Strength of concrete under combined tensile-compressive stresses

Summary Strength of plain concrete under combined tensile-compressive stresses has been studied by conducting splitting tests on cubes, cylinders, prisms and ellipses. Using these results the influence of lateral compressive stress on the longitudinal tensile strength of concrete has been determined. The results have been critically examined and a failure criterion in the form of an interaction diagram has been given.

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Résumé On étudie la résistance du béton armé sous des efforts combinés en traction-compression au moyen de l'essai brésilien sur des cubes, cylindres, prismes, et des éprouvettes à section elliptique. A l'aide de ces résultats, on détermine l'influence de l'effort de compression latérale sur la résistance en traction longitudinale. Après analyse des résultats, on donne un critère de rupture sous la forme d'un diagramme d'interaction.

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Mechanical stability of iron under hydrostatic stresses

A comprehensive investigation of the mechanics of iron subjected to arbitrary fluid pressure has been carried out. Apart from the classical elastic moduli (k, , and ) and conventional elastic moduli (Green and stretch moduli) computations are carried out for a family of generalised moduli of which the conventional moduli are just specific members. With the generalised moduli the mechanical stability of iron is investigated through Born criteria. It is found that classical stability, Green stability and stretch stability are all represented uniquely by the present generalised scheme. The definition of effective classical moduli under stresses enabled the amalgamation of the Born criteria of lattice stability into the single classical criteria of lattice stability of cubic crystal under hydrostatic loading environment. Computations are also carried out to investigate the coordinate and stress dependence of Young's modulus of elasticity, Poisson's ratio, mean velocity of elastic wave, and Debye temperature. Surprisingly, it is found that all these properties of solids play an important role in representing the mechanical stability of the solid. The path of uniaxial loading of iron is also investigated along with its internal energy variation on this path. This indicated the existance of stress-free fcc phase of iron on the path of uniaxial deformation at cell length a=3.6444 Å giving enthalpy of transformation (bccfcc) of 1.1 kJ/mol in good agreement with experimental results.     

Fatigue crack propagation model and size effect in concrete using dimensional analysis

It is well known that fatigue in concrete causes excessive deformations and cracking leading to structural failures. Due to quasi-brittle nature of concrete and formation of a fracture process zone, the rate of fatigue crack growth depends on a number of parameters, such as, the tensile strength, fracture toughness, loading ratio and most importantly the structural size. In this work, an analytical model is proposed for estimating the fatigue crack growth in concrete by using the concepts of dimensional analysis and including the above parameters. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between different parameters involved. It is shown that the proposed fatigue law is able to capture the size effect in plain concrete and agrees well with different experimental results. Through a sensitivity analysis, it is shown that the structural size plays a dominant role followed by loading ratio and the initial crack length in fatigue crack propagation.     

Numerical investigation of through crack behaviour under welding residual stresses

Numerous engineering structures operate under the presence of residual stresses resulting from welding or other manufacturing processes. In the present work, the effect of typical residual stress fields on stress intensity factors and crack propagation angle of cracks developing into the residual stress field under mixed mode loading conditions is studied. For the calculations a numerical methodology based on linear elastic finite element analysis is used. The presented results provide a useful tool for an efficient assessment of the influence of residual stress field on the crack evolution behaviour.     

The effect of a circular inclusion on the stresses around a line crack in a sheet under tension

Based on the two-dimensional theory of elasticity and by the use of Muskhelishvili technique, the effect of a circular inclusion of different elastic material on the stress state around a line crack in an infinite plate subject to tension is discussed. Here, the circular inclusion is supposed to be on the line of prolongation of the crack.Numerical calculations were carried out and the variation of the crack-tip stress intensity factor due to the geometry and elastic properties of two media was clarified.

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Zusammenfassung Es wurde der Effect einea zirkularen Einschlusses verschiedener-elatischer Materiale auf den Druckzustand um einen Linienriss in einer unendlichen Platte, die Spannung ausgesetzt ist, diskutiert. Der zirkulare Einschluss wurde hier auf der Verlängerungslinie des Risses angenommen.Numerische Berechnungen wurden ausgeführt. Die Variation des Rissspitzen-Druckintensitäts-Faktors, die auf die geometrischen and elastischen Eigenschaften der zwei Medien gegründet ist, wurde geklärt.

