A dislocation network model of recovery-controlled creep

A new model of recovery-controlled creep deformation, based on the jerky glide motion of dislocations between obstacles, is proposed. A three-dimensional distribution of dislocation links is visualized such that only links which attain a certain threshold size,λ _a, through recovery can glide rapidly until they are again arrested at the next obstacle. The rate of mobilization of arrested dislocations is shown to be directly proportional to the annihilation rate, ?_a. The strain rate, γ, during transient creep is related to the annihilation rate, the obstacle spacingL and the Burgers vectorb of the dislocations according to the expression $$\gamma = \alpha _1 \psi (t)\dot \varrho bL$$ where α₁ is a geometrical constant and ψ(t) is a time-dependent parameter whose value is determined by the instantaneous (free) dislocation density as well as some salient features of the dislocation distribution. At steady state, ψ(t) translates into a constant which is stress and temperature independent. The average effective dislocation velocity is also shown to be directly proportional to the annihilation rate. The model is used to rationalize the familiar creep transients which are usually observed when the stress is altered abruptly during recovery creep.     

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.     

High-temperature creep of the particlehardened commercial Al-Li-Cu-Mg alloy 8090

Creep of the particle-hardened commercial Al-Li 8090 alloy has been studied at temperatures of 425 and 445 K. The measured stress sensitivity of the minimum creep rates changes abruptly at a given applied stress with stress exponents being around 4–6 at low stresses and 30–40 at high stresses. Creep activation enthalpies were determined by both temperature cycling and by comparing creep rates at two temperatures at a given applied stress, the results from both gave the same unrealistically high values. The internal stresses, _i, developed during creep were determined using the strain-transient dip test. These increased linearly with the applied stress, _a, at low stresses and were effectively constant at high stresses. The minimum creep rate was found to be a simple function of the effective stress, _a-_i, with a stress exponent of between 5 and 6, at all applied stresses. The dislocation and precipitate structure of the alloy was examined before and after creep using thin-film electron microscopy. The initial structure consisted of pancake grains with a well-developed {1 1 0}1 1 2 type texture. The grains contained well-developed sub-cells and and S precipitates. The structure developed during creep consisted of dislocation pairs, single dislocations and dislocations loops. There was evidence to suggest that slip took place on both {1 0 0} and {1 1 1} planes. The dislocation loops were most likely to have been Orowan in character and around the rodlike S precipitate, with the coherent precipitate being sheared by pairs of dislocations. The measured internal stresses result from inhomogeneity of plastic deformation. These stresses increase continuously with applied stress up to the observed macroscopic yield stress, and then become constant. The internal stresses are likely to have arisen from the Orowan loops around S and the behaviour of sub-grain boundaries. The increases in internal stress may have resulted from an increased loop density with increasing applied stress. This rate of increase is likely to slow down if S particles are sheared or fractured at high applied stresses.     

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.     

Creep Behavior of Mullite Short Fiber Reinforced ZL109 Alloy Composites at High Temperature

The creep behavior of AI203.SIO2 fiber reinforced ZL109 composites has been investigated at four temperatures ranging from 553 to 623 K. The results show high stress exponent and highapparent creep activation energy. A good correlation between the normalized creep rate and normalized effective stress means that the true stress exponent of minimum creep strain rate of the composite is very close to 5, and the minimum creep strain rate is matrix lattice diffusion     

Transient Creep Associated with Grain Boundary Sliding in Fine-Grained Single-Phase Al2O3

Transient creep data for high-purity polycrystalline alumina are examined at the testing temperature of 1150–1250 °C. The data are analysed in terms of the effect of stress and temperature on the extent of transient time and strain.In order to explain the observed transient creep, a time function of creep strain is proposed from a two-dimensional model based on grain boundary sliding. The grain boundary sliding is assumed to take place by the glide of grain boundary dislocations accommodated by dislocation climb in the neighboring grain boundaries. The time function for a creep strain obtained from the model is given in a form

Application of a modified strain transient dip test in the determination of the internal stresses of PVC under tension

A modified strain transient dip test which involves the design of a load reduction apparatus to perform rapid step unloading and extrapolating to zero extension rate has been developed to measure the internal stresses (recovery and effective stress) of PVC under uniaxial tension. This simple technique appears to be consistent with other internal stress measurement techniques. It was found that the effective stress approaches a limiting value with applied strain and an extrapolated yield point could be defined. The limiting value is a function of the strain rate during the initial load application. The general increase in applied stress (at fixed applied strain) with crosshead speed was attributed to the increase in magnitude of the effective stress. The maximum peak ratio of effective over recovery stress, at each crosshead speed, could indicate that it was the energy-dissipating part of the material that played a dominant role in the early stages of the deformation while the energy-storage part dominated the latter stages.     

