Showing papers on "Stress–strain curve published in 1979"

Plastic-Fracturing Theory for Concrete

Abstract: Incremental plasticity and fracturing (microcracking) material theory are combined to obtain a nonlinear triaxial constitutive relation that is incrementally linear. The theory combines the plastic stress decrements with the fracturing stress decrements, which reflect microcracking, and accounts for internal friction, pressure sensitivity, inelastic dilatancy due to microcracking, strain softening, degradation of elastic moduli due to microcracking, and the hydrostatic nonlinearity due to pore collapse. Failure envelopes are obtained from the constitutive law as a collection of the peak points of the stress strain response curves. Six scalar material functions are needed to fully define the monotonic response. One function, the dilatancy due to microcracking, is determined theoretically based on Budianski-O’Connell’s calculation of the effective elastic contents of a randomly microcracked elastic material by the self consistent method for composites.

Constitutive Model for Short-Time Loading of Concrete

Abstract: A constitutive model based on nonlinear elasticity is proposed, where the secant values of Young’s modulus and Poisson’s ratio are changed appropriately. This alteration is obtained through the use of a nonlinearity index that relates the actual stress state to the failure surface. The model simulates the strain hardening before failure, the failure itself and the strain softening in the post-failure region. The dilation of the concrete and the influence of all three stress invariants are considered. All stress states including those where there are tensile stresses can be dealt with; however, the model is calibrated using experimental data obtained by a uniaxial compressive and tensile test only. The model predictions are demonstrated to be in good agreement with experimental results involving a wide range of stress states and different types of concrete.

Deformation of Polycrystals

Abstract: SUMMARY Deformation of polycrystals is treated as the average behavior of an agglomerate of individual crystallites and their interaction across the grain boundaries. After considering the effect of grain boundaries on yield, in a rather general way the similarities between stress strain curves of single crystals and polycrystals are discussed, including the implication for commonly used stress strain relationships. Since - as known from polyslip in single crystals - the polycrystal curve consists of two stages (II and III) which are differently affected by deformation temperature, these two stages are treated separately. The range of athermal hardening (stage II) is described quantitatively by incorporating the processes of dislocation storage near the grain boundary into the well established stage II theories of single crystals. It is concluded from this discussion, that the influence of grain size on yielding and on work hardening at low strains is phenomenologically well explored and rather well understood theoretically. The range of temperature dependent work hardening (stage III) is interpreted as being the stage where the dislocation structure evolves towards a well defined cell structure, which approaches a steady state pattern as strain proceeds. The influence of temperature and strain rate on steady state appears to be the same for single crystals (deformed in polyslip) and polycrystals in the normal range of grain sizes. Although the differences between different materials can be related to the values of certain material parameters, understanding of stage III suffers from our ignorance of the basic dislocation mechanisms which control cell formation. In the last part effects of very large strains are shortly considered. Texture development is taken as an example how information about details of the deformation of the grains can be deduced from a comparison of experimentally obtained and of theoretically derived pole figures. Eventually it is discussed that at very large strains new effects appear, which are beyond the scope of the common theoretical concepts of work hardening and plastic flow.

On the determination of stress state in the simple shear apparatus

Abstract: The simple shear apparatus is one of the few commonly available laboratory apparatus that permits the application of controlled rotations of the principal axes of stress and strain to soil samples. However, because of the boundary conditions in the apparatus the soil sample does not respond as a single element, and this should be reflected in the analysis of test results. In the Cambridge University simple shear apparatus, the sample is surrounded by an array of load cells (contact stress transducers) that measure the complete distribution of boundary stresses throughout a test. For simple shear test results to be presented in terms of useful stress parameters, a procedure for computing the stress state from the load cell measurements is required. Such a procedure is described, making use of the concept of an average stress tensor to determine a representative stress state in the central part of the sample, which is least influenced by the ends of the apparatus. Less complex and expensive apparatus exist that can only measure the average normal and shear stresses applied to the top and bottom horizontal boundaries of the sample. Patterns of soil response have been determined from tests on Leighton Buzzard sand in the more elaborately instrumented Cambridge apparatus, and a method is described for using these patterns to deduce the complete stress state in the less complex apparatus.

Uniaxial Cyclic Loading of Elastic-Viscoplastic Materials

Abstract: : Elastic-viscoplastic constitutive equations based on two internal state variables are utilized to determine material response for uniaxial cyclic loading conditions. These equations are capable of representing the principal features of cyclic loading behavior including softening upon stress reversal, cyclic hardening or softening, tendency towards a stable limit cycle, cyclic relaxation, and cyclic creep. Calculations were performed for various stress and strain controlled conditions using material constants intended to represent commercially pure titanium and aluminum and OFHC copper. Capabilities and limitations of the analytical formulations are discussed in relation to computed results and corresponding test data. (Author)

A mathematical description of the deformational behaviour of concrete under complex loading

Abstract: Synopsis A mathematical description of the deformational behaviour of concrete under any type of short-term static loading is developed, using a model material with the same strength characteristics. The mechanical properties of the model are defined by analysing experimental data obtained at Imperial College from tests on concrete under various states of multiaxial stress. The testing techniques used have been validated by comparing the results obtained with those produced by other institutions investigating the behaviour of concrete under similar stress conditions but with different apparatus. In the analysis, each stress and strain state is resolved into a hydrostatic and a deviatoric component and it is assumed that any non-linear material behaviour is dictated mainly by fracture processes occurring under increasing stress.

