Showing papers on "Stress–strain curve published in 1968"

Singular behaviour at the end of a tensile crack in a hardening material

Abstract: D istributions of stress occurring at the tip of a crack in a tension field are presented for both plane stress and plane strain. A total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used. For applied stress sufficiently low such that the plastic zone is very small relative to the crack length, the dominant singularity can be completely determined with the aid of a path-independent line integral recently given by rice (1967). The amplitude of the tensile stress singularity ahead of the crack is found to be larger in plane strain than in plane stress.

On the generalized stress-strain behavior of wet clay

Abstract: THE BASIC CAMBRIDGE THEORY OF THE STRESS-STRAIN BEHAVIOUR OF WET CLAYS, AS DEVELOPED FOR 'TRIAXIAL' (AXI-SYMMETRIC) COMPRESSION TEST CONDITIONS, IS EXTENDED TO INCLUDE GENERALIZED THREE-DIMENSIONAL STRESS AND STRAIN CONDITIONS. THE THEORY IS DEVELOPED IN THE LIGHT OF A NEW WORK EQUATION PROPOSED BY BURLAND. TWO OTHER NEW CONCEPTS ARE INTRODUCED. FIRST, A NEW YIELD LOCUS TO TAKE ACCOUNT OF THE SHEAR DISTORTION THAT OCCURS, WITHOUT PLASTIC VOLUME CHANGE, FOR STATE PATHS BENEATH THE STATE BOUNDARY SURFACE. SECONDLY, THE MOHR-COULOMB CRITERION IS INCORPORATED IN THE THEORY TO PREDICT RUPTURE WHEN WET CLAYS ARE SUBJECTED TO STRESS PATHS IN THREE-DIMENSIONAL STRESS SPACE. THE MECHANICAL BEHAVIOUR OF A GIVEN WET CLAY UNDER SUCH A GENERAL SYSTEM IS PREDICTED FROM THE THREE SOIL CONSTANTS, M, LAMBDA AND KAPPA OBTAINED FROM TRIAXIAL COMPRESSION TESTS. AFTER SHOWING THAT TRIAXIAL EXTENSION TEST RESULTS CAN BE SATISFACTORILY PREDICTED FROM TRIAXIAL COMPRESSION DATA, PARTICULAR ATTENTION IS PAID TO PLANE STRAIN WHICH IS SO FREQUENTLY RELEVANT IN PRACTICAL PROBLEMS. THE PLANE-STRAIN BEHAVIOUR AS PREDICTED FROM TRIAXIAL DATA IS COMPARED WITH OBSERVATIONS IN A PLANE-STRAIN APPARATUS, AND A SIMPLE-SHEAR APPARATUS. EXCELLENT AGREEMENT IS OBTAINED, AND CONFIRMS THE PREDICTION THAT FOR WET CLAYS THE ANGLE OF INTERNAL FRICTION IN DIRECT SHEAR TESTS IS LESS THAN THE TRIAXIAL VALUE. TO ILLUSTRATE THE POWER AND PRACTICAL SIGNIFICANCE OF THE THEORY, IT IS USED TO PREDICT THE STRAINS THAT ARE REQUIRED TO DEVELOP THE ACTIVE AND PASSIVE RANKINE STATES IN A MASS OF WET CLAY. THESE PREDICITIONS ARE IN AGREEMENT WITH EXPERIENCE. /RRL/A/

Plastic stress and strain fields at a crack tip

Abstract: Further details of the stress and strain fields associated with the dominant singularity governing the plastic behaviour at a crack tip are presented for conditions of plane stress and plane strain for cracks in both far tensile and far shear fields. Results are obtained for a power hardening material. Limiting cases for non-hardening materials are shown to correspond to certain perfect plasticity solutions.

The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics

Abstract: A new model is proposed to describe the large recoverable extensions which can be observed with high polymers below their glass transition points. The model consists of a Hookean spring in series with an Eyring dashpot and rubber elasticity spring in parallel. Conventional stress-strain curves for cellulose nitrate and cellulose acetate sheet and PVC are compared with those predicted by the model. In this way many of the characteristic features of the stress-strain curves of plastics can be illustrated. Differences between the stress-strain curves of a number of polymers are discussed in terms of the model, and the tendency of a polymer to show necking is related to the ultimate network strain (limiting elongation) under the conditions of the test.

