Showing papers on "Creep published in 1991"
TL;DR: In this paper, the role of non-deforming particles in reinforcing ductile matrix materials against plastic flow and creep is investigated within the framework of continuum plasticity theory using cell models to implement most of the calculations.
Abstract: A theoretical investigation is made of the role of non-deforming particles in reinforcing ductile matrix materials against plastic flow and creep. The study is carried out within the framework of continuum plasticity theory using cell models to implement most of the calculations. Systematic results are given for the influence of particle volume fraction and shape on the overall behavior of composites with uniformly distributed, aligned reinforcement. The stress-strain behavior of the matrix material is characterized by elastic-perfectly plastic behavior or by power-law hardening behavior of the Ramberg-Osgood type. A relatively simple connection is noted between the asymptotic reference stress for the composite with the power-law hardening matrix and the limit flow stress of the corresponding composite with the elastic-perfectly plastic matrix. The asymptotic reference stress for the composite with the power-law matrix is applicable to steady-state creep. A limited study is reported on the overall limit flow stress for composites with randomly orientated disc-like or needle-like particles when the particles are arranged in a packet-like morphology.
474 citations
TL;DR: In this article, a simple expression to evaluate the residual stress in a plasma-sprayed coating is given for the case where the coating thickness is much smaller than the substrate thickness.
460 citations
TL;DR: In this article, the bulk mechanical properties of samples of nanocrystalline Cu and Pd consolidated from powders prepared by inert gas condensation were studied. But the results of the study were limited.
Abstract: This report gives results of a study of the bulk mechanical properties of samples of nanocrystalline Cu and Pd consolidated from powders prepared by inert gas condensation. Fourier analysis x-ray diffraction techniques, used to determine average grain size and mean lattice strains of the as-consolidated samples, show grain sizes in the range of 3–50 nm and lattice strains ranging from 0.02–3%. Sample densities range from 97–72% of the density of a coarse-grained standard. Microhardness of the nanocrystalline samples exceeds that of annealed, coarse-grained samples by a factor of 2–5, despite indications that sample porosity reduces hardness values below the ultimate value. Uniaxial tensile strength of the nanocrystalline samples is similarly elevated above the value of the coarse-grained standard samples. Restrictions on dislocation generation and mobility imposed by ultrafine grain size are believed to be the dominant factor in raising strength. Residual stress may also play a role. Room temperature diffusional creep, predicted to be appreciable in nanocrystalline samples, was not found. Instead, samples appear to show logarithmic creep that is much smaller than the predicted Coble creep.
459 citations
01 Jan 1991
TL;DR: This paper describes extensive work within Nuclear Electric, to develop a procedure which assembles knowledge in structural mechanics and materials science for assessment of components operating in the creep range.
Abstract: This paper describes extensive work within Nuclear Electric, to develop a procedure which assembles knowledge in structural mechanics and materials science for assessment of components operating in the creep range. The procedure, called R5, is written in seven parts, or volumes. These volumes and the associated failure modes which are addressed are described.
357 citations
TL;DR: In this paper, the authors investigated the effect of orthopyroxene activity and loading orientation on the creep behavior of San Carlos olivine in controlled chemical environments at a total pressure of 0.1 MPa.
Abstract: To investigate the rheological behavior of the Earth's upper mantle, over 100 high-temperature deformation experiments have been performed on single crystals of San Carlos olivine in controlled chemical environments at a total pressure of 0.1 MPa. Constitutive equations have been determined which describe the dependence of creep rate on applied stress, temperature and oxygen fugacity in terms of power law relations. In addition, the effects of orthopyroxene activity and loading orientation on the creep behavior have been investigated. For samples of each of three compression directions, [101]c, [011]c and [110]c, buffered by orthopyroxene or magnesiowustite, either two or three power law equations are required to describe the dependence of strain rate at fixed stress on temperature and oxygen fugacity over the full range of experimental conditions. It is proposed that in each power law regime a different creep mechanism controls the creep rate. For all of the experimental conditions, the activation energy for creep is independent of the stress level and the stress exponent is constant at 3.5±0.1. Activation energies for the various creep mechanisms varied from 230 to 1000 kJ/mol; and oxygen fugacity exponents lie in the range −0.03 to 0.4. From the constitutive equations determined based on the power law equations for all of the creep mechanisms, e˙-T-fo2 deformation maps were constructed at a stress of 1 MPa for olivine.
