Shape Of Creep Curves Research Articles

Some Aspects of Mechanisms and Modelling of Creep Behaviour of 2.25 Cr-1 Mo Steel.

The present work attempts to establish experimentally the dominant mechanism based model for describing the shape of creep curve at any arbitrary stress and temperature. Creep data were collected from literature and some were generated experimentally under different microstructural conditions of 2.25Cr-1Mo steel. Influence of thermal aging and pre-strain on the shape of creep curve have also been studied. The analysis of creep data clearly revealed that irrespective of initial microstructures, thermal aging significantly increases the tendency to soften whereas pre-strain results in marginal strengthening. Softening due to carbide coarsening was thus established as the dominant mechanism of creep in 2.25Cr-1Mo steel. A numerical procedure was developed to extract the parameters of the model, describing the kinetics of carbide coarsening directly from creep curves. A fairly accurate prediction of creep strain up to 5% was obtained using this approach. The kinetics of carbide coarsening was found to depend on the applied stress.

固溶化熱処理および熱時効したNi-22Cr-18Fe-9Mo合金のクリープ曲線形状

Change in creep curve shapes of a Ni-22Cr-18Fe-9Mo alloy developed for an intermediate heat exchanger of high temperature gas-cooled reactors has been investigated with the following results: (1) Creep curves at 800°C for this alloy, in the solution-treated and aged conditions, are tertiary creep dominated ones where most of the life is an accelerating creep stage although a primary creep stage is slightly recognized in some cases. (2) Creep curves at 1000°C for this alloy in a solution treated condition are irregular ones which have a region with a low creep rate preceding the steady-state creep rate and accelerating creep rate. This low creep rate stage diminishes after aging at 1000°C. Creep curves at 1000°C for the aged alloy are normal type ones. (3) Creep rates at 800 and 1000°C increase after aging at 1000°C. This effect is small under low stresses at 1000°C. Rupture strain of the aged alloy increases because carbides formed on grain boundaries by aging suppress the formation and growth of voids and cracks.

High-Temperature Creep Behavior in Ni<SUB>3</SUB>(Al, Ta) Single Crystals with Different Orientations

High temperature creep behavior of a nickel-rich Ni 3 (Al, Ta) with the LI 2 structure is investigated in order to clarify the influence of crystallographic orientation. The single crystals with four different orientations are deformed in compressive creep at the temperatures ranging from 1123 to 1273 K under a constant load with initial shear stresses being from 35 to 120 MPa for the (111)[101] slip system. The results show a distinct orientation dependence of creep strength, although shape of creep curves, stress exponent and the activation energy seem to be independent on orientation. It is shown, however, that the internal stress measured by strain transient dip tests is found to be orientation-dependent and that the creep behavior is independent on orientation if these are analyzed with the effective stress instead of the applied shear stress.

Estimations of Creep Behavior and Failure Life for a Circumferentially Notched Specimen.

No method with which to characterize and/or illustrate total creep behavior for specimens with notches, holes or cracks has been proposed. In this paper it is proposed that most creep curves can be drawn with a master curve for each creep test whenever test conditions and failure modes are similar to each other, and the lifetime ratio normalized by the rupture time is introduced. Using smooth and circumferentially notched specimens of 2.25 Cr-1 Mo steel, creep tests were performed at 600°C for examination of this concept. Furthermore, a θ projection method was used to describe creep curves for notched specimens and to extrapolate longer creep lives. Then, the whole creep curve shape for notched specimens could be easily drawn, except for that in the vicinity of the rupture point. However, longer creep lives of notched specimens were underestimated in comparison with a simple extrapolation of the experimental data. This resulted from the negative dependence of the parameter of θ3 on the applied stress.

