Showing papers on "Stress–strain curve published in 1989"

Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties

Abstract: A microporous, anisotropic form of expanded polytetrafluoroethylene has been found to have a large negative major Poisson's ratio. The value of Poisson's ratio varies with tensile strain and can attain values as large as -12. The microporous structure of the material is described and the mechanisms that lead to this large negative Poisson's ratio are identified. Micro-rotational degrees of freedom are observed, suggesting that a micropolar elasticity theory may be required to describe the mechanical properties.

Mechanical properties of model polyethylenes: tensile elastic modulus and yield stress

Abstract: Etude sur un polyethylene lineaire et un copolymere ethylene-butene-1, entre 175 o K et 260 o K

A study of the rapid deformation behaviour of a range of polymers

Abstract: Polymers are increasingly being used in applications where they are rapidly deformed. However, compared with metals, relatively few studies of their mechanical properties at high rates of strain have been published. This paper describes an investigation of the rapid deformation behaviour in compression of a number of widely used polymeric materials. The necessity of properly characterizing polymers is discussed, as the variation of commercial grades bearing the same name is considerable, and furthermore these materials are much more susceptible to change during storage than say metals. The importance of thermal properties to rapid, and hence adiabatic, deformation is pointed out, and tables of such properties are presented. Extensive use was made of high-speed photography (interframe time 7 $\mu $s) to study qualitatively the behaviour of solid discs of polymers at strain rates of 2.5 $\times $ 10$^{3}$ s$^{-1}$. The framing speed was sufficiently fast to capture fracture initiation and subsequent failure of all the polymers studied, including polycarbonate (PC), which fails in an almost explosive manner. The darkening of heat-sensitive film in contact with deforming discs was also investigated. Quantitatively, this technique was used to check the applicability of Avitzur's analysis (Avitzur (Israel J. Technol. 2, 295-304 (1964)) of a deforming annulus to polymers. Agreement was found to be good and hence friction could be measured during deformation at high rates of strain for the first time. Studies were also carried out to determine the best lubricant for rapid compressive testing. Petroleum jelly was found to reduce the friction closest to zero. An optically identical system was set up in an Instron mechanical testing machine both to perform friction studies and to explore deviation from incompressible behaviour. Agreement with Avitzur's analysis was found to be poorer, and no lubricant was found to reduce friction below about 3-4%. PC, with a very high value of frictional stress, showed evidence of a change in volume. Allowances were made for the elastic indentation of the anvils. Higher strain rates were achieved by using an instrumented drop-weight machine and a direct impact Kolsky bar, both developed in this laboratory. Care was taken to eliminate sources of error, including friction and calibration errors. The strain rate sensitivity of the polymers ranged from 5-15 MPa per decade of strain rate. However, most showed some softening as the strain rate was raised from 10$^{3}$ to 10$^{4}$ s$^{-1}$, the exceptions being polybutylene teraphthalate (PBT) and polyvinylidene difluoride (PVDF).

Plastic yielding of partially crystalline polymers

Abstract: : Measurements are described of characteristic stress strain properties in tension for several representative partially crystalline polymers, prepared by cooling from the melt. Striking differences were found in the natural draw ratio, ranging from 2X to 11X. They are interpreted in terms of a simple molecular model of the yielding process in which polymer chains, folded to different degrees in the crystallites, are pulled taut. Values of yield and draw stress were found to be of the same order as the free energy Um of melting, suggesting that yielding and drawing take place by stress-induced disruption of crystallites, analogous to melting. The mechanical work of drawing was similar to, but generally larger than, that required for melting, ranging from Um to about 4Um. The difference is attributed to strain energy of drawn material and possible recrystallization during drawing. Keywords: Crystalline, Deformation, Drawing, Plastic, Polymers, Strain, Tension, Yielding.

Interpretation of moduli from self-boring pressuremeter tests in sand

Abstract: The pressuremeter is a unique method for assessing directly the in situ shear stiffness of soils. However, the correct interpretation and application of the measured modulus must account for the relevant stress and strain level acting around the pressuremeter during the test. A method to correct the measured unload-reload shear modulus from self-bored pressuremeter tests in sands is proposed. The method has been evaluated using extensive data obtained from 47 tests performed in a large calibration chamber using pluvially-deposited silica sand and from 25 tests performed in situ in a natural deposit of relatively clean silica sand at the River Po, Italy. A consistent relationship was obtained between the corrected unload-reload shear modulus and the small strain shear modulus determined from resonant column tests and field cross-hole tests. Suggestions are given to link the measured moduli with moduli values required for geotechnical design problems. The importance of strain level, stress-strain model, yie...

Constitutive relations and finite deformations of passive cardiac tissue II: stress analysis in the left ventricle.

