On diffusion creep of polycrystals

We present a variant of diffusion creep in polycrystalline bodies, which is based on solving a diffusion-viscous flow model problem. A polycrystal is treated as a composite material and the relevant boundary-value problem is solved through approximation of the self-consistent method. Simple expressions have been derived for viscosity coefficients of the polycrystal and grain boundaries. The creep equation is analyzed for a uniaxial compression case. The conclusions inferred from this equation are qualitatively consistent with the available experimental findings. Translated from Problemy Prochnosti, No. 3, pp. 14–24, May–June, 2009.     

Time-dependent creep stress redistribution analysis of thick-walled functionally graded spheres

Time-dependent creep stress redistribution analysis of thick-walled spheres made of functionally graded material (FGM) subjected to an internal pressure and a uniform temperature field is performed using the method of successive elastic solution. The material creep and mechanical properties through the radial graded direction are assumed to obey a simple power-law variation. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are time, temperature and stress dependent. Using the equations of equilibrium, compatibility and stress–strain relations a differential equation, containing creep strains, for radial stress are obtained. Ignoring creep strains, a closed-form solution for initial thermoelastic stresses at zero time is presented. It has been found that the material in-homogeneity parameterβ has a substantial effect on thermoelastic stresses. From thermoelastic analysis the material identified by β=2 in which a more uniform shear stress distribution occurs throughout the thickness of the FGM sphere is selected for time-dependent stress redistribution analysis. Using the Prandtl–Reuss relations and Norton’s creep constitutive model, history of stresses and strains are obtained. It has been found that radial stress redistributions are not significant, however, major redistributions occur for circumferential and effective stresses. It has also been concluded that stresses and strains are changing with time at a decreasing rate so that there is a saturation condition beyond which not much change occurs. Indeed after 50 years the solution approaches the steady-state condition.     

A mechanical model for creep,recovery and stress relaxation in polymeric materials

A mechanical model is presented, in which viscoelastic response is described by the action of time-dependent latch elements. The model represents viscoelastic changes occurring through incremental jumps as opposed to continuous motion. This is supported by the observation that polymeric creep, recovery and stress relaxation can be correlated with stretched exponential functions, i.e. Weibull and Kohlrausch-Williams-Watts, since (i) the former is also used in reliability engineering to represent the failure of discrete elements and (ii) there is evidence of the latter being an approximation to the Eyring potential energy barrier relationship, which describes motion in terms of molecular jumps.     

The correlation between creep deformation and stress relaxation in concrete

Summary The functional relation between creep deformation and stress relaxation can be represented by the Volterra integral equation. By substituting the creep function and the relaxation function into this equation and comparing coefficients it is possible to obtain an expression which relates the ultimate creep to the relaxed stress at time t=∞. The rate at which the stress decreases at the begenning of the experiment is proportional to the creep velocity, and the constant of proportionality is the modulus of elasticity. It is shown the half-life time of the relaxation process is always smaller than the corresponding half-life time of the creep process. The derived equations are compared with experimental results described in the literature.

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Résumé On peut traduire la relation entre fluage et relaxation par l'équation intégrale de Volterra. La substitution des fonctions ?fluage? et ?relaxation? dans cette équation et la comparaison des coefficients permet d'obtenir une expression qui relie le fluage final et la contrainte relachée au tempst=∞. Le taux de décroissance au début de l'expérience est proportionnel à la vitesse de fluage; la constante de proportionnalité est le module d'élasticité. On montre que la mi-temps du processus de relaxation est toujours plus petite que la mi-temps correspondance du processus de fluage. On compare les équations dérivées avec les résultats expérimentaux décrits dans la littérature.

     

A comparative study of the stress relaxation in aged and un-aged high-purity aluminium polycrystals

Stress relaxation in 99.996% aluminium polycrystals of average grain-diameter 0.30, 0.42 and 0.51 mm, annealed at 500°C and aged for six months at room temperature, has been studied as a function of initial stress level from which relaxation at constant strain was allowed to start. Data were also obtained with annealed but un-aged aluminium specimens of the same purity and grain size for comparison. The grain size has no notable effect on the strength parameters and stress-relaxation rate in both aged and un-aged aluminium. The room-temperature ageing causes significant increase in the yield stress, while tensile strength and fracture stress remain un-effected. The intrinsic height of the thermally-activable energy barrier (1.64 eV) evaluated for aged aluminium is comparable with that (1.94 eV) for un-aged aluminium, and is of the order of magnitude for recovery processes. In aged specimens, the relaxation rate at a given stress level is 30% larger and associated activation volume is accordingly smaller than that in un-aged specimens. This is most probably due to the diffusion of vacancies and/or residual gaseous and metallic impurity atoms to the cores of edge dislocations in aged specimens.     