Orientation Dependence of High Temperature Creep Strength and Internal Stress in Ni3Al Alloy Single Crystals

ABSTRACTHigh temperature creep behavior of a nickel-rich Ni3(Al,Ta) with the L12 structure is investigated in order to clarify the influence of crystallographic orientation with respect to the stress axis. The single crystals with four different orientations are deformed in compressive creep at temperatures ranging from ‘M 23 to 1273 K under a constant load, initial shear stress being 35 to 120 MPa for (111)[101] slip system. The results show a distinct orientation dependence of creep strength, although shape of creep curves, stress exponent and the activation energy seem to be independent of the orientation. It is shown, however, the internal stress, being measured by strain transient dip tests, is found to be orientation dependent and the creep behavior is independent on orientation if it is interpreted using the effective stress instead of the applied shear stress.

A micromechanical model for creep in short fibre reinforced aluminium alloys

Three elementary microstructural processes control creep of short fibre reinforced, squeeze cast aluminium alloys: (i) loading of fibres by dislocations through the formation of a work hardened zone (WHZ), (ii) a recovery mechanism which decreases the dislocation density in the WHZ, and (iii) multiple breakage of fibres. A uniaxial micromechanical model is presented which is based on these three elementary processes. The model rationalizes the shape of individual creep curves as well as the temperature and stress dependence of the minimum creep rate. The minimum creep rate is shown to result from a superposition of primary (loading of fibres by dislocations) and tertiary (breakage of fibres and shortening of the length of the recovery path) processes. † On leave from: Institute of Physical Metallurgy, Academy of Sciences of the Czech Republic, Zizkova 22, 616 22 Brno, Czech Republic.

アルミナ短繊維強化6061 Al合金複合材料のクリープ特性

Creep tests were carried out at temperatures from 573 to 773 K on the 6061Al matrix composites reinforced with 11 vol% and 18 vol% alumina short fibers to examine the effect of short fibers reinforcement on the creep rate and the creep curve shape, and their stress and temperature dependences. Furthermore, the density change by creep deformation was measured to examine the formation of cavities during creep of the short fiber reinforced composites.Creep curve shape changed with stress as follows: In the low stress range, the tertiary creep occurred after small extent of the primary stage, so that the creep curve was dominated by the tertiary creep without being related to the occurrence of necking in the specimen. With increasing the stress, the extent of primary and secondary stages became large and occupied a large part of the creep curve in the high stress range at low temperature.The higher the creep temperature and the lower the creep stress, the larger was the density change by creep deformation. It showed that the tertiary creep was associated with the formation of cavities, especially at the fiber/matrix interface and at the grain boundaries at high temperature (773 K).The θ-projection method was useful in describing the creep curve shape of the short fiber reinforced composites and it’s variation with stress and temperature. It was found that rate parameters θ2 and θ4 describing the primary and tertiary creep were about equal, at least at 573 and 673 K, as proposed by Maruyama et al.These results were compared with the creep behaviour of Al matrix composite reinforced with the same short alumina fibers as the present composites and the effect of matrix alloy on creep was discussed.

Estimation of Creep Curve Shapes after Increase of Applied Stresses Using the .THETA. Projection Concept.

The θ projection concept was proposed to describe a wide range of creep curve shapes, and has been mainly studied for ferritic steels in which applied stresses were kept constant until rupture. In this paper, we examined whether it could also predict creep behavior when the applied stress was changed during creep deformation. Conventional creep tests of an austenitic stainless steel were conducted at 700°C. In a series of stress-change creep tests, the initial stress of 90 MPa was loaded for a given test duration, after which the stress was increased to 140 MPa. Creep strain produced by the initial stress was determined to range from the primary to the tertiary stage of creep. Employing the θ projection concept and the strain hardening law, creep behavior after the change of the applied stress was estimated. Estimated creep curves agreed well with experiments when the creep strain due to the initial stress was within the early part of the tertiary stage.

The high-temperature creep behaviour of an Al-1 wt% Cu solid-solution alloy

The creep behaviour of an Al-1 wt% Cu solid-solution alloy is investigated at a temperature of 813 K under stress range of 0.5–5 MPa. The creep characteristics of the alloy including the stress dependence of the steady-state creep rate (n=4.4), the shape of creep curve (normal primary stage), the transient creep after stress increase, and the value of the true activation energy for creep, suggest that some form of dislocation climb is the rate-controlling process at higher stresses above 1 MPa. However, at low stresses (< 1 MPa), the creep curves show no distinguished steady state, and the stress dependence of the minimum creep rate is as high as ∼ 8. The creep behaviour of the alloy is discussed based on recent theories available for describing creep in solid-solution alloys.

