The influence of grain size on the creep of uranium dioxide

The creep of uranium dioxide has been investigated as a function of grain size. At high stresses, when creep is controlled by dislocation movement, grain boundaries exert a strengthening effect and this strengthening is correlated with the Hall-Petch equation. The degree of strengthening diminishes with increases in temperature. At lower stresses, when creep is controlled by mass transport, grain boundaries exert a weakening effect owing to the reduction in diffusion path length as grain size is reduced. In this range behaviour is correlated with the Nabarro-Herring equation with stress replaced by an effective stress _E=–₀ where ₀ is a threshold stress for diffusional creep associated with the limitation of the ability of boundaries to emit and absorb vacancies. ₀ appears to decrease as grain size is increased.     

Steady-state creep in a 25 wt % Cr-20 wt % Ni austenitic stainless steel

Steady-state creep behaviour of a 25 wt % Cr-20 wt % Ni stainless steel without precipitates was studied in the stress range 9.8 to 39.2 MPa at temperatures between 1133 and 1193 K. The results of stress-drop tests indicate that, in the steady-state creep region, diffusion-controlled recovery creep is dominant. Such recovery creep can be accounted for in terms of the composition of the internal stress, _i=_s+_c, except in the case of fine-grained specimens where d<80 m, whered is the mean grain diameter, _s is possible to reduce easily and is comparable to the driving stress for creep, and _c is the persistent stress field due to metastable substructure. In the fine-grained specimens, it is suggested that the steady-state creep is dominantly controlled by grain boundaries.     

Creep of medium and high strength aluminum alloys at normal temperature in moist atmospheres

Direct data have been obtained for the creep of high- and medium-strength aluminum alloys in the stress range of O.6–1.2 of the nominal yield strength _0.2 in laboratory air and in aqueous NaCl solution at room temperature. On this basis using known theories approximating functions have been determined for the creep curves. Stress _0.2 serves as a natural boundary for the macroelastic and macroplastic regions in the first of which creep is only transient, and in the second there are transient, quasisteady-state, and accelerated stages. Extrapolated estimates of creep strain in the macroelastic region from data measured in the macroplastic region are not physically competent. However, a tendency towards an increase in ductility with an increase in time to failure at stresses greater than _o.2 makes it possible to estimate by extrapolation the time for onset of the accelerated creep stage with low test stresses from measured values at greater stresses in the macroplastic region. Fractographic and strain indices revealed the harmful effect of moist atmospheres on the deformation and failure resistance of alloys with prolonged loading.Translated from Problemy Prochnosti, No. 1, pp. 50–58, January, 1990.     

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.     

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.     

Examining the temperature dependence of the mechanical properties for materials in large-diameter tubes

Measurements have been made on the mechanical properties of largediameter tubes made of 09G2S, 14G2SAF, and 17G1S steels and on welded joints in them at strain rates of 200 sec^–1 and 113–293 K. Fivefold microspecimens 1.2 mm in diameter have been employed. The parameters have been determined in the temperature-rate dependence of the Yaroshevich yield point, lower brittleness temperature, and fracture resistance as affected by the ferrite diameter. A method is proposed for predicting the brittleness range from the dependence of the notch bottom narrowing B on the generalized parameter = S_f/_y — _t/_i for a Menaget specimen.Translated from Problemy Prochnosti, No. 4, pp. 43–50, April, 1994.     

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 internal stress and activation volume in polymers

The two-site model is developed for the analysis of stress relaxation data. It is shown that the product of d In (– )/d and (- _i) is constant where is the applied stress, _i is the (deformation-induced) internal stress and = d/dt. The quantity d In ( )/d is often presented in the literature as the (experimental) activation volume, and there are many examples in which the above relationship with (- _i) holds true. This is in apparent contradiction to the arguments that lead to the association of the quantity d In (– )/d with the activation volume, since these normally start with the premise that the activation volume is independent of stress. In the modified theory presented here the source of this anomaly is apparent. Similar anomalies arise in the estimation of activation volume from creep or constant strain rate tests and these are also examined from the standpoint of the site model theory. In the derivation presented here full account is taken of the site population distribution and this is the major difference compared to most other analyses. The predicted behaviour is identical to that obtained with the standard linear solid. Consideration is also given to the orientation-dependence of stress-aided activation.     

