Subgrain Interior Research Articles

Composite Model of Internal Stress Field in the Steel P91

One of the refined versions of the composite model suggested by Sedláček et al. is adopted in a modeling of the local stress field in the steel type P91. The microstructure of the steel is considered as a one-dimensional substructure in which the subgrain interiors represent soft regions and sub-boundaries discontinuously decorated by carbide particles are hard regions. Two limiting structures locally approximating the real substructure, i.e., a substructure with particle-free and a substructure with particle-decorated sub-boundaries, are considered. In the latter case, the model takes into account different elastic moduli of the hard and the soft regions. As an application to experimental data, some predictions for the internal stress and for the changes of the stress field due to evolution of microstructure in creep are discussed.

Composite Model of Internal Stress Field in the Steel P91

One of the refined versions of the composite model suggested by Sedláček et al. is adopted in a modeling of the local stress field in the steel type P91. The microstructure of the steel is considered as a one-dimensional substructure in which the subgrain interiors represent soft regions and sub-boundaries discontinuously decorated by carbide particles are hard regions. Two limiting structures locally approximating the real substructure, i.e., a substructure with particle-free and a substructure with particle-decorated sub-boundaries, are considered. In the latter case, the model takes into account different elastic moduli of the hard and the soft regions. As an application to experimental data, some predictions for the internal stress and for the changes of the stress field due to evolution of microstructure in creep are discussed.

Advances in Physical Metallurgy and Processing of Steels. Strengthening Mechanisms of Creep Resistant Tempered Martensitic Steel.

The creep deformation resistance and rupture life of high Cr ferritic steel with a tempered martensitic lath structure are critically reviewed on the basis of experimental data. Special attention is directed to the following three subjects: creep mechanism of the ferritic steel, its alloy design for further strengthening, and loss of its creep rupture strength after long-term use. The high Cr ferritic steel is characterized by its fine subgrain structure with a high density of free dislocations within the subgrains. The dislocation substructure is the most densely distributed obstacle to dislocation motion in the steel. Its recovery controls creep rate and rupture life at elevated temperatures. Improvement of creep strength of the steel requires a fine subgrain structure with a high density of free dislocations. A sufficient number of pinning particles (MX particles in subgrain interior and M 23 C 6 particles on sub-boundaries) are necessary to cancel a large driving force for recovery due to the high dislocation density. Coarsening and agglomeration of the pinning particles have to be delayed by an appropriate alloy design of the steel. Creep rupture strength of the high Cr ferritic steel decreases quickly after long-term use. A significant improvement of creep rupture strength can be achieved if we can prevent the loss of rupture strength. In the steel tempered at high temperature, enhanced recovery of the subgrain structure along grain boundaries is the cause of the premature failure and the consequent loss of rupture strength. However, the scenario is not always applicable. Further studies are needed to solve this important problem of high Cr ferritic steel. MX particles are necessary to retain a fine subgrain structure and to achieve the excellent creep strength of the high Cr ferritic steel. Strengthening mechanism of the MX particles is another important problem left unsolved.

Modelling the Work Hardening in Cold Rolled and Annealed Aluminium Sheet

A recently developed work-hardening model has been applied in an attempt to describe the deformation behaviour during tensile testing of cold rolled, partially annealed and recrystallised aluminium sheet. The model is based on a microstructural concept comprising three elements, the subgrain size, δ, the misorientation, θ, and the dislocation density in the subgrain interior, ρ i . Effects of solutes and particles on the work hardening behaviour have been accounted for in 0-temper (recrystallised) variants of the investigated alloys. The model is also able to handle the effect of a fine grain structure reasonably well.

Microstructural evolution during high temperature deformation of lamellar Ti48Al–2Nb–2Cr

The microstructural evolution of lamellar Ti48Al–2Nb–2Cr during deformation at temperatures between 1000 and 1200 K was investigated by light optical and electron microscopy. The lamellar structure which initially covers more than 95% of the volume transforms during deformation into a globular structure consisting of equiaxed subgrains with a significant amount of large angle boundaries (<30%). The steady state subgrain size and the spacing of dislocations in the subgrain interior vary in inverse proportion to shear modulus normalized stress. Based on the steady state data the evolution of the volume fraction with globular (subgrain) structure and the characteristic spacings is quantified.

