Showing papers on "Stress–strain curve published in 1973"

The effect of strain rate and heat developed during deformation on the stress-strain curve of plastics

Abstract: Polymethylmethacrylate, cellulose acetate butyrate, polypropylene and nylon 6–6 have been characterized in compression at various strain rates from 10−4 s−1 to 103 s−1 at room temperature. A medium strain-rate machine and a split-Hopkinson-bar apparatus are used in conducting the experiments. The temperature rise developed during deformation is also measured by using a thermocouple. All four materials tested definitely show a viscous effect at the beginning of the deformation and a plastic flow follows thereafter. Test results also indicate that the temperature rise developed during deformation cannot be neglected in determining the dynamic response of those materials investigated in this study.

Stress‐strain behavior of a granodiorite and two graywackes on compression to 20 kilobars

Abstract: The complete stress-strain equation of state for a granodiorite and two graywacke sandstones has been determined on loading to 20 kb axial stress at room temperature. Data under conditions of hydrostatic, uniaxial stress at various confining pressures and uniaxial strain loading are synthesized to define the behavior of these rocks. For the granodiorite it is observed that the onset of dilatancy as well as intersection of the failure envelope is independent of loading path. No dilatant behavior is observed on uniaxial strain loading to 12 kb axial stress. Both sandstones are observed to load below the hydrostat (increased compressibility) in either uniaxial stress or uniaxial strain loading. This enhanced compaction at relatively low pressures is believed to result from the influence of the additional shear stresses, which facilitate intergranular movements in these porous rocks. Dilatant behavior greatly diminishes at higher mean stresses where the rock undergoes a transition in failure mechanism from throughgoing narrow tensile and shear fractures (predominantly intergranular) to pervasive small-scale fracturing (predominantly intragranular). Dilatancy again becomes important at the highest stresses, where most of the initial porosity has been removed. The data on both rocks are used to delimit areas of characteristic behavior that are uniquely defined in stress space, independent of loading path.

Fracture in cold upset forging -a criterion and model

Abstract: Deformation behavior and fracture of three iron alloys during cold working conditions were studied systematically under a range of stress and strain states by means of the upset test. As described in a previous publication by the authors, an anomalous strain behavior and sub-surface void formation are observed prior to fracture at the bulge surface. This anomaly, in the form of a perturbation in the strain path, has features that are similar to the strain instability in biaxial stretching of sheet material. Based on these experimental observations, a mathematical model of localized necking and fracture is presented that permits evaluation of the effects of material characteristics and process parameters. A fracture criterion involving total strains at failure is also proposed. The criterion accurately fits experimental data obtained in this study as well as that presented by other investigators. Essential features of the fracture criterion can be derived from the mathematical model of instability and fracture.

Crazing, yielding, and fracture in polycarbonate and polyethylene terephthalate at low temperatures

Abstract: Tensile behavior over the temperature range 4.2 to 350°K is reported for amorphous polyethylene terephthalate and polycarbonate. Three regimes in tensile behavior are distinguished and the transitions between these regimes are correlated with molecular relaxation processes. The [dtilde]-process at about 50°K is associated with the onset of anelasticity in the stress strain behavior. Below the β-temperature, fracture stresses fall off markedly with decreasing temperature, suggesting that stress concentration effects are active. The effect of the [dtilde]-relaxation on tensile properties is more pronounced in polycarbonate than in polyethylene terephthalate and agrees with the relative relaxation peak intensities. Over the gamma relaxation region, 170 to 200°K, there occurs a broad drop in yield stress in polycarbonate. In polyethylene terephthalate a transition from brittle to yield behavior is observed. Crazing occurs in both polymers over two distinct temperature regimes, one over an approximate...

Strain hardening equation and the prediction of tensile strength of rolled polymers

Abstract: A number of thermoplastic polymers were tested in tension to investigate their strain hardening behavior. A strain hardening equation has been proposed in terms of the true stress, true strain and two constants σo and m. The three material constants, viz. σom and the true fracture strain, are shown to be adequate to describe completely the material's nonlinear viscoelastic or the so-called “plastic” behavior. The true stress-strain data for the polymers rolled to varying amounts of cold-work fits the strain hardening plot of the unrolled material. The same strain hardening equation, therefore, applies to rolled materials as well. The procedure for predicting the tensile strength of rolled materials is given.

