Steady Creep Stage Research Articles

Creep and Creep Rupture of 63 Sn-37 Pb Solder.

This paper studies the creep and creep rupture properties of 63 Sn-37 Pb solder. Creep and creep rupture tests were carried out using 63 Sn-37 Pb solder specimens at 313 K, 353 K and 398 K to develop a creep constitutive equation and to obtain rupture time. Short primary and long tertiary creep stages were found but there was no clear steady creep stage at the three temperatures. A creep constitutive equation was proposed as a function of stress and temperature. The proposed equation predicted the experimental creep strain within a factor of 1.25. A new equation for predicting creep rupture time was also proposed. The equation predicted the experimental rupture time within a factor of two.

Effect of phase transformation and predeformation on creep characteristics of Al–40 wt% Zn alloy

The change in the steady state creep rate of Al–40 wt% Zn alloy is studied under constant stresses ranging from 42 to 50.3 MPa and at different temperatures ranging from 503 to 623 K. The study is extended to samples given different degrees of torsional predeformation in the same investigated temperature range. The stress sensitivity parameter m' is found to decrease from 5 to 2.3 by increasing the working temperature. The energy activating the steady state creep is found to be 78 kJ/mol in the temperature range from 513 to 533 K and 128.5 kJ/mol in the temperature range from 603 to 623 K characterizing a grain boundary diffusion mechanism of Zn in β-phase and of Al in α-phase, respectively. The activation energy 105.7 kJ/mol obtained in the temperature range from 573 to 593 K may characterize volume self-diffusion of Zn. These values decrease by increasing the degree of predeformation which is associated with creep strain rates. The analysis of the microstructural variations confirms that the above-mentioned mechanisms are expected to take place during the investigated steady state creep stage.

A planar model study of creep in metal matrix composites with misaligned short fibres

The effect of fibre misalignment on the creep behaviour of metal matrix composites is modelled, including hardening behaviour (stage 1), dynamic recovery and steady state creep (stage 2) of the matrix material, using an internal variable constitutive model for the creep behavvour of the metal matrix. Numerical plane strain results in terms of average properties and detailed local deformation behaviour up to large strains are needed to show effects of fibre misalignment on the development of inelastic strains and the resulting over-all creep resistance of the material. The creep resistance for the composite is markedly reduced by the fibre misalignment and the time needed to reach an approximate steady state is elongated due to the strain induced rotation of the short fibres in the matrix.

Positive feedback fracture process induced by nonuniform high‐pressure water flow in dilatant granite

During forced water infiltration into a dry granite rock in the dilatant state, migration of a water front and a clear positive feedback between acoustic activity and water flow into microcracks were revealed by means of AE hypocenter locations and velocity tomography. Water was injected into a cylindrical granite sample subjected to 40 MPa confining pressure and constant axial stress equal to about 70% of short‐term dry strength. The injection water pressure was held constant at 17 MPa until failure occurred. Soon after water injection into the bottom end of the sample, AE hypocenters began near the bottom end. Subsequently, they moved up with a strong preference for the region where a weak concentration of AE events had been observed during a steady state creep stage before the water injection. The P wave velocity structure was determined in the section parallel to the loading axis and crossing the cluster of AE hypocenters. The velocity structure, reconstructed by seismic tomography, showed a nonsymmetric distribution of the velocity with regard to the loading axis during the injection. The strong concentration of AE hypocenters suggests that water flow channels are preferentially formed in a very limited region in the dilatant rock. The concentration of AE events and formation of these water channels marks a positive feedback process in which the local strength of the rock is reduced by the decrease of the effective confining pressure caused by increasing pore pressure which, in turn, triggers more microfracturing.

大島カコウ岩におけるクリープ時のAE発生の確率過程と震源の空間分布

Stochastic process of the occurrence of AE events and their spatial distribution during creep in granite were studied. In the stage of steady creep, linear increments of volumetric and circumferential strains accompanied with a steady AE activity. A transition point from steady creep to tertiary creep estimated by the strain data agrees with that estimated by the change of AE activity. Frequency distribution of AE rate during steady creep shows Poisson distribution, according to X2-test with a significance level of 0.05. In the stage of tertiary creep, however, Poisson process of the occurrence of AE has disappeared. Spatial distributions of hypocenters exhibit concentration patterns during steady creep. The temporal randomness of the occurrence of AE events cannot always correspond to the spatial randomness. The present results suggest that the transition from steady creep to tertiary creep may be characterized by the occurrence of AE events with large amplitude, their aftershocks, change of stress distribution in the rock and migration of hypocenters. There seems to be a close relation between stochastic process of the occurrence of AE events and the manner of the AE emanation. Taking similarities between AE events and earthquakes into account, a study of stochastic process in microearthquake occurrence will play an important role for the earthquake prediction study.