281 citations
TL;DR: A physically-based theoretical model for describing the phenomenon of indentation creep over the whole temperature range, from 300 K to melting, was developed in this paper, in agreement with experimental data.
Abstract: A physically-based theoretical model is developed for describing the phenomenon of indentation creep over the whole temperature range, from 300 K to melting. In agreement with experimental data col ...
211 citations
IBM1
TL;DR: The microindenter has proven to be a powerful device in the characterization of the mechanical properties of thin films as discussed by the authors, which allows for other mechanical properties, in addition to hardness, to be acquired.
Abstract: The microindenter has proven to be a powerful device in the characterization of the mechanical properties of thin films. The machine has both high resolution in the applied load and penetration depth measurements, as well as the versatility to perform different types of testing. The former provides the capability to deal with extremely thin films, while the latter allows for other mechanical properties, in addition to hardness, to be acquired. Four types of tests, namely indentation, scratch, load relaxation, and indentation fatigue tests can currently be conducted using the microindenter via different operating procedures. Only the scratch and load relaxation techniques will be covered in this paper. In a microscratch test, the normal load, tangential load, scratch length, and acoustic emission are monitored simultaneously during an entire scratch process for the purposes of measuring the critical load and studying the failure mechanisms of the deposited films. The adhesion strength, scratch hardness, fracture toughness, and friction are the mechanical properties which are possible to obtain by using this technique. Results from aluminum, carbon, and zirconia coatings will be discussed. The load relaxation test provides information on the creep properties of the films and results in an empirical constitutive relation between the applied stress and plastic strain rate. The creep properties of DC sputtered Al films will be used as an illustration of this.
197 citations
TL;DR: In this article, a combination of mechanical and microstructural results for experimentally deformed albite aggregates of 2-10 μm grain size indicates a regime of grain boundary diffusion creep that depends upon the presence of water, temperature and strain rate.
190 citations
TL;DR: In this article, a sliding crack model is proposed to predict the dependence of the stress-strain curve on the applied strain rate, and the model is able to predict both transient and tertiary creep in brittle rocks.
176 citations
TL;DR: In this article, the deformation and failure history of a pipe weldment using a finite element creep continuum damage mechanics model, which incorporates the characteristic material properties of the parent metal, the weld metal and heat-affected zone microstructures of the weldment.
Abstract: Predictions have been made of the deformation and failure history of a pipe weldment using a finite element creep continuum damage mechanics model, which incorporates the characteristic material properties of the parent metal, the weld metal and heat-affected zone microstructures of the weldment. It is shown that the computer predictions are in close agreement with the results of large-scale pressure vessel tests, provided that the material characterization is carried out correctly, and that the constitutive equations which control the evolution of creep strain and damage, represent the dominant physical mechanisms present.
142 citations
TL;DR: In this article, the authors investigate the behavior during compaction under diagenetic conditions and evaluate the importance of stress-induced solution transfer (9pressure solution9) as a compaction mechanism.
Abstract: Experiments have been carried out on dry and fluid-saturated quartz sands to investigate the behaviour during compaction under diagenetic conditions and to evaluate the importance of stress-induced solution transfer (9pressure solution9) as a compaction mechanism. The experiments were performed at temperatures ( T ) in the range 150–350°C, applied effective stresses (σ e ) up to 20.7 MPa and pore fluid pressures (P 1 ) of 12.5 and 15.5 MPa, using material with a grain size ( d ) in the range 20–100 μm and an initial porosity of 45–52%. Dry quartz sands underwent significant compaction during the loading stage, but showed very little compaction creep once full load was achieved (i.e. essentially time-independent compaction). In contrast, fluid-saturated material at constant applied effective stress showed substantial time-dependent compaction (i.e. creep). With increasing temperature, there is a decreasing number of grains in the wet-compacted sand which show intragranular cracks and an increasing number of grains which show dissolution features at contacts with adjacent grains. In addition, there is a decreasing dependence of the volumetric strain rate, β on σ e , with both increasing volumetric strain (e v ) and increasing σ e and a decreasing dependence of β on e v with increasing temperature. These observations suggest that, for wet quartz sand, a gradual change might occur from compaction creep controlled by time-dependent microcracking, at T = 250–300 °C, to compaction creep controlled by stress-induced intergranular solution transfer at T = 300–350 °C.