Abstract: We present a new approach for estimation of transmural distributions of stress and strain in the equatorial region of a passive left ventricle. We employ a thick-walled cylindrical geometry, assume that myocardium is incompressible, and use a three-dimensional constitutive relation that yields a material symmetry consistent with observed transmural variations in muscle fiber orientations. Moreover, we consider finite deformations including inflation, extension, twist, and transmural shearing and suggest a new method for determination of the requisite deformation parameters directly from experimental strain data. We show representative transmural distributions of stress and strain, and perform a parametric study to illustrate differing predictions of stress induced by varying boundary conditions, muscle fiber orientations, or modes of deformation. Our analysis can be used to guide and check future predictions of cardiac stresses, and to guide experimentalists by suggesting the accuracy of measurements essential for stress analysis in the heart.

Thermo-viscoelastic analysis of composite materials

Abstract: The thermo-viscoelastic boundary value problem for anisotropic materials is formulated and a numerical procedure is developed for the efficient analysis of stress and deformation histories in composites. The procedure is based on the finite element method and therefore it is applicable to composite laminates containing geometric discontinuities and complicated boundary conditions. Using the present formulation, the time-dependent stress and strain distributions in both notched and unnotched graphite/epoxy composites have been obtained. The effect of temperature and ply orientation on the creep and relaxation response is also studied.

Morphological studies of blends containing liquid crystalline polymers with poly(ethylene terephthalate)

Abstract: The investigation involved the structure–property behavior of extruded cast films prepared from blends of thermotropic liquid crystalline copolyesters with poly(ethylene terephthalate) (PET). Data were obtained which showed not only the temperature dependence of the moduli and stress–strain behavior but also the orientation effects that must be prevalent in order to explain the differences between the moduli measured parallel and perpendicular to the extrusion direction. Only at high liquid crystal polymer (LCP) composition is the modulus particularly increased. The modulus enhancement with lower LCP content and utilization of process variables are discussed with respect to the induced morphological textures and nature of the process equipment. Specifically, the process variable extruder gear pump speed did not enhance Young's modulus at the same LCP content as extensively as did the process variable of extruder screw speed.

Moment-curvature relations for a pseudoelastic beam

Abstract: Pseudoelastic bodies have very simple stress-strain diagrams for uniaxial tensile and compressive loading. In particular, yield and recovery occur at fixed stresses. And yet, the moment-curvature diagrams for bending and unbending of a beam are fairly complex, because the stress and strain fields are non-uniform. The paper shows stress profiles within the beam for pure bending and arrives at explicit equations for loading and unloading curves.

Study on the drawing behavior of poly(l-lactide) to obtain high-strength fibers

Abstract: The tensile drawing behavior of poly(L ‐lactide) has been studied in order to obtain high strength fibers Elongational viscosity measurements indicated that the hot drawing can take place in two temperature regions with different activation energies Up to 180°C, the deformation proceeds in the semicrystalline state of the polymer having an activation energy of 15–28 kJ/mol, presumably by shear deformation In the range of 180–190°C, the deformation proceeds in the liquid state of the polymer having an activation energy of 145–165 kJ/mol, leading to a semicrystalline state by strain hardening after displacement of topological defects By using high deformation rates during drawing in a temperature gradient (tube drawing), the deformation will principally proceed in the semicrystalline region and inhomogeneous draw will take place leading to inferior fiber properties, unless the deformation rate and drawing temperature are strictly adjusted Homogeneous drawing can be achieved by applying low deformation rates so that the deformation may take place in the liquid state of the polymer in which individual chains can be easily aligned and topological defects can be removed Poly(L ‐lactide) fibers with tensile strengths of 23 GPa have been produced in this way

Effect of plastic deformation on the microstructure and properties of amorphous polycarbonate

Abstract: Polycarbonate specimens were subjected to a plastic strain cycle at room temperature by means of a computer-controlled shear apparatus. The strain-cycling has several consequences: it softens the further plastic behaviour of the material, it increases the β relaxation peak observed between 300 and 400 K by dynamic mechanical analysis, and it generates an exothermic shoulder in the differential scanning calorimetry plot at 350 K. The experimental results are analysed in terms of a model which, during shear straining, involves the nucleation of quasi-point defects of higher molecular mobility. These defects persist in large density after strain cycling and are responsible for the changes in material behaviour reported. In particular, the evolution of the loss tangent spectra was analysed quantitatively by means of a computer simulation based on the elimination of the defects.

Creep-fatigue interactions in solders

Abstract: Solders in surface-mount-technology (SMT) joints are subjected to high homologous temperatures that cause the solder to deform and accumulate damage by both time-dependent and instantaneous mechanisms. The effects of frequency, stress range, mean stress, waveform (hold times on and off load), and mechanical history are investigated in bulk uniaxial solder in the as-cast condition. Strain is measured on a per-cycle basis as well as cumulatively, to separate the mechanisms of strain storage and damage storage. At hold times less than about 10 s, a significant part of the strain is recoverable, time dependent, and nondamaging. By this strain storage mechanism, life, measured either by cycles to failure or by time on load, can be increased by at least a factor of 5. At lower frequencies the damage is stored as a function of time on load and stress (creep damage). The effective stress for a cyclic creep test is defined in terms of the stress sensitivity of the solder in creep. A technique for measuring damage for life predictions is developed and examined. This technique involves the grain boundary embrittlement of partially fatigued specimens and the statistical analysis of the voids on the surfaces. >

Introduction to mechanics of materials

Abstract: Introduction to Stress, Strain, and Their Relationships. Axial Loading: Applications and Pressure Vessels. Torsional Loading. Flexural Loading: Stresses. Flexural Loading: Deflections. Statically Indeterminate Beams. Stress and Strain Transformation Equations. Combined Static Loadings. Columns. Inelastic Behavior. Energy Methods. Appendices. Answers. Name Index. Subject Index.

