Negative creep and recovery during high-temperature creep of MgO single crystals at low stresses

High-temperature creep equipment with very high precision has been used to measure the creep of MgO single crystals above 1948 K and stresses lower than 4 MPa. A transition in exponent,n, from 3 at stresses higher than 2 MPa to almost unity at lower stress region was observed. Since in a single crystal deformation can only occur by the generation and movement of dislocations, the transition in stress exponent from high to low stress region cannot be interpreted in terms of a change from dislocation to diffusional creep processes. Decreasing the stress by a small amount during steady-state creep resulted in an incubation period of zero creep rate before creep commenced at lower stress. However, large stress reduction led to a period of negative creep during which the dislocation substructure coarsens and the subgrain cell boundaries straighten. On the basis of dislocation substructure studies, it is proposed that the kinetics of backflow are thought to be based on the local network refinement caused by the reverse movement of dislocations and that recovery is necessary before further movement of dislocation can occur. It is shown that the network theory proposed by Davis and Wilshire can satisfactorily account for all stress reduction observed during forward creep.     

Newtonian flow process in polycrystalline silicon carbides: diffusional creep or Harper-Dorn creep?

Some previous studies on hot-pressed and sintered SiC polycrystalline materials have been reexamined. Mechanical data and microstructures strongly suggest that the Newtonian creep behaviour observed in these SiC materials was induced by a dislocation process operating in Harper-Dorn creep, rather than by diffusional creep as concluded before. The supporting evidence for this suggestion includes extensive development of dislocation substructures, no dependence of creep rate upon grain size, and the measured creep rates being far faster than those predicted by the model of diffusion creep, but consistent with those estimated by the model of Harper-Dorn creep.     

Investigation of the effects of microstructure on creep deformation in α2-based titanium aluminide intermetallics

The results of a systematic investigation of the effects of microstructure/substructure on the secondary creep behaviour of α2-based titanium aluminide alloys are presented. This includes a study of the effects of heat treatment on the steady-state creep behaviour of α2+β-processed Ti-24Al-11Nb and Ti-25Al-10Nb-3V-1Mo at 540, 650 and 760°C, and an investigation of the effects of creep deformation on dislocation substructures in Ti-24Al-11Nb. The parameters that control secondary creep deformation are identified for both alloys, and the results are compared with data obtained for conventional high-temperature near-α titanium alloys and β-forged Ti-24Al-10Nb-3V-1Mo. This revised version was published online in November 2006 with corrections to the Cover Date.     

The creep and fracture behaviour of tempered martensitic steels

Creep strength enhanced ferritic steels contain 9 to 12% Cr and were developed to exhibit excellent high temperature properties. These should be achieved when the microstructure exhibits a tempered martensitic matrix containing a substructure with a high dislocation density and a uniform dispersion of fine, second phase precipitates. It is interesting to note that when properly processed the typical alloy compositions for these steels provide reasonable strength but can exhibit brittle creep behaviour. The levels of ductility required in engineering applications necessitate proper control of composition (including trace elements), steel making and processing and all heat treatments. The properties needed for modern design methods can only be obtained using validated procedures for both uniaxial and multiaxial testing and documentation to establish the mechanisms controlling deformation and fracture for relevant stress states.     

偏心支撑框架空间子结构混合试验边界条件模拟方法

数值子结构的建模精度和子结构的边界条件模拟是子结构混合试验中的两个关键问题。为进一步研究这种新型结构试验方法对于空间框架结构的适用性,基于高强钢组合Y形偏心支撑框架模型展开研究。首先建立了一套由OpenSees, OpenFresco试验平台以及MTS加载系统组成的混合试验系统。然后分别针对2层、3层和4层3跨高强钢组合Y形偏心支撑框架,取底层带有偏心支撑的框架部分作为试验子结构,其余部分作为数值子结构在OpenSees中进行模拟。在混合试验之前,利用已有单榀试件拟静力试验结果对数值子结构的建模方法进行了数值模拟验证。最后选取El Centro波作为原始输入地震波,针对试验子结构的平动模拟和竖向荷载作用进行了一系列空间子结构混合试验。结果表明:通过数值模拟验证拟静力试验结果的方式,可以为混合试验中数值子结构的建模提供参考依据;采用双作动器水平加载来实现试验子结构的平动,可以有效考虑数值子结构对试验子结构的边界约束;竖向荷载的考虑,可以更真实的模拟试验子结构的重力二阶效应。     

