Showing papers on "Stress–strain curve published in 1986"

Tensile Tests and Failure Analysis of Concrete

Abstract: The tensile strength of concrete is receiving an increasing amount of attention since the loading capacity and durability of structures are being studied more thoroughly, and since nonlinear fracture mechanics and numerical methods require a complete stress deformation relation. The theoretical background of the application of the tensile strength of concrete in fracture analysis is given. Test results are presented that were obtained from deformation‐controlled uniaxial tensile tests under static and cyclic loading of lightweight and normalweight concrete. The results have been used to establish material models for finite element calculations. Numerical examples show the usefulness of these models for static and cyclic loading conditions.

Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction

Abstract: Recent field and laboratory studies have shown that, even at very small strains, many soils exhibit non-linear stress–strain behaviour. Nevertheless, because of its convenience, linear elasticity will continue to play an important role in the analysis of such problems as settlement, deformation and soil–structure interaction. In this Paper the measured non-liqear stress–strain properties of a low plasticity clay are used in the finite element analysis of footings, piles, excavations and pressuremeter tests to assess the influence of small strain non-linearity in comparison with linear elastic behaviour. In all cases non-linear behaviour results in the concentration of strain and deformation towards the loading boundaries. This is shown to have important consequences for soil–structure interaction problems such as settlement profiles, pile group interaction and contact stress distributions. Small strain non-linearity also has a significant influence on the interpretation in terms of equivalent elastic modu...

Mechanics of engineering materials

Abstract: Preface to second edition. Preface to first edition. Notation. 1. Statically Determinate Force Systems. 2. Statically Determinate Stress Systems. 3. Stress-Strain Relations. 4. Statically Indeterminate Stress Systems. 5. Torsion. 6. Bending Stress. 7. Bending: Slope and Deflection. 8. Statically Indeterminate Beams. 9. Energy Methods. 10. Buckling Instability. 11. Stress and Strain Transformations. 12. Yield Criteria and Stress Concentration. 13. Variation of Stress and Strain. 14. Application of the Equilibrium and Strain-Displacement. 15. Elementary Plasticity. 16. Thin Plates and Shells. 17. Finite Element Method. 18. Tension, Compression, Torsion and Hardness. 19. Fracture Mechanics. 20. Fatigue. 21. Creep and Viscoelasticity.

Concrete structures: Stresses and deformations

Abstract: Preface to the third edition Acknowledgements Note The SI system of units and British equivalents Notation 1 Creep and shrinkage of concrete and relaxation of steel 11 Introduction 12 Creep of Concrete 13 Shrinkage of Concrete 14 Relaxation of prestressed steel 15 Reduced relaxation 16 Creep superposition 11 The aging coefficient ?: definition 18 Equation for the aging coefficient ? 19 Relaxation of concrete 110 Step-by Step calculation of the relaxation function for concrete 111 Age-adjusted elasticity modulus 112 General 2 Stress and strain of uncracked sections 21 Introduction 22 Sign convention 23 Strain, stress and curvature in composite and homogeneous cross-sections 24 Strain and stress due to non-linear temperature variation 25 Time-dependent stress and strain in a composite section 26 Summary of analysis of time-dependent strain and stress 27 Examples worked out in British units 28 General 3 Special cases of uncracked sections and calculation of displacements 31 Introduction 32 Prestress loss in a section with one layer of reinforcement 33 Effects of presence of non-prestressed steel 34 Reinforced concrete section without prestress: effects of creep and shrinkage 35 Approximate equations for axial strain and curvature due to creep 36 Graphs for rectangular sections 37 Multi-stage prestressing 38 Calculation of displacements 39 Example worked out in British units 310 General 4 Time-dependent internal forces in uncracked structures: analysis by the force method 41 Introduction 42 The force method 43 Analysis of time-dependent changes of internal forces by the force method 44 Movement of supports of continuous structures 45 Accounting for the reinforcement 46 Step-by-step analysis by the force method 47 Example worked out in British units 48 General 5 Time-dependent internal forces in uncracked structures: analysis by the displacement method 51 Introduction 52 The displacement method 53 Time-dependent changes in fixed-end forces in a homogeneous member 54 Analysis of time-dependent changes in internal forces in continuous structures 55 Continuous composite structures 56 Time-dependent changes in the fixed-end forces in a composite member 57 Artificial restraining forces 58 Step-by-step analysis by the displacement method 59 General 6 Analysis of time-dependent internal forces with conventional computer programs 61 Introduction 62 Assumptions and limitations 63 Problem statement 64 Computer programs 65 Two computer runs 66 Equivalent temperature parameters 67 Multi-stage loading 68 Examples 69 General 7 Stress and strain of cracked sections 71 Introduction 72 Basic assumptions 73 Sign convention 74 Instantaneous stress and strain 75 Effects of creep and shrinkage on a reinforced concrete section without prestress 76 Partial prestressed sections 77 Flow chart 78 Example worked out in British units 79 General8 Displacements of cracked members 81 Introduction 82 Basic assumptions 83 Strain due to axial tension 84 Curvature due to bending 85 Curvature due to a bending moment combined with an axial force 86 Summary and idealized model for calculation of deformations of cracked members subjected to N and/or M 87 Time-dependent deformations of cracked members 88 Shear deformations 89 Angle of twist due to torsion 810 Examples worked out in British units 811 General 9 Simplified prediction of deflections 91 Introduction 92 Curvature coefficients, k 93 Deflection prediction by interpolation between uncracked and cracked states 94 Interpolation procedure: the 'bilinear method' 95 Effective moment of inertia 96 Simplified procedure for calculation of curvature at a section subjected to M and N 97 Deflections by bilinear method: members subjected to M and N 98 Estimation of probable defection: method of 'global coefficients' 99 Deflection of two-way s