Experimental and theoretical studies of workpiece deformation, stress, and strain during flat rolling

Abstract: A review of experimental and theoretical studies of the flat rolling process is presented. An ‘applied mechanics’ view of the rolling process is adopted to study metal flow, pressure, stress, and d...

Study of dislocation cell structures from uniaxial deformation of AISI 4340 steel

Abstract: A considerable interest has focused on the role of substructure during the uniaxial deformation of pure metals and alloys. To elucidate this role further, the evolution of dislocation cell structures during the tensile straining of AISI 4340 steel was investigated by transmission electron microscopy. It was found that substructural evolution reflects the inhomogeneous distribution of stress and strain in a composite material consisting of ferrite and pearlite. Cell formation occurs at different stages in the phases, with a more advanced state of cell development in ferrite grains indicating higher dislocation mobility. The strength of 4340 steel appears to be largely due to the pearlite. Work hardening by cell mechanisms occurs in the ferrite only after stresses exceed the pearlite strength. The dependence of dislocation cell size on flow stress σ was also studied and σ is found to be linearly related to the inverse cell size, indicating the operation of similitude in the “meshlength” theory of work hardening over most of the strain range. The breakdown of this relationship at higher strains is related to the transition to stage IV hardening behaviour, where increased dislocation mobility through profuse cross slip results in a very low hardening rate and nearly constant cell size.

Nonlinear Mechanical Properties of a Thermoset Matrix Composite at Elevated Temperatures

Abstract: Models are presented for describing the stress-strain relationships and the strengths of a thermoset matrix composite exposed to elevated temperature. The models take into account the nonlinear elastic characteristics of the material. For Fiberite 976 resin and for unidirectional Fiberite T300/976 composite the constants required in the models were determined by measuring the tensile, compressive, and shear properties, and Poisson ratios at 75, 250, 300, and 350°F. The strengths, initial (stress → 0) moduli, and initial Poisson's ratios of the unidirectional composite were calculated from the known resin and fiber properties using micromechanics equations. A procedure is also described which, together with the stress-strain-strength models developed in this study, can be used to calculate the deformations and strengths of loaded multidirectional laminates at high temperatures. To evaluate the accuracies of the models and the calculation procedure deformations and strengths of multidirectional Fiberite T30...

Temperature Dependence of Plastic Deformation in White Tin Single Crystals

Abstract: Tensile experiments have been carried out over a wide range of temperatures on single crystals of high-purity white tin with low dislocation density. From the observations of slip lines it is found that different slip systems are activated for different temperature regions and for different orientations of specimens. By deformation with the (100)[010] slip system the cell structure is formed in the specimen. The critical-resolved shear stress of this system shows a similar temperature dependence to that of cubic metals. In the case of the (10)½[111] slip system, only isolated dislocations are formed during deformation and the yield point phenomenon occurs. The critical-resolved shear stress of this system shows a strong temperature dependence not found in cubic metals. It increases nearly exponentially with decreasing temperature and attains a factor of 200.

Improved characterization model for granular bases

Abstract: Laboratory resilient modulus tests were conducted on granular materials at stress states exceeding the materials' static shear strengths. The test results show that, above the static strength, the modulus decreases with increasing stress levels. These data were used to develop a characterization model that is a modification of the commonly used k-theta-n model. The modification consists of the addition of a stress ratio (stress/strength) parameter. The stress ratio model was used in the finite element program ILLI-PAVE to analyze typical flexible pavement sections. The analysis results are compared with similar analyses using the Mohr-Coulomb stress adjustment model normally used with ILLI-PAVE. The comparison shows that similar stress and strain patterns are predicted by both models but that the stresses predicted in the granular base by the stress ratio model appear to be more realistic. Also, the stress ratio model provides a means for analyzing the structural effects of granular materials having different shear strength characteristics.

Use of modified standard 20-node isoparametric brick elements for representing stress/strain fields at a crack tip for elastic and perfectly plastic material

Abstract: The analysis of defects in engineering structures and components has to take into account the singular strain field at the crack tip. The problems encountered in such analyses have unique geometries, have some non-linear elastic plastic behaviour and are three-dimensional in nature. Their solution calls for the use of the finite element method. Two-dimensional fracture mechanics analysis methods have been developed and proved by other researchers to show that 8-noded collapsed finite elements have the required singular strain fields for both the elastic and perfectly plastic material conditions. This paper proves the conditions under which three-dimensional collapsed elements represent the stress/strain fields at a crack tip required for elastic and perfectly plastic material, including crack tip blunting in the latter case. The collapsed elements presented can be used with confidence and give large savings in computing time, which is an essential point in three-dimensional finite element calculations.