A coupled creep damage evolution model and creep life evaluation

Due to the damage accumulation during creep deformation, creep failure after a certain service time is the most important failure mode for metal structures working at high temperatures. Considering the coupled damage evolution of geometric and material’s damage, a creep life evaluation method based on continuum damage mechanics has been proposed and examined. It is found that the geometric damage evolution model can be deduced theoretically from the creep constitutive equation, while the material’s damage evolution can be assumed in the same way as that for static fatigue problems. Through solving the coupled damage evolution models, creep lives under various stress levels and temperatures can be evaluated in a unified way, just by several material constants which can be determined by some creep tests only.     

Creep behaviour and dislocation substructure evolution in the KBr-Kl system

Creep behaviour and dislocation substructure as a function of strain was investigated for two solid solution alloys and the pure components in the KBr-Kl system. The creep characteristics for the KBr-Kl alloys are in good agreement with creep behaviour observed in other ionic and class I metallic solid solution alloys, where the creep rate is controlled by a viscous dislocation glide process. The creep resistance of the KBr-KI alloys is higher than that for the pure components at the same value of homologous temperature. The dislocation substructure of the KBr-Kl alloys and pure components at large strains consists of well defined subgrains. Subgrain formation is shifted to larger strains in the alloys compared to the pure components as a result of solute drag forces on dislocations during glide.     

Creep behaviour and creep microstructures of a high-temperature titanium alloy Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.35Si–0.06C (Timetal 834): Part I. Primary and steady-state creep

The tensile creep behaviour of the high-temperature near -Ti alloy Ti–5.8Al–4.0Sn–3.5Zr–0.7Nb–0.35Si–0.06C (Timetal 834) with a duplex microstructure has been extensively investigated in the temperature range from 500°C to 625°C and the stress range from 100 to 550 MPa. Both primary and secondary creep are being considered. The results of the primary creep are analysed in terms of the dependencies of stress on strain (strain hardening) and on strain rate (strain rate sensitivity). It is shown that the strain-hardening exponent depends on temperature, and takes values between 0.5 for 500°C and 0.33 for higher temperatures; this would give a dependence of the primary creep strain of σ² and σ³. The strain rate exponents obtained in both primary and secondary creep have been found to be similar; this is also the case for the activation energies. It is thought that, in the stress and temperature range investigated, creep is controlled by bow-out and climb of dislocation segments pinned at lath boundaries and second-phase particle. Analysis of the dislocation substructure is presented to give some support for this mechanism.     

Exact eigenvalue calculations for structures with rotationally periodic substructures

The theory presented enables rotationally periodic (i.e. cyclically symmetric) three-dimensional substructures to be included when using existing algorithms to ensure that no eigenvalues are missed when the stiffness matrix method of structural analysis is used, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. A substructure can be connected in any required way to a parent structure which shares its rotational periodicity, or can be connected by nodes at each end of its axis of periodicity to any parent structure, i.e. the parent structure need not be periodic. The theory uses complex arithmetic, involves only one of the rotationally repeating portions of the substructure, allows nodes and members to coincide with the axis of rotational periodicity, permits efficient multi-level use of rotationally periodic substructures, and gives ‘exact’ eigenvalues if the member equations used are those obtained by solving appropriate differential equations. The competitiveness of the method is illustrated by approximate predictions of computation times and savings for two structures which contain rotationally periodic substructures.     

Failure time in creep

This brief note proposes a method to estimate the useful life of a component subjected to constant load creep, using the total displacement or strain at any instant and the elapsed time. In contrast to the conventional methods based on the minimum creep rate or the steady state creep rate, the present method gives a more realistic and less conservative estimate of the ‘failure time’ in creep of a material, and hence predicts a longer design life for the component or structure.     