General stress-strain-time function for soils

Abstract: The stress-strain-time behavior of soils may assume a variety of form depending on such factors as soil type, soil structure, stress history, drainage conditions, and type of loading. Generalizations concerning creep in soils suggested by various investigators are sometimes contradictory. However, test results show that there exist linear relationships between logarithm of strain rate and logarithm of time for a given stress and between logarithm of strain rate and stress at any given time, provided the creep stress level is between the practical limits of about 30% to 90% of the initial soil strength. These findings lead to a simple three-parameter general stress-strain-rate-time relationship. Integration of this relationship yields creep curves which are observed to agree in form with the experimental results.

Local heating by plastic deformation at a crack tip.

Abstract: : This paper presents calculations of the temperature elevations accompanying rapid plastic deformation near a crack tip. Solutions for the stress and strain distribution in non-hardening materials are employed as a basis for the heating rate distribution. Results are approximate in that temperature independent mechanical and thermal properties are assumed and thermal stressing is neglected. Two cases are considered: a stationary crack under increasing load, and a running crack with locally constant speed and plastic zone size. Numerical results are presented as based on properties of 2024 aluminum alloy, 6Al-4V titanium alloy, and mild steel. Temperature rises predicted for test conditions on these metals seldom exceed 100C. This may, nevertheless, be large enough to influence fracture and to account for the observed rise in roughness at very fast rates. Consequences are examined for the assumption that the localized tip temperature elevation alone governs fracture toughness at very fast rates. (Author)

A comparative study of numerical methods of elastic-plastic analysis.

Abstract: WO general methods have been developed for the elasticplastic analysis of continuous solid bodies. The method of "thermal" or "initial strains"1 is based on the idea of modifying the elastic equations of equilibrium to compensate for the fact that the plastic strains do not cause any change in stress. On the other hand, the tangent modulus method2 is based on the linearity of the incremental laws of plasticity. The load is applied in increments, and at each stage, a new set of coefficients are obtained for the equilibrium equations. Both methods have been used in conjunction with finite element theory. The matrix equations for finite element analysis using the method of initial strains were developed in Refs. 3-5, whereas the equations for the tangent modulus method were developed in Refs. 6-8. Since both methods solve the same problem, there should be a close relation between them, and perhaps a comparison could lead to a better understanding of the original problem. This note addresses itself to such a comparison. II. Elastic-Plastic Stress-Strain Relations The linear relation between the increments of stress and strain developed in Marcal and King8 is taken here as the point of departure. With the definition of the elastic components of the strain increments,

Internal microcracking, mortar-aggregate bond and the stress-strain curve of concrete