TL;DR: In this paper, the authors provide an alternative phenomenology for flux creep in high temperature superconductors by the more recent collective pinning theories, including long-time relaxation, flux-creep annealing and studies near T c.
Abstract: Magnetic studies of flux creep in high temperature superconductors show many features unexpected in the conventional Anderson-Kim theory, which assumes a thermal activation mechanism and uncorrelated motion of vortex bundles. An alternative phenomenology is provided by the more recent collective pinning theories. Experiments probing this new phenomenology are reviewed, including long-time relaxation, flux-creep annealing and studies near T c .
TL;DR: In this article, cyclic fatigue, and specifically fatigue-crack propagation in ceramics, is reviewed both for monolithic and composites systems, and implications are discussed in terms of the primary crack-tip shielding (toughening) mechanisms and potential mechanisms of cyclic crack advance.
Abstract: Cyclic fatigue, and specifically fatigue-crack propagation, in ceramic materials is reviewed both for monolithic and composites systems. In particular, stress/life (S/N) and crack-propagation data are presented for a range of ceramics, including zirconia, alumina, silicon nitride, SiC-whisker-reinforced alumina and a pyrolytic-carbon/graphite laminate. S/N data derived from unnotched specimens often indicate markedly lower lives under tension-compression compared to tension-tension loading; similar to metals, 108-cycle “fatigue limits” generally approach -50% of the tensile strength. Crack-growth results, based on studies on “long” (>3mm) cracks, show fatigue-crack propagation rates to be markedly power-law dependent on the applied stress-intensity range, ΔK, with a threshold, ΔKTH, of the order of -50% of Kc. Conversely, for “small” (<250μm) surface cracks, fatigue-crack growth is seen to occur at ΔK levels some 2 to 3 times smaller than ΔKTH, and to show a negative depen-dency on applied stress intensity. At ambient temperatures, lifetimes are shortened and crack-growth rates are significantly accelerated by cyclic, compared to quasi-static loading, although limited data suggest the reverse to be true at very high temperatures in the creep regime. Such results are discussed in terms of the primary crack-tip shielding (toughening) mechanisms and potential mechanisms of cyclic crack advance. Finally, implications are discussed of long and small crack cyclic fatigue data to life prediction and safetycritical design of ceramic components.
TL;DR: The GLOSS analysis is emerging as a useful technique for determining multiaxial stress relaxation, follow-up, creep damage, inelastic strain concentrations and low-cycle fatigue estimates, limit analysis and issues pertaining to stress classification as discussed by the authors.
Abstract: The underlying theory relates redistribution of inelastic stresses at a given location under consideration to the uniaxial stress relaxation process. GLOSS analysis is emerging as a useful technique for determining multiaxial stress relaxation, follow-up, creep damage, inelastic strain concentrations and low-cycle fatigue estimates, limit analysis and issues pertaining to stress-classification
TL;DR: In this paper, the authors reported that nanocrystalline TiO[sub 2] with densities higher than 99% of rutile has been deformed in compression without fracture at temperatures between 600[degrees] and 800[degree] C.
Abstract: This paper reports that nanocrystalline TiO[sub 2] with densities higher than 99% of rutile has been deformed in compression without fracture at temperatures between 600[degrees] and 800[degrees] C. The total strains exceed 0.6 at strain rates as high as 10[sup [minus]3] s[sup [minus]1]. The original average grain size of 40 nm increases during the creep deformation to final values in the range of 120 to 1000 nm depending on the temperature and total deformation. The stress exponent of the strain rate, n, is approximately 3 and the grain size dependence is d[sup [minus]q] with q in the range of 1 to 1.5. It is concluded that the creep deformation occurs by an interface reaction controlled mechanism.
TL;DR: In this article, the authors investigate the yielding behavior of waxy crude oils and identify three distinct characteristics of the yielding process, namely, a solid (Hookean) behavior, a slow deformation (creep), and a sudden failure of the sample that closely resembles the brittle or ductile fracture of solids.