Analysis of stress-strain relations by use of an anisotropic hardening plastic potential

Abstract: A method of analyzing plastic behavior by use of an anisotropic hardening plastic potential is proposed. The plastic potential surface in deviatoric stress space is assumed to be the same as the equi-plastic-strain surface. Stress-strain relations in combined loading and in multi-axial cyclic loading are calculated by use of the anisotropic hardening plastic potential and the normality rule of the plastic strain increment vector to the plastic potential surface, which are experimentally determined or confirmed by subjecting thinwalled tubular test specimens of 60 40 brass to combined axial load, internal pressure and torsion. The calculated results agree fairly well with the experimental observations.

The Stress-Strain Behaviour of Axially-Loaded Butt Joints

Abstract: The effects of the stress distribution in the adhesive layer of axially loaded butt joints have been examined theoretically and experimentally. It has been shown that the measured stress–strain behaviour of a butt joint is dependent on the triaxial stress state induced in the adhesive by the restraint of the adherends. This causes a butt joint to yield at a stress which is greater than the uniaxial yield stress of the adhesive. Conversely, the presence of stress concentrations can cause a butt joint to fail at a lower tensile stress than the failure stress of a bulk specimen tested in uniaxial tension. Therefore, the relationship between the strength of a butt joint and that of a bulk specimen of the same adhesive depends on the ductility of the adhesive. Furthermore, if the adhesive obeys a pressure-dependent yield criterion, the compressive yield stress of a butt joint can be much greater than the tensile yield stress of a similar joint and, under some circumstances, compressive yielding of a butt joint...

Stress-strain isotherms for polymer networks at very high elongations

Abstract: Some polymer networks show an anomalous increase in the modulus or reduced stress at very high elongations This behavior has now been investigated definitively by determining stress-strain isotherms for both crystallizable and noncrystallizable networks, prepared using several curing techniques (carried out so as to yield a wide range in degree of cross-linking) The networks were studied unfilled at a number of temperatures, and at several degrees of swelling The results clearly implicate strain-induced crystallization as the origin of the upturn in the modulus, and thus demonstrate that the wide spread interpretation of this upturn in terms of limited chain extensibility is incorrect

Numerical study of initiation, stable crack growth, and maximum load, with a ductile fracture criterion based on the growth of holes

Abstract: Considering a material at the ductile plateau, fracture tests on small specimens in generalized yielding conditions are common. We need to extract from them adequate information to characterize the fracture resistance properties of the material. We also need to predict initiation, crack growth, and maximum load for a crack found in a ductile structure. But the real problems are three-dimensional; for instance, semi-elliptical surface cracks or through-cracks in "small" thicknesses (tunneling and mixed-mode fracture). Moreover, they are not only in the symmetrical Mode I case (angled crack extension). The common denominator of all these phenomena is the ductile fracture processes in the material at the crack border; these micromechanisms extend over some characteristic length which needs to be introduced at a crack tip because of the very intense strain gradient. We thus need a ductile fracture damage function belonging to the continuum mechanics frame and related to the history of stresses and strains averaged over such a characteristic volume. In this numerical feasibility study, using elastic-plastic finite-element computations and guided by a ductile fracture model in three stages-void nucleation, void growth, and coalescence-we tried such a differential damage history, in a most simplified form. We integrated this during the whole stress and strain history in each finite element along the crack path, and we studied the influence of the mechanical and numerical parameters playing a role in this methodology. We describe herein the evolution, which results from this criterion, of some parameters used in the literature as initiation and crack growth criteria.

Nonlinear Stress-Strain Response of Laminated Composites

Abstract: This paper presents a simplified method of predicting the nonlinear stress-strain curves upt to the tensile and compressive failures for an unidi rectionally orthotropic lamina, symmetric biaxial and triaxial laminates. The analytical procedure is based on the classical Laminated Plate Theory (L.P.T.). With applying L.P.T. to the small sress or strain increments of the stress-strain curve, nonlinear stress-strain curve is continuously predicted for various laminates. Comparisons are made between analytical predic tions and experimental results. As the results, the nonlinear stress-strain curves for various cases could be estimated and the results have consider ably good agreement with experimental ones.

