interior of the specimens. The one direct method of measuring _gbin the interior used oxide markers introduced by extruding a composite billet. The values of _gbobtained from the offsets in these interior markers were found to agree with those given by the three sets of measurements made on the surface, but not with those from the indirect method for the interior which relies on the measurement of grain strain via grain shape changes.     

Instantaneous plastic strain associated with stress changes during the steady state creep of Al and Al-4.20 at% Mg alloy

The instantaneous strains resulting from stress changes during steady state creep of polycrystalline aluminium and an Al-4.2 at % Mg alloy in the temperature range 100 to 300° C, have been determined. Instantaneous plastic strains were found in both materials for stress increments and decrements. For polycrystalline aluminium the instantaneous plastic strain on a stress increment, (+), was considerably larger than the instananeous strain on a stress increment, (–), whereas for Al-4.2 at % Mg (+) was approximately equal to (–). Work hardening rates determined from (+) and (–) for polycrystalline aluminium vary from about one-tenth to one-half of Young's modulus and depend strongly on temperature and stress. The need to improve existing creep theories to include both climb (recovery) and glide components is suggested.On leave from Department of Engineering Materials, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

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.     

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.     

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.