Search

Poly(m-phenyleneisophthalamide) films were drawn and heat-treated inglycol solution of N, N-dimethylformainide or N, N-dimethylacetamide, and the fine structure and mechanical properties of thus treated films were investigated, comparing them with those treated in aqueous solution.It was found that filmscould be drawn in N, N-dimethylformamide solution at lower temperature and at lower concentration than in aqueous solution. Improvement of orientation, initial modulus and tensile stress at break by drawing or heat-treatment in glycol solution was of similar extent to those in aqueous solution, but the former solution was slightly more effective for improving the elongation at break and crystallinity than the latter.In order to evaluate the degree of crystallinity and orientation, the amorphous X-ray diffraction pattern was determined and the intrinsic birefringence of poly(m-phenyleneisophthal-amide) was estimated; and the finestructure of films was discussed in more detail from the changes in the degree of crystallinity and orientation.

Plated wires, 2.5 and 5.0 mils in diameter, have been obtained from various sources and compared to our own 2.5 mil diameter wire made on both copper-beryllium and tungsten substrates. The wires have been tested for their digit, word, and shmoo windows, pulse output and uniformity of output, skew and magnetostriction and their uniformity, the tension and torsion stress changes in the above characteristics, the thickness of the magnetic layer, stability during accelerated aging, and their mechanical characteristics. The characteristics of the wires in the unstressed condition were all adequate for memory application. Differences in signal output and location of the operating windows could be correlated with differences in film thickness and wire diameter. Pulse signal fluctuations were found to be directly proportional to magnetostriction fluctuations. There were great differences observed in the behavior of the samples under stressed conditions. These differences were shown to arise from differences in the local fluctuations in magnetostriction, the modulus and diameter of the substrate, and differences in the metallurgical and magnetic structure of the permalloy film. Accelerated aging showed 2:1 differences in rate between some samples.

The effect of soil modulus, mode of wall movement and base friction conditions, on lateral earth pressure distribution and pattern of failure development in the soil mass is brought out.

The behavior of an inclusion in a host material subjected to a stress system depends primarily on the ratio of the tangent moduli,E inclusion/E host. An inclusion of suitable material used in the form of a gage will give an identifiable photoelastic-fringe pattern. This pattern is related to the applied biaxial stresses in the diametral plane of the gage, and is independent of the actual modulus and strains in the host material provided that the moduli ratio is more than 300. A program of work has been carried out to verify the use of such an inclusion gage in low-modulus nonlinear viscoelastic materials. The gage geometry used in this work consisted of a hollow cylinder of birefringent material with a ratio of outside diameter to inside diameter of 5 to 1. The host materials were either unfilled or highly filled carboxyl-terminated polybutadiene rubbers. The moduli ratios for both host materials were such that the gages act as rigid inclusions. A theoretical study has also been conducted to find the optimum measuring points within the gage and the fringe patterns created by selected biaxial-stress ratios. The study also showed that the gage sensitivity is virtually independent of Poisson's ratio but depends on the biaxial ratio of the stresses. The values of the sensitivity factor obtained experimentally were close to those derived theoretically. The stressfringe order at the optimum measuring points was obtained by Tardy compensation, and the biaxial-stress ratio determined either from fringe-pattern recognition or by measuring points. Future applications and uses of such a stress-measuring technique will be described.

The properties and structure of natural cellulosic fibers were investigated by sonic velocify, visible dichroism and x-ray diffraction methods. The following results were obtained: (1) There is a good agreement between the orientation factor determined from the x-ray diffraction method and the visible dichroism of dyestuffs. (2) A linear relation exists between the sonic velocity (C) and the orientation factor from x-ray diffraction (fx); C=8.54fx-0.72(km/sec)for0.6

The elastic properties of copper have been compiled and reviewed. Polycrystalline elastic constants included are: Young's modulus, the shear modulus, the bulk modulus, and Poisson's ratio. Single‐crystal constants of second‐, third‐, and fourth‐order are included. Over 200 references to the experimental literature are given. A few theoretical numbers are included. When sufficient data exist, best values are recommended together with their standard errors. Effects on the elastic constants of temperature, pressure, and mechanical (plastic) deformation are included. The Cauchy (central‐force) relationships and the single‐crystal—polycrystal relationship are also discussed.