Abstract: Statically cooled samples of waxy crude oil possess a complex yielding behavior that cannot be described by existing yield stress fluid models nor by the description and modeling of thixotropic materials. Three distinct characteristics of the yielding process, namely, a solid (Hookean) behavior, a slow deformation (creep), and a sudden failure of the sample that closely resembles the brittle or ductile fracture of solids, have been identified by four different techniques−the vane technique, the cone and plate viscometer (constant rotation), constant stress rheometry, and oscillatory (dynamic) testing. A capillary viscometer or pilot scale pipeline presents technical difficulties which make it unsuitable for investigating the yielding behavior of waxy crude oils. The shear stress at fracture is the value of most interest to pipeline designers and the one most often taken as the yield point. Means of obtaining reproducible yield stress and fracture stress data are discussed.
TL;DR: In this paper, a formulation for the noblinear analysis of two-dimensional steel frames under fire conditions using the finite element method is presented, which includes the effects of geometric nonlinearity, temperature dependent nonlinear material behaviour and variations in temperature distributions both along and across each member.
TL;DR: In this paper, the porosity of fine-grained quartz aggregates was investigated in the presence of dissolution-precipitation processes in the form of ridges, plateaus and flatbottomed pores on interfaces.
Abstract: Rapid compaction creep has been achieved in fine-grained quartz aggregates during hydrothermal isostatic pressing (HTIP) at 1200K, a confining pressure of 300MPa and a pore water pressure of 200 MPa. While raising the pressure and temperature over a period of three hours, the porosity decreased by over 50%. During subsequent HTIP for periods up to 4 hours, further porosity reduction occurred at compaction creep rates between 10−5 and 10−6 s−1. Changes in grain shapes, grainsize distribution, pore geometry and microstructures on grain surfaces, together with an absence of substantial brittle or intragranular plastic deformation, indicate that compaction creep has occurred largely by dissolution-precipitation processes. Interpenetration of grains and grain-shape truncation are well-developed at grain contacts. Arrays of fine-scale ridges, plateaus and flat-bottomed pores on interfaces indicate that the fluid distribution on actively dissolving interfaces is a dynamic structure that is not controlled entirely by equilibrium wetting angles.
TL;DR: In this paper, constant stress creep tests were combined with detailed transmission electron microscopy in order to characterize and explain the intermediate temperature creep properties of Ni 3 Al, and it was observed that octahedral glide, the mechanism associated with the anomalous yielding behavior of this alloy, is exhausted during primary creep.
Abstract: In this study, constant stress creep tests were combined with detailed transmission electron microscopy in order to characterize and explain the intermediate temperature creep properties of Ni 3 Al. It was observed that octahedral glide, the mechanism associated with the anomalous yielding behavior of this alloy, is exhausted during primary creep. Primary creep does not lead to steady state creep but is instead followed by inverse creep. TEM observations indicate that the Kear-Wilsdorf locks that are formed during primary creep do lead to the exhaustion of octahedral glide, but that given sufficient time and temperature these cross-slipped segments are able to bow out and glide on the cube cross-slip plane. This dislocation generation, and subsequent glide, on the (010) plane is the basis for the observation of inverse creep in this alloy. Dislocation motion on the cube plane is a thermally activated process and as such is able to explain the strong temperature dependence that was observed for the intermediate temperature creep strength of Ni 3 Al.
TL;DR: In this article, the authors reviewed the creep mechanisms in ceramics and compared experimental data, showing that there are three major types of creep behavior: a stress exponent close to 5 due to control by dislocation climb and fully ductile behaviour; a stress expander close to 3 due to controlling by climb from Bardeen-Herring sources and less than jive interpenetrating independent slip systems; and a stress extraction close to 1 due to diffusion creep.
Abstract: The creep mechanisms in ceramics are reviewed briefly and then compared with experimental data. It is shown that there are three major types of creep behaviour: a stress exponent close to 5 due to control by dislocation climb and fully ductile behaviour; a stress exponent close to 3 due to control by climb from Bardeen–Herring sources and less than jive interpenetrating independent slip systems; and a stress exponent close to 1 due to diffusion creep. The role of interface reaction control and the transitions from diffusion to power law creep are also examined.MST/1389
TL;DR: In this article, a study of the creep and creep rupture behavior of hot-pressed silicon nitride reinforced with 30 vol% SiC whiskers was presented. But, the authors did not consider the effect of whisker additions on the creep rate.