Creep deformation of evgineering alloys: Developments from physical modelling.

Differences in the creep behaviour of particle-strengthened engineering alloys relative to simple solid solutions are reviewed and their implications for the mechanisms of high temperature deformation in these materials are considered. Constitutive equations describing the shapes of creep curves, based on physical models of the important types of damage are considered. These are incorporated in a computer software package, designated CRISPEN, that allows the analysis of creep data, the development of a database of model parameters and the simulation of the strain/time trajectory for arbitrary loading conditions. Examples of the application of CRISPEN to a range of alloys and loading conditions are described.

Shape of creep curves in frozen soils and polycrystalline ice: Fish, A M Can Geotech JV24, N4, Nov 1987, P623–629

Shape of creep curves in frozen soils and polycrystalline ice: Fish, A M Can Geotech JV24, N4, Nov 1987, P623–629

Prediction of the Microyield Strength of Polymer Matrix Composites

A theory for the prediction of the creep and the microyield strength of composite laminates with viscoelastic matrices has been developed and tested. Precise creep curves from three laminates with arbitrary orientations provide the necessary input data. The time-dependent lamina properties are derived for subsequent use with standard laminate codes. Both the level and the shape of creep and strain recovery curves can be predicted. Extensions of the theory to include the effects of microcracking are outlined.

Effects of Structure on Creep of Ti-53.4mol%Al Intermetallics

ABSTRACTConstant stress compression creep behavior at elevated temperature was investigated on Ti-53.4mol%Al polycrystalline intermetallics of gamma single phase in different grain morphologies: coarse columnar grains, fine recrystallized grains and equiaxed grains. The shape of creep curves depended on the applied stress: normal primary transient followed by steady creep was found at higher stresses, but at lower stresses steep acceleration was observed after taking minimum creep rates. This behavior was common to all the grain morphology. The creep rate itself was not greatly different among the three types of structure, and the stress exponent of about 4 and the apparent activation energy of about 340kJ/mol at 0.3 true strain were common to all three types. The shape and size of grains do not affect the essential creep features of this material.

Shape of creep curves in frozen soils and polycrystalline ice

A new method was developed for determining creep parameters, particularly the time to failure, from a single linear plot in which an individual creep curve forms a straight line for primary and tertiary creep. Secondary creep is considered to be a principal point on this line that predetermines the onset of failure. The times to failure can be predicted even when creep tests are not complete by extrapolating information obtained for primary creep. Based upon T. H. Jacka's test data, prediction of creep strain was evaluated using the constitutive equation of A. M. Fish for entire creep and compared with the modified Sinha equation of M. F. Ashby and P. Duval for attenuating creep as well as with models for primary and secondary creep. It is shown that the shape of the creep curves, and thus the creep parameters, varies with stress, temperature, and other factors. Hence, a family of creep curves cannot be described by a constitutive equation with a single set of creep parameters that do not take into account these variations without loss in the accuracy of the creep strain calculations. Key words: frozen soil, polycrystalline, ice, creep, failure, time to failure, attenuation, constitutive modelling.

Alternative methods of parameter estimation in exponential descriptions of normal creep curves

In an earlier analysis, creep strain/time curves obtained using high-precision creep equipment were used to compare two equations developed to describe the shapes of normal creep curves. Constant stress data are reported for 1/2Cr1/2Mo1/4V steel in this paper. Topics considered include chromium-molybdenum steels, creep, strains, vanadium alloys, measuring instruments, and stress analysis.