The effect of cold rolling on the mechanical properties of polymers, viz., acetal, nylon 66, poly(vinyl chloride) and polycarbonate has been studied. The yield strength, Young's modulus, and hardness increase with increasing cold work, except for a slight drop in these properties at low values of cold work. The ductility increases with rolling to a maximum and drops with further reduction. At the same time, the tensile strength increases continuously with rolling. This conspicuous occurrence of the increase in ductility with a simultaneous increase in tensile strength for polymers, unlike that in metals, is explained considering the morphological changes produced in polymers upon cold rolling. It is shown that this typical behavior is not due to the unique loading or heating and cooling cycle involved in the rolling process.

A series of rigid polyurethane foams of densities varying from 65 kg/m−3 to 400 kg/m−3 have been tested in compression as a function of rate and temperature. It has been found that a linear relation exists between density and modulus if the data is referred to a constant thermodynamic temperature.

A method for the routine stabilization and heat-treatment of rayons to prepare them for carbonization and graphitization has been developed. After treatment by this method, which employs either air or pure oxygen, the yarn is suitable for fast, continuous stress-carbonization and stress-graphitization. Routine processing conditions yield “carbon fibres” with a filament modulus of fifty million psi. This procedure, which produces a carbon yield between 16 and 21 %, has been successfully applied to rayons produced by five different manufacturers. The steps necessary to accommodate the process to different sources of precursor materials are discussed, and the final product properties obtained are presented.

At first a survey is given on the thermodynamics of rubber-elasticity and the results of the statistical theory of molecular networks. Experimental data of torsional vibrations, stress–strain measurements (simple extension and uniaxial compression) and photoelastic properties in dependence of temperature are reported. The measurements have been carried out on dry and swollen crosslinked polymers, especially poly(methyl methacrylate) (crosslinked in bulk or in solution), natural rubber, trans-polypentenamer and poly(butadiene). The modulus–temperature curves were always linear in the rubbery region when the samples had been carefully extracted. For poly(methyl methacrylate) the curve of retractive force against temperature showed a bend at a distinct temperature. Below this temperature the slope of the curve is lower than above. This behaviour can be explained by the existence of long living associations in poly(methyl methacrylate)–solvent systems already known by measurements on the corresponding solutions. The associations are able to form physical crosslinks. Most elastomers do not behave ideally in the sense of the theory: they are not purely entropy-elastic but show also an energy elasticity term of the modulus. The energy elasticity part is not constant but increases with the network density and the degree of swelling. From this it is concluded that the energy elasticity contribution is not only an intramolecular effect caused by rotational isomerism. The energy elasticity may also depend on other intramolecular effects and intermolecular sources. The existence of short chains in the network seems to be one essential reason for the nonconstancy of the energy elasticity contribution. Photoelastic measurements in dependence of the degree of swelling show that we must assume a short-range order in amorphous polymers. Following a newer theoretical consideration, the second term of the Mooney–Rivlin equation for the stress–strain behaviour of unswollen elastomers can be explained by the co-operation of the short-range order and the chain-length distribution in the random polymer network.

The regular Tromp curve is a log-normal probability (K—Kolmogoroff) function; it is, however, also a modified RRS (Rosin-Rammler-Sperling) or GGS (Gates-Gaudin-Schuhmann) function. The exponent m (distribution modulus) is a measure of the slope of the functions, i.e. Tromp curves and can be used instead of the indices Ep or I to characterize the efficiency of the various separating (sorting or classifying or sizing) equipments. The relationship Im ⋍ constant is valid.

The elastic constants and Vickers hardness of B2O3-PbO glasses have been determined. The data obtained for Vickers hardness, isotropic wave velocities, bulk modulus, shear modulus and Young's modulus are listed in Table I and II together with the density and molar volume. The variation of these data with composition of the glasses are shown in Fig. 1∼3. It can be seen that both the elastic constants and Vickers hardness increase with increasing PbO content up to its maximum value at about 42 mole percent PbO and then decrease; that is, beyond this further addition of PbO produces a softer glass. The increase of the elastic constants and hardness in the composition range of approximately 20∼42 mole percent PbO is interpreted based on the evidences that the four-co-ordinated borons are present and the type of lead-oxygen association becomes more covalent bonding.