Effective and recovery stresses in deformation studies of polyvinyl chloride and polypropylene using the modified strain transient dip test

Partitioning the applied stress into internal stress components (effective and recovery) using the modified strain transient dip test is a useful approach towards a better understanding of the viscoelastic nature of polymers. The internal stresses of polyvinyl chloride (PVC) and polypropylene (PP) were measured successfully using this test on a computer-controlled electro-servo hydraulic tensile testing machine which was designed for rapid step unloading in less than 1 s to avoid memory effects of the polymers. A power-law relationship can be used to describe the variation of the internal stress components with strain. Actual yield strains occurred at smaller values (less than 2%) than those obtained from a conventional stressstrain diagram (which for PVC and PP exceed 3.5% and 7%, respectively). This observation indicated that plastic yielding occurred much earlier and yield strains from conventional stress-strain diagrams may be overestimates. For very ductile material (PP) the activation volumes were comparable in magnitude to that obtained conventionally; whilst for less ductile material (PVC), the activation volume was four times higher. One of the main advantages of stress partitioning is for the detailed definition of the extrapolated yield point which otherwise will be missed out in a conventional plot of applied stress and strain.     

The Bailey-Orowan equation

A simple derivation of the Bailey-Orowan equation, , which is based on the spurt-like glide of dislocations during recovery-creep, is presented. It is demonstrated that this equation is valid for steady state but not for transient creep. A dislocation network model is employed to show that the values ofR andH which are measured by stress-change techniques do not represent the true values of the recovery and work-hardening rateS. However, the ratio of the measured values is always equal to the strain rate during transient or steady state creep.     

Breakdown of the power-law creep in a Class I Al-10 at % Zn alloy

The creep behaviour of Al-10 at% Zn at 573 K is divisible into three deformation regions; low stress region, intermediate stress region and high stress region. The creep characteristics of the low stress region and intermediate stress region are consistent with dislocation climb and viscous glide, respectively. In the high stress region, the stress exponent,n increases with stress, the activation energy is higher than those observed in the other two regions, the activation area is slightly decreasing with stress and the internal stress is almost negligible. Present analysis shows that these characteristics are consistent with the thermally-activated glide motion of dislocations as a rate controlling mechanism at high stresses.[/p]     

Rheological analysis of stress change experiments during high temperature creep

The main results of stress drop experiments during high temperature creep (i.e. the occurrence of zero and sometimes negative creep rates, the existence of two parts with different slopes in the curves of the incubation time t_r versus the stress decrement , the zero or positive values of the stress variations in stress relaxation tests) are analysed from a rheological point of view. The basis of the proposed interpretation is the existence of a creep criterion, represented by a limit surface in the stress space, which explains through the usual plastic flow rules the occurrence of zero or negative creep rates. The work hardening splits into a translation (kinematic hardening) and a deformation of this limit surface. The recovery of kinematic hardening is slower than the recovery of deformation. On this basis, the concept of internal stress used either in the activated glide of dislocations or in the Bailey-Orowan relationship and the nature of negative creep rates are discussed.     

Primary and Anelastic Creep of a Near α-Ti Alloy and Their Dependencies on Stress and Temperature

The primary creep behaviour of a high temperature near -Ti alloy Ti6242Si has been investigated in the temperature range from 500 to 625°C, and the stress range from 80 to 450 MPa. The results are analysed in terms of the dependencies of stress on strain (strain hardening) and on strain rate (strain rate sensitivity). Furthermore, full unloading experiments were conducted in order to gain additional information as to the nature of primary creep. It is shown that primary creep can be described by an athermal component, strain hardening, with a mean strain hardening coefficient of 0.37, and a thermally activated component, strain rate sensitivity, with a strain rate sensitivity coefficient suggesting a mechanism based on climb controlled recovery. This is confirmed by the activation energy of 259 kJ/mol determined at different stresses, which is similar to the activation energy of Ti self diffusion in -Ti. The anelastic strain obtained on full unloading was analysed in its fast stage in a similar way. The kinetics of anelastic creep and its activation energy are in many aspects very similar to those of primary creep. It is thought that, in the stress and temperature range investigated, primary creep is to a relatively high extent anelastic in nature, and is controlled by the climb controlled bow out of pinned dislocation segments, particularly dislocations pinned at lath boundaries.     

Effect of precipitate type and morphology on high-temperature creep and internal stress in Al-Li based alloys

The tensile creep of a series of aluminium-lithium-based alloys, two binary alloys containing precipitate, and the 2090 alloy containing and T₁ precipitate, has been studied over a range of stresses at 150°C. In some cases the internal stress developed during creep has been determined using the strain transient dip test. The results have been compared with similar data previously obtained for the 8090 alloy containing and S precipitates. The solid solution alloy and the binary alloy containing shearable particles exhibited normal Class II behaviour, with the development of sub-grains and a stress dependence of the creep rate given by a single stress exponent,n, between 4 and 5 at all applied stresses. The alloys containing particles not easily sheared by dislocations, coarse , S and T₁, exhibited similar stress dependencies of the creep rate at low stresses but exhibited large values ofn, between 18 and 35 at high stresses. The internal stress, _i, in these alloys was found to be approximately constant at high stresses possibly due to partial shearing of the coarse , T₁, and the S on sub-boundaries. The stress dependence of the minimum creep rate, , could be represented at all applied stresses, _a, by , where (_a–_i) is the effective stress driving dislocations during creep, andn is a single stress exponent of between 5 and 6 for all applied stresses. The internal stress, which increases with applied stress, at least at a low applied stress, arises from inhomogeneity of plastic deformation, due to hard sub-boundaries or hard particles which are Orowan looped. These two types of contribution to the internal stress are of similar magnitude in the alloys containing coarse and T₁ but the majority of the internal stress in the 8090 alloy may arise as a result of the hardening of sub-boundaries by the S precipitate.     