In-Plane Shear Stress-Strain Response of Unidirectional Composite Materials

Abstract: The experimental determination of the in-plane or longitudinal shear stress-strain response of a unidirectional composite material usually presents a difficult task. Several test techniques have been proposed for determining this quantity: (1) Pure torque applied to a tubular specimen (Adams and Thomas [ 1 ] ), (2) Cross-sandwich beam test (Shockey and Waddoups [2] ), (3) Rail shear test (Whitney, Stansbarger, and Howell [ 3 ] ), and (4) ±45 balanced angle-ply laminate subjected to uniaxial tension (Petit [4] and Rosen [ 5 ] ).

Moisture Content Effect on Tensile Properties of Individual Douglas-Fir Latewood Tracheids

Abstract: A testing system was developed to determine tensile properties of single wood fibers under precisely controlled relative humidity conditions. Individual delignified Douglas-fir summer-wood tracheids were tested axially in tension at moisture contents of 0, 6, 12, 18% and in a water-soaked condition. Load-elongation curves were predominantly linear to failure and curve shape was unaffected by moisture content, implying that stresses in tracheids were borne primarily by a structural framework with a high degree of crystallinity. Moisture content significantly affected tracheid tensile properties. Tracheids tested wet exhibited the lowest strength and elasticity. The overall relationship between strength properties and moisture was curvilinear with maxima in tensile strength and modulus of elasticity at about 12 and 6% moisture content, respectively. Tensile strengths obtained were higher than published values for other cellulosic fibers. Maximum internal stresses on the cellulosic framework of tracheids were considered to approach those theoretically calculated for cellulose chain seission, suggesting highly crystalline microfibrils containing an extended-chain crystal lattice structure.

Mitral-valve mechanics—stress/strain characteristics of excised leaflets, analysis of its functional mechanics and its medical application

Abstract: The stress/strain characteristics of mitral-valve leaflets are determined. The leaflet elements exhibit the characteristic nonlinear stress/strain behaviour with a transition point; the posttransition-point modulus being orders of magnitude greater than the pretransition modulus. An element closer to the chordae tendineae has an initial modulus 4–5 times that of an element in the centre of the cusp; its transition point also occurs at a lower strain. These tests provide information on the strength characteristics of the mitral-valve leaflets.

Mechanics of Solids and Structures

Abstract: The first part of this book deals with fundamental principles of the theoretical analysis of stress and strain, and applies these principles to common engineering problems. The chapter headings of Part 1 are: (1) Statically determinate frames and beams; (2) Statically determinate stress systems; (3) Stress-strain relations; (4) Displacements in statically determinate structures; (5) Statically indeterminate stress systems; (6) bending: stresses; (7) Bending: slope and deflection; (8) Elastic strain energy; (9) Theory of torsion; (10) Statically indeterminate beams and frames; (11) Buckling instability; (12) Stress and strain transformation and relationships; (13) Analysis of variation of stress and strain; (14) Some applications of the equilibrium and strain-displacement relationships; (15) Theories of yielding; (16) Thin plates and shells; (17) Stress concentration; (18) Elementary plastic and viscoelastic analyses. Part 2 deals with mechanical properties and testing of materials, and consists of the following chapters: (19) Tension, compression and torsion; (20) Hardness and other tests; (21) Toughness and unstable fracture; (22) Fatigue; (23) Creep; (24) Non-metallic materials. Part 3 covers some of the most common methods used in experimental analysis of stress and strain, and is presented under the following chapter headings: (25) Resistance strain gauges; (26) Photoelasticity; (27) Other methods of strain measurement. /TRRL/

Electric contacts. II. Mechanics of closure for gold contacts

Abstract: We describe equipment and report results of a study of the mechanics of closure for gold electric contacts cleaned by sputtering and closed with precise control of mechanical and environmental variables. The ultrahigh‐vacuum system, in which measurements are performed, is isolated from building vibrations. Our measurements include contact resistance, load, cold welding, creep, anelastic strain recovery, stress strain, yield stress, and strain hardening. We calculated an activation energy of 1200 ± 100 cal/mole for low‐temperature creep in gold.