A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—II. Study of classical plasticity for ideal-plastic phases

Abstract: The response of phase-transforming steels to variations of the applied stress (i.e. the ∑-term of the classical plastic strain rate Ė cp defined in Part I) is studied both theoretically and numerically for ideal-plastic individual phases. It is found theoretically that though the stress-strain curve contains no elastic portion, it is nevertheless initially tangent to the elastic line with slope equal to Young's modulus. Moreover an explicit formula for the beginning of the curve is derived for medium or high proportions of the harder phase, and a simple upper bound is given for the ultimate stress (maximum Von Mises stress). The finite element simulation confirms and completes these results, especially concerning the ultimate stress whose discrepancy with the theoretical upper bound is found to be maximum for low proportions of the harder phase. Based on these results, a complete model is proposed for the ∑-term of the classical plastic strain rate Ė cp in the case of ideal-plastic phases.

A rationalization of stress-strain behavior of two-ductile phase alloys

Abstract: An extensive literature review indicated that the law of mixture rule can at times account for stress-strain behavior of two-ductile phase alloys in terms of the stress-strain behavior of component phases. In the present investigation, various factors which can contribute to the stress-strain behavior of two-ductile phase alloys are considered, using Ti-Mn alloys as the model system. Particular attention is focused on the effect of elastic, elasto-plastic, and plastic interactions between the phases on the stress-strain behavior. It is shown that the law of mixture cannot adequately explain the stress-strain behavior. The following equation is proposed to describe the stress-strain behavior of two-ductile phase alloys: Pα-β = fαPαc+ fβPβc+ Iα-βp, where Pα-β is a given stress-strain property, fα and f/gb are respective volume fractions of α and β-phases, Pαc and Pβc are corrected properties of α and β-phases, and Iα-βp is the interaction term. It is found that for α- β Ti-Mn alloys, for 0.2 pct yield strength, Iα-βp is positive, negative, or zero depending on the microstructure; but Iα-βp is always positive for the ultimate tensile strength and strain hardening rates and its magnitude depended on the microstructure. The reasons for the nature or sign of the interaction parameter for a given property are discussed in detail.

Confined Compression Tests of Cement Paste and Concrete up to 300 ksi

Abstract: Tests of cylindrical specimens of O. 75 in. diameter up to 300.000 psi axial compression stress have been conducted for hardened portland cement paste as well as concrete with !Is in. aggregate. The specimens tightly fit into a cylindrical cavity in a pressure vessel and are loaded axially by a hard piston. The pressure vessel is very stiff, forcing the lateral expansion of specimens to be so small that the strain is almost uniaxial. Sophisticated analysis is used to evaluate material proper­ ties from measurements of force and displacement on the loading piston outside the test cavity. The results indicate [hat an initial de­ crease of the tangent modulus is followed by a continuous increase reaching values that exceed the initial modulus. This stiffening is at­ tributed to pore closure; however. not all pores can yet be closed at the peak pressure. Unloading and reloading reveals relatively low hysteresis at these high pressures. Reloading beyond the previous maximum strain returns the response to the virgin diagram. Creep is found to exist at these high press ures. with a similar value of creep coefficient as that applicable for the service stress range. The results are presented in the form of diagrams as well as smoothing formulas. The tests reproduce well and the scatter is small.