Interpretation of constant-load and constant-stress creep behavior of a magnesium alloy produced by rapid solidification

The creep behaviour of an Mg–Zn–Ca–Ce–La alloy produced by rapid solidification was investigated by means of constant-load creep tests carried out at 498, 523 and 548 K. The analysis of strain rate as a function of applied stress suggests that in the ranges of stress and temperature studied, the creep mechanism is glide on basal plane controlled by cross-slip on non-basal planes or dislocation glide limited by the nucleation of kinks. This behaviour contrasts with previous results obtained in pure Mg where cross-slip on non-basal planes was the rate-controlling mechanism only at higher temperatures. The different behaviour of this alloy is attributed to the very fine grain size typical of rapidly solidified material. The enhancement in strain rate observed in the present alloy can be attributed to grain-boundary sliding accommodating the strain produced by dislocation creep mechanisms (glide on non-basal plane controlled by cross-slip or dislocation glide limited by the nucleation of kinks) that operate in the subgrain interior.

Analysis of creep transients in pure metals following stress changes

The analysis of creep transients associated with stress change tests is reviewed, with an emphasis on using the results of these experiments to characterize the kinetics of deformation under conditions of nominally constant structure. In order to develop a common framework for the description of results obtained by various authors, operational definitions of the characteristic strain rates observed after stress changes are adopted. The data for aluminum reported by numerous investigators provide a consistent picture over a broad range of temperatures and initial creep stresses. These results show that transient creep after stress reductions occurs by two parallel processes of dislocation glide within subgrain interiors and dynamic recovery associated with subgrain boundary migration. Following relatively large stress reductions, the creep transient is dominated by the subgrain boundary migration processes. After relatively small changes in stress, thermally activated motion of dislocations within subgrain interiors is the predominant mechanism of deformation. In this regime, the creep transients can be described by a thermally activated rate law, thereby enabling various activation parameters to be evaluated from the data. In particular, the true activation areas are found to be equal to the dislocation spacing within subgrain interiors, hence are consistent with thermally activated cutting of forest dislocations. Limited results for other f.c.c. metals and related materials are shown to follow the trends established for aluminum. In particular. it is demonstrated that the data for pure copper and LiF at high temperatures and after small stress changes are also consistent with a description based on thermally activated glide. However, the true activation areas in copper are about five times greater than the dislocation spacing. This difference between copper and aluminum is attributed to the fact that the former has a substantially lower stacking fault energy. It is argued that the resulting wider separation of partials makes the thermally activated cutting of forest dislocations more difficult.

Modelling high temperature creep of academic and industrial materials using the composite model

The composite model of plastic deformation of materials developing a subgrain structure provides a framework for coupling the deformation of the soft subgrain interior and the hard subgrain boundaries through internal stresses. By specifying the kinetic laws for deformation of soft and hard regions according to the dominant dislocation obstacles, the model has been applied to three materials: pure aluminium, the Ni-based alloy NiCr22Co12Mo (Inconel 617) and the ferritic 12% Cr steel X 20 CrMoV 12 1. The formulation of the kinetic laws for the soft region was based on thermally activated glide through the dislocation structure in the case of aluminium and on solute and particle hardening in the case of the alloys. The kinetic laws for the hard region were similar in all cases, differing mainly in the amount of particle hardening. It is shown that the model is capable of modelling the transient creep of pure aluminium between two different steady states, accounting for strain hardening due to the formation of the subgrain structure during the primary creep of NiCr22Co12Mo and estimating the degree of softening which can be expected as a result of subgrain growth and particle coarsening during the long-term creep of the 12% Cr steel.

Stress reduction tests on Nb-1wt.%Zr at 1300 K

The objective of this paper is to analyze the stress reduction behavior of b.c.c. Nb-1wt.%Zr at 1300 K (0.47 of the melting point T m). After small reductions in stress an increasing strain rate was observed, while after large stress reductions a decreasing strain rate was observed. The reduced strain rate normalized by the intial strain rate plotted semi-logarithmically as a function of the reduced stress normalized by the initial stress showed two branches ( i.e. a low and high stress sensitivity region) indicating that two different dislocations mechanisms are operating. From the high stress sensitivity branch a true activation area was calculated, which was in the range of the true activation area for cutting of forest dislocations. The normalized true activation area was found to be less than the empirically predicted dislocation spacing in the subgrain interior. Similar behavior was observed for aluminum and Al-5at.%Zn. Extrapolating the low stress sensitivity branch to σ/σ 0 equaling one shows that 10% of the total strain rate is owing to the dislocation mechanism operating at the low stress sensitivity region. The mechanism operating at the low stress sensitivity region was assumed to be subgrain boundary migration.

