Function Of Strain Amplitude Research Articles

超音波疲労試験による１０５０アルミニウムの疲労変形

Ultrasonic fatigue tests have been performed on commercial 1050 aluminum. Internal friction (Q-1) has been measured during fatigue tests and as a function of strain amplitude (ε). It is shown that more than 109 cycles test is necessary in order to determine the fatigue limit. Q-1 versus ε curves have the inflection points at particular strain amplitude which corresponds to the strain at fatigue limit. Below this strain amplitude, Q-1 does not change and any slip bands are not observed on the specimen surface fatigued for 1010 cycles.

Internal Friction Study of Microplasticity of Aluminum Thin Films on Silicon Substrates

Internal friction in aluminum thin films 0.2 to 2.0 μm thick on silicon substrates has been investigated between 180 and 360 K as a function of strain amplitude by means of a free-decay method of flexural vibration. According to the constitutive equation, the internal friction in the film alone can be evaluated separately from the data on the film/substrate composite. The amplitude-dependent part of internal friction in aluminum films is found in the strain range approximately two orders of magnitude higher than that for bulk aluminum. On the basis of the microplasticity theory, the amplitude-dependent internal friction can be converted into the plastic strain as a function of the effective stress on dislocation motion. The mechanical responses thus obtained for aluminum films show that the plastic strain of the order of 10 -9 increases nonlinearly with increasing stress. These curves tend to shift to a higher stress with decreasing film thickness and also with decreasing temperature, both indicating a suppression of the microplastic deformation. At all temperatures examined, the microflow stress at a constant level of the plastic strain varies inversely with the film thickness, which qualitatively agrees with the variation in macroscopic yield stress.

Dynamic properties of short fiber–EPDM matrix composites as a function of strain amplitude

AbstractThe dynamic properties of composite materials consisting of an ethylene–propylene rubber matrix (EPDM) and short polyester polyethylene‐terephthalate (PET) fiber vary with dynamic stress amplitude applied to the material. These variations support the statement that fiber treatment with 1,4‐carboxy‐sulphonyl‐diazide, which acts as a bridge between the fiber and the matrix and hence enhances the strength of the interface enabling it to resist greater strain applied to the composite and, as a consequence, yielding greater retention values of the storage modulus, measured longitudinally to preferential fiber orientation, E′L. By means of transversal measurements of the storage modulus, E′T, of these materials it is possible to determine a parameter b, which eventually indicates the degree of matrix–fiber bonding and which is consistently higher for materials filled with surface‐treated fiber. This enhanced phase adhesion is further confirmed by higher equivalent interfacial thickness values, ΔR, which, in addition, vary less with increasing dynamic strain amplitude. Finally dissipated energy variation or mechanical energy loss, Eloss, is studied as a function of fiber content and strain amplitude. Experimental findings show Eloss to increase with fiber content and strain amplitude, when measured at constant strain amplitude ϵ0, and to yield higher values for treated fiber samples. © 1994 John Wiley & Sons, Inc.

