Influence of load amplitude and uniaxial tensile properties on fatigue crack growth

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

Modified entropic elasticity of rubberlike materials

In the first part of the paper, consisting of Sections 2 and 3, physical grounds are adduced for weakening the concept of strictly entropic elasticity as applied to elastomeric materials. The resulting notion of modified entropic elasticity is shown to provide an alternative formulation of a model of rubberlike thermoelasticity proposed by Chadwick (1974). In the second part (Sections 4 and 5) Chadwick's model is generalized by allowing the deformation-dependent part of the internal energy to be a symmetric function of the principal stretches rather than depending only on their product, as in the original development. Consistently with the molecular theory of polymer networks, and with experimental findings, the extended model predicts that the deviatoric stress is not entirely entropic in origin, but arises in part from changes of internal energy. The energetic fraction of the retractive force in an extended cylinder is calculated and discussed in some detail and the paper concludes with a correlation of theoretical results with measurements on specimens of a lightly cross-linked natural rubber.     

Effective elasticity tensor of a periodic composite

The effective elasticity tensor of a composite is defined to be the four-tensor C which relates the average stress to the average strain. We determine it for an array of rigid spheres centered on the points of a periodic lattice in a homogeneous isotropic elastic medium. We first express C in terms of the traction exerted on a single sphere by the medium, and then derive an integral equation for this traction. We solve this equation numerically for simple, body-centered and face-centered cubic lattices with inclusion concentrations up to 90% of the close-packing concentration. For lattices with cubic symmetry the effective elasticity tensor involves just three parameters, which we compute from the solution for the traction. We obtain approximate asymptotic formulas for low concentrations which agree well with the numerical results. We also derive asymptotic results for C at high inclusion concentrations for arbitrary lattice geometries. We find them to be in good agreement with the numerical results for cubic lattices. For low and moderate concentrations the approximate results of Nemat-Nasseret al., also agree well with the numerical results for cubic lattices.     

Application of quasilinearization technique to the vertical channel flow and heat convection

The quasilinearization technique, also known as the generalized Newton-Raphson method, is employed to solve the problem of fluid injection through one side of a long vertical channel. With very approximate starting values, only a few iterations are needed to obtain a result with high accuracy. The results are compared with those obtained by the perturbation technique. Although the perturbation technique is perhaps the simplest and the most straight-forward method to achieve solutions to non-linear boundary value problems, the limitation on the magnitude of perturbed parameters hinders its applicability.     

Active feedback control of a beam subjected to a nonconservative force

This study examines the possibility of controlling through feedback a thin cantilevered beam subjected to a nonconservative follower force. A converging frequency flutter instability which occurs in this model is similar to classical bending-torsion flutter of an aircraft wing. Because of the similar nature of the instabilities, the beam under the follower force can be a useful vehicle for investigating the fundamental aspects of stabilization of wing flutter by feedback control. A modal approach is used for obtaining the mathematical model and control laws. A standard root locus technique for simple analytical models is also used to understand and explain the control of the beam. Experiments are carried out to verify the validity of this theoretical model. Good correlation is shown between theoretically and experimentally determined stability boundaries as well as for modal frequency and damping variation with follower force.     

The influence of finite rates of temperature change in the creepT-jump experiment

Summary General equations for nonisothermal creep of a linear viscoelastic solid are presented. Both the time dependent strain and strain rate are predicted for an arbitrary temperature history. The creepT-jump experiment (imposition of a sudden temperature change on a creeping specimen) is analyzed using these equations in order to understand the influence of non-instantaneous temperature changes on the experimental observations. It is shown that an increase in the time required to impose the temperature change causes an increase in the activation energy,H _exp, determined via creepT-jump. This effect is most pronounced for materials with large activation energies. Appropriate extrapolation techniques can be used to obtain the result expected for an instantaneous temperature change. Verification of the theoretical prediction was obtained from isothermal and nonisothermal creep experiments on polymethylmethacrylate in the linear viscoelastic region. The activation energy for a nearly instantaneous temperature change was 43 ± 2 kcal/mol. As the rise time of the temperature change was increased to 600 seconds,H _exp increased to 70 ± 2 kcal/mol. The effects of the rate of temperature change on other aspects of the creepT-jump experiment were also found to be in keeping with the predictions of the nonisothermal linear theory.