Abstract: This paper presents a study of the creep and creep rupture behaviour of hot-pressed silicon nitride reinforced with 30 vol% SiC whiskers. The material was tested in both tension and compression at temperatures ranging from 1100 to 1250°C for periods as long as 1000 h. A comparison was made between the creep behaviour of whisker-reinforced and whisker-free silicon nitride. Principal findings were: (i) transient creep due to devitrification of the intergranular phase dominates high-temperature creep behaviour; (ii) at high temperatures and stresses, cavitation at the whisker-silicon nitride interface enhances the creep rate and reduces the lifetime of the silicon nitride composite; (iii) resistance to creep deformation is greater in compression than in tension; (iv) the time to rupture is a power function of the creep rate, so that the temperature and stress dependence of the failure time is determined solely by the temperature and stress dependence of the creep rate; (v) as a consequence of differences in grain morphology and glass composition between whisker-free and whisker-reinforced material, little effect of whisker additions on the creep rate was observed.
TL;DR: In this paper, the creep and fracture behavior of two hot-pressed aluminas are presented, for both flexural and tensile testing, and three distinct fracture regimes are found.
Abstract: The creep and creep fracture behavior of two hot-pressed aluminas are presented, for both flexural and tensile testing. Steady-state power-law creep is observed with a stress exponent of about 2 for each material. Three distinct fracture regimes are found. At high stress in flexure, fracture occurs by slow crack growth with a high stress dependence of the failure time. At intermediate stresses, in both flexure and tension, creep fracture occurs by multiple microcracking after modest strains. Failure times exhibit a modest stress dependence (stress exponent of 2.5 in tension and 3 in flexure), with a constant failure strain equal to 0.09. The failure times are considerably longer in flexure than in tension, because of the constraint imposed on crack growth by the bending geometry. We conclude that flexure cannot be used for creep lifetime assessment, even in simple, single-phase materials such as Al2O3. At low stresses, in tension, failure also exhibits a modest stress dependence but with a much higher failure strain. The material shows the onset of super-plastic behavior.
TL;DR: In this article, the creep strengthening imparted by reinforcements is shown to be limited by diffusional assisted flow, and a critical reinforcement aspect ratio is identified, above which the strengthening can be retained.
Abstract: The creep strengthening imparted by reinforcements is shown to be limited by diffusional assisted flow. Diffusional flow is demonstrated to be rapid at low strain-rates and small particle sizes, causing the strengthening to be eliminated. However, a critical reinforcement aspect ratio is identified, above which the strengthening can be retained. This aspect ratio is sensitive to the allowable strain-rate, the reinforcement radius and the temperature. Predictions are validated by comparison with experimental data obtained for γ-TiAl reinforced with Ti2AlC-platelets.
TL;DR: In this paper, the strength and lifetime in creep rupture of carbon-epoxy microcomposites consisting of seven carbon fibres (Hercules IM6) within an epoxy matrix (Dow DER 332 epoxy with Texaco Jeffamine T403 curing agent) in an approximately hexagonal configuration.
Abstract: Experimental results are presented for the strength and lifetime in creep rupture of carbon-epoxy microcomposites consisting of seven carbon fibres (Hercules IM6) within an epoxy matrix (Dow DER 332 epoxy with Texaco Jeffamine T403 curing agent) in an approximately hexagonal configuration. Special attention was paid to clamping, specimen alignment, shock isolation and accurate lifetime measurement. The results were analysed using a previously developed model, which involves a Weibull distribution for fibre strength and micromechanical stress redistribution around fibre breaks where the matrix creeps in shear following a power law. The model yields Weibull distributions for both microcomposite strength and lifetime where the respective shape and scale parameters depend on model parameters such as the Weibull shape parameter for fibre strength, the exponent for matrix creep, and the effective load transfer length and critical cluster size for failed fibres. Experimental results were consistent with the theory, though a fractographic study suggested time-dependent debonding along the fibre-matrix interface as being a key mechanism. Arguments were given to suggest, however, that the overall analytical forms would essentially be preserved. The results were compared with earlier results using a different epoxy system (Dow DER 331 epoxy with DEH 26 curing agent). Values for the matrix creep exponent and the effective load transfer length were about double and triple respectively the values from the earlier study, leading to slightly reduced strength, about one-half the variability in lifetime, but almost one-half the value of the exponent for the power law relating microcomposite lifetime to stress level.
TL;DR: In this article, a review of work on ordered Fe-Al based intermetallics for potential high temperature applications is presented with emphasis on improvements in mechanical properties achievable by processing and compositional control.