Abstract: INTERNAL CRACKING OF CONCRETE IS OBSERVED DIRECTLY WITH A MICROSCOPE AND WITH A NEWLY DEVELOPED X-RAY TECHNIQUE. CRACKS ARE OBSERVED BOTH AT THE INTERFACE BETWEEN COARSE AGGREGATE AND MORTAR, AND DIRECTLY THROUGH THE MORTAR. TO INVESTIGATE THE SIGNIFICANE OF THESE TWO TYPES OF CRACK, AND OF THE PRESENCE OF INTERFACIAL CRACKS BEFORE ANY LOADING, TENSILE AND SHEAR BOND STRENGTHS OF THE MORTAR-AGGREGATE INTERFACES ARE MEASURED AND COMPARED WITH STRENGTHS FOR MORTAR AND PASTE ALONE. THEORETICAL MODELS RELATING BOND STRENGTHS TO MICROCRACKING WERE DEVELOPED AND TESTED BRIEFLY. STRESSES FROM VOLUME CHANGES ON SETTING AND HARDENING ARE CONSIDERED. BOND BETWEEN PASTE OR MORTAR AND AGGREGATE IS FOUND TO BE MUCH WEAKER THAN ANY OF THE CONSTITUENTS ALONE. CONCRETE SPECIMENS ARE UNIAXIALLY LOADED, BOTH CONCENTRICALLY AND ECCENTRICALLY, IN COMPRESSION TO VARIOUS STRAINS UP TO FAILURE. INTERNAL MICROCRACKING, DISTINGUISHED AS TO BOND OR MORTAR CRACKING, IS RELATED TO AMOUNT OF STRAIN, AND A PHYSICAL, SEMI-QUANTITATIVE PICTURE OF THE PROGRESS OF CRACKING UP TO FAILURE IS DEVELOPED. THE STRAIN GRADIENT IN ECCENTRICALLY LOADED SPECIMENS SEEMS TO RETARD NOTICEABLY THE AMOUNT OF CRACKING TRHOUGH MORTAR. PROGRESSIVE DEVELOPMENT OF MICROCRACKING IS APPARENTLY DIRECTLY RELATED TO THE SHAPE OF THE STRESS-STRAIN CURVE IN SHORT-TERM COMPRESSION. THE HETEROGENEITY INDUCED BY AGGREGATES SEEMS TO BE RESPONSIBLE FOR BOND CRACKING AND THEREFORE FOR MOST OF THE SHORT-TERM INELASTIC BEHAVIOR OF CONCRETE. /A/RRL/

26—structural and non-structural effects in the observed stress-strain curve for wet wool fibres

Abstract: This paper describes a detailed theoretical and experimental investigation into the relationship between wool-fibre non-uniformities and stress-strain behaviour. The shape of the stress-strain curve in the yield region is closely related to the fibre cumulative cross-sectional-area distribution. The fibre-material yield slope is found to be nearly zero, and the changes from Hookean to yield region and from yield to post-yield region for the material are quite sharp. The observed relative yield slope (relative to the stress at 15% extension) and the coefficient of variation of area interact in the manner predicted except that there are quantitative differences between the experimentally and theoretically derived relationships; these deviations are interpreted as structural effects due to fluctuations in the stress at 15% extension along the fibres, a variation that is relatively independent of the changes in cross-sectional area along the fibres. The mean effective coefficient of variation of area due to t...

The Stress-Strain Behavior of Concentric Composite Cylinders:

Abstract: An analytical model was developed for the elastic-ideally plastic behavior of concentric cylindrical composites under uniaxial tension. The model predicted the creation of transverse stresses in the composite during axial loading. The existence of these stresses was experimentally verified in a 4140 steel core-18% Ni maraging steel case composite system by examining the effects of the trans verse stresses on the composite axial stress-strain curve and the composite tangential surface strain ratio curve.

The effect of strain rate on the stress–strain curve of oriented polymers. I. Presentation of experimental results

Abstract: The stress-strain curves of viscose, nylon 66, poly(ethylene terephthalate), polyacrylonitrile, and polypropylene have been determined at a large number of different strain rates between 10−4 and 330 sec−1 The shape of these stress-strain curves and its change with strain rate is shown to depend upon whether the material is tested above or below its glass temperature The stress-strain curves of materials tested below their glass temperature consists of an initial straight portion followed by a yield point at a few per cent strain The breaking strain is only slightly affected by strain rate, and the energy to rupture increases with increasing rate For materials tested above their glass temperature the initial portion of the stress-strain curves in nonlinear, and the yield strain is much higher than for the other materials There is a small range of strain rate, in which the breaking strain falls sharply to the yield strain with increasing rate, and the energy to rupture also decreases Outside this range the energy to rupture increases with increasing rate

The effect of strain rate on the stress–strain curve of oriented polymers. II. The influence of heat developed during extension

