Sinusoidal Stress Research Articles

Fatigue Failure Under Complex Stress Histories

An expression for predicting fatigue failure of a structure subjected to sinusoidal stress cycles of different amplitudes and different mean values is derived. The derivation is based on a steady-state model of fatigue crack growth. For two cases, predicting in-service fatigue failure and predicting crack growth in a laboratory test, the derived expression is substantially equivalent to the classical linear damage rule. The crack-growth derivation extends the classical linear damage concept to the problem of predicting the remaining fatigue life of a partially damaged structure.

A two-layer frictional model of wind-driven motion in a rectangular oceanic basin

A study is made of the circulation in a two-layer ocean with rectangular boundaries driven by a zonal wind stress. The dynamics is linear, with bottom and interface stresses. A non-linearity arises from finite variations in layer depths. In the case where the lower layer is much deeper than the upper layer the equations can be integrated exactly. The solution gives a directly wind-driven gyre in the upper layer, with an interior Sverdrup regime and a western boundary current. In the lower layer there is no interior motion but a recirculating boundary current develops. The total transport is thereby intensified near the coast while a counter-transport develops at the outer edge. The boundary current width varies with the current depth and the latitude. The key parameter in the model is ? = (D/F)(H/h 0 ) , where D and F are the “frictional depths” applicable at the interface and the bottom, H and h 0 are the total depth and the upper layer depth. Numerical examples are worked out for a sinusoidal wind stress distribution in the case ? = 1. DOI: 10.1111/j.2153-3490.1966.tb01443.x

A two-layer frictional model of wind-driven motion in a rectangular oceanic basin

A study is made of the circulation in a two-layer ocean with rectangular boundaries driven by a zonal wind stress. The dynamics is linear, with bottom and interface stresses. A non-linearity arises from finite variations in layer depths. In the case where the lower layer is much deeper than the upper layer the equations can be integrated exactly. The solution gives a directly wind-driven gyre in the upper layer, with an interior Sverdrup regime and a western boundary current. In the lower layer there is no interior motion but a recirculating boundary current develops. The total transport is thereby intensified near the coast while a counter-transport develops at the outer edge. The boundary current width varies with the current depth and the latitude.The key parameter in the model is ε = (D/F)(H/h0), where D and F are the “frictional depths” applicable at the interface and the bottom, H and h0 are the total depth and the upper layer depth. Numerical examples are worked out for a sinusoidal wind stress distribution in the case ε = 1.

Dynamic Response of a Lined Rigid Inclusion

A theoretical analysis is made to predict the dynamic response of an elastically lined cylindrical rigid inclusion subjected to plane compressional sinusoidal stress waves. Solutions in the form of infinite series involving Hankel functions of the first and second kinds for the wave equations are determined from the prescribed boundary conditions. The nondimensional parameters are then identified and typical material properties are used in numerical calculations. It is found that the angular distribution of the maximum dynamic stresses follows a certain pattern depending on the wave number. In addition, the lining-inclusion density ratio and the lining thickness also have strong influence on the critical stresses. The translation of the rigid inclusion, although having similar response characteristics against wave number as the stresses, always reaches its critical value at a lower wave number than do the stresses.

Transient Response in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling

The transient response of a semi-infinite, viscoelastic rod after application of a sinusoidal stress variation at one end has been investigated by a numerical method. Account has been taken of temperature dependence of properties and of thermomechanical coupling. It is found that, with values of physical properties typical for polymeric materials, temperature approaches steady state several orders of magnitude more slowly than would be the case for stress and strain in the absence of thermomechanical coupling.

The Study on the Fatigue Strength by Varying the Stress-Amplitude withd the Superposed Mini-Sinusoidal Stress Wave on the Based Sinusoidal Stress Wave : Report 1, Some Experimental Results of Fatigue Test by New Simple Device for Superimposing Secondary Mini-Stress Wave

The Study on the Fatigue Strength by Varying the Stress-Amplitude withd the Superposed Mini-Sinusoidal Stress Wave on the Based Sinusoidal Stress Wave : Report 1, Some Experimental Results of Fatigue Test by New Simple Device for Superimposing Secondary Mini-Stress Wave

Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling

A numerical method is developed for the analysis of one-dimensional wave propagation in viscoelastic media with temperature-dependent properties when thermomechanical coupling is significant. The method is applied to a specific case of longitudinal wave propagation in a finite rod with essentially sinusoidal stress variation at the two ends. The results show that, contrary to the usual assumption, such a system does not have the same response as a single-degree-of-freedom elastic system with viscous damping, as long as a realistic stress-strain relation is used.

