Showing papers on "Elastic modulus published in 1969"

On the overall elastic moduli of composite materials

Abstract: The overall elastic moduli of some solid composite materials are evaluated, first by bounding them precisely, and secondly by a ‘self-consistent’ estimate. Transversely isotropic inclusions of ‘needle’ and ‘disc’ shapes are particularly considered, at both random and aligned orientations, and at arbitrary volume concentration.

Static Anisotropic Elastic Properties of the Aorta in Living Dogs

Abstract: Static anisotropic elasticity was studied in the middle descending thoracic aorta of 14 living dogs. Special transducers were used to measure radius and longitudinal stress at several pressures in situ in an isolated vessel segment. From these data, moduli describing elastic properties of the vessel wall were calculated. Results indicate that (1) at a physiologic pressure of 154 cm H2O (extension ratio of 1.52 circumferentially) the mean values for the incremental elastic moduli in the radial, circumferential, and longitudinal directions were 5480, 7510, and 10,100 g/cm2, respectively; (2) these moduli increased with an increase in intravascular pressure; and (3) the longitudinal modulus decreased when the vessel was studied in vitro (from the removal of longitudinal tethering).

Length Optimization for Constrained Viscoelastic Layer Damping

Abstract: Viscoelastic materials are used extensively to damp flexural vibrations of metallic structures; it has been known for some time that the energy dissipation due to shear strain in the viscoelastic layer can be increased by constraining it with a stiffer covering layer. In this paper, we will discuss a method for increasing this damping by cutting the constraining layer into appropriate lengths. The analysis for a single layer of this treatment is relatively straightforward. The damping can be increased still further by using several layers; in this case, the analysis is based upon effective complex elastic moduli of an equivalent homogeneous medium. One result found from this analysis is that, if the element length of the constraining layer is optimum, the damping depends primarily upon the stiffness of the constraining layer and the loss coefficient of the viscoelastic material, and only indirectly on the shear modulus of the viscoelastic layer. Experimental data is presented for comparison with the theoretical predictions.

Closure on vibration modulus of normally consolidated clay

Abstract: THE WRITERS ARE GRATEFUL TO WHITMAN, HOLT AND MURPHY, AND DOBRY AND POBLETE FOR DEMONSTRATING THE GOOD AGREEMENT BETWEEN VALUES OF THE SHEAR MODULUS CALCULATED IN THE PRESENTED EQUATION AND SHEAR WAVE VELOCITIES MEASURED IN THE FIELD BY GEOPHYSICAL METHODS AT TWO DIFFERENT SITES. TEST RESULTS SHOW THE EFFECT OF VOID RATIO, AMBIENT STRESS, STRESS HISTORY, FREQUENCY, AND STRAIN AMPLITUDE ON THE VIBRATION SHEAR MODULUS OF THESE UNDISTURBED SAMPLES. INDEX PROPERTIES IN THE CLASSIFICATION OF VARIOUS UNDISTURBED COHESIVE SOILS TESTED ARE PRESENTED IN A TABLE AND THEIR PARTICLE SIZE DISTRIBUTIONS SHOWN IN A FIGURE. THE VALUES OF VOID RATIO ARE PRESENTED IN A FIGURE. ANOTHER FIGURE PRESENTS THE EFFECT OF ISOTROPIC COMPONENTS OF STRESS ON UNDISTURBED SAMPLES. THE EFFECT OF OVERCONSOLIDATION RELATIONSHIPS ARE PRESENTED. WHITMAN, HOLT AND MURPHY HAVE PRESENTED A FIGURE SHOWING A CURVE BY WHICH THE MODULUS FOR HIGHER STRAIN AMPLITUDES MAY BE COMPUTED FROM THE MODULUS AT SMALL STRAIN AMPLITUDES. RESULTS ARE PRESENTED IN A FIGURE OF (1) COHESIVE SOIL AND (2) DRY SANDS WHICH WERE TESTED AT DIFFERENT FREQUENCIES AND NUMBERS OF CYCLES. DATA FOR BOTH HOLLOW AND SOLID CYLINDRICAL SPECIMENS SHOWED THE EFFECT OF THE VARIATION OF STRAIN WITHIN THE SPECIMEN TO BE SMALL. THIS IS ALSO TRUE FOR LARGE STRAIN AMPLITUDES PROVIDED THE MEASURED PARAMETERS ARE CORRELATED TO THE AVERAGE SHEAR STRAIN AMPLITUDE IN THE SPECIMEN. THE RESULTS FOR TWO SENSITIVE CLAYS ARE SHOWN IN A FIGURE. THE SPECIAL STRUCTURE OF HIGHLY SENSITIVE CLAYS APPEARS TO INCREASE THE MODULUS ABOVE THAT FOR LESS SENSITIVE SOILS WITH SIMILAR VOID RATIO AND STATE OF STRESS. REFERENCES: VIBRATION MODULUS OF NORMALLY CONSOLIDATED CLAY, BOBBY O. HARDIN, WILLIAM L. BLACK, ASCE PROCEEDINGS PAPER 5833, MARCH, 1968.