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Zusammenfassung Es werden allgemeine Gleichungen für das nichtisotherme Kriechen eines linear-viskoelastischen Festkörpers abgeleitet. Sowohl die zeitabhängige Dehnung als auch die Dehngeschwindigkeit werden für eine beliebige Temperaturvorgeschichte vorausgesagt. Das Kriech-T-Sprung-Experiment, d.h. die Aufbringung einer plötzlichen Temperaturänderung bei einer Kriechprobe, wird mit diesen Gleichungen analysiert, um den Einfluß von kontinuierlichen Temperaturänderungen bei experimentellen Beobachtungen verständlich zu machen. Es wird gezeigt, daß eine Verlängerung der Zeitdauer zur Erzeugung der Temperaturänderung ein Anwachsen der AktivierungsenergieH _exp, verglichen mit derjenigen beim Kriech-T-Sprung, zur Folge hat. Dieser Effekt tritt am ausgeprägtesten bei Stoffen mit großen Aktivierungsenergien auf. Angepaßte Extrapolationsmethoden lassen sich anwenden, um das für eine plötzliche Temperaturänderung erwartete Ergebnis zu erhalten. Die theoretischen Voraussagen wurden mit Hilfe isothermer und nicht-isothermer Kriechexperimente an Polymethylmethacrylat im linearviskoelastischen Bereich verifiziert. Die Aktivierungsenergie für eine nahezu plötzliche Temperaturänderung ergab sich zu 43 ± 2 kcal/mol. Wenn das Zeitintervall für die Temperaturänderung auf 600 Sekunden erhöht wurde, stiegH _exp auf 70 ± 2 kcal/mol. Die Auswirkungen der Temperaturänderungsgeschwindigkeit bezüglich anderer Gesichtspunkte beim Kriech-T-Sprung-Experiment ergeben sich ebenso in Übereinstimmung mit den Voraussagen der nicht-isothermen linearen Theorie.

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With 15 figures     

Laser-generated rayleigh waves in graphite/epoxy composites

This study explores the potential for application of laser-induced surface or Rayleigh waves on graphite/epoxy composites. Rayleigh waves were generated by a Q-switched ruby laser in the ablation regime and detected by a pinducer which permitted accurate phase-velocity measurements. The Rayleigh wave velocity was measured in various directions relative to the fiber direction. Experimental results agreed closely with numerical predictions in the thick plate, but showed some increase of phase velocity in the thin plate. Laser-generated Rayleigh waves, particularly along the fiber direction, showed good potential for applications in NDT.     

The grid-shift technique for moiré analysis of strain in solid propellants

Moiré principles and procedures were surveyed with a view toward adaptation to measurement of complex strain distribution in solid propellants. Compliant coating and photosensitive materials were selected for grid reproduction. The most flexible of the several possible procedures for recording moiré data was found to be grid photography. A novel “grid-shift” technique employing coarse grids was developed for point-by-point determination of surface displacement derivatives, and the grid-shift relations for large strain and large rotation were derived. The technique is extremely versatile, permitting the analysis of strain of dynamically deformed specimens in nonambient environmental conditions of temperature, pressure or atmosphere. The utility of the technique was demonstrated by application to static and dynamic problems.     

Nonlinear stability analysis of miscible displacements

A simulator for three-dimensional horizontal miscible displacements in porous media is developed. Using this simulator, we examine the initiation and development of instabilities, viscous fingers and gravity tongues.With the only perturbations to the system being truncation and round-off errors, a density ratio (the ratio of the density of the displacing fluid to that of the displaced fluid) different from one is responsible for the initiation of the instabilities, and an unfavorable mobility ratio (the ratio of the viscosity of the displaced fluid to that of the displacing fluid) is responsible for the growth of the instabilities.