Strain dependence of the volume fraction of hard regions in the composite model of plastic deformation and related substructural quantities

Methods of estimating the volume fraction of hard and soft regions from substructural quantities obtained in transient creep are discussed. It is shown that the volume fraction can be assessed from the subgrain misorientation and either subgrain diameter or dislocation density in subgrain interiors. The procedure which tries to relate strain with substructural quantities is critically revised. It is shown that the procedure can give values of the product of stress and strain which correlate quite reasonably with the experimental data. Finally, an approximate formula is suggested for the estimation of volume fraction in an equilibrium state.

A model for dislocation creep

Experimental results of dynamic modulus and internal friction, measured directly during creep deformation, and back-stress data from dip test measurements are considered for an explanation of the power law of creep. The explanation is essentially based on the assumption that stationary creep depends on dislocations in the subgrain interior with zones of accumulation near to the subboundaries which are conditioning for the emission processes. The power law is related to the tendency, of the dislocation segments, to approach to the lengths of superior backstress limit, the more the higher the applied stress.

Constant substructure creep of aluminum following stress reductions

A series of stress reduction experiments was conducted on high purity polycrystalline aluminum. Initial stresses of 8.27, 10.3 and 12.4 MPa at 573 K and 3.44 MPa at 673 K were used, and stress reductions were made during steady state creep at approximately 22% true strain. For each initial stress, the constant substructure strain rates are characterized by an exponential dependence of rate on the reduced stress. These data are consistent with an exponential form of the kinetic law for flow within subgrain interiors, which is based on the theory of obstacle-controlled dislocation glide. In addition, the experimentally determined slopes for each set of constant substructure strain rate-vs-reduced stress data vary approximately as the inverse of the initial stress. This finding suggests that the strength of the microstructure scales with the initial applied stress. Finally, it is proposed that the activation energy for dislocation glide can be determined from a combination of constant structure and steady state creep data. The results of this analysis suggest that the thermal activation process may be controlled by lattice self-diffusion.

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 (τ 0, or the stress necessary to cause dislocation motion in the absence of a dislocation substructure) and dislocation (αGbϱ 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 toτ 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.

Synchrotron radiation studies of defect structure evolution in aluminium during creep

Results are reported of in situ observations (using synchroton radiation) of the nonmonotonic evolution of the structural parameters of polycrystalline aluminium deformed under creep at intermediate temperatures. As an explanation of the experimental data, a theoretical model is proposed of dislocation ensemble transformation: chaotically distributed (in subgrain interiors) dislocations → sub-boundary dislocations.

Stress dependence of the creep rate at constant dislocation structure

Stress reduction tests were performed during steady state compressive creep of pure aluminum at 523 K and of Al-5at.%Mg at 573 K in order to determine the dependence of the creep rate ϵdotr at constant (steady state) dislocation structure on (reduced) stress σr. Forward flow with ϵdotr > 0 was found in the whole range σr ⩾ 0, i.e. even after (nearly) full unloading, implying the existence of internal stresses in both materials. For aluminum the relation between log ϵdotr and σr consists of two branches with different stress sensitivities, indicating that the dominant mechanisms of dislocation motion are different for small and for large stress reductions. An interpretation is given in terms of the composite model, which assumes that the thermally activated glide in the (soft) subgrain interior and the recovery processes at (hard) subgrain boundaries are coupled by internal stresses. In the case of AlMg, on the contrary, the shape of the log ϵdotrvs. σr curves indicates that glide and recovery are not separable.

On the interpretation of the “Internal stress” determined from dip tests during creep of Al-5at.%Mg

Stress change test have been performed during creep of Al-5at.%Mg at σ = 30 MPa and 573 K. Transmission electron microscopy observations after creep showed that a subgrain structure develops for a strain of 0.3 although the creep behaviour is characteristic of the “alloy” class of materials (class A). The instantaneous strain response to a change in stress can be characterized by an elastic modulus E s which is equal to the dynamic elastic modulus. This indicates that there is no anelastic back flow during unloading. A (net) non-elastic back strain is observed only for stress reductions above 40%. The reduced stress σ i for which a non-elastic back strain of 10 −5 is observed is 0.52 of the creep stress. It does not vary significantly with strain in spite of the change in dislocation structure. The physical meaning of σ i is discussed on the basis of the anelastic and plastic strain contributions from free dislocations and subgrain boundaries. It is shown that σ - σ i can be explained as the average of a wide distribution of effective stresses acting on the dislocations in the subgrain interior. This explanation is shown to be an alternative to the “loop model” of Mills et al.