Response of Quasi-Isotropic Carbon/Epoxy Laminates to Biaxial Stress

Abstract: The results of biaxial tension tests on AS4/3501-6 carbon/epoxy are presented for a quasi-isotropic [90, ±45,0]s laminate. These tests were performed using a tubular spec imen subjected to internal pressure and axial tension. The specimen design appears to minimize stress concentrations in the gage section. The measured stress-strain response shows a small but definite reduction in stiffness associated with progressive matrix failure. The failure stresses and strains are consistent with a maximum fiber strain failure criterion, and are most accurately modeled with a progressive failure model that incor porates ply stiffness changes.

Plastic anisotropy and texture development in calcite polycrystals

Abstract: In the past, most information on the plasticity of rocks has been derived from axisymmetric compression experiments. These data are the basis for Arrhenius-type flow laws which relate stress and strain, treating them essentially as scalars and not accounting for the deformation history. This assumption is valid for a very limited range of mechanisms, for example, superplastic flow, dislocation climb, and some mechanisms of recrystallization. Wherever dislocation glide is involved in the deformation process, preferred orientation develops which depends on the strain mode. The development of texture has a profound influence on the stress-strain curve: (1) a geometric factor due to crystal orientation and expressed by the Taylor factor, (2) strain hardening due to interaction of dislocations in active slip systems, and (3) latent hardening because of microstructural difficulties in activating inactive slip systems at expected critical shear stresses. We have analyzed the influence of geometric factors on the plasticity of calcite polycrystals using the full constraint Taylor theory and observed that effects of strain mode are even stronger than in metals where the anisotropy of plastic flow was first documented. For example, at low temperature in axial deformation the specimen hardens rabidly, whereas in plane strain it softens during straining. The differences can be attributed to activation of different slip systems (number and relative importance) in each case, particularly the role of mechanical twinning. Wherever dislocation glide is significant, anisotropic flow laws should be considered, also in geological materials, to explain deformation. Particularly emphasized is the importance of deformation experiments in geometries different from axisymmetric compression.

Stresses and Deformations in Composite Tubes Due to a Circumferential Temperature Gradient

Abstract: A linear elasticity solution for determining the response of composite tubes subjected to a circumferential temperature gradient is presented. Numerical examples are used to show that, in a single layer tube, fiber orientation strongly influences response. When the fibers are aligned axially, all stress components in the tube are small. When the fibers are aligned circumferentially, the hoop stress becomes large. This difference in behavior is due to the large difference between the radial and circumferential coefficients of thermal expansion when the fibers are oriented circumferentially. In multilayer tubes, stresses are quite high and just two constants characterize the overall bending and axial deformations of the tubes.

Determination of various deformation processes in impact-modified PMMA at strain rates up to 105%/min

Abstract: The deformation processes in impact-modified PMMA, which deforms homogeneously, were determined by means of the stress/strain experiment (α, ɛ) with simultaneous lateral strain measurement (elat) in a wide range of strain rates (ɛ) up to 105%/min (impact stress). The elastic, plastic cavitation and plastic shear processes were determined as a function of strain. Therefore we calculated the elastic strain (ɛel), the elastic volume expansion (ɛvol el), the cavitation strain (ɛcav), which is identical with the plastic volume expansion (ɛvol pl), the shear strain (ɛsh) and the energy densities (Wel, Wcav, Wsh) related to these three processes.

The biaxial deformation and yield behavior of bisphenol‐a polycarbonate: Effect of anisotropy

Abstract: The biaxial tension stress-strain-yield behavior of glassy bisphenol A-polycarbonate has been investigated at constant octahedral shear stress rate and at 25°C and −40°C. The specimens possess a small amount of anisotropy. Hill′s criterion for yielding of anisotropic materials is modified to take into account the sensitivity of the yield locus to the hydrostatic stress component. This modified yield criterion fits the 25°C data quite well. However, the data at −40°C cannot be fitted using reasonable parameters.