Benchmark for finite element analysis of stress redistribution induced by creep damage

A benchmark test for finite element analysis of stress redistribution induced by material creep damage is proposed using a two-bar model structure. It is directly based on the analytical solution reported earlier by Gonçalves Filho [Int. J. Solids Struct. 32 (1995) 3087] and actual creep data for the Ti–6Al–2Cr–2Mo titanium alloy. The new benchmark is used to assess the accuracy of the implicit time integration scheme employed in the in-house finite element code developed by this author for solution of engineering creep damage problems. By allowing the calculation of the true relative errors in alternative numerical solutions, the designed test enhances the set of benchmark tests recently proposed by Becker et al. [Comput. Mater. Sci. 25 (2002) 34].     

Early age creep and stress relaxation of concrete containing blended cements

The main objective is to investigate key properties that influence the stress development in concrete at early ages and the effect of using blended cements. Mineral additives and amount by weight of total binder used in the blended cements are fly ash (25%), ground granulated blast furnace slag (25%), and silica fume (10%). The properties investigated include tensile creep, elastic modulus, split tensile strength, and autogenous shrinkage. The relaxation modulus used for stress prediction was obtained from the creep data fitted using a log-power creep function. These findings show that tensile creep and stress relaxation are important properties of Portland cement concrete. These properties however are reduced in concretes containing blended cements. Blended cements affect the early age strength and elastic modulus moderately but significantly alter the autogenous deformation. Water/cement ratio (w/c), type and dosage of mineral additives were found to influence the magnitude of autogenous deformation. This deformation was found to be significant in low water-cement ratio concretes and should be included in early age stress calculations.

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Résumé L'objectif principal de cette étude est d'explorer les propriétés importantes qui influencent le développement des contraintes dans le béton au jeune age et particulièrement les effets dus à l'utilisation de ciments composés. Les additifs minéraux utilisés et leur poids en proportion du ciment composé sont: 25% de cendres volantes (FA), 25% de laitiers de hauts-fourneaux granulés (GGBS) et 10% de fumée de silice. Les propriétés étudiées comprennent le fluage en tension, le module d'élasticité, la résistance en tension (essai brésilien), et le retrait endogène. Le module de relaxation utilisé pour la prédiction des contraintes a été obtenu à partir des essais de fluage utilisant une fonction logarithmique. On observe que le fluage en tension ainsi que la relaxation des contraintes sont des propriétés importantes qui diminuent avec l'utilisation de ciments composés. Le rapport eau/ciment, le type et le dosage d'additifs minéraux influencent la valeur du retrait autogène. On trouve que cette déformation est importante et doit être prise en considération dans le calcul des contraintes au jeune age.

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Editorial Note Prof. Will Hansen is a RILEM Senior Member. He participates in the work of RILEM TC 181-EAS: ‘Early age shrinkage induced stresses and cracking in cementitious systems’.     

Viscoplastic analysis of structural polymer composites using stress relaxation and creep data

A structural carbon based composite material has been investigated for its high temperature viscoplastic properties using a model based on an overbearing stress concept and using the data obtained from load relaxation and creep. The time dependent viscoplastic properties were obtained at several load and temperature levels. An elastic–viscoplastic constitutive model (proposed by Gates) was used for the modeling efforts. The model is based on an overstress concept appropriate to inelastic properties of composites. The materials parameters for the model are obtained from a set of load relaxation experiments. The model predictions have been compared to the results of creep tests. The results show that the model is capable of predicting the creep behavior at shorter time periods and lower temperatures. As the temperature is increased or as the creep is prolonged the model predictions deviate from the experimental results.     

A unified model of stress relaxation and creep applied to oriented polyethylene

The stress relaxation behaviour of high-modulus oriented polyethylene fibre has been studied with regard to the response to successive small strain increments imposed on an initial relatively large strain deformation. For isotropic polymers, the results of such experiments have previously been interpreted in terms of a single thermally activated process modified by strain hardening. It has been found that, although this approach can describe satisfactorily some of the stress relaxation experiments on the oriented polyethylene fibres, it is unsatisfactory once the strain increments have exceeded a certain size, and that it is at variance with stress recovery experiments. It is shown that both the present stress relaxation and stress recovery experiments can be interpreted in terms of a model comprising two thermally activated processes acting in parallel. Furthermore, the parameters obtained for the stress relaxation data are consistent with those required to fit creep data obtained in a comparable stress range. The essential feature of the mechanical behaviour which was previously attributed to strain hardening can now be seen to arise from the transfer of stress between the two thermally activated processes in the two-process model.     

Micromechanism for anomalous creep of MoSi2 polycrystals

A theoretical model is proposed for an anomalous creep effect in MoSi2 polycrystals (characterized by an anomalous dependence of the plastic strain rate on the grain size). In this model the micromechanism for anomalous creep is represented as the diffusioncontrolled climb of grain-boundary dislocations in grain-boundary planes. Pis’ma Zh. Tekh. Fiz. 25, 69–73 (June 12, 1999)     

High temperature creep of ultrafine-grained Fe-doped MgO polycrystals

Creep deformation in ultrafine-grained (0.1 to 1μm) Fe-doped magnesia polycrystals is studied in compression, at temperatures of 700 to 1050° C, and constant loads of 50 to 140 MPa. The stress exponent observed to be nearly unity and the strong grain size sensitivity (ė∼d ^−2.85) suggest that diffusional creep mechanisms dominate the deformation. In the grain size range of the present study the grain boundary diffusion contribution is significantly more important than lattice diffusion. Magnesium is tentatively identified as the rate-controlling species along grain boundaries from an analysis of the diffusivities inferred from the present work and from other authors for Fe-doped magnesia. Associated with the CNRS.     