Pronounced effects of thermal treatment on the properties of graphite fiber/ polycarbonate and glass fiber/polycarbonate composites have been demonstrated and explained. At 20 volume percent loading of random-in-a-plane, discontinuous fibers, both specimen strength and modulus in both fiber systems were found to increase dramatically upon molding above 260-265 C, whereas only the graphite system was further improved by subsequent annealing. In the latter case, property improvement is due to generation of a crystalline inner layer at the interface, which apparently transfers the stresses more effectively from fiber to fiber. Regardless of the type of fiber, molding at 275 C (slightly above 260-265 C, the melting point of crystalline polycarbonate) results in improved properties due to better wetting of the fibers by the resin. Hot forming of graphite reinforced polycarbonate composites between the molding and annealing steps takes advantage of the higher process-ability of the unannealed material in addition to providing increased modulus and strength in the final molded article.

The effects of dimensions and supporting conditions on the compressive strength and deformation of polyvinylchloride pipes under external pressure were discussed. The following four kinds of pipe supporting conditions were used; (A) compression between two steel plates, (B) compression between a steel plate and a concave wooden block, (C) compression between two concave wooden blocks, and (D) compression between two concave hard rubber supporters. The main results obtained are as follows.(1) The relation between the compressive strength P and the dimensions of PVC pipe is given by the following formula, similar to the mid load bending for a both end fixed straight beam with a rectangular section;P=4σb·l·t2/3·Dm·c1 (a)where, l, t and Dm are the length, thickness and diameter of pipe, respectively, c1 the correction coefficient according to pipe supporting conditions, and σb the bending stress in kg/mm2. The value of correction coefficient c1 was 0.81∼1.35 for A-method, 1.35 for B-method, 8.0 for C-method and 2.3 for D-method, respectively.(2) The deflection δ under elastic deformation is given by the following formula;δ=P·Dm3/8E·l·t3c2 (b)where, E is Young's modulus in kg/mm2 of pipe material, and c2 the correction coefficient similar to c1. The value of c2 was 2.22 for A-method.(3) It seems reasonable, therefore, that the theory of straight beam may be applied to the compressive strength and deflection of plastics-pipe under external pressure by using the correction coefficient c1 or c2.

Longitudinal waves at the liquid-gas interface of a liquid layer with finite thickness, on a solid substrate, are considered. The thin liquid layer contains surface active material and exchange during wave propagation, between the interface and the liquid layer is assumed to be controlled by diffusion. For this case the dispersion equation for the longitudinal waves and an expression of the complex dilational modulus are obtained. This general equation for the complex dilational modulus contains the already known expressions for infinite layer thickness and for finite layer thickness assuming that diffusion equilibrium is achieved.

A method of applying linear programming to evaluate the elastic moduli of unidirectionally fiber-reinforced composite materials is presented. Based on the theory of elasticity, the stresses and displacements of the fiber and of the resin are expressed in terms of harmonic series. The coefficients of the series are determined by the simplex algorithm to minimize the deviations which occur when the stresses and displacements are matched at the fiberresin interface and at the outer boundary of the representative element of the composite. By applying the energy principle, the Young's modulus in the fiber direction and the major Poisson's ratio of the E-glass/resin composite are found to be in good agreement with existing results, while the gap of the bounds for its bulk modulus is considerably narrowed in comparison to earlier results.

This paper concerns the effects that slight deviations in fiber directions have on the stress field in composite plates. The fiber reinforced plates are represented by the equivalent modulus theory as homogeneous transversely isotropic regions and the deviations in fiber directions are incorporated by varying the directions of the axes of the material symmetry.

A method is developed based on the use of a model kinetic equation with a shock frequency ω = v/l (l is the mean length of the free flight path; v is the modulus of the molecular velocity). The method is tested on several classical problems.

The short-time behavior of viscoelastic materials has been traditionally studied on the millisecond time scale using steady sinusoidal excitation to measure the complex modulus and optical functions. A technique has now been developed for determining the short-time inverse optical-creep function on the microsecond time scale, using wave propagation in a rod. The method is demonstrated by characterizing an epoxy material in the time regime from 1 μs to 100μs.