Creep of medium and high strength aluminum alloys at normal temperature in moist atmospheres

Direct data have been obtained for the creep of high- and medium-strength aluminum alloys in the stress range of O.6–1.2 of the nominal yield strength _0.2 in laboratory air and in aqueous NaCl solution at room temperature. On this basis using known theories approximating functions have been determined for the creep curves. Stress _0.2 serves as a natural boundary for the macroelastic and macroplastic regions in the first of which creep is only transient, and in the second there are transient, quasisteady-state, and accelerated stages. Extrapolated estimates of creep strain in the macroelastic region from data measured in the macroplastic region are not physically competent. However, a tendency towards an increase in ductility with an increase in time to failure at stresses greater than _o.2 makes it possible to estimate by extrapolation the time for onset of the accelerated creep stage with low test stresses from measured values at greater stresses in the macroplastic region. Fractographic and strain indices revealed the harmful effect of moist atmospheres on the deformation and failure resistance of alloys with prolonged loading.Translated from Problemy Prochnosti, No. 1, pp. 50–58, January, 1990.     

Apparent activation volume for creep of copper and alpha brass at intermediate temperatures

Experimental measurements of the apparent activation volume for creep,V ^*, of Cu and Cu-30% Zn conducted at intermediate temperatures showed two types of strain dependencies. At the lower temperatures and higher stresses,V ^* decreased with increasing creep strain, ε, while at higher temperatures and lower stresses,V ^* was essentially independent of strain. The low temperature-high stress behaviour for Cu and Cu-30% Zn was found to be consistent with the dominance of a dislocation intersection mechanism. The high temperature-low stress data for the pure metals suggest that the rate-controlling process involves the nonconservative motion of jogs on screw dislocations. For the latter conditions, an additional contribution from solute drag-limited dislocation glide also appears to be important in governing the creep behaviour of the alloy.     

Dislocation analysis of die-cast Mg–Al–Ca alloy after creep deformation

Tensile creep tests were combined with detailed transmission electron microscopy in order to characterize the dislocation movements during creep and to explain the creep properties of the Mg–Al–Ca AX52 die-cast alloy at 473 K and stresses from 15 to 70 MPa. TEM observations indicate that dislocations are generated within the primary α-Mg grain in the die-casting process, which consist of both the basal and non-basal segments. The basal segments of dislocations are able to bow out and glide on the basal planes under the influence of a stress, and the jogs follow the basal segments with the help of climb during creep. The creep mechanism for the alloy is deduced as dislocation climb due to the formation of sub-boundaries during creep, while the easy glide of the basal segments of dislocations is controlling the creep rates immediately after the stress application of creep tests.     

Dynamical recovery

Robert Cahn demonstrated, many years ago, that purely thermal recovery at high temperatures occurs by polygonisation, the first seen example of cell formation in a dislocated crystal. Here, we now consider low temperature recovery which, because of the essential role played in it by an applied stress large enough to cause plastic yielding, is known as dynamical recovery or work softening. The dominant features, which can lead to this recovery appearing in the spectacular form of a yield drop, are the creation of cellular dislocation structures in the work hardened state, with most of the glide dislocations densely packed in the cell walls where they face a forest of other dislocations as obstacles; the back stress exerted by the obstructed dislocations on the interiors of the cells so that, even though these are soft, they are prevented from yielding until the applied stress is raised further; and the stress-driven but thermally activated cutting of the glide dislocations through the forest obstacles. The way these combine to give yield drops is discussed.     

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.     

Asymmetry Behaviour between Tension and Compression for Prestrained Materials under Cyclic Loading

The prestrained metals show substantial asymmetry between tension and compression in addition tothe softening under cyclic loading, thus the cyclic creep takes place at a load-control test. The soft-ening reflects the decrease in density of dislocation and total internal stress, and the creep implies theasymmetry in back stress between tension and compression, The mechanical behaviour of the soft-ening is similar for materials with different slip modes, but their features of creep differ significantly.The creep of planar slip Cu-Zn alloy exhibits“explosively”, while that of wavy slip Cu and low car-bon steel occurs continuously and slowly. The explanation of creep behaviour via the internal dislo-cation structure was presented in this paper. According to asymmetw behaviour, it can be concludedthat the internal processes of softehing also strongly depend on the slip mode. In addition, underhigh stress amplitude the opposite asymmetries take place for Cu and Cu-Zn alloy, it indicates thatasymmetric back stresses developed in pretension have been eliminated even though the density andthe configuration of dislocations have not reached equilibrium.