Abstract: Recent work on the ordered Fe-Al based intermetallics (B2-FeAl and D03-Fe3Al) for potential high temperature applications is reviewed with emphasis on improvements in mechanical properties achievable by processing and compositional control. Constitution and microstructure as well as the role of crystalline defects, including vacancies, dislocations, tubes, antiphase boundaries and grain boundaries are discussed. The influence and behaviour of these defects with respect to strength, work hardening, ductility and fracture are analysed. Proposed mechanisms for deformation and recent investigations on creep and fatigue of these materials are also reviewed. Current literature on ternary additions, multi-phase alloys and non-equilibrium processing is discussed.
TL;DR: In this article, the free water content of concrete underlies the various physical mechanisms that shape its mechanical behaviour, and it is shown that properties from creep to dynamic behaviour can be explained with reference to the process of cracking.
Abstract: The free water content of concrete underlies the various physical mechanisms that shape its mechanical behaviour. This Paper attempts to show that properties from creep to dynamic behaviour can be explained with reference to the process of cracking. Assumptions are made concerning the physical mechanisms involved, with a view to understanding what happens inside the material rather than to give rise to quantitative predictions.
TL;DR: In this paper, the influence of stress ratio on the tensile fatigue behavior of a unidirectional SiC-fiber/Si,N.,-matrix composite was investigated at 1200°C.
Abstract: The influence of stress ratio on the tensile fatigue behavior of a unidirectional SiC-fiber/Si,N.,-matrix composite was investigated at 1200°C. Tensile stress ratios of 0.1, 0.3, and 0.5 were examined. Fatigue testing was conducted in air, at a sinusoidal loading frequency of 10 Hz. For peak fatigue stresses below the proportional limit of the composite (approximately 195 MPa at 1200°C) specimens survived 5 X lo6 cycles, independent of stress ratio. At peak stresses above the proportional limit, fatigue failures were observed; fatigue life decreased significantly as the stress ratio was lowered from 0.5 to 0.1. Creep appears to be the predominant damage mechanism which occurs during fatigue below the pro
TL;DR: In this paper, the effect of green density on both the densification rate and the creep rate was measured simultaneously during sintering by loading dilatometry, and the results showed that the rate of densification at any temperature increases significantly with decreasing green density.
Abstract: The effect of green density on both the densification rate and the creep rate was measured simultaneously during sintering by loading dilatometry. The experiments were performed on zinc oxide powder compacts with five different green densities covering a range of 0.39 to 0.73 of theoretical. The samples were heated at a constant rate of 4°C/min up to 1100°C in air. The densification rate at any temperature increases significantly with decreasing green density. The data for the densification rate and creep rate as a function of density show two quite distinct regimes of behavior; the rates were strongly dependent on density below 0.80, while above this value they were weakly dependent on density. The ratio of the densification rate to the creep rate was almost independent of temperature but increased almost linearly with increasing green density. The representation of the data in terms of models for sintering and creep is discussed.
TL;DR: In this article, the authors presented the formulae for the prediction of basic creep of concrete, i.e. creep at no moisture exchange, which takes into account simultaneous ageing, satisfies all the basic thermodynamic requirements, and avoids divergence of creep curves.
Abstract: The second part of this series presents the formulae for the prediction of basic creep of concrete, i.e. creep at no moisture exchange. The formulae give the secant uniaxial compliance function which depends on the stress level, and, as a special case, the compliance function for linear structural analysis according to the principle of superposition. The formulae are based on the recently developed solidification theory for concrete creep which takes into account simultaneous ageing, satisfies all the basic thermodynamic requirements, and avoids divergence of creep curves. The formulae, which describe both creep and elastic properties, involve only four free material parameters. All four appear linearly, so that optimum data fits can be obtained by linear regression. For the frequent situations where no test data for the particular concrete to be used are available, empirical formulae for predicting these four parameters from the concrete mix composition and the standard compressive strength are given. These formulae, however, involve considerable error. To avoid it, one should, whenever possible, carry out measurements of the elastic modulus and, if possible, also the short-time creep of 7 to 28 days duration. With such measurements, greatly improved predictions can be achieved. The predictions are compared with 17 extensive data sets taken from the literature, and the coefficients of variation of the deviations are found to be smaller than with previous models.