Creep behaviour of a heat-resistant ferritic chromium steel in terms of stress exponents

In many publications the high-temperature deformation behaviour of materials is described by the stress sensitivity of steady-state creep rate, the creep exponent, n. In order to investigate the mechanisms of dislocation motion, it is more promising to evaluate the constant structure creep properties. This leads to the constant structure creep exponent, m, which is not influenced by the stress dependence of the substructure. Therefore, the investigation of deformation mechanisms is less difficult. Additionally, m is the basis for the calculation of the effective stress exponent, m, of dislocation velocity, which permits the investigation of the strength of interactions between alloying atoms and moving dislocations. It is shown that the creep exponent, n, is between 5 and 10 in the power-law creep region (where diffusion-controlled glide processes of dislocations cause deformation). However, it increases to about 50, if exponential creep is working (in this region the glide processes are thermally activated but diffusion is not the rate-controlling mechanism). The constant structure creep exponent, m, is relatively small and independent of stress in the power-law creep region. It increases almost linearly with the applied stress, if thermally activated glide dominates creep. The evaluation of the stress exponent, m, which can be calculated from m and the effective stresses, showed that dislocation motion is influenced by alloying atoms as long as power-law creep works. There is experimental evidence that power-law breakdown is due to a breakdown of the alloying effect, because dislocations can escape from their dragging Cottrell clouds at high applied stresses.     

A case for Taylor hardening during primary and steady-state creep in aluminium and type 304 stainless steel

Previous elevated-temperature experiments on 304 stainless steel clearly show that the density of dislocations within the subgrain interior influences the flow stress at a given strain rate and temperature. A re-evaluation shows that the hardening is consistent with the Taylor relation if a linear superposition of solute hardening ( ₀, or the stress necessary to cause dislocation motion in the absence of a dislocation substructure) and dislocation (Gb ^1/2) hardening is assumed. The same Taylor relation is applicable to steady-state structures of aluminium if the yield stress of annealed aluminium is assumed equal to ₀. New tests on aluminium deforming under constant-strain-rate creep conditions show a monotonic increase in the dislocation density with strain. This and the constant-stress creep trends are shown to be possibly consistent with Taylor hardening.     

On the dislocation density in aluminum during Harper-Dorn creep

In research on high temperature, low stress, creep in aluminum, Lacombe and Beaujard's etchant has been used to determine dislocation densities. This work has led to the suggestions that the density is about 10⁸ m⁻² or less and independent of stress and that for Harper-Dorn creep the density must be below a critical value of about 2×10⁹ m⁻². Here, the characteristics of the etchant have been reviewed and it has been shown that they are complex and that pit densities are generally unreliable measures of dislocation populations. The purpose of this note is to point this out and to suggest that further work on dislocation populations during Harper-Dorn creep is warranted.     

Optimal modal reduction of vibrating substructures

A structure which consists of a main part and a number of attached substructures is considered. A ‘model reduction’ scheme is developed and applied to each of the discrete substructures. Linear undamped transient vibrational motion of the structure is assumed, with general external forcing and initial conditions. The goal is to replace each discrete substructure by another substructure with a much smaller number of degrees of freedom, while minimizing the effect this reduction has on the dynamic behaviour of the main structure. The approach taken here involves Ritz reduction and the Dirichlet‐to‐Neumann map as analysis tools. The resulting scheme is based on a special form of modal reduction, and is shown to be optimal in a certain sense, for long simulation times. The performance of the scheme is demonstrated via numerical examples, and is compared to that of standard modal reduction. Copyright © 2003 John Wiley & Sons, Ltd.     

A comparison of impression and compression creep behavior of polycrystalline Sn

This paper reports on the application of a miniaturized impression creep test to measure the creep behavior of pure polycrystalline Sn, and compares the results to compression creep data on the same sample, in order to experimentally determine a scaling constant to formulate the equivalent uniaxial creep constitutive law from the impression creep data. The creep parameters determined via impression and compression creep are found to be identical, with n ∼ 5 and Q ∼ 42 kJ/mol, indicating that over the tested stress–temperature range, the mechanism is core diffusion controlled dislocation creep. In conjunction with results from previous modeling work, a single conversion factor, κⁿ/C, which depends on material properties, is shown to be usable for converting the impression creep relation to the equivalent uniaxial creep relation, and the experimentally determined value of κⁿ/C for polycrystalline Sn is very close to that obtained via modeling.