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Résumé En se basant sur la théorie de l'élasticité bidimensionnelle, et en ayant recours à la technique de Muskhelishvili, on discute l'effet de la présence d'une inclusion circulaire d'un matériau de propriétes élastiques distinctes, sur l'état de tension dans le voisinage d'une fissure linéaire sise dans une plaque infinie soumise à traction. On suppose dans le présent mémoire que l'inclusion circulaire se situe sur une ligne prolongeant la fissure.On a procédé à des calculs numériques et l'on a pu ainsi mettre en évidence la variation du facteur de concentration de contraintes à la pointe de la fissure en fonction de la géométrie et des propriétés élastiques des deux milieux considérés.

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On leave from Dept. of Mechanical Engineering, Tohoku University, Sendai, Japan     

FEM analysis of crack closure and delay effect in fatigue crack growth under variable amplitude loading

An analysis of fatigue crack closure under variable amplitude loading was made by using the finite element technique. Two basic types of variable amplitude loading were selected for the analysis; constant amplitude loading with a single overload and block loading. A characteristic variation of a crack closure level was found to exist for both types of loading: the trace of the crack closure level vs crack length rose to a maximum value and then decreased asymptotically. The characteristic behavior was explained in terms of the residual stress which had been induced by an overload or a load preceding to the variation. The predicted fatigue crack growth behavior which was obtained analytically was consistent with the experimental results, and it was concluded that the retardation and acceleration phenomena are closely correlated with the crack closure.     

Significant effect of thermal stresses on fatigue crack propagation properties

Fatigue crack propagation properties of low-alloy ferritic steel were investigated using 50-mm-wide compact-type (CT) specimens and 200-mm-wide center-cracked-type (CCT) specimens at room temperature and 300°C. Most of the stress ratios were nearly equal to zero. Significant differences in fatigue crack propagation rate in the CCT specimen, which was heated to the test temperature only locally near the crack plane, were compared with the rates for the CT specimen which was enclosed completely by a furnace. It was found that the differences were related to the compressive stresses arising from the thermal gradients.

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Résumé On étudie les propriétés de propagation des fissures de fatigue dans un acier ferritique faiblement allié à l'aide d'éprouvettes de traction compactes CT longues de 50 mm et d'éprouvettes de traction à fissure centrale (CCT) longues de 200 mm, à température ambiante et à 300°C. Dans la plupart des cas, les rapports de contraintes R sont égaux à zéro. On constate et on compose des différences importantes de vitesses de propagation en fatigue sur les éprouvettes CCT où le chauffage jusqu'à température d'essai est appliqué localement au voisinage du plan de la fissure, par rapport aux vitesses de propagation constatées sur les éprouvettes CT complètement insérées dans un four. On trouve que ces différences sont liées aux contraintes de compression associées aux gradiants thermiques.

     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Fatigue crack growth in a welded rail under the influence of residual stresses

The effect of welding residual stresses on fatigue crack growth in rail welds is studied. Finite element analysis is used to calculate residual stresses in a flash-butt welded rail. The calculated residual stresses are found to be in good agreement with experimentally determined residual stresses in a welded rail. The redistribution of residual stresses in the welded rail is simulated for a straight track, during heavy-haul operation conditions, using a train-track model. Fatigue crack growth of defects in the weld region is studied using fracture mechanics. In the investigation, a number of parameters such as the axle load, crack location, crack size and rail temperature are varied.     

Elastic-plastic analysis of a stationary crack under cyclic loading and effect of overload

A recently proposed elastoplastic constitutive model has been implemented in a finite element code to study crack front behaviour under variable loading. The importance of proper modelling of a material's behaviour becomes evident when a variable loading condition is considered. We present stress, strain and displacement distribution along a stationary crack front for constant amplitude cyclic loading with an overload cycle. The analysis predicts a decreased tensile stress and damage accumulation following an overload.     

The effect of couple stresses on the stress field around a penny-shaped crack

The present paper is concerned with the influence of couple stresses on the stress concentration around a penny-shaped crack in an infinite body within the framework of both the micropolar and couple stress (indeterminate) theory. Taking into account the symmetry of the boundary value problem considered this one is converted into solving dual integral equations, and finally into a Fredholm integral equation of the second kind. Approximating the kernel the latter is solved analytically.

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Résumé Dans le cadre de la théorie des contraintes micropolaires et des couples, on étudie l'influence d'un couple et d'une concentration de contraintes sur une fissure en ongle dans un corps infini. En prenant en compte la symétrie qui caractérise les contours du problème considéré, celui-ci est ramené `a la solution d'une double équation intégrale, et ensuite à une équation intégrale de Fredholm du second genre. Celle-ci est résolue par voie analytique en faisant une approximation sur le noyau.