Bending effects on flow localization in metallic sheets

Abstract: In the present work the dependence of critical strain on thickness in finitely stretched metallic sheets is investigated. A finite strain axisymmetric shell theory is developed for the modelling of the punch stretching of a thick circular plate and a consistent onset of localization criterion for the shell is proposed. Experimental results as well as numerical calcutions, in the case of mild steel plates deforming under the action of a frictionless hemispherical punch, show that if the onset of strain localization is used as the failure criterion, the material’s thickness has very little influence for plate thicknesses usually used in sheet forming. The opposite held viewpoint in the literature that the sheet thickness significantly affects the critical strain is due to the experimental use of the fracture strain as the failure strain.

A cyclic multiaxial model for concrete

Abstract: A rate-independent plasticity constitutive model is proposed, for the stress-strain and strength behavior of plain concrete, under complex multiaxial stress-paths, including stress reversals. The only material parameters required by the model are the uniaxial cylinder strength f cand the strain at the peak of the monotonic stress-strain curve, e0 . The model is based on a bounding surface in stress space, which is the outermost surface that can be reached by the stress point. When the size of the bounding surface decreases with increasing maximum compressive principal strain emax on the material, strength degradation during cyclic loading as well as the falling “post-failure” branch of the stress-strain curves, can be modeled. The distance from the current stress point to the bounding surface, determines the values of the main parameters of the inelastic stress-strain relations, i.e. of the plastic shear modulus H P, and the shear-compaction/dilatancy factor β Strains are almost completely inelastic from the beginning of deformation. The inelastic portion of the incremental strain is computed by superposition of 1) the deviatoric strain increment, which occurs in the direction of the deviatoric stress and is proportional to the octahedral shear stress increment and inversely proportional to the plastic shear modulus 2) the volumetric strain increment, which consists of a portion which is proportional to the hydrostatic stress increment, and another which equals the product of the octahedral shear strain increment and the shear compaction/dilatancy factor β Stress reversals are defined separately for the hydrostatic and the deviatoric component of the stress tensor, and the parameters of the inelastic stress-strain relations are given as different functions of the stress and strain history, for virgin loading, unloading, reloading, or for the “post-failure” falling branch. The incremental stress-strain law is set in the form of incremental compliance and rigidity matrices, and implemented into a nonlinear dynamic finite element code.

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

Abstract: The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.

Determination of geotextile stress strain characteristics using a wide strip test

Abstract: The effect of specimen dimensions and strain rate upon the measured stress strain characteristics of geotextiles is investigated. In particular, it is shown that the geotextile modulus may be quite sensitive to the specimen dimensions and strain rate when testing high modulus fabric to be used as reinforcement. Based on these results it is suggested that a 500 mm wide by 100 mm gauge length specimen should be used for determining design properties for reinforcing fabrics at a strain rate not exceeding 2 per cent/ min (a).

Prediction of the creep behaviour of polyethylene and molybdenum from stress relaxation experiments

Abstract: In many applications it is useful to be able to convert observed creep data of a material to corresponding stress relaxation data or vice versa. If the material exhibits non-linear viscoelasticity such a conversion can be rather difficult. In this paper two semi-empirical flow equations, the power law and the exponential law, are used to convert stress relaxation data into corresponding creep behaviour data. These two flow equations are often used to describe non-linear viscoelastic behaviour. The procedure adopted here is based on the assumption that the creep data during the experiment decrease due to an increase in the internal stress level, thus decreasing the effective stress for flow. The conversion method is applied to high density polyethylene and polycrystalline molybdenum at room temperature. In general predictions using the power law are in better agreement with the experimental results than predictions using the exponential formula. The concepts of secondary and ceasing creep are discussed in terms of build-up of internal stress during the creep process.

The Stress and Strain-Rate Dependence of Spall Strength in Two Aluminum Alloys

Abstract: The spallation behavior of 6061-T6 and AMg-6 aluminum alloys was studied as a function of loading stress and initial pulse duration for stress amplitudes ranging from 5–20 GPa and for pulse durations spanning the range of 0.06–0.9 μs. These experiments show that the spallation strength varies from about 0.7–1.4 GPa for strain rates varying from 0.15–1 μs−1 and for impact stresses from 5–20 GPa.