Creep During Dehydroxylation of Magnesium Hydroxide

The creep deformation of cold compacts of Mg(OH)2 during the dehydroxylation reaction was studied. The overall creep behavior can be divided into three stages. The initial stage is initiated by the dehydroxylation reaction. During the second or steady state creep stage the highest creep rate was obtained. The steady state creep rate was determined as a function of temperature, pressure, and relative density of the green compact. The results are represented by ė=Aσn=1ρ-1 exp(-17,500/RT)s-1. Particle sliding was considered to be the mechanism for creep in the second stage. During the last stage, the creep rate asymptotically approached zero. The reduction of the creep rate and the surface area at this stage may be due to coalescence or beck-growth between the freshly formed MgO particles.

Creep of Cylindrical Tube Subjected to Combined Axial Load and Internal Pressure at Elevated Temperatures

The following conclusions have been derived from the present analytical and experimental studies on the creep of a cylindrical tube of low carbon steel subjected to internal pressure at 450°C. In the cylindrical tube with an arbitrary radius ratio K, subjected to combined axial load and internal pressure, it was found that the following assumption was efficiently suitable for the creep analysis of the tube in the transient or steady state creep stage. The present assumption is the constancy of both the equivalent stress σav and the stress ratio A at the mean radial distance of the cylindrical tube during the creep, where the stress ratio A was defined as the ratio of average tangential stress σθav to the axial stress σzav.The first of the present verification was made through the aspect of the influences of K and A on the analytical results of the creep of the cylindrical tube. It was concluded that the analytical results were in good agreement with the experimental results. The second of the present verification was performed from both the types of the creep tests of the tubular specimens under the periodic stress variation along the single Mises-stress ellipse and under that along the two Mises-stress ellipses. It was also concluded that the analytical results were closely like the results of the experiments made under the general loading condition of both the variation of axial load and of internal pressure during the creep tests. Therefore, it was found that both the influences of the change in the equivalent stress at the mean radial distance of the tube during the creep and of the multiaxiality of the stress or the stress ratio at the mean radial distance were not predominant in the creep analysis of the high pressure tube. By such simple assumption, the creep strain distributions along the radial distance of the tube were easily calculated from the information of simple tensile creep. It should be noted, however, that the present analytical result gives a slightly higher estimation of creep strain than the measured values in the case of variation of the equivalent stress.

Creep of Thick-Walled Cylinders under Repeated Varying Internal Pressure

Concerning the problems respecting the creep under non-steady multiaxial stress conditions, there are two cases in the state of stress encountered. The first is the case in which the principal stress directions are kept constant, and the second is the case in which those are variable with varying stresses. In order to investigate a creep behavior under such conditions, the creep of thick-walled cylinders of low carbon steel and 21/4Cr-1Mo steel under stepwise changing internal pressure of periodic rectangular wave was studied. This is one of the fundamental problems on non-steady multiaxial stress conditions under constant direction and constant ratio of principal stresses. Furthermore, such a situation is present in boiler tubes and pressure vessels subjected to internal pressure. It is necessary, therefore, to consider the problem with the aim of predicting the creep strength of thick-walled pressurized cylinders under varying stress.As the results of the experimental and analytical study. It was found that the law of“the mechanical equation of state in solid”was not valid for the creep of the materials tested both in the case of varying uniaxial tension and also in the case of varying multiaxial stresses. The strain rate at the period of reloading was about 20% higher than that under steady load, and the rupture life in the tests under cyclic stress was about 20% shorter than that of the reference tests under constant stress. In the stage of steady state creep, creep recovery came to an almost constant value independent of the amount of strain. These tendencies were quite the same in the creep of the thick-walled cylinders under varying internal pressure. It is considered that residual stresses in the cylinder at the period of pressure removal have little effect on the stress distribution after reloading, and it seems to be appropriate to assume in the analysis that there is no rotation in the principal directions of creep rate and that the material is isotopic under cyclic loading and unloading. This leads to the conclusion that the creep strength under non-steady multiaxial stress condition of constant stress direction and constant ratio of principal stresses can be estimated from the results of the creep tests under varying uniaxial tension by the use of the multiaxial creep theory based on the relationship between the static creep strength of the uniaxial stress and that of the multiaxial stresses.