In this paper we establish three theorems concerning the asymptotic distributions of ordinary least-squares estimates of the parameters of a stochastic difference equation. We show that, if there is at least one root of the associated characteristic equation with modulus less than one and if all the roots have moduli different from one, the vector of least-squares estimates converges in distribution to a normally distributed vector. The distribution of the limiting vector is degenerate if there is at least one root with modulus greater than one. The results we obtain represent extensions of results proviously obtained by H. B. Mann and A. Wald, H. Rubin, J. S. White, T. W. Anderson, M. M. Rao, T. J. Muench, and the author.

The longitudinal thickness-shear behavior of a rectangular cross-section prism containing circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Saint-Venant flexure problem modeled by a tip-loaded cantilever composite beam and solution is obtained by the boundary-point least-squares method. It is shown that the longitudinal thickness-shear modulus is much greater than the in-plane shear modulus for a monofilament composite and therefore an independent analysis is necessary to predict the longitudinal thickness-shear behavior of the composite. Numerical results are presented in graphical form for various values of fiber volume fraction and material parameters typical of modern advanced composites.

Mechanical and thermal properties of several kinds of plywoods, which were trially manufactured for the thermal barrier of the LNG carrier, were experimentally proved.Material tests were carried out at room temperature, -78°C (dry-ice) and -196°C (liquid nitrogen).The results are as follows : (1) The obtained coefficients of variation are for the most part distributed within 20 percent and those of Young's modulus around 10 percent.(2) Breaking strength and Young's modulus are proportional to the specific gravity.(3) Breaking strength, proportional limit and Young's modulus have tendency to increase in cryogenic temperature region.(4) Regarding size effect of test specimen, the mean values do not show evident difference, but the standard deviations decrease evidently according to the increase of size.

Experiments are described in which the fracture toughness,K c, of PMMA has been determined in the temperature range −190 to + 80° C and over the crack speed range of 10−2 to 102 mm sec−1. Single edge notch tension was used for instability measurements but the other data were obtained using the double torsion method. In the range −80 to + 80°C the variations inK c may be described in terms of modulus changes and a constant crack opening displacement criterion. Crack instabilities are correlated with isothermal-adiabatic transitions at the crack tip. Below −80° C there is an inverted rate dependence associated with thermal effects during post-instability crack propagation.

A theoretical analysis using finite element methods has been applied to oriented short-fiber composites and spherical particle composites in order to predict the influence of a finite layer at the interface on mechanical properties. In this study the interfacial layer has been modeled by assuming that a layer surrounds the interface and that this layer has a modulus of elasticity different than both the fiber and the matrix. The stress distribution near the interface has been determined as a function of the elastic constants of the interface layer and the interface layer volume fraction. This analysis has also been performed for two volume fractions of fibers and two fiber length to diameter ratios. From this stress distribution, the composite modulus and toughness have been determined as a function of interface modulus. It is theoretically shown that the toughness, measured by amount of strain energy absorbed, can be maximized by controlling the interface modulus. Furthermore, recent experimental results appear to verify the theory.

Electron microscopy studies indicate that the microfibrils are a well defined element of many uniaxially oriented polymers. On the basis of these results it was inferred that the mechanical responses of uniaxially oriented polymers are similar to those of a parallel ensemble of the microfibrils. An important consequence of this microfibrillar model is that the type of load transfer is independent of crystallite aspect (length/diameter) ratio. The analysis of anisotropy in modulus of uniaxially oriented nylon 6, however, indicates that the load transfer characteristics of these polymers are dependent on crystallite dimension. A series response is observed only with fibers or films of low and intermediate draw ratio. Highly oriented structures, however, exhibit a nearly isotropic response in load transfer. These results show that uniaxial polymers must be analyzed in terms of a model where the crystallites are embedded in an “amorphous” matrix. The equations are derived for modulus, strength, and coefficient of diffusion in terms of crystallite dimensions, and the results compared with the experimental data.

The mechanical properties of a series of thermoplastics reinforced with unidirectionally oriented short fibers are reported. Both organic and inorganic fiber reinforcements were used in fiber volume fractions of 0.10 to 0.50. A number of these composites were found to have excellent strength and stiffness properties combined with good toughness and low density. The dependence of composite properties on the properties of the constituent materials is discussed. Fiber efficiency factors for strength and modulus are presented and models for predicting composite mechanical behavior are reviewed.