Strength, Fracture Mode, and Thermal Stress Resistance of HfB2 and ZrB2

Abstract: Zirconium diboride and hafnium diboride were fabricated by hot-pressing at 1800°C and 120,000 psi. Bend strengths were measured on the fully dense materials from 25° to 1400° C in an argon atmosphere. These diboride compounds do not exhibit any gross plastic flow in the temperature range studied. The bend strengths go through a maximum between 700° and 1000°C and vary from 39,000 to 68,000 psi for HfB2 and 30,000 to 56,000 psi for ZrB2. The maxima in strength correspond to maxima in the fraction of transgranular fracture. The bend strength and room-temperature elastic modulus measurements were combined with available thermal conductivity and expansion data to calculate thermal stress resistance parameters. Under steady-state heat flow conditions, the calculated thermal stress resistance parameters of the borides are higher than those calculated for other refractory compounds.

Stability of Polycarbonate

Abstract: Although a wide range of aromatic polycarbonates has been synthesized and examined [1–3], the term polycarbonate usually refers to the commercially available poly[2,2-propane-bis(4-phenyl carbonate)], i.e., and this polymer is discussed exclusively in the present review. Polycarbonate possesses a number of attractive mechanical properties [1,3] e.g., high impact strength, high elastic modulus, and creep resistance. These features, coupled with the fact that the polymer is almost unaffected by water and many inorganic and organic solvents, permit its use in a variety of applications. In such applications the mechanical properties may alter with time because of the viscoelastic nature of the material.

The End Problem for a Laminated Elastic Strip — II. Differential Expansion Stresses

Abstract: A plane elasticity solution is presented for the state of stress resulting from differential expansion in a composite made up of two rectangular strips bonded on an interface. The stress field that has long been known to exist in the middle of such a laminated strip (to the St. Venant approximation) includes neither normal nor shear traction on the bonded interface. These stress components are shown to be significant only within a distance from each end equal to the total thickness, and their distribution is determined for a wide range of elastic moduli and strip dimensions.It is found that the distribution of normal stress at the interface is quite sensitive to the modulus and thickness ratios of the laminae. By making use of the form of this dependence, it may be possible to design bonded structures to withstand curing and/or temperature changes which would otherwise cause failure.

Elastic and Anelastic Behavior of V2O5·P2O5 Glasses

Abstract: The internal friction of several compositions of V2O5·P2O5 glasses has been measured in the kHz region from 100° to 400°K. A relaxation peak strongly dependent upon composition exists below room temperature in these glasses. The activation energies of the peaks lie between 0.1 and 0.2 eV. The isotropic elastic moduli and densities were measured for some compositions. These glasses are n‐type semiconductors. Direct current electrical conductivities ranged from 6×10−2 to 4×10−6 Ω·cm−1 at 100°C over the composition region studied. The connection between the internal friction and the dc electrical conductivity is discussed.

Creep and Dynamic Mechanical Properties of Filled Polyethylenes

Abstract: The creep and dynamic mechanical properties are reported for a series of filled and unfilled polythylenes. The fillers (untreated and treated with silanes) were kaolin and wollastonite. The variables studied include filler concentration, silane treatment, water soaking, temperature, and load. Most of the creep data can be explained, and semiquantitatively predicted, in terms of the increase in elastic modulus of the materials as a result of the incorporation of the filler. However, there are some secondary effects due to filler‐polymer interactions which apparently change the properties of the polymer phase and result in a further reduction of creep and an increase in damping. The presence of the filler greatly reduces creep, increases the stiffness, and increases the loss modulus of polyethylenes. Silane treatment generally reduces creep and increases modulus somewhat. An unexpected long‐time aging effect at room temperature was found which makes the polyethylenes more creep resistant. If allowance is made for the aging effect, soaking in water increases the creep of filled polyethylenes.

Shrinkage Stresses in Two-Phase Materials

Abstract: Shrinkage stresses produced during the curing of the matrix in a two-phase material were studied. Specimens representing a typical two-phase material made of unplasticized epoxy as inclusions and plasticized epoxy as the matrix were studied photoelastically.The magnitude of stresses at the interface of a single inclusion in an infinite matrix during the transient period of curing depended only on the constant elastic modulus of the inclusion and on the instantaneous value of the matrix elastic modulus and it was independent of the amount of shrinkage of the matrix. In the case of a square array of inclusions in close proximity, the stress-distribution depended on both elastic moduli and the amount of shrinkage. The influence of the ratio of the space between inclusions and their diameter on the magnitude of stresses was also studied, in the case of already set matrices.