An experimental determination of the true uniaxial stress-strain behavior of brittle rock

Abstract: An Experimental Determination of the True Uniaxial Stress-Strain Behavior of Brittle Rock Results are presented of an experimental study of the behavior of six rock types deformed under uniaxial compression into their respective post-failure regions. Based on the observation that a rock sample in a post-failure state can be considered to be composed of broken and unbroken rock and assuming that the reduction in load-bearing capability of rock in the post-failure region is due to a reduction of the effective cross-sectional area of the specimen resulting from the growth of large cracks within the rock sample, we show that there is a maximum true stress that the unfractured solid rock can sustain without inelastic deformation. This stress is constant and is defined to be the true failure strength of the rock. The value of this stress is calculated by dividing the force on the rock sample at any point along the post-failure curve by the true load-bearing cross-sectional area of the rock sample at that point. Theoretical and experimental techniques are developed which allow an estimate of the true load-bearing area of the rock sample at any point along the post-failure curve of the sample. For the rock types used in the study, which were deformed to preselected positions along their respective post-failure curves and with the assumption that the fractured rock carried none of the applied load, the two techniques of measuring the effective load-bearing area give results which are equivalent.

Influence of deformation history on the yield locus and stress-strain behavior of aluminum and copper

Abstract: Thin-walled tubular specimens of 1100-0 aluminum and OFHC copper were loaded biaxially through the application of simultaneous axial load and internal pressure. The effects of loading path and deformation history on the stress-strain and yield locus characteristics were studied at strains less than 2.0 pct. The observed plastic strains for both materials depended on the loading path to a given stress point, whereas the loading path during prestraining did not affect subsequent deformation. Deformation subsequent to prestraining depended on the prestraining magnitude and direction at strains less than 0.2 pct and only on the magnitude at larger strains. The resulting plastic response was, therefore, anisotropic at small strains and isotropic at large strains. The small strain behavior cannot be predicted by present continuum plasticity theories, whereas the large strain behavior agrees with the isotropic hardening rule. It was also found that a prestraining operation of sufficient plastic strain can erase some of the prior deformation history.

A stress-strain relationship for concrete at high temperatures

Abstract: Synopsis This paper reviews some data on the effects of temperature (up to 7000°C) upon the relationship between stress and strain for concrete under compression. It is shown that the effects of temperature can be represented by an equation of the form σ/σmax = f(ϵ/ϵmax), where f is a functional form independent of temperature, and σmax and ϵmax are the values of stress and strain at the point of maximum stress, which vary with temperature. This scaling law is used to derive a relationship for the variation of the modulus of elasticity with temperature.

Deformation and Failure of Boron-Epoxy Plate with Circular Hole

Abstract: The behavior under uniaxial tension of a boron-epoxy composite plate with a circular hole was studied by means of experimental stress analysis and finite-element methods. The specimens were 10 by 26 in boron-epoxy panels of [0/′45/0/90] s layup. They were instrumented with strain gages, photoelastic coatings, and moire grids. The latter were analyzed using moire fringe multiplication techniques. Strain distributions as a function of applied nominal stress were obtained along the axes of symmetry and around the boundary of the hole. Young's modulus and Poisson's ratio were computed from the far-field strains. Tensile and compressive strain concentrations were computed for the linear range of strain response. Experimental results were compared with those obtained by homogeneous anisotropic elasticity and by finite-element analysis. The mode of failure was a combination of interlaminar shearing and tensile cracking starting at the hole boundary off the horizontal axis, at a point where the elastic shear stress and strain reach their maximum and where the tangential normal and shear strains increase rapidly and nonlinearly with load. The average applied stress at failure was 42 200 psi compared with a coupon strength of 94 000 psi. The average ultimate tensile strain at the hole boundary on the horizontal axis was 8 X 10 - 3 in./in. compared with a coupon ultimate strain of 6.8 X 10 - 3 in./in. At higher loads the peak of the tensile strain shifted, resulting in a higher ultimate strain away from the boundary.