Investigation of the thermodynamic criterion of crack resistance of steels

The article shows the validity of the previously proposed criterion K_Ic = K_Ic ^* + _0.2iK_Ic/_0.2 (K_Ic is reduced crack resistance, _0.2i is internal component of yield strength _0.2) for a wide range of body-centered cubic metals such as iron—carbon alloys (cast iron; low-, medium-, and high-strength carbon and alloy steels). It examines the relationship between this criterion and energy and force concepts of the fracture micromechanism. Existence of a common temperature dependence of the effective yield strength component in ferrite—pearlite carbon and alloy steels in the annealed, normalized, and heat-treated states is established. It is shown that the fraction of effective stress In the total yield strength, i.e., _0.2 ^*/_0.2 controls crack resistance K_Ic over a wide range of temperatures and deformation rates. For impact strength KCV, linear dependences of KCV — KCV/_0.2 and KCV-KCV/HB are observed In the zone of transition temperatures and cold brittleness threshold. A correlation equation connecting KCV and K_Ic over the indicated range is obtained. An applied software package has been worked out for computer-aided prediction of crack resistance and impact strength.Translated from Problemy Prochnosti, No. 8, pp. 14–22, August, 1993.     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

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.     

Effects of precracked specimen geometry on local cleavage fracture stress σf of low alloy steel

An elastic-plastic finite element method (FEM) is used to analyze the stress distributions ahead of crack tips for three types of COD specimens with different precracked depth a/W and height W of a low alloy steel, and the tensile and COD tests are carried out at various temperatures. By accurately measuring the distances of the cleavage initiation sites from the blunted crack tips, the local cleavage fracture stresses _f are measured. With increasing precrack depth a/W, specimen height W and test temperatures in a certain range, it was found that the _f essentially does not change. The _f is a steady inherent parameter of the material whose value is independent of the precracked specimen geometry.     

Effective conductivity of a composite of poly-dispered spherical particles in a linear continuum

Rayleigh's method is used to find the electric potentials of a composite of poly-dispered spherical particles in a linear continuum in an external electric field. Based on the solutions of potentials, analytical formula for the effective electric conductivity is derived. Based on the formula, several factors, such as the number of spherical inclusions, the spatial distribution of the spheres, the contrast ratio _i / _h (where, _i and _h are the conductivities of the spherical inclusion and the host medium, respectively) and volume fraction of the inclusions, are discussed. Our results show that at high volume fraction, the effective conductivity is also affected by the spatial distribution of the inclusions.     

The influence of antimony-additions on the creep behaviour of a 25wt% Cr-20wt% Ni austenitic stainless steel

The effect of antimony on the creep behaviour (dislocation creep) of a 25 wt% Cr-20 wt% Ni stainless steel with ~ 0.005 wt% C was studied with a view to assessing the segregation effect. The antimony content of the steel was varied up to 4000 ppm. The test temperature range was 1153 to 1193 K, the stress range, 9.8 to 49.0 MPa, and the grain-size range, 40 to 600m. The steady state creep rate, , decreases with increasing antimony content, especially in the range of intermediate grain sizes (100 to 300m). Stress drop tests were performed in the secondary creep stages and the results indicate that antimony causes dislocations in the substructure to be immobile, probably by segregating to them, reducing the driving stress for creep.Nomenclature _a Creep stress in a constant load creep test without stress-drop - _A Initial applied stress in stress-drop tests - Stress decrement - ( _A-) Applied stress after a stress decrement, - t _i Incubation time after stress drop (by the positive creep) - _C Strain-arrest stress - _i Internal stress - _{s s}-component (= _i- _c) - Steady state creep rate (average value) in a constant load creep test - Strain rate at time,t, in a constant load creep test - New steady state creep rate (average value) after stress drop from _A to ( _A-) - Strain rate at time,t, after stress drop.     