The Nature of Fatigue

Abstract While the fundamental nature of fatigue is not well understood, many of the phenomenological aspects of the problem have been sorted out. A general outline of the problem, methods of presenting data, types of fatigue and the factors involved are discussed. The fundamentals of the problem and what is known about fatigue today are outlined, and the implications of this knowledge in terms of possible treatments, inspection, etc., particularly as related to the drilling industry, are presented. Introduction Fatigue is a strange and exceedingly dangerous problem. Fatigue failure occurs with little or no warning under repeated applications of a load which the metal would support indefinitely if the load were applied statically. The problem was first recognized in 1850, but it has become progressively more prevalent as technology has developed machines and equipment subjected to repeated loading and vibration. Today fatigue accounts for about 90 per cent of all service failures due to mechanical causes. Causes of Fatigue Failure Much has been written about fatigue and a great many people have studied and continue to study it, using the most modern techniques and ingenious experiments. While a great deal is known about the phenomenon, we do not understand the basic mechanism or nature of the problem. Three basic factors are, however, necessary to cause fatigue failure. These are: a maximum tensile stress of a sufficiently high value; a large enough fluctuation in the value of the applied stress; and a sufficiently large number of cycles of the fluctuating applied stress. While these are sufficient to cause fatigue, there are a host of other variables which alter the conditions for fatigue, such as temperature, crystal system of the metal, grain size, environment (corrosive or otherwise), metallurgical structure, stress system, etc. Fluctuating StressThe general types of fluctuating stresses which can cause fatigue are illustrated in Fig. 1. The first represents an idealized situation wherein the net resultant stress is zero, fluctuating in a sinusoidal fashion from tensile to compressive. This is the most common form used to study fatigue in a laboratory, but is also approached in service by a rotating shaft operating at a constant speed without overload. The second shows the sinusoidal stress form but here the resultant (or mean) stress is not zero. The third shows an irregular or random stress cycle of the type most frequently encountered in actual service, and of course is of the type found in drilling operations. S-N Curves The most common method of presenting fatigue data is by means of the stress-number (S-N) curve, which relates the number of cyclic stresses imposed on a specimen to failure with the maximum stress applied. These data are generally obtained by imposing a sinusoidal stress pattern with a net resultant (or mean) stress of zero as shown in Fig. 1.Fig. 2 shows a typical S-N curve for a ferrous and nonferrous material. The fatigue life of the nonferrous material is very short for high stresses, but this life becomes increasingly longer as the magnitude of the maximum stress is reduced. For the case of the ferrous metals, a plateau is reached when the stress is reduced below a certain level. This means that for a stress equal to or less than the plateau value, the specimen will support an infinite number of cycles without failure. This plateau value is the maximum stress for infinite life, and is called the fatigue or endurance limit. Most nonferrous metals such as aluminum, magnesium and copper alloys do not have a true fatigue limit because the S-N curve never becomes horizontal and they will eventually fail at any value of an applied cyclic load. JPT P. 869ˆ

Anelasticity and viscoelasticity in glass

Experiments on glasses under conditions of constant stress, constant strain and sinusoidal stress are briefly reviewed. These experiments are related to some papers presented at two recent meetings on the anelastic and viscoelastic properties of glasses.

Comparison of Stress Response and Fatigue Test Results under Random and Sinusoidal Acoustic Loading

For several configurations of aircraft structure, measured values of stress response under random loading are compared to those computed from sinusoidal stress response data. Predictions of long-life allowable random loads are made from fatigue test data obtained under sinusoidal loading. These predictions are compared with those inferred from failures in accelerated tests under random forcing. It is concluded that the convenient and relatively inexpensive sinusoidal test provides a simulation of random loading of sufficient accuracy for use in the design of structural components.