Effects of misalignment on the pre-macroyield region of the uniaxial stress-strain curve

Abstract: Some bending usually occurs in uniaxial testing systems due to small unavoidable misalignment. The resulting elastic strain gradient can lead to significant differences between axial strain and extreme surface bending strains, especially at small strains. A three-point microstrain measurement around a cylindrical sample permits evaluation of the extreme strains and of the precision of alignment. A three-point, parallel-plate capacitance strain gage having a linear output with displacement was designed to evaluate bending of tensile samples in the microstrain range. The resolution of the gage was 3 parts in 10,000 at plate separations of 0.010 in. Varying misalignment resulted in extreme elastic bending strains at the sample surface of the order of tens to hundreds of micro-in. per in. larger than the axial strain. Analysis of the mechanics of bending in uniaxial loading demonstrated that: 1) the average applied stress divided by the average elastic strain always gives a unique number, Young's modulus, and 2) the average microplastic strain is not uniquely related to the average applied stress, but rather depends upon precision of alignment. The influence of bending on the determination of the average stress at which microplastic flow initiates is discussed, and a method for making meaningful comparisons of plastic microstrain data generated with significant misalignment is suggested.

Failure criteria developed from aasho road test data

Abstract: Theoretical models of pavement deformation behavior such as elastic-layered theory can only be used for design purposes when failure criteria are specified. Although such models can be used to predict stress and strain states, they in no way indicate whether the material in the pavement can withstand the predicted deformations. For elastic-layered theory, limiting values of strain or stress need to be defined before the theory can be used to assist practicing engineers in the design of asphalt pavements. There is general agreement in the literature that horizontal tensile stress or strain at the bottom of a thick asphalt layer is the controlling criterion for design to prevent retetitive load cracking. Although such strains were not measured at the bottom of the asphalt layer at the AASHO Road Test, they can be inferred from a knowledge of the material characteristics mechanism of initial failure at the Road Test. Since the bituminous base sections provided a complete range of performance, from failures to survivors of over 1 million load repetitions it was possible to describe the strain history of these test sections in terms of performance. The bituminous base sections fell into three performance classifications, depending upon whether they failed the first spring of testing, survived the testing period with a low serviceability rating or survived the testing without any change in serviceability. The horizontal tensile strain, horizontal tensile stress and vertical strain on top of the subgrade data were computed for each test section in each performance classification. Asphalt moduli for a wide spectrum of deflection measurements were input into the stress and strain computations. Moduli values were determined from dynamic loading in compression. Subgrade moduli were inferred from the deflection measurements. The results of the elastic-layer computations showed that there were indeed large differences in horizontal tensile strain, horizontal tensile stress and vertical strain in the subgrade, depending upon the performance classification. Secondly, the level of strain or stress for each performance classification was a function of the asphalt base stiffness at the asphalt layer bottom. From the horizontal strain results it was apparent that asphalt pavements can tolerate higher strains at lower stiffnesses. The horizontal tensile strain and stress relationships with asphalt stiffness were converted into "load repetition to failure" relationships by relating two performance classifications to the number of load repetitions to failure. A log-log relationship was assumed. The resulting family of "fatigue-like" curves for a range of asphalt stiffnesses has been used by Witczak and is the subject of another paper to this conference. /Author/

Dislocation Mechanics at High Strain Rates

Abstract: In this paper a high strain rate is defined as high if the dislocations that produce the plastic strain must move at velocities of the order of, or larger than the shear wave velocity a2. Except possibly in the initial portions of stress strain curves dislocation velocities are much smaller than a2. Only in shock loaded specimens should very fast dislocation velocities exist. An approximate analysis is made to show how supersonic dislocations in a shock wave interface (the Smith interface) can produce a hydrostatic stress behind the interface.

Predicting the stress-strain behavior of polycrystalline α-lron containing hard spherical particles

Abstract: Recent interest in the work hardening of metal crystals containing a dispersion of hard particles has resulted in analytical expressions relating the work hardening to strain, particle diameter, and volume fraction as well as other material parameters. In this study, these models have been used to calculate the tensile stress-strain behavior of polycrystalline α iron containing dispersions of the intermetallic compound Fe2Ta. The structural characteristics of the Fe-Ta alloys were thoroughly evaluated. The particle morphology was measured for randomness, mean particle diameter, standard deviation of the particle diameter, volume fraction, and planar interparticle spacing. Also, the matrix flow strength, composition, crystallographic randomness, dislocation morphology and grain size were evaluated. It was found that an Orowan type relationship as modified by Ashby satisfactorily described the yield strength as a function of the interparticle spacing and particle diameter. An experimental slope of 11.1 x 10-5 kg-cm/mm2 and a calculated slope of 9.75 x 10-5 kg-cm/mm2 were found. Both the Hart revised FHP work hardening model and Ashby’s model based on the generation of secondary dislocations were in good agreement with the experimental data. Hart’s revised FHP model required the use of empirically obtained values for the particle volume fraction which differed by a factor of 10 from the measured volume fraction and therefore is not suitable for predictive purposes. At tensile strains greater than 5 pct, the work hardening was characteristic of the matrix without particles; therefore, deviation between the experimental and calculated results based on Ashby’s model occurred at large strains. It is hoped that this study represents a step towards applying work hardening models to more complex polycrystalline alloys.