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Internal and effective stresses in high-temperature creep evaluated from transient dip tests and dislocation bowing

Because creep of metals and alloys is modelled on the basis of microstructural observations, it has been shown that there is a difference between the mathematical treatment of high-temperature deformation and the real material behaviour. One idea to consider is to split the applied stress into a part depending on the substructure (the internal stress which has to be reached to start dislocation motion) and a part describing the resistance to the glide motion of dislocations (the effective stress). For ferritic chromium steel these quantities have been measured by means of the stress transient dip test technique. This leads to mean values of internal and effective stresses for the whole specimen. Additionally, local stresses acting on individual dislocations are evaluated from dislocation bowing for a wide range of applied stresses. The results show that the ratio of internal to applied stress decreases with increasing applied stresses, which, on the other hand, causes a large increase of effective stresses. Dislocation bowing stresses show a similar dependence. Compared to the results of dip tests, the determination of local stresses leads to less accurate results and to a large deviation of results within small regions of one specimen. Therefore, it is only valuable for comparison purposes.     

Some features of indentation creep of LiF single crystals

The dependence of the size of the indentation and dislocation rosettes on loading time was investigated on the (001) plane of LiF single crystals. The measurements were performed in temperature range from room temperature to 170° C. The indentation time was varied from 0.2 to 10³ sec. It was revealed that the change of the indentation size during creep was more significant than the change in dislocation ensemble tracks in the field of the concentrated load. It was shown that the dependence of the length of the dislocation rosette edge arms on loading time, when plotting in double logarithmic scale, was linear. This fact allowed the determination of parameterm, characterizing the dependence of the dislocation velocity on stress, using creep experiments. The values ofm proved to be in good agreement with the results obtained by different methods.     

Bending and creep buckling response of viscoelastic functionally graded beam-columns

The viscoelastic creep response of flexural beams and beam-columns made with functionally graded materials is numerically investigated. The paper highlights the challenges associated with the modeling and analysis of such structures, and presents a nonlinear theoretical model for their bending and creep buckling analysis. The model accounts for the viscoelasticity of the materials using differential-type constitutive relations that are based on the linear Boltzmann’s principle of superposition. The model is general in terms of its ability to deal with any material volume faction distribution through the depth of the beam, and with different linear viscoelastic laws, boundary conditions, and loading schemes. The governing equations are solved through time stepping numerical integration, which yields an exponential algorithm following the expansion of the relaxation function into a Dirichlet series. A numerical study that examines the capabilities of the model and quantifies the creep response of functionally graded beam-columns is presented, with special focus on the stresses and strains redistribution over time and on the creep buckling response. The results show that the creep response of such structures can be strongly nonlinear due to the variation of the viscoelastic properties through the depth, along with unique phenomena that are not observed in homogenous structures.     

Internal stress and unloading experiments in creep

Internal stresses are developed during deformation and have an important role in determining the mechanical properties and, in particular, the creep properties of crystalline materials. The strain transient dip test is the generally accepted method for the determination of internal stresses developed during creep. The strain transient dip test has been analysed using a number of very general creep models and it is concluded that, for glide-controlled creep, the dip test can only be interpreted if the relation between dislocation velocity and the force on the dislocation is linear. When this is the case it measures not an average internal stress but an average back stress for all the dislocations, mobile and immobile, where the back stress is the resolved component of the internal stress plus the glide component of the line tension force divided by the Burgers vector. The dip test does not allow separation of the back stress into internal stress and line tension components. For recovery models the results of the dip test cannot be simply interpreted because expressions for the creep rate do not define a unique average internal stress or back stress. However, for the recovery model in which strain occurs by athermal or jerky glide there will be a reverse yield stress, i.e. there will be a stress reduction below which there will be instantaneous reverse strain followed by reverse creep. By averaging the instability condition for all the dislocations participating in jerky glide it is shown, subject to assumptions, that the sum of the average internal stress experienced by dislocations involved in both forward and reverse creep can be obtained from the reverse yield stress. Separate values for these internal stresses cannot be obtained, however. Determination of the reverse yield stress for recovery creep is the experiment equivalent to the strain transient dip test for glide-controlled creep.Research visitor from University of Aix-Marseille 11, France.