The dynamic stress-intensity factor about the tip of a rapidly moving crack ( K D ) in polymethylmethacrylate (PMMA) has been measured, using ultra-high speed photographic techniques to record the photoelastic patterns produced around the crack tip. From the same photographs, the velocity of the moving cracks was determined. A gross roughening of the fracture surface was found to appear at crack speeds of 1,300 ft sec−1 (396 m sec−1). From the geometry of the surface markings associated with the roughening, a dynamic value of Young's Modulus for PMMA was obtained over the velocity range 1,300–2,300 ft sec−1 (400–700 m sec−1). These dynamic values of Young's Modulus were used to interpret the variation of the stress intensity factor, K D , with crack velocity, and its relation to fracture morphology.

Response of individual piles to externally applied loads is one of the most complex soil-structure interaction problems in the field of foundation engineering. For any realistic analysis of this problem, it is essential to take into account both the elastic and plastic properties of the soil, as both these states occur along the embedded length of the pile. Herein, analysis and results are presented for the problem of axially and laterally loaded piles, taking into account elasto-plastic nature of the soil for both cohesive and cohesionless soils. The results indicate that the flexural behaviour of laterally and axially loaded pile in an elasto-plastic soil is considerably influenced by type of variation of plastic resistance, soil modulus variation and the boundary conditions at the top.

A shock tube technique was utilized to assess the impact fracture of bovine femur compact bone, in the form of cylindrical tube specimens. The effect of wall thickness on the fracture pressure was established and an unique hoop stress (= 18.0 MN m−2) for fracture obtained. In addition, the effect of crack length and radius of curvature of the crack tip on the fracture hoop stress was established, together with a determination of Young's modulus at the shock loading rate. The possible correlations of these results with fracture mechanics concepts are discussed.

The low compressive strength of Kevlar 49® unidirectional composites cannot be satisfactorily explained in terms of current theories which assume that failure is due to the matrix material. For a given matrix, Kevlar 49 composites are considerably weaker in compression than those based on other comparable high strength, high modulus filaments. Fracture is found to occur before any plastic deformation of the matrix is observed.

Let t i = X i/s, i = 1, 2 be noncentral Student t-variates with noncentrality parameters δi, where x 1, x 2 and s are independent. The simultaneous distribution of t 1 and t 2 is studied and the power function of the studentized maximum and minimum modulus tests are tabulated for significance level 0.05, degrees of freedom 1, 2, 5, 10, 20, 50, ∞ and δ1, δ2 =0(1)5. Asymptotically exact approximations to these power functions are discussed. The marginal power of the maximum modulus test is also tabulated.

M. L. Cartwright has given ((2), 180–181) the following theorem, together with a neat proof of it.Theorem C.Suppose that f(z) is regular andin the half-strip Sof the complex plane.Suppose also that for some constant α in αas y→∞. Then for every δ>0.uniformly asy→∞ for α+δ≦x≦β–δ.

Polycrystalline spinel (MgA12O4), hot-pressed in graphite dies, yielded densities ranging from ∼64 to ≊100% of theoretical. Average grain size of compacts varied from 4 to 125μ depending on hot-pressing conditions. Room-temperature mechanical properties also varied widely; average strengths for the 15 experimental combinations ranged from 3500 to 34,000 psi in bending and from 21,700 to 389,000 psi in compression, and Young's modulus ranged from 0.54 X lo7 to 3.5 X 107 psi. Variations in bulk density, average grain size, room-temperature transverse and compressive strengths, and Young's modulus of elasticity were separately expressed as multiple quadratic regressions in terms of 1/T (temperature), In t (time), and P(pressure) over the hot-pressing range 1227’to 1750°C, 5 to 320 min, and 1000 to 3000 psi. From these regressions, empirical equations expressing mechanical properties in terms of regression solutions of density and grain size were derived which statistically indicate a principal dependence on density and only a minor grain size dependence.