A finite-element method for the plastic buckling analysis of plates

Abstract: Finite element technique extended for plastic buckling of flat plates, using Stowell theory

Anisotropic and composition effects in the elastic properties of polycrystalline metals

Abstract: The expressions giving the variations in Young's modulus E and the modulus of rigidity G with direction in cubic single crystals are combined to form the relationship 2/E+1/G=S44+2S11, which is independent of direction for a given crystal providing the effective or mean value of = Σ l2m2 (direction cosines) is the same for the two measurements. Experimental measurements for polycrystalline steel have shown that 2/E+1/G is equal to a constant which is also independent of direction, and this result has proved of value in distinguishing between the effects of composition variations which are likely to be obscured by varying degrees of anisotropy. Experimental measurements of Poisson's ratio have also been interpreted.

The Time Effect of Auxin and Calcium on Growth and Elastic Modulus in Hypocotyls

Abstract: The relationship between Young's modulus and longitudinal growth has been studied on growing segments of etiolated sunflower hypocotyls. The modulus was determined by means of the resonance frequency method. IAA in a concentration of 2.8 10−5 M produces a decrease in the modulus with a time lag of 4 minutes, while an increase in growth is observable only after 6 minutes. Addition of IAA results in a stronger decrease in the modulus if the segments are placed in a solution of 0.1 M mannitol rattier Hum in water. Through plasmometric measurements it has been found that the elastic extensibility is insignificant compared with the growth. After the addition of IAA, there occurs a marked elongation both in 0.1 M mannitol and in water, and at the same time a decrease in the elastic extensibility of the segments is observed. In the growing segments an increased modulus causes an in creased elastic extensibility, a matter which is directly contrary to the relationship found in a physical system with an applied external force. An explanation of this discrepancy has been given. With an excess of calcium the modulus increases, while the elongation decreases. Calcium deficiency implies both a decreased modulus and a decreased growth. With the addition of 10−3 M Ca(NO3)2 to segments raised without calcium the modulus increases after only 10 minutes, while an increase in longitudinal elongation is observable after 30 minutes. With the addition of IAA to the calcium deficient segments the modulus decreases to the same extent as in an optimal supply o f calcium. The results are discussed with reference to other investigations about elasticity and growth. It has been concluded that plastic extensibility cannot he of great importance in longitudinal growth. Time studies of the auxin effect and I he interaction between auxin and calcium have confirmed the hypothesis that one of the primary actions of auxin consists in a loosening of the cell wall matrix. Calcium always increases Youngs modulus and gives the cell wall a more rigid structure. Furthermore, calcium in a certain concentration is necessary for longitudinal growth.

Bounds for the real and imaginary parts of the dynamic moduli of composite viscoelastic systems

Abstract: If a system , consisting of firmly bonded isotropic linearly viscoelastic phases, behaves macroscopically as a homogeneous isotropic material under oscillatory deformation, upper and lower bounds can be set to both the real and imaginary parts of the complex rigidity and bulk moduli of the system. These reduce to the Voigt and Reuss bounds on the elastic moduli when the phases are purely elastic, and to the corresponding bounds on the shear viscosity and bulk viscosity when the phases are purely viscous.

The effect of time and temperature on the mechanical behavior of a 'plasticized' epoxy resin under different loading modes

Abstract: Epoxy–Versamid specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine mode of failure, yield stress and strain, and tangent and relaxation moduli. Stress-strain curves were used to define brittle, ductile, ductile-rubbery, and rubbery modes of behavior which prevailed in different temperature-strain rate regions. The time-temperature superposition principle was applied to yield stress, initial tangent moduli, and relaxation moduli data for all three types of loading. The transition regions, tangent and relaxation moduli, and shift factors were the same in tension, compression, and flexure. Thus the most convenient mode of loading can be used to determine the general time-temperature dependence. The ratio of compressive-to-tensile yield stress was almost constant over the entire ductile region. Flexural yielding data were used to predict yield stress in tension and compression, and stress relaxation master curves were shown to be related to elastic modulus vs. strain rate curves. The yielding phenomenon was interpreted using Eyring's theory of non-Newtonian viscoplastic flow. The apparent activation energy and activation volume were larger for tension than compression. A theory is offered to explain why yielding can occur in a cross-linked system.

Structure of Oxidized Polyacrylonitrile

Abstract: CURRENT commercial methods for converting polyacrylonitrile based textile fibre to high elastic modulus carbon fibre usually1 but not essentially2 involve a first stage of heating to a temperature between 200 and 300° C in air. During this so-called preoxidation stage, a proportion of oxygen is taken into the modified polymer structure to produce a black, heat resistant fibre3.

Bulk Modulus Shrinkage and Thermal Expansion of a Two Phase Material

Abstract: A simple theoretical approach is used to obtain expressions for bulk modulus, shrinkage and thermal expansion of a two phase material. To apply the expressions it is necessary to know the bulk modulus of a composite containing pores in place of the aggregate particles.