Energy dissipation in inelastic flow of saturated cohesionless granular media

The results of a study of energy dissipation in cohesionless granular media are presented. The relation between the excess pore water pressure, accumulated in a water-saturated granular mass, and the corresponding external work in undrained cyclic loading is studied experimentally, under displacement-controlled conditions. A micro-mechanical model of internal energy dissipation due to slip between contacting granules is introduced, and the results are compared with experimental measurements. The specimens are subjected to two sequences of loading with an intermediate reconsolidation to simulate reliquefaction. External work per unit volume is calculated from the experimental results, and its correlation with the excess pore water pressure is examined. In the first loading, a unique non-linear relation exists between the excess pore water pressure and the external work per unit volume which is independent of the shear strain amplitude. In the second loading this relation is a function of strain amplitude. Based on a micromechanical model, it is shown that the internal dissipation per unit volume in cohesionless granular media can be expressed in terms of the time history of the applied effective pressure and a single scalar parameter which depends on the density and strain amplitude. The model is further validated by torsion tests with random variation in the applied strain amplitude, and excellent agreement with the experimental results is obtained. L'article présente les résultats obtenus au cours d'une étude sur la dissipation de l'énergie dans des milieux granulaires pulvérulents. La relation existant entre l'excès de pression interstitielle d'eau, accumulé dans une masse granulaire saturée, et le travail extérieur associé apparaissant au cours de cycles de chargement non-drainés, à déplacement contrôlé, est étudiée expérimentalement. Une modélisation micromécanique de la dissipation d'énergie interne liée au glissement entre grains jointifs, est proposée. Les résultats obtenus à l'aide de ce modèle sont comparés aux mesures expérimentales. Les échantillons sont soumis à deux cycles de chargement, séparés par une reconsolidation permettant de simuler la reliquéfaction. Le travail extérieur, par unité de volume, est calculé à partir des résultats expérimentaux. La corrélation pouvant exister avec l'excès de pression interstitielle est étudiée. Lors du premier chargement, il n'existe qu'une seule relation entre l'excès de pression interstitielle et le travail extérieur, cette relation étant indépendante de l'amplitude de la déformation au cisaillement. Lors du second chargement, cette relation devient dépendante de l'amplitude de cette déformation. U apparaît, à partir du micromodèle, que la dissipation interne, par unité de volume d'un milieu granulaire pulvérulent, peut s'exprimer en fonction de l'historique de la pression effective appliquée et d'un paramètre scalaire unique dépendant de la densité et de l'amplitude de la déformation. Le modèle est ensuite validé à l'aide d'essais de torsion, pour des variations aléatoires de l'amplitude de déformation. La correspondance avec les résultats expérimentaux est excellente.

Fabrication and damping capacity of CuZnAl matrix composites processed by powder metallurgy route

Cu-26.5Zn-4Al (wt.%) alloy (as a matrix) and each of three different Fe-based ferromagnetic alloy flakes (as a reinforcing material) were processed into three different composites via conventional cold compaction; this was followed by hot isostatic pressing. The sliced sheets of the composites were heat-treated at 1073 K and quenched into ice water to introduce a martensitic structure. The damping capacity and the storage modulus were measured for three different composites as functions of strain amplitude and frequency. The microstructure of the composites was characterized by use of optical microscopy, scanning electron microscopy and scanning transmission electron microscopy in order to examine the martensite, the flake morphologies and the interfaces. In all three composites, the loss factor increased from 0.02 (with a strain of f100 × 10 −6) to approximately 0.05 (with a strain of 300 × 10 −6). In particular, the FeCr flakes/CuZnAl composites exhibited a maximum loss factor near a strain of 165 × 10 −6 , owing to the damping of the FeCr flakes.

Hysteresis loop shape in fatigue of CuZn alloys

Hysteresis loop shapes in 70Cu30Zn, 75Cu25Zn and 80Cu20Zn alloys were studied as a function of strain amplitude and holding stress during load interruptions. Three loop shapes, designated as I, II and III, were found. The strain amplitude at which transition from Shape I to Shape II and Shape II to Shape III occurs, decreases with decreasing Zn content. The characteristic shapes of these loops were considered to arise from Zn segregation to dislocations and from Bauschinger stress behavior as a function of half-cycle strain. Holding during cycling produced anisotropic loop shapes. The magnitudes of these distortions increased with holding time, eventually producing burst and yielding behavior. Explanations for anisotropic loop shapes were also based on Zn segregation to dislocations and on changes in Bauschinger stress as a function of half-cycle strain.

Strain-amplitude-dependent internal friction and microplasticity in alumina with microcracks

Abstract Internal friction in polycrystalline alumina subjected to thermal shock has been measured as a function of strain amplitude by means of the free-decay method of flexural vibration. The curves of the amplitude dependence show a more rapid rise with increasing thermal shock damage. The data have been analysed on the basis of the phenomenological theory of microplasticity assuming a friction-type hysteresis. Thus the internal friction in alumina with microcracks is transformed into a microplastic strain of the order of 10—9. The stress-strain responses show that the microplastic strain increases nonlinearly with increasing stress under conditions where macroscopic plastic flow can never be observed. The variation in the microplastic flow stress corresponds well to the decrease in the macroscopic fracture strength resulting from the formation of microcracks and crack propagation.