Superposition of alloy hardening, strain hardening, and dynamic recovery

Abstract: The principles and heuristics of flow stress superposition are illustrated for the case that one of the components is due to dislocation/dislocation interactions and is the only one that changes with strain. A simultaneous investigation of the flow stress and its rate sensitivity as a function of strain then allows one to confirm or refute postulated superposition laws and, in addition, to separate the effects of alloying or heat treatment on yield stress and on strain hardening. The slope of the observed stress strain curve depends on the form of the superposition law even if there is no physical influence of alloying on the dislocation storage rate; the frequently observed low initial strain hardening associated with a higher yield stress may in some cases be merely a consequence of a nonlinear superposition. At higher strains, the influence of alloying on dynamic recovery becomes the predominant effect; it also controls the high-temperature creep strength. When dynamic recovery plays an important role, it provides a further straining mechanism which, however, is not additive to the low-temperature strain rate; a form of the superposition law for long-range slip and this dynamic recovery strain is proposed. An application of these principles has demonstrated thatmore » dynamic strain aging is due to an effect of mobile solute atoms on the strain-hardening component of the flow stress, not on the friction stress.« less

Cyclic deformation behavior of type 304 stainless steel at elevated temperature

Abstract: Samples of 304 stainless steel were subjected to a variety of deformation histories at 300 and 560°C. The deformation histories included both periods of constant stress amplitude cyclic loading and constant strain rate tensile deformation. It was found that changes in the plastic strain amplitude during cycling were not always correlated with changes in the tensile flow stress. This indicates that a mechanical equation of state based on the flow stress as the only state variable cannot adequately describe the mechanical behavior of 304 stainless steel at these temperatures. Transmission electron microscopy on deformed samples showed that an increase in the plastic strain amplitude during cycling at constant stress amplitude was correlated with the rearrangement of the dislocations into a tight cellular structure. This rearrangement was found to have no effect on the tensile deformation behavior of the material beyond a brief transient. It is suggested that another state variable, in addition to the flow stress, be introduced into the equation of state formulation to allow the description of the observed cyclic behavior. This additional state variable would be associated with the arrangement of the dislocations in the material.

Creep Damage under One-Dimensional Variable Tensile Stress.

Abstract: : A nonlinear damage relation, containing the axial strain history and a time integral over the stress history, is proposed for the case of one-dimensional time dependent tensile stress. Nonlinear steady and transient creep terms are included in the axial strain relation, and elastic and creep Poisson's ratios are introduced into the lateral strain relation. Using these relations, complete damage solutions are obtained for the constant stress rate, step stress, relaxation and constant load tests. Observations are made concerning the associated rupture times. (Author)

Effect of stress path on the behavior of concrete under triaxial stress states

Abstract: Previous investigations of the behavior of concrete under multiaxial loading configurations have identified levels of significant change in the behavior of the material under increasing stress and have established the envelopes which are formed by the variation of these levels in stress and strain space. Tests on a particular concrete using different stress paths in the triaxial stress domain indicate that these envelopes are path dependent. The effect of stress path on each of the envelopes has been quantified and the paths giving the most critical envelopes identified. /Author/

Stress-strain characteristics of concrete confined in steel spirals under repeated loading

Abstract: Repeated loadings tests have been conducted on 150 mm dia.×300 mm high concrete cylinders with circular steel spiral confining the concrete. Stress-strain curves obtained in the experiments are presented. Equations are proposed for the envelope, unloading and reloading curves of the stress-strain curves and compared with test results.

Complete stress-strain curve of concrete and nonlinear design

Abstract: Difficulties of experimentally obtaining the descending part of the stress-strain curve of concrete in uniaxial compression and methods of overcoming these difficulties are described. The influence of testing parameters on the stress-strain curves are presented. Based on the experimentally observed stress-strain relationship, an analytical model was developed to predict the moment-curvature relationships of reinforced concrete sections. These moment-curvature relationships are compared with some available experimental data obtained and with those obtained by two other analytical models.

Sample Disturbance and Stress-Strain Behavior

Abstract: Different effects of sample disturbance were simulated in a resonant column apparatus that clearly show the change in stress-strain behavior when the sample is subjected to swelling, reconsolidation, shear strain, or total stress changes. A new framework that applies the concept of “reference strain” is suggested for considering disturbance effects on stress-strain behavior, based on results of laboratory and field measurements. The normalized behavior of a soil can be determined with high accuracy in the laboratory. By also measuring the shear strength and initial tangent modulus in the field it is possible to accurately describe in situ stress-strain behavior.

Apparatus for determining the stress-strain properties of viscoelastic materials in the molten state

Abstract: Apparatus for determining the stress-strain characteristics of materials in the viscoelastic state, especially polymer melts, in which a bar-shaped test specimen arranged vertically in a thermostable bath is stretched by means of a tape attached to a motor-driven reel and the tensile forces are continuously measured by a load cell arranged below the specimen and within the bath.