     

Size effect of concrete members applied with flexural compressive stresses

In this study, two types of special experiments are carried out to understand flexural compressive strength size effect of concrete members. The first type is an ordinary cylindrical specimen (CS) with a fully penetrated and vertically standing plate type notch at the mid-height of the specimen, which is loaded in compression at the top surface (e.g., in the parallel direction to the notch length). The second type is a general double cantilever beam (DCB), which is compression loaded in axial direction (e.g., in the parallel direction of the notch). For CS, an adequate notch length is taken from the experimental results obtained from the compressive strength experiment of various initial notch lengths. The trial tests to select the effective initial notch length show that CS with an initial notch length approximately greater than four times the maximum aggregate size fails without an additional increased load and in stable manner under Mode I failure mechanism. Therefore, the initial notch length to the maximum aggregate size ratio of 4.0 is used for all size specimens. For DCB, the eccentricity of loading points with respect to the axial axis of each cantilever and the initial notch length are varied. In both specimens, the compressive loads apply flexural compressive stresses on the crack tip region of the specimens. These two types of specimens fail by Mode I crack opening mechanism. By testing 3 geometrically proportional size specimens for CS and DCB, the experimental datum for flexural compression size effect of concrete are obtained. Using the obtained flexural compressive strength size effect datum, regression analyses are performed using Levenberg-Marquardt's least square method (LSM) to suggest new parameters for the modified size effect law (MSEL). The analysis results show that size effect is apparent for flexural compressive strength of specimens with an initial notch. For CS, the effect of initial notch length on flexural compressive strength size effect is apparent. For DCB, flexural compressive size effect is dependent on the eccentricity of loading points with respect to the axial axis of the cantilever beam. In other words, if DCB specimen is applied with greater tensile stress at the crack tip, the size effect of concrete becomes more distinct. The results show that the flexural compressive strength size effect of initial notch length variation of DCB exists but directly dependent on the loading location. This is due to the fact that the sizes of fracture process zone (FPZ) of all DCB specimens are similar regardless of the differences in the specimen slenderness ratio, but the flexural compressive and tensile stress combinations resulting in stress concentration at the crack tip region has direct effect on size effect of concrete members.     

The stresses in the neighborhood of a crack tip under effects of electromagnetic forces

In recent work, some basic problems of the stresses in the neighborhood of a crack tip under the effects of electromagnetic forces are studied, and the basic concept of Maxwell electromagnetic stress tensor is illustrated and used to express the effects of the electromagnetic field to the solid body. The basic governing equations of elastic stress of both potential electromagnetic force and Maxwell stress tensor and the approaches for solving these equations are provided. Two kinds of affects of the electromagnetic field on stress singularity of a crack tip are presented and analyzed. Lastly, several examples about the stress analysis on the effects of the electromagnetic field are provided     

Numerical analysis of the influence of residual stresses on crack closure in rings

The stress intensity factors which result when an axially cracked ring containing residual stresses is subjected to an external load have been calculated using a numerical method. When partial crack closure occurs, it has been taken into account. The computations show that residual stresses can cause both cracking problems in service and scatter in experimental data. The method uses a finite-element procedure that is similar to those used with contact problems to provide the basis for a numerical solution. The procedure can be applied to any geometrical configuration that can be analyzed with the finite-element method.     

Experimental study on dynamic damage evolution of concrete under multi-axial stresses

The effect of stress state on the dynamic compressive strength and the dynamic damage evolution process of concretes are investigated by use of a Spilt Hopkinson Pressure Bar (SHPB) and the ultrasonic technique. The columned concrete specimen is encircled by a steel sleeve. The multi-axial loading includes the axial and the radial loadings. The axial loading is supplied by the incidence bar, and the radial ones are produced by the steel sleeve. Analysis of the dynamic damage evolution of the samples is based on the measurement of the changes of ultrasonic wave velocities before and after the impact tests. The waveforms in the test bars, the stress strain curves, the confining pressure of the specimen, the dynamic compressive strength and other information about the samples are obtained during the SHPB experiments. The results of the tests show that the loading rate and stress states of the specimen apparently influence the damage evolution process in concretes. The dynamic damage evolutions are accelerated with the increase of the strain rate and are delayed significantly under the confined pressure.