Microplasticity and Dislocation Mobility in Copper-Nickel Single Crystals Evaluated from Strain-Amplitude-Dependent Internal Friction

Internal friction in copper-0.4 to 7.6 at% nickel single crystals is measured as a function of strain amplitude at various temperatures. Analysis of the data on the amplitude-dependent internal friction yields the relation of effective stress and microplastic strain of the order of 10−9. The stress-strain responses thus obtained exhibit that the microplastic flow stress increases more rapidly on alloying than the macroscopic yield stress. The mean dislocation velocity is also evaluated from the internal-friction data, which corresponds well to the etch-pit data. It is shown that the dislocation motion is impeded by friction due to dispersed solute atoms. Die innere Reibung von Kupfer-0,4 bis 7,6 at% Nickel-Einkristallen wird als Funktion der Dehnungs-amplituden bei unterschiedlichen Temperaturen gemessen. Die Analyse der Daten der amplitudenabhängigen inneren Reibung ergibt das Verhältnis von Effektivspannung und mikroplastischer Verformung in der Größenordnung von 10−9. Das erhaltene Spannungs-Dehnungs-Verhalten zeigt, daß nach dem Legieren die mikroplastische Fließspannung stärker als die makroskopische Streckgrenze zunimmt. Die mittlere Versetzungsgeschwindigkeit wird außerdem aus den Daten der inneren Reibung ermittelt, in guter Übereinstimmung mit den aus Ätzgrübchen ermittelten Werten. Es wird gezeigt, daß die Versetzungsbewegung durch die Reibung aufgrund verteilter Fremdatome bestimmt wird.

Shear Indxuced order of Cncenirated Dispersions

ABSTRACTThe microstructure or interparticle ordering in concentrated dispersions of colloidal pmma (polymethylnethacrylate) particles in a mixture of tetralin and decalin have been monitored using light scattering techniques. These sterically stabilized, uniformly sized, nearly hard, colloidal spheres are observed to exhibit an equilibrium phase transition from a liquid-like ordering to a crystal-like ordering of suspended particles as the volume fraction of solids increases. The crystals have a close packed - random stacked structure. At the largest volume fractions a nonequilibrium glassy phase results.Samples at different volume fractions are subjected to steady and oscillatory shear flow. Four basic structures are observed to exist: liquid or distorted liquid-like, string-like, sliding or randomly stacked layers, and face centered cubic (FCC) structures. Oscillatory shear studies will be reported here and are made as a function of strain amplitude and shear history, in addition to volume fraction. Generally, oscillatory shear is effective in ordering samples. For example, an unstable FCC ordering can be induced in an equilibrium liquid-like sample.

Amplitude internal friction peaks associated with the interaction between dislocation kinks and solute atoms in aluminium

Early in 1950, Kê observed in slightly cold-worked dilute aluminium-copper solid solutions a pronounced low-frequency internal friction peak around room temperature as a function of strain amplitude in which the high-amplitude side of the peak decreases rapidly to a very small value. This paper reviews the experimental results since the work of Kê, with emphasis on cold-worked aluminium containing Cu or Mg as substitutional solute atoms. A dislocation kink dragging and break away model is suggested. The latest results show that this internal friction peak around room temperature consists of two separate peaks. The amplitude peak accompanying the lower temperature peak shifts toward lower amplitudes and that accompanying the higher temperature peak shifts toward higher amplitudes with an increase of temperature of measurement. The former amplitude peak appears at an amplitude range lower than that of the former peak. A mechanism of the double amplitude peaks is suggested in terms of the simultaneous occurrence of longitudinal core diffusion (LCD) and transverse core diffusion (TCD) of the solute atoms during the to and fro sidewise motion of the dislocation kinks. Some conclusions concerning the mechanism of Hasiguti peaks are drawn from the comparison with studies on the internal friction peaks associated with the interaction between dislocation kinks and solute atoms.

Fatigue life response of ASME SA 106-B steel in pressurized water reactor environments

Fatigue strain-life tests were conducted on ASME SA 106-B piping steel base metal and weld metal specimens in 288°C (550°F) pressurized water reactor (PWR) environments as a function of strain amplitude, strain ratio, notch acuity, and cyclic frequency. Notched base metal specimens tested at 0·017 Hz in 0·001 part per million (ppm) dissolved oxygen environments nearly completely used up the margins of safety of 2 on stress and 20 on cycles incorporated into the ASME Section III design curve for carbon steels. Tests conducted with smooth base metal and weld metal specimens at 1·0 Hz showed virtually no degradation in cycles to failure when compared to 288°C air test results. In all cases, however, the effect of temperature alone reduced the margin of safety offered by the design curve in the low cycle regime for the test specimens. Comparison between the fatigue life results of smooth and notched specimens suggests that fatigue crack initiation is not significantly affected by 0·001 ppm dissolved oxygen, and that most of the observed degradation may be attributed to crack growth acceleration. These results suggest that the ASME Section III methodology should be reviewed, taking into account the PWR environment variables which degrade fatigue life of pressure-retaining components.