Crack-tip damaged zones in rubber-toughened amorphous polymers: a micromechanical model

The various stages of crack propagation in rubber-toughened amorphous polymers (onset and arrest, stable and unstable growth) are governed by the rate of energy dissipation in the cracktip damaged zone; hence the relationship between the applied stress intensity factorK ₁ and the damaged zone size is of utmost importance. The size of the crack-tip damaged zone has been related toK ₁ via a parameter which is characteristic of the material in given conditions: this factor is proportional to the threshold stress for damage initiation in a triaxial stress field, and has been denoted by ^*. Theoretical values of ^* have been calculated by means of a micromechanical model involving the derivation of the stresses near the particles and the application of damage initiation criteria. The morphology, average size and volume fraction of the rubbery particles have been taken into account together with the nature of the matrix. The calculated values of ^* have been successfully compared with the experimental ones, for a wide set of high-impact polystyrenes (HIPS) and rubber-toughened poly(methyl methacrylate) (RTPMMA).Nomenclature PS; HIPS polystyrene; high-impact polystyrene - PMMA; RTPMMA poly(methyl methacrylate); rubber-toughened PMMA - MI; CS/H; CS/R particle morphologies (multiple inclusion; hard core - rubber shell; rubber core - rigid shell) - K _r;K _g bulk moduli of rubber and glassy materials - G _r;G _g shear moduli of the same materials - v _p particle volume fraction - L mean centre-to-centre distance between neighbouring particles - B; H; W standard names for the dimensions of the compact tension specimen - R _y size of the crack-tip plastic zone in a homogeneous material - h half thickness of the crack-tip damaged zone - r; polar coordinates around the crack tip (Fig. 1) - r;r _p distance from particle centre; particle radius - p normalized distance from the particle (Equation 5) - K ₁;K _1c;K _1p stress intensity factor; critical values ofK ₁ at the onset of and during crack growth - G _1c plane strain energy release rate - _y yield stress in uniaxial tension - _th macroscopic threshold stress for the onset of local damage initiation in a composite material - ^* characteristic parameter (Equation 3) - ⁰; ₁ ⁰ ; ₂ ⁰ ; ₃ ⁰ applied stress tensor and its three principal stresses - ⁰ uniaxial applied stress - ; ₁; ₂; ₃ local stress tensor and its three principal stresses - A tensor which elements are the ratios of those of over those of ⁰ (Equation 4) - v Poisson's coefficient of the matrix - g triaxiality factor of the crack-tip stress field - _e; _p Mises equivalent stress; dilatational stress (negative pressure) - I ₁;I ₂ invariants of the stress tensor - U ₁;U ₂ material parameters for argon and Hannoosh's craze initiation criterion (Equation 12)     

Hydrodynamics of rising bubbles and drops

Conclusion An analysis of the problem concerning the interaction of moving single formations (bubbles and drops) with the surrounding carrying medium shows the possibility of describing real physical processes within the frameworks of the models of ideal and viscous liquids. Generalization of experimental and theoretical data is made by constructing charts of flow modes. A successful selection of the dimensionless numbersR andR as coordinates made it possible to arrange in an ordered fashion in the diagram all of the media by means of the parameter M, with the data for each specific medium being located on a certain straight line whose slope is determined by M. Vast computational data both of the present author and of other investigators for the region of small and intermediate values of dimensionless parameters, converted into theR ,R functions, made it possible to fully display the region inaccessible for investigation when the effect of all the parameters is significant and their number cannot be reduced. The use of these very parameters for correlating the data of the problem of steady rise of a drop made it possible to simply demonstrate the influence both of the presence of the medium itself and its motion on the drop rise. Comparison of the data with the problem of bubble rise can be made by simple superposition of diagrams. The logical clarity of the parametersR , which is equal to the ratio of the equivalent radiusa of a bubble (drop) to the capillary constant of the surrounding medium , allowed the determination of a certain critical sizea after which waves appear on the surface at the back side of the bubble (drop) when the value ofa is higher than 2-3. Another form of instability of steady rise is associated with the formation of a stagnant zone and with the separation of flow from the surface of a bubble or drop characteristic for surrounding media with small values of M. The use of the parametersR andR will definitely significantly simplify the analysis of more complex problems, for example, the problems of the motion of bubbles and drops in tubes with liquid and also the change in the external conditions (reduced or increased gravitation).Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 1, pp. 93–123, January, 1994.     