On the origin of the stress decrease for nickel polycrystals with few grains across the thickness

The mechanical behaviour under uniaxial and loading/unloading tensile tests of high purity nickel with different number of grains across the thickness is studied experimentally. The specimens have a constant 500 μm thickness and the mean number of grains across the thickness (i.e., thickness “t” to grain size “d” ratio) lies between 0.9 and 15. An extended microstructural study is operated and no change of the microstructure appears with a modification of t/d. The experimental results show that the t/d ratio affects the hardening stages, flow stress, intragranular and intergranular backstress of the samples. For specimens with few grains across the thickness, the flow stress is reduced due to a decrease in the intragranular backstress. The main explanation of these results is a delay of the generalization of cross-slip for the lowest t/d ratio specimens due to surface effects.     

A semi-empirical model for stress relaxation including primary and secondary creep stages

A universal creep law which incorporates both primary and secondary creep has been used to develop a semi-empirical model for stress relaxation. The modelling was performed by comparing computer simulated relaxation curves with experimental data. Contrary to most models for stress relaxation, the results indicate that relaxation life should be divided into two stages, a primary stage with increasing internal stress and a secondary stage during which the internal stress falls as the applied stress decreases.     

Observation of the relation between uniaxial creep and stress relaxation of filled rubber

This paper presents an experimental evaluation of the stress relaxation and creep of filled rubber. A detailed study of the influence of different test programs, where the main variable was the load sequence on the creep and relaxation processes, is discussed. The final goal of the research is to find a method to predict stress relaxation from known creep, or vice versa, in a simple way that would give sufficiently accurate results over both primary and secondary creep regions. Therefore suggestion for converting the creep test result into a stress relaxation curve and vice versa is presented. The idea is based on the assumption that both processes (creep and stress relaxation) are the result of the same viscoelastic mechanism and that the stress relaxation can be treated as creep under decreasing stress. Experimental data shows these assumptions to be correct. For the conversion of the creep parameters into stress relaxation parameters a reverse stress-strain curve is needed, therefore factors affecting the unloading stress-strain curve are also presented. Finally, the transition from the suggested conversion to the final method will be discussed.     

Quantification of stress redistribution due to mismatch in creep properties in welded branch pipes

This paper reports steady‐state stress distributions within the weld metal in a welded branch component, via detailed three‐dimensional elastic‐creep finite element analyses. The creep exponent and constants for the base and weld metal are systematically varied to simulate under‐matching, even‐matching and over‐matching conditions in creep. Various loading conditions are also considered to see the effect of the loading mode. It is found that the mismatch effect in creep on steady‐state stresses within the weld metal can be uniquely quantified by the mismatch factor, defined as a function of creep exponent and constant. Ratios of section‐averaged (effective and maximum principal) stresses for the mismatched case to those for the even‐matched case are linearly dependent on the mismatch factor.     

Physical and thermodynamic aspects of the glassy state,and intrinsic non-linear behaviour of creep and stress relaxation

Rheology in the highly viscous liquid and the glassy state is reviewed and discussed. A distribution relaxation time due to the co-operative molecular motion is exhibited both in the highly viscous liquid and in the glassy states. However, only in the glassy state has the structure been frozen-in at some particular internal state resulting from the incomplete establishment of a thermodynamic equilibrium state. Therefore, the intrinsic non-linear rheological behaviour of the glassy state is explained from the physical and thermodynamic aspects in the glass transformation region. The volume relaxation of soda-lime-silica glass and the thermal history of glass during forming process have been studied. Finally, the role of rheology in thermal stress and fracture mechanics is also mentioned, which subsequently will allow us to re-evaluate the mechanisms of toughening and weakening of composite materials.     

The significance of weldment material mis-matching on stress redistribution and creep cracking of high temperature components

A large circumferentially oriented crack was discovered in a weld of a double T-piece in the main steam pipe of a Swedish power plant. The pipe and the weld were manufactured from 0.5Cr0.5Mo0.25V steel. In this paper a nominal creep life assessment and an assessment considering mis-matching are carried out for a defect free component and for a component with a crack. While the nominal prediction of a defect free component indicates a creep life of approximately 2200000 hours, a creep life of 550000 hours is obtained when mis-matching effects and enhanced axial stresses due to system loads are considered. If mis-matching is not taken into account, as opposed to if it is, the estimated incubation plus creep crack growth time is approximately 30–70% longer.