The Behaviour of a Vibrating Visco-elastic Cylinder

The general differential equation of wave-motion for a Burgers body is used to express the attenuation and retardation time of a visco-elastic material in terms of the mechanical quality factor of a cylinder of the material set into forced vibration. It is assumed that the vibrations are induced by the action of a sinusoidal stress at one end of the cylinder.

Viscoelastic Behavior of Polyisobutylene under Constant Rates of Elongation

Abstract A variety of methods has been used to study the viscoelastic properties of polymeric materials. These methods include the response to sinusoidal stress (dynamic measurements), stress relaxation, and creep under constant load and constant stress. The present investigation was made to determine whether or not the viscoelastic properties of rubberlike materials over an extended time scale could be obtained from stress-strain curves measured at different strain rates and temperatures. Polyisobutylene of high molecular weight was selected for study, since its viscoelastic properties have been investigated extensively in a cooperative program sponsored by the National Bureau of Standards. From the data obtained, Marvin has derived the distribution functions of relaxation and of retardation times over a time scale of 10−10 to 107 sec. These functions show quantitatively a change in properties from liquidlike to rubberlike to glasslike with decreasing time scale. The equilibrium stress-strain curves for lightly crosslinked rubber and other elastomers are closely linear for elongations up to 100 per cent. The non-equilibrium (viscoelastic) stress-strain curves for similar and noncrosslinked elastomers might be expected to be linear viscoelastic, as a first approximation, at temperatures above the glass transition, provided the strain and the strain rate are not excessively large. Nonlinear viscoelastic effects are usually pronounced for materials in their glasslike state and at large strains.

LXXI. The propagation of stress pulses in viscoelastic solids

Abstract The propagation of short mechanical pulses along rods of three polymers, polythene, polystyrene and polymethylmethacrylate, has been investigated experimentally. The pulses were produced by the detonation of small quantities of explosive at one end of a rod and a condenser microphone was employed to record the displacement of the opposite end. It is shown that if the response of the material to sinusoidal stresses over a wide frequency range is known, the pulse shapes can be predicted accurately by means of a numerical Fourier synthesis. Further, that where the damping loss is not too large and is constant over a wide frequency range, as it is for many polymers, a general solution of the problem can be obtained which gives the pulse shape for all such polymers and for all distances of travel. Some experiments on pulses through blocks of plastic are also described.

The creep of metals under interrupted stressing

The creep behaviour of polycrystalline lead subjected to interrupted stress, or ‘stress pulses’, has been examined with an apparatus which enables the creep curve to be recorded as a magnified photographic trace. When the metal is reloaded after an interruption, a new creep transient is exhibited which can be adequately expressed by assuming a fraction n of the material to have recovered its original Andrade β -flow properties, whilst the remaining fraction (1 — n ) continues to deform as if unloading had not occurred. It is shown that this analysis is valid whether the material exhibits a finite Andrade K -flow or not. The variation of n with the time of creep ( T ) previous to the interruption, for a constant recovery time ( R ), and the variation of n with R for a constant T , are each investigated. The full component analysis is worked out for four stages, but the exact calculation rapidly becomes too unwieldy, and approximations are developed to deal with the case of regular repetitive stress pulses. It is shown that the creep under these conditions may be very closely formulated from measurements of uninterrupted creep coupled with knowledge of the value of n for the first interruption. The problem of a constant stress cycle, i. e. ɤ + R = constant (= λ ), is specially treated, and the significant effect of the ɤ/λ ratio is demonstrated; it is, for example, possible, with a given duration of test, for interrupted stress to bring about a greater creep strain than uninterrupted creep at the same stress. Because of the character of the β -againststress curves, nearly square β -pulses can occur in structures subjected to sinusoidal stress cycles, and the treatment has, therefore, a very wide application.

The Response Characteristics of Linear Systems

For a linear system, steady-state response to sinusoidal stress cannot have a unique dynamic modulus and phase shift, but these quantities must be related to rate of creep; particularly they cannot be independent of external frequency. A proof is given that such linear system is always equivalent to a viscoelastic system. Finally the discrepancy between the relations deduced and experimental results of various authors is pointed out and discussed.