Recovery behaviour after stress reductions during the steady state creep of Al-14wt.%Zn

Stress reduction tests were carried out during the steady state creep of Al-14wt.%Zn under different constant applied stresses σ app reduced in steps of (0.3-0.1) σ app to determine the internal stress σ in, the flow stress σ flow(= σ app − σ in) and the density ϱ is of mobile dislocations under a steady state strain rate at the dissolution temperatures of Guinier-Preston (GP) zones and β phase. After a small stress reduction, the internal stress σ in and the dislocation density ϱ i in the subgrain interior were found to decrease rapidly to a minimum value at the dissolution temperatures of GP zones and β phase, while the steady state strain rate ϵ dot st , the flow stress σ flow and the density ϱ is of mobile dislocations were found to increase to a peak value at these dissolution temperatures. The results support the concept that the dynamic recovery behaviour of mobile dislocations and the flow stress which drives these dislocations are strongly dependent on the applied and internal stresses during the dissolution of GP zones and β phase.

Evolution of internal stresses and substructure during creep at intermediate temperatures

Secondary creep has most generally been associated with a rather steady structure. Many models have been suggested to explain the constant strain rate in terms of the effective stress which is determined by the structurally-dependent internal stresses. The internal stresses deduced macroscopically have been of the order of half the applied stress. In this article, by pinning the dislocations under load in an Al-Zn alloy, the evolution of the structure and local effective stresses with strain has been identified by electron microscopy. Values of local effective stresses at the subgrain boundaries ranging between 10–20 times the applied stress have been measured. The emission of dislocations from these boundaries and the evolution of substructure within the subgrain interior indicate that the controlling mechanism during the creep process is the relaxation of internal stresses by this emission. At the same time, the subboundary stress-fields existing in different subgrains determine their different behaviour as a function of time. Hard and soft subgrains alternate in the deformation process to produce overall uniform strain.

Coarsening of the dislocation structure after stress reduction during creep of NaCl single crystals

Abstract The dislocation structure during compressive creep of NaCl single crystals has been investigated by means of the etch pit technique. The steady-state subgrain size L is about 27 times the average distance of dislocations in the subgrain interior, (pi)−1/2, and scales inversely proportional to the compressive stress normalized by the shear modulus. ‘Nests’ of etch pits of relatively high density are found in small subgrain sections at a distance of ≍ 3 L and are interpreted as indicating dissolving subgrain boundaries. After a load reduction during creep at 923 K, corresponding to a decrease in stress from 1.20 to 0.50 MN/m2, L and pi −1/2 increase and reach their new steady-state values within 3 to 6% transient strain. The distribution of subgrain intercepts broadens during transient creep, indicating that subgrain boundary migration is involved in the coarsening process. There is no significant difference between the stress exponents of the steady-state creep rate determined from load reduction tests and from constant load tests.

Observations of anelastic backflow following stress reductions during creep of pure metals

The anelastic contribution to creep transients in pure f.c.c. metals has been studied by conducting experiments in which nearly the entire applied stress is removed. The observed anelastic strains range from as little as one quarter of the calculated elastic contraction for Pb to 7 or 8 times the elastic contraction for pure Al. The recoverable strains in Cu are generally about equal to the elastic strains. For Al, the magnitude of the recoverable strain increases with prior creep strain. Both the magnitude and kinetics of backflow are similar for polycrystalline and single crystal specimens. Consideration of the kinetics of backflow suggests that there are at least two rate controlling mechanisms which operate during this process. An attempt has been made to determine the physical mechanisms which contribute to creep anelasticity. Based on a qualitative consideration of the kinetics and magnitude of the anelastic transients, the most likely mechanism involves motion of dislocations from subgrain interiors to the subgrain walls and is driven by long range internal back stresses. Other simple mechanisms cannot account for the large recoverable strains, although they may make additional contributions to the overall transient.