Investigation has been made on viscoelastic properties of moderately concentrated high-polymer solutions of the order of small percentage. Tschoegl, Ferry et al. have developed a general theory on the viscoelasticity of random coiled chain polymers, adopting into it the so-called hydrodynamic interaction effect and the excluded volume effect between the segments from the well-known Rouse-Zimm theory, Making a comparison between their theoretical complex modulus and experimental ones, they have pointed out that the hydrodynamic interaction seems to decrease with increasing concentration of solutions and increasing molecular weight of polymers. With increase of interpolymer interactions the polymers will behave with increased free-draining coils.This is rather a strange thing from the theoretical view-point. It even betrays some discrepancy between the theory and the experimental results in some cases. Though the Tschoegl's calculation shows the relation G"-ωηs>G' excepting very high frequency region corresponding to the minimum relaxation time, there are some systems that give the inverse relation G"-ωηs

Stereoscan electron microscope studies and measurements of tensile strength and Young's modulus have been made on chrysotile and five naturally-occurring fibrous amphiboles. The effect of heat on the modulus and fracture mechanism has also been examined. With the exception of tremolite which has a different microstructure from the remaining amphiboles, the moduli and strengths were similar. The loss of strength which occurs when the fibrous amphiboles, and to a lesser extent, chrysotile are heated below their decomposition temperature is shown to be due to an increase in interfibrillar bonding causing the material to become notch-sensitive

It is a well-known fact that the magnetic properties of a reversible iron-nickel alloy, especially of 78.5% Ni, are largely modified by rapid cooling from 600°, namely, by the so-called permalloy treatment. Two theories have been advocated on the physical meaning of this treatment; one is the super lattice (Ni3Fe) theory, and the other the plastic flow theory in magnetic domain. We carried out an experiment on the change of Young's modulus by the permalloy treatment and attempted to decide which theory is more reasonable of the two. By the lateral vibration method we measured the modulus of specimens cooled slowly after vacuum annealing at 1000_??_1100° for 20 hours, and then of specimens cooled rapidly from 600° in air after reheating to 1000°. Rapid cooling general, seems to decrease Young's modulus in both ranges reversible and irreversible. The marked decrease of the modulus occurs in the magnetically modifiable range of alloys (50_??_85% Ni). Moreover, the curve of the percentage decrease of the modulus to composition is quite similar to that of magneto-striction in longitudinal magnetic field. Similarity of these two curves suggests that some relation may exist between the change of Young's modulus by rapid cooling and the degree of plastic flow in magnetic domain. The decrease of magneto-striction by cooling in field was related directly to the degree of plastic flow of magnetic domains by Bozorsh and Dillinger, and afterwards was supplemented by Becker and During as a trans formation from cubic atom arrangement to somewhat tetragonal one. The decrease of Young's modulus by rapid cooling may be attributed to the degree of transfor-mation of atom arrangement from cubic to tetragonal.

An apparatus is described for the measurement of Young's modulus, E , and the energy loss per cycle, Δ W/W, of small beam-shaped rock samples, over the frequency range 2 to 40 c/s. Results are given for seven sedimentary and two igneous types of rock. An increase of between 1 % and 3 % in E, and of up to 100 % in Δ W/W, occurred over this range. Experiments on rocks containing moisture showed a decrease in the magnitude of E (at 2 c/s), an increased frequency variation of E, and a greater and almost linear increase of Δ W/W with frequency. The effect of oil was similar except that the magnitude of E at 2 c/s was unaffected. It is suggested that the moisture and oil results are due to viscous movements of fluid through the pores in the rock, and that the changes in E and Δ W/W with frequency, in dry rocks, are due to a small viscous mechanism operative at low frequencies.

Hydrogen electrolyzed into palladium changes the internal friction. In torsional oscillations at 0$\cdot $54 and 0$\cdot $22 c/s an immediate large increase of internal friction is observed after charging, or after removing some of the hydrogen by electrolysis. On ageing, the internal friction in such specimens falls to a limiting value, without appreciable loss of hydrogen. This decrease of internal friction obeys approximately a unimolecular rate law, with velocity constant markedly affected by the grain size of the metal. Decay is fastest in annealed specimens with large grain sizes, where in the limit the internal friction returns almost to the value for pure palladium, notwithstanding the presence of about 0$\cdot $6 H/Pd. In fine-grained charged specimens the internal friction decays to limiting values rather larger than for the pure metal. The observations on palladium/hydrogen suggest that there is a diversity of relaxation processes in the alloy. Electrolysis produces large but temporary 'cold-working' which is accompanied by high internal friction. Rested alloys show permanent relaxation effects related to the initial grain size. Brief discussion is given of measured effects of hydrogen on Young's modulus and the rigidity modulus of palladium, both of which are somewhat decreased on charging with hydrogen.