The Bauschinger Effect of Sheet Metal Under Cyclic Reverse Pure Bending

AbstractIn some sheet metal forming operations, metal flow involves a series of bending and unbending steps. In any such bending sequence the occurrence of the Bauschinger effect is likely. Correct process modelling of such forming operations therefore requires inclusion of the Bauschinger effect. This paper presents results of an experimental procedure developed for the determination of the Bauschinger effect. Sheet strips were subjected to a series of bending and reverse bending steps by means of a pure moment bending device. Results show the Bauschinger effect in steel and aluminum sheet as a function of strain amplitude, prestrain, and sheet thickness.

Shear modulus and internal friction of calcite rocks at seismic frequencies: pressure, frequency and grain size dependence

The shear modulus G and associated internal friction Q −1 have been measured at seismic frequencies for a suite of four essentially monomineralic, calcite rocks with grain sizes ranging from 4 to 1000 μm. The measurements are based on a previously described technique for the observation of forced torsional oscillations of a series combination of a rock cylinder and a steel standard under high confining pressure at room temperature. The behaviour of each rock has been studied as a function of strain amplitude (10 −8–10 −6 maximum at surface), pressure (0 – 300 MPa) and oscillation period (1 – 300 s). No evidence is found of any departure from linearity in the range of strain amplitudes studied. Corrections, which are significant only at the shortest periods (1 – 3 s), have been applied to the raw data to account for the influence of torques exerted on the specimen assembly by the gas pressure medium. Up to about 100 MPa, increase in pressure results in a marked increase in G and decrease in Q −1, attributable to the closure of crack porosity—except in the fine-grained Solnhofen limestone in which both G and Q −1 are insensitive to change in pressure, indicative of the virtual absence of crack porosity. At higher pressures, G is much less pressure-sensitive and Q −1 is essentially pressure-independent, with values less than 0.001 in all four rocks. Since the rock specimens were jacketted under conditions of normal humidity, these relatively low values of Q −1 indicate a diminished role for adsorbed water in the anelasticity of rocks at high effective pressures. Within the pressure-independent regime, Q −1 is essentially independent of frequency for periods of 3–100 s and increases by only 30% as the grain size decreases from 1000 to 4 μm. Thus, within this regime, it is concluded that the observed value of Q −1 results to a large degree from an intracrystalline mechanism with a broad range of relaxation times. The possibility of significant dislocation damping will be discussed.

Mechanisms governing cyclic fracture in an Al–Cu–Li alloy

AbstractThe fracture behaviour of a peak-aged, partially recrystallized Al–4·5Cu–1·21Li–0·51Mn–0·20Cd alloy has been investigated as a function of strain amplitude, stress intensity, and environment. It was found that the failure was predominantly intergranular separation, regardless of the environment, stress intensity, or strain amplitude, and that the fracture behaviour was influenced mostly by intrinsic microstructural features, rather than the nature of the environment. The shearable nature of matrix strengthening precipitates, large recrystallized grains, and precipitate-free zones along the high-angle grain boundaries aid in localizing the deformation, resulting in low-energy intergranular fracture. The iron- and silicon-rich intermetallic precipitates in the alloy promote void nucleation following fracture of the particle. A model is proposed which suggests the need for high stresses and strains for the initiation and spontaneous growth and coalescence of microvoids. The mechanisms of fracture beh...

Anomalously amplitude dependent effect of the low-temperature internal-friction peaks in cold-worked dilute aluminium-copper solid solution

The composite internal friction peak (versus temperature) assumed to be consisted of a relaxation peak and a phase transformation peak previously observed in cold-worked Al-0.50wt% (0.21at%) Cu at temperatures below room temperature are now resolved into two separate peaks. Internal friction peaks as a function of strain amplitude (the amplitude peak) are observed around the temperature region of both peaks for the first time.