Abstract: The temperature changes which take place in a yarn during extension are considered. From thermodynamical considerations and the heat-transfer coefficient it is shown that extension of the yarns studied will take place isothermally at strain rates below 0.04 sec.−1 and adiabatically at rates above 4 sec.−1 It is not possible to make an accurate estimate of the magnitude of the temperature rise during adiabatic extension, because of the lack of information on internal energy changes during irreversible extension, but by assuming these to be zero it is estimated that the temperature is likely to rise by 20–30°C. at strains above 10%. Results from a study of the effect of strain rate on the stress-strain curves of five different yarns show in all these materials a range of strain rate in which the stress that produces a given strain increases less rapidly with strain rate than elsewhere. For viscose and poly(ethylene terephthalate) this effect occurs in the expected range of strain rate, and its magnitude is of the correct order for it to be attributed to the temperature rise resulting from the transition from isothermal to adiabatic extension. For the other materials the transition does not seem likely to provide a complete explanation of this effect. There is no evidence that the transition significantly affects the breaking properties.

Plastic stress and strain concentration factors in a strip with a hole or notches under tension

Abstract: Spread of plastic region and influence of severity of constraint are observed and concentration factors are evaluated by photoplasticity of celluloid. Suitability of photoplasticity for solution of practical problems is discussed.

Deformation mechanisms in hot working

Abstract: 1. During deformation at a constant temperature above 0.5Tm, there is a steady-state regime where both stress and strain rate remain constant independent of strain. 2. The interdependence of stress, strain rate and temperature during steady-state hot working and secondary creep are similar. 3. During the hardening stage, simultaneous dynamic recovery causes the dislocations to arrange into sub-boundaries. 4. During the steady state, the balance between hardening and recovery maintains the dislocation density constant as subgrains of constant size and misorientation. 5. The subgrains remain equiaxed, indicating that the sub-boundaries continuously break up and reform. It is proposed that this process inhibits recrystallization during high strain-rate deformation. 6. The size of the subgrains and the neatness of their boundaries increase as the temperature increases and the strain rate decreases.

Effects of molecular weight and strain rate on the flexural properties of polycarbonate

Abstract: The effects of changes in molecular weight (7000 to 22,000) and strain rate (0.0001 to 4 min.−1) on the flexural properties of polycarbonate have been examined in detail with the use of speciments of different molecular weight prepared by high-energy electron irradiation. The results have been plotted as surfaces which show the dependence of both stress and strain on molecular weight and strain rate, and these surfaces have been described in terms of brittle, transitional, and ductile regions. The relationships between stress or strain and molecular weight in the brittle region have been shown to be hyperbolic. A single failure locus has been found to include all the corresponding stress and strain data obtained at the various molecular weights and strain rates. In the low strength region this locus exhibits a proportionality between stress and strain, while at high strength values, strain becomes a logarithmic function of stress. Stress–molecular weight data obtained at the various rates have been superimposed to form a single composite curve, and the corresponding crossplots of stress–log rate have been treated similarly. It is concluded from these superpositions that an equivalence exists between changes in both molecular weight and strain rate such that a tenfold change in strain rate corresponds approximately to a change of 1000 in molecular weight. Strain-strain rate data obtained at the various molecular weights have also been superimposed in a similar manner. Modulus is shown to increase slowly with decrease in molecular weight and appears to be relatively insensitive to changes in strain rate.

Numerical Solutions of Two-Dimensional Elastic, Plastic Problems by Conformal Mapping and Finite-Difference Method : 3rd Report, Elasto-Plastic Torsion of Circumferentially Grooved Shafts

Abstract: In this report, the problem of elasto-plastic torsion of circumferentially grooved shafts is solved by the same numerical method as presented in the 1st report. The solutions based on both flow and deformation type theories are obtained for the Ramberg-Osgood material. The numerical calculations are carried out for several characteristic parameters of material, then the stress and strain concentration factors, stress distributions, the angle of twist, etc. are presented. The results calculated by the flow theory are experimentally verified, and comparing them with the deformation theory, it is proved that both results coincide fairly well with each other about the angle of twist, but about other quantities, for example, the stress and strain concentration factors, the difference between both results becomes larger as torque increases.

Proof stress indicator

Abstract: A proof stress indicator for use with a stress/strain testing apparatus in which there is produced during the testing of a specimen two electrical signals which are respective analogues of the increases in the stress and strain of the specimen above the particular values thereof obtained at a selected earlier stage of the testing and being operable for providing a response when the strain electrical signal has increased above the stress electrical signal by an amount which is an analogue of a preselected proof stress percentage.