Two silicon carbides with different fracture surface energies were subjected to increasingly severe thermal shock; the damage was monitored by changes in the specific damping capacity, elastic modulus, and fracture strength. The fracture strength followed predicted trends, but the strength losses did not correlate with the changes observed in damping and modulus. The differences in thermal-shock resistance of the materials were related to the fracture surface energy; the body with the higher fracture energy had superior resistance to thermal-shock damage.

Experimentally, a rubber cord seems to have characteristics of a string on one hand, and of a beam on the other. Equation of motion with a term of damping was introduced as for a rubber cord. Then the solution was compared with the results of experiments, and the dynamical characteristics of rubber obtained as rubber vibration isolators were taken into account. 1) Vibration of rubber cord with a concentrated mass. Linear vibration with one degree of freedom was assumed. Elastic modulus E calculated from this experiment was compared with static modulus. Values of E are thought to be adequate when the ratio between dynamic and static moduli is taken into consideration. 2) Torsional vibration of rubber cord. Shear modulus G^- calculated in the same way was compared with the static shear modulus. 3) Free damped vibration of rubber cord. A term of damping was added to an ordinary equation of string. Results of experiments could be explained by an equation ∂2y/∂t2=a2(∂2y/∂x2)-2c(∂/∂t)(∂2y/∂x2), when an effective value of tension was taken into account.

The numerical solution described in the preceding section shows that the heterogeneity of a plate affects seriously the strain distribution but not so much the stress distribution (although this need not be true in general). This conclusion which cannot be immediately introduced from the known knowledge of elasticity, tends to support the assumption made by Muller and Macherauch. Electronic computers allow to find numerical solutions of complicated differential equations. But direct application of an electronic computer to the evaluation of a problem such as treated here is not possible, since the boundary conditions are not prescribed concretely. The solution obtained in this paper also applies to more complicated problems, such as the problems of heterogeneous plates containing holes or notches, because it represents the solution at points distant from the holes or notches. Using this solution, one can prescribe the boundary conditions for those problems concretely, hence numerical solutions can be obtained by the use of an electronic computer.

A comprehensive compilation is given of elastic properties of iron‐nickel alloys. When sufficient data exist, preferred values are recommended. This compilation covers, besides pure iron and pure nickel, the entire binary composition range, both b.c.c. and f.c.c. phases. Elastic constants included are: Young's modulus, shear modulus, bulk modulus (reciprocal compressibility), Poisson's ratio, and single‐crystal elastic stiffnesses, both second‐order and higher‐order. Data are compiled for variation of elastic constants with composition, temperature, pressure, magnetic field, mechanical deformation, annealing, and crystallographic transitions. An overview is given from the vantage points of the electron theory of metals, elasticity theory, and crystallographic theory. Also included are discussions of iso‐thermal and adiabatic elastic constants, interrelationships among engineering elastic constants, computation of the latter from single‐crystal elastic stiffnesses, and similar topics. Where key data have n...

Experimental studies are described in which two different types of air shock are used to induce stress waves in an elastically confined, cylindrical specimen of sand, the objective being to permit direct observation of the effects of unloading on the dynamic response of granular material. In one case, “pure” unloading waves are generated by suddenly subjecting the end of a prestressed specimen to pressures below atmospheric. In the second type of test, the specimens are impacted at one end by an air shock which has the form of a sharp front followed immediately by a rapid exponential decay of pressure. The decay of the shock pressure generates unloading waves which cause attenuation of the wave as it propagates in the granular material. As a result of the tests, it is suggested that seismic-wave velocity may be correlated to the modulus of unloading cycles in a quasi-static test and that, when strainrate effects are included, a relatively simple model may be used to predict the dynamic response of granular materials.

Numerous experiments have already been published on the strength of wood and other substances, as far as regards their cohesion and elasticity; but I am not aware of any extensive table of the modulus of torsion of different species of wood, deduced from experiments conducted upon a proper scale, and with the necessary care. To supply this defect, and to furnish the practical engineer and mechanic with useful data, and with rules for their application, is the object of the pre­sent communication, consisting of a copious table of the results of my experi­ments, made at various times, and upon substances of considerable variety of dimensions within the ordinary limits of practice.

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.