Creep Behaviors of 2 1/4Cr-1Mo Steel under Cyclic Unloading and Reloading

Structural members which are subject to load at high temperature are, in general, not in a steady condition of applied stress and temperature. In this paper, as one of fundamental problems, the creep behaior under cyclic stress removal is discussed. If a specimen of metals is creeping under constant load, at high temperature and on the way, the load is removed, elastic strain and creep strain recovery which seems like elastic-after-effect occur. After the period of stress removal, when reloaded, creep recovery which is based on the recovery of work-hardning in each crystal, strain aging and precipitation in commercial materials, take place. When the cyceic stress removal is given creep curves, show the differences from steady load creep curve.As the a result of this experiment, creep curves of stress removal are shown upper or lower than steady load creep curves, but the difference between lower creep curve of stress removal and steady load curve is very small. So in this experiment, by considering creep recovery only, creep curve of stress removal can be estimated well. But as for cases when stress cycle or period of stress removal is changed, this result has some questions. As test temperature is rised, creep recovery is much remarkable. If stress amplitude is synchronized with temperature cycle, the influence of creep recovery is much striking. Experimental results may be summarized up as follows:(1) Under a high stress and high temperature, creep recovery is much remarkable.(2) In the eary stage of transient creep, creep recovery is much larger and therafter gradually decreases. In the stage of steady creep, creep recovery reaches almost constant value.(3) Strain increment in cyclic stress removal test is affected not only by creep recovery but also by precipitation, aging and phase change. etc.(4) In this experiment, this strain increment is well expressed by the following equation:Δe=a log (1+Ctr)Δe: strain increment, tr: rest timea, c: constant in constant strain, temperature and stress.

温度変動下のクリープおよびクリープ破断

Structure members which are subjected to load at high temperature are, in general, not in a steady condition of applied stress and temperature. Therefore, the studies on creep of structures under cyclic temperatures or cyclic stressing are important problem. In this paper, the influence of temperature history on creep is discussed. Experimental and analytical relationships of the creep and the rupture life under temperature cycling or under combined variation of stress and temperature to the static creep and the rupture life are presented.(1) The effect of temperature history on creep is composed of transitional change in internal yield stress, that is, recovery or aging, where the internal yield stress is defined as the local stress at which deformation begins without the aid of thermal fluctuation. The influence of the temperature history results in the existence of “induction period” or transitional increase in creep rate immediately after the change of temperature. However, these effects are negligible small in most metallic materials and the concept of “mechanical equation of state in solid”or the Robinson's hypothesis is applicable for preduction of creep or rupture life under cyclic temperatures.(2) By adopting the assumption the creep strain in the stage of transient or steady state creep under temperature cycling can be predicted analytically from the data of static creep test in transient stage, by introducing the equivalent steady temperature. The equivalent steady temperature means the temperature at which the transient creep strain under cyclic temperatures is equivalent to the strain in the static creep test. In like manner, creep rupture life under temperature cycling can also be estimated analytically from the data of static creep rupture test by introducing the equivalent steady temperature for creep rupture life. These analysises are usefull if severe metallurgical change such as microstructural phase change or corrosion does not occur. The assumption is also applicable for prediction of creep or the rupture life under combined variation of stress and temperature. However, under the condition that the stress amplitude which is synchronized with temperature cycle is large, the influence of recovery must be considered.

The Initial Stage of Plastic Deformation in Lead Under Compression

In the steady-creep stage in metals, stress (or resistance to deformation) is related to the velocity of deformation, in accordance with the hyperbolic-sine law, or the exponential law. These laws, however, fail completely to describe the initial stage of plastic deformation in lead. The present series of tests is an investigation of this initial stage in compression. An optical lever system and high speed kymograph have been employed. The photographic records obtained show the progress of deformation with time. The duration of the initial stage increases with the compressing load. For a load of 120.0 kg the duration is about 0.16 sec. It is found that a unique, initial deformation, independent of time, is associated with each load. From measurements on the deformation curves, resistances as functions of time have been calculated. These data indicate a linear relationship between the resistance R and time t: R=l+mt,where l=a parameter of small value, evidently a correction term, and m=rate of increase of resistance. Using this equation and the dynamic constants of the apparatus, deformation curves in good agreement with experiment have been derived. Resistance in the initial stage appears to be only approximately a function of deformation alone