Stress-strain behavior of cold-welded copper-copper microjunctions in vacuum as determined from electrical resistance measurements

Abstract: True stress-strain curves, developed from contact-resistance measurements be­ tween two OFHC copper specimens loaded and unloaded in vacuum, showed that the coldwelded junctions exhibited an amount of ductility generally characteristic of the specimen material. Junction ductility was greater when the experiment was kept vibration free. Deliberate vibration introduced during the loading cycle lowered the junction ductility. The contact-resistance-against-load data also seemed to indicate that impulsive forces could increase the a rea of contact under fixed load to a point where the contact a rea might revert to an elastic condition.

A comparison of stress-strain behavior in cutting and high strain-rate compression tests

Abstract: Stress-strain relations derived from orthogonal cutting of 1100-0 aluminum and of annealed electrolytic tough pitch copper are compared on an effective stress–effective strain basis with compression test data obtained for these metals at comparable strain rates. To facilitate such a comparison, three series of compression tests were made at strain rates of 10−3/sec, 1/sec and 103/sec. The high strain rate tests were carried to large strains by a repeated application of Kolsky's impact technique. The strain rates in metal cutting were estimated by associating with the zone of chip formation the zone of micro-hardness variation. The results for both aluminum and copper indicate that the effective flow stress derived from the cutting data is about 10% lower than the effective flow stress at the corresponding strain and strain rate derived from the compression data. Possible reasons for this discrepancy are discussed.

Strength and stress-strain properties of rapidly heated laminated ablative materials

Abstract: : It is shown that the mechanical properties of rocket nozzle liners and reentry vehicle ablation materials can be determined by tests in which a high temperature plasma arc is used as a heat source. The arc flow is used to heat slender specimens, and a pneumatically actuated loading frame is used to apply stress. This method of testing provides heating and loading in time periods typical of the rapid heating during rocket firing or reentry, on the order of 10 sec. Earlier investigations of similar ablative materials have used specimens heated and charred (degraded) slowly prior to the application of load. Strength and stress-strain properties in the warp direction were determined for carbon, graphite, and silica phenolic materials. The method appears promising for the determination of properties in various loading-laminate orientations and during thermal expansion, and for studies of heating and strain rate effects on strength at elevated temperatures.

The relationship between stress and deformation of polymers in the linear stress state

Abstract: The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).

The Theories of Fracture in Viscoelastic Bodies

Abstract: Two theories of fracture of viscoelastic materials are hereunder proposed, the one based on a simple model and the other generalized thereupon, and an attempt is made to explain the dependence of stress and strain at break on temperature and strain rate as particularly was called the failure envelope by T.L. Smith.The model of the first simple theory consists of two Maxwell elements (system 1 and 2) connected in parallel and the following criteria for fracture are introduced.(1) Fracture occurs first at the system 1, and then at the system 2 where the whole load is applied.(2) Fracture of the system 1 occurs either when the spring reaches the critical strain e11c (in the case of large strain rate) or the dashpot does so to e12c (in the case of small strain rate).For the deformation of constant rate R, the following results are obtained, which explain the experimental behaviors well at least qualitatively.at larger strain ratesat smaller strain rateswhere σ, e, G and τ follow the ordinary use and suffices 1 and 2 mean system 1 and 2 respectively and the suffix b does so "at break".Next the above model theory is so extended to the generalized Maxwell bodies as to read that the stress of deformation at constant rate is expressed by the equationIn this case the storage energy Wst and the dissipation energy Wdis of deformation are calculated after Landel, and the following criterion is introduced, that is, the sample breaks either when the elastic part with its own modulus G0 (the instantaneous modulus) reaches the critical strain e1c or the viscous part with its steady flow viscosity η0 reaches the critical strain e2c.The results are given asat larger strain ratesat smaller strain rateswhere G' and η' are dynamic modulus and viscosity respectively. Considering the dependence of G' and η' on shear rate and temperature, the failure envelope can be explained with these equations.