A Dislocation Pinning in KCl Crystals Annealed in Chlorine Gas

On KCl crystals annealed in chlorine gas, the internal friction was measured as a function of strain amplitude by the Marx's method. The experimental results were analysed by the Granato-Lucke model of vibrating dislocations. It was found that the internal friction is remarkably decreased with X-irradiation. It was indicated that chlorine molecular ions introduced in crystals by the annealing were changed to pinning elements on the dislocations with the X-irradiation. With repeated measurements in the range exceeded the break points, the internal friction irreversibly increased. The fact was interpreted by vanishing of the pinning elements with breakaway of the dislocations from them. The pinning element was supposed to be chlorine molecule ion Cl 2 - captured on dislocation.

Role of Adhesion in Viscoelastic Properties of Rubber-Tire Cord Composites

Abstract Dynamic mechanical measurements have been carried out on samples of rubber and PET cord-rubber composites, with and without adhesive, as a function of strain amplitude, temperature, pretension, angle of strain application and time of cycling. The results show that mechanical loss and dynamic modulus depend on these variables as well as the presence and type of adhesive at the cord-rubber interface. Based on these results, we conclude that adhesion plays a significant role in the viscoelastic properties of a composite and it is an important factor along with the properties of components in the analysis of tire performance in terms of composite properties. This study clearly shows that the maximum adhesion may not be the optimum adhesion in tire technology. The most relevant question, i.e., the determination of the optimum level of adhesion for a specific tire, however, remains unanswered. The viscoelastic properties of the composites decrease with time of cycling but the rate of decrease depends upon the level of adhesion in the starting material. This result could be important in the development of a more realistic dynamic adhesion test. Attempts to use the viscoelastic experiments with small amplitude, high frequency strain to determine the onset of fracture in the composite specimen appears to be promising. Work is in progress to determine the potential of this method in the analysis of adhesion.

Amplitude dependence of dislocation damping in high-purity copper after quenching and during 1-MeV electron irradiation

Dislocation damping as a function of strain amplitude following quenching and during 1-MeV electron irradiation was investigated by measuring Young’s modulus and the logarithmic decrement in high-purity polycrystalline copper. A ’’peaking effect,’’ an initial increase and subsequent decrease in the damping, was observed at all strain amplitudes during electron irradiation. A somewhat subdued peaking effect was observed only at high strain amplitudes following quenching.

Automatic resonant-bar apparatus for plotting of internal friction against strain amplitude

Describes an automatic apparatus for plotting internal friction Q-1 and sample resonant frequency as functions of strain amplitude. Q-1 is measured from the ratio of driving force to strain amplitude, while the sample is held at resonance by a phase-locked loop and the strain amplitude is automatically varied following a chosen function of time. This method allows continuous Q-1 measurement, while an appropriate choice of the amplitude variation rate ensures that the measure Q-1 corresponds to a definite strain amplitude rather than being averaged over an amplitude interval as is the case with other techniques. The system incorporates a resonance apparatus which employs an electrostatic drive without DC bias, but any type of resonance apparatus can be used with minor adjustments. The ranges of Q-1, strain amplitude and operating frequency are those of the resonance apparatus employed.

Dynamic‐mechanical behavior of poly(vinyl chloride), PVC, and chlorinated PVC compounds in the range of processing temperatures

AbstractBoth real and imaginary components of the complex shear viscosity have been determined as a function of strain amplitude, frequency and temperature for various samples of poly(vinyl chloride), PVC, and chlorinated PVC of increasing chlorine content, with the aid of a Rheometrics mechanical spectrometer using eccentric rotating disk geometry. Different methods of sample preparation (low temperature dry‐blending, high temperature extrusion or calendering) were used to study thermomechanical history effects. Results obtained in the region of “linear” viscoelastic behavior were compared with those of capillary flow experiments: at relatively high temperatures the validity of the Cox‐Merz relationship was confirmed. Use of time‐temperature superposition procedures made it possible to predict the important variation of viscosity over a broad range of shear rates. The experimental results in particular with regard to the strong influence of temperature and thermal history, were tentatively interpreted in terms of a supermolecular structure due to the presence of ordered domains (microcrystallites) of variable amount and size. This interpretation was shown to be consistent with differential scanning calorimetry.