A comparison of extrapolation techniques for long-term creep strain and creep life prediction based on equations designed to represent creep curve shape

High-precision creep data obtained for 1 2 Cr 1 2 Mo 1 4 V steel at temperatures from 808 K to 868 K in tests having a maximum duration of only about 1000 h have been used to predict the full creep strain and creep life properties expected under conditions giving lives up to 100 000 h and more. Excellent agreement with published long-term behaviour was achieved using an extrapolation procedure, referred to as the θ Projection Concept, which envisages normal creep curves as the sum of a decaying primary and an accelerating tertiary component. With this approach, the increase in creep strain ε c with time t can be described as ε c = θ 1 (1 − e −θ 2t ) + θ 3 ( e θ 4t − 1) where θ 1 and θ 3 define the strains and the rate constants θ 2 and θ 4 quantify the curvatures of the primary and tertiary stages respectively. In contrast, a significantly poorer correlation between actual and predicted long-term properties was found when the curves were described using the equation ε c = A (1 − e −αt) + B ( e αt − 1) where the same rate constant, α, is used to define the curvatures of the primary and tertiary stages.

A minimal network model for creep

We present a minimal rheological network model for the creep function in plastic flow. The model has a very small number of elements—a maximum of two linear springs, two Newtonian dashpots and a frictional mass. No non-Newtonian dashpots or other nonlinear elements are invoked. A wide variety of creep-curve shapes including those with inflection points across which the curvature changes sign are shown to be reproduced by the model and its sub-cases.

Shape of transient creep curves following stress change during steady state creep

AbstractThe shape of the strain transient following a sudden stress change (drop or increment) during steady state creep has been investigated for AI, AI–Mg alloys, AI–Li alloys, Cu, and Zr−1 wt-%Nb over a range of temperatures. The strain transients were classified as N type, for which the initial creep rate is high but decreases with time eventually reaching a constant value, or I type, for which the creep rate gradually increases to a constant value. The shape after a stress increment can be used as a guide to the rate controlling process of creep with pure metals and Class 2 alloys in which recovery is rate controlling showing an N type transient, and Class 1 alloys in which viscous glide is rate controlling showing I type transients. The shape of the strain transient after a sudden stress drop gives no clear indication of the rate controlling mechanism since, in general, pure metals and Class 1 and Class 2 alloys each show I type transients.

A phenomenological theory of transient creep

Abstract A new creep theory is proposed which takes into account the strain generated during the annihilation of dislocations. This contribution is found to be very significant when recovery is appreciable, and is mainly responsible for the decreasing creep rate associated with the normal primary creep of class II materials. The theory provides excellent semiquantitative rationalization for the types of creep curves presented in the preceding paper. In particular, the theory predicts a change in the shape of the primary creep curve from normal to inverted as recovery becomes less important, i.e. as the applied stress and/or temperature decrease(s). It also predicts a minimum creep rate under certain circumstances, hence pseudo- tertiary behaviour. These different types of creep curves are predicted even though the net dislocation density decreases monotonically with time in all cases. Qualitative rationalization is presented for the inverted transient which always follows a stress drop in class II materia...

Heat treatment effects on creep and rupture behavior of annealed 2.25 Cr-1 Mo steel

The strength of 2 1/4 Cr-1 Mo steel depends on the microstructure, which, in turn, de-pends on the heat treatment. In the fully annealed and isothermally annealed conditions, the microstructure is primarily proeutectoid ferrite with varying amounts of bainite and pearlite. The relative amounts of the latter constituents depend on the cooling rates during the anneal. The creep and rupture properties were determined for steel plates (from a single heat) given three different annealing treatments: two were fully annealed, but cooled at different rates from the austenitizing temperature, and the third was iso-thermally annealed. Properties were determined at 454, 510, and 566°C. At 454 and 510°C, the cooling rate had a significant effect on the creep and rupture properties, with the ma-terial cooled fastest being the strongest. Although at 510°C strengths at short rupture times differed widely, the properties approached a common value at longer rupture times. The properties differed very little at 566°C, even for short rupture times. The effect of heat treatment was concluded to be the result of interaction solid solution hardening, a dislocation-drag process. This process gave rise to nonclassical creep curves (as op-posed to classical curves with single primary, secondary, and tertiary stages). By examining the creep-curve shape, it was possible to interpret the heat treatment effects on the creep-rupture properties.