Failure criteria developed from aasho road test data

Abstract: Theoretical models of pavement deformation behavior such as elastic-layered theory can only be used for design purposes when failure criteria are specified. Although such models can be used to predict stress and strain states, they in no way indicate whether the material in the pavement can withstand the predicted deformations. For elastic-layered theory, limiting values of strain or stress need to be defined before the theory can be used to assist practicing engineers in the design of asphalt pavements. There is general agreement in the literature that horizontal tensile stress or strain at the bottom of a thick asphalt layer is the controlling criterion for design to prevent retetitive load cracking. Although such strains were not measured at the bottom of the asphalt layer at the AASHO Road Test, they can be inferred from a knowledge of the material characteristics mechanism of initial failure at the Road Test. Since the bituminous base sections provided a complete range of performance, from failures to survivors of over 1 million load repetitions it was possible to describe the strain history of these test sections in terms of performance. The bituminous base sections fell into three performance classifications, depending upon whether they failed the first spring of testing, survived the testing period with a low serviceability rating or survived the testing without any change in serviceability. The horizontal tensile strain, horizontal tensile stress and vertical strain on top of the subgrade data were computed for each test section in each performance classification. Asphalt moduli for a wide spectrum of deflection measurements were input into the stress and strain computations. Moduli values were determined from dynamic loading in compression. Subgrade moduli were inferred from the deflection measurements. The results of the elastic-layer computations showed that there were indeed large differences in horizontal tensile strain, horizontal tensile stress and vertical strain in the subgrade, depending upon the performance classification. Secondly, the level of strain or stress for each performance classification was a function of the asphalt base stiffness at the asphalt layer bottom. From the horizontal strain results it was apparent that asphalt pavements can tolerate higher strains at lower stiffnesses. The horizontal tensile strain and stress relationships with asphalt stiffness were converted into "load repetition to failure" relationships by relating two performance classifications to the number of load repetitions to failure. A log-log relationship was assumed. The resulting family of "fatigue-like" curves for a range of asphalt stiffnesses has been used by Witczak and is the subject of another paper to this conference. /Author/

Stress-strain relationship during transformation enhanced plasticity

Abstract: The effects of a deformation induced reaction kinetics upon the stress-strain curve of materials which transform during deformation is theoretically discussed. It is shown that the observed work hardening rate, dσ*/de*p depends on both the occurrence of a transformation and on the instantaneous rate of the reaction.

Stress-strain characteristics and slip band formation in copper-base alloy crystals

Abstract: The plastic properties at room temperature of extended copper crystals alloyed with aluminium, germanium and silicon were examined as a function of crystal orientation, alloy concentration and nature of solute. A strong orientation dependence was observed on the gross shape of the shear stress/shear strain diagram in all of the alloy crystals examined. In those crystals exhibiting a well-defined two-stage hardening curve, the extent of shear associated with stage I and the shear hardening coefficients of stages I and II are significantly dependent on orientation, nature and concentration of solute. On the other hand, the shear stress defining the onset of stage II is constant and independent of crystal orientation. Variations in the gross shape of the shear stress/shear diagram and in the parameters defining the two-stage hardening curve are correlated with changes in slip line development. No evidence of Luders band propagation, kink band development or twinning, was observed.

Yield Criterion and Second-Order Effects in Plane-Stress

Abstract: A yield criterion in planestress state is derived here based on isotropic representation of a scalar valued function depending upon symmetric 2×2 stress and strain matrices. The material has been assumed to be incompressible. In particular, for tension-torsion loading the yield surface is nonsymmetric with respect to the torsional stress axis. Due to the non-symmetry, the yield condition describes the second-order effect relating to axial-strain accumulation in cyclic torsion, and at the same time it has got a very simple form compared to other yield conditions describing this effect.