The stress dependence of the crack growth rate during creep

An equation is derived for the crack growth rate under creep conditions. In the model, the propagation of a grain boundary crack is controlled by the plastic growth of cavities located in the grain boundaries ahead of the crack. It is assumed that the cavities grow by power law creep in the elastic crack tip stress field. Hence, the stress dependence of the crack velocity is provided through the elastic stress intensity factor, i.e., dC/dt=BK _I ^p .The cavity spacing, , appears as an important factor in the coefficient,B ^–(p–2)/2. At large values of , corresponding to less severe creep damage in the grain boundaries, the above equation would predict very low values for the crack velocity. Under such conditions, we suggest that another mechanism, whose stress dependence is provided through the net section stress, becomes active, i.e., dC/dt=B _net ^p . Since increases with decreasing applied stress, one should observe the _net correlation at low stresses. The results of recent creep crack growth experiments which tend to support this hypothesis are presented.

---

Résumé On dérive une équation décrivant la vitesse de propagation d'une fissure dans les conditions de fluage. Dans ce modèle, la propagation d'une fissure aux frontières de grains est contrôlée par la croissance dans le domaine plastique de cavités situées aux frontières de grains en avant de la fissure.On suppose que les cavités s'étendent dans le champ de contraintes élastiques situées à l'extrémité de la fissure en suivant une loi de fluage parabolique. Dès lors, la dépendance de la vitesse de la fissuration en fonction de la contrainte est fournie par un facteur d'intensité de contrainte élastique, c'est-à-dire dC/dt=BK _I ^p .L'espace entre les cavités, , apparaît être un facteur important dans les coefficientsB. Pour de grandes valeurs de , qui correspondent à un dommage moins sévère par fluage aux frontières des grains, l'équation ci-dessus permettrait de prédire des valeurs très faibles de la vitesse de fissuration.Sous ces conditions, il est suggèré qu'un autre mécanisme, dont la dépendance de la contrainte est fournie par la contrainte agissant sur la section droite, devient plus actif; on a alors dC/dt=B _nette ^p .Comme augmente lorsque la contrainte appliquée diminue, on devrait observer une corrélation de nette à basses contraintes.Les résultats d'essais de croissance de fissure sous des conditions de fluage effectués récemment tendent à supporter cette hypothèse et sont présentés.

     

Fracture toughness of eutectic Al-Si casting alloy with different microstructural features

The static fracture toughness of a series of eutectic Al-Si casting alloy with different microstructural features has been evaluated. The dominant influence of eutectic silicon in controlling the fracture toughness is thus clarified. The relationship between the fracture toughness and the microstructure was established. Fracture toughness was found to be strongly associated with the size and morphology of silicon particles. The other feature which greatly influences the fracture toughness is the ratio (/DE)_Si, i.e. the silicon particle spacing divided by the equivalent particle diameter, rather than the silicon particle spacing, _Si. Fracture toughness also correlates well with the void growth parameter, VGP (=_y (/DE)_Si), proposed by the authors. The results of the present work can be used to develop an understanding of the variation of fracture toughness with the microstructural features of eutectic Al-Si alloys.     

Effects of sizes of ferrite grains and carbide particles on toughness of notched and precracked specimens of low-alloy steels

Four point bending (4PB) tests of notched specimens and COD tests of precracked specimens were carried out on two steels; one steel was treated into two groups with the same ferrite grain size but different carbide sizes, the other steel with different ferrite grain sizes but similar carbide sizes. The results of the tests show that the toughness measured in notched specimens is mainly determined by the grain sizes, which define the local fracture stress _f; the size of carbide particle plays a minor role. However, on the contrary, in precracked specimens the toughness is sensitive to the carbide sizes, which affect the critical plastic strain _pc for initiating a crack nucleus; the effect of grain size is indistinct. By these inferences the behavioral discrepancy of large grain steel in improvement of crack fracture toughness while reducing the notch toughness is explained.