Harper-Dorn Creep Research Articles

Comments on the internal stress model of Harper-Dorn creep

At intermediate to high temperatures single and polycrystalline metals, alloys, ceramics and minerals often deform by the diffusion-controlled dislocation mechanism of power law creep at high stresses, but of Harper-Dorn (H-D) creep at low stresses. H-D creep is characterized by a stress exponent n of unity and an activation energy - equal to that for power law creep and creep rates that are insensitive to grain size. Recently, a model was proposed to explain H-D creep, based on the assumption of the presence of an internal stress [sigma][sub i], which arises from the random dislocation density [rho] within subgrains. This internal stress model has been used to predict the H-D creep behavior in pure metals, alloys, ceramics and NaCl. It is the intent of this communication to show that this model only provides an approach to unify the low stress (n = 1) and high stress (n = 5) data, but reveals no information about the Newtonian viscous flow mechanism at low stresses, H-D creep or diffusional creep.

On the transition from power law creep to Harper-Dorn creep

At intermediate to high temperature single and polycrystalline metals, alloys, ceramics and minerals often deform by the diffusion-controlled dislocation mechanism of power law creep at high stresses, but by a mechanism of Harper-Dorn (H-D) creep at low stresses. H-D creep is characterized by a stress exponent n of unity and an activation energy equal to that for power law creep and a strain rate independent of grain size. Several dislocation mechanisms have been proposed for H-D creep. Langdon and Yavari explain H-D creep from the climb of edge dislocations under conditions of vacancy saturation. According to Weertman and Blacic, H-D creep may be produced by a low-amplitude thermal cycling effect which causes a cyclic change in equilibrium point defect concentration. Raj postulated a mechanism with the generation of dislocations from surface sources controlling the strain rate. Ardell and Lee considered H-D creep as the result of a dislocation network coarsening. Based on the assumption of the presence of internal stress, Wu and Sherby and Ruano et al. treated Harper-Dorn creep as an extension of power law creep into the low stress region. It is the intent of this communication to show that H-D creep starts to operate at stresses equalmore » to the Peierls stress.« less

Significance and Role of Deformation Micromechanisms in Life-Predictive Modeling of Aging Structures

Transitional creep mechanisms are exhibited by materials used in power systems and a thorough knowledge of these is a prerequisite in reliable extrapolations of short-term data to service conditions mainly due to the dominance of viscous creep mechanisms such as Nabarro-Herring, Coble and more importantly Harper-Dorn creep at low stresses. The paper summarizes the deformation mechanisms pertinent to various classes of materials. It is shown that blind extrapolation of the short-term laboratory test results to long-term service conditions leads to nonconservative predictions of the creep-rates and life times of the structural materials. Application of such transitional creep mechanisms to the prediction of dimensional changes of Zircaloy cladding in light water reactors is summarized.

Harper–Dorn and Power‐Law Creep in Single‐Crystalline Magnesium Oxide

The creep behavior of single‐crystalline MgO tested in the 〈100〉 direction is reviewed in the temperature range 1300° to 1800°C. At low stresses, the stress exponent is equal to about unity, and the deformation process is attributed to Harper–Dorn creep. At high stresses, the stress exponent is equal to approximately 5 and the deformation process is attributed to dislocation glide controlled by climb. The creep behavior in both regions is successfully predicted by an internal stress model for Harper–Dorn creep.

An examination of the metals deforming by Harper-Dorn creep at high homologous temperatures

At low stresses and high homologous temperatures, metals exhibit Newtonian viscosity with a stress exponent of 1. This behavior is attributed to either Harper-Dorn creep arising from a dislocation process or Nabarro-Herring creep resulting from the stress-directed diffusion of vacancies. By analysing experimental data where the occurrence of Harper-Dorn creep is unambiguous, a relationship is derived for the transition between the two processes. It has been suggested recently that several experiments, using the zero creep technique on wires and foils, are consistent with Harper-Dorn creep. Using the transition relationship, it is demonstrated that these experiments are instead within the regime of Nabarro-Herring creep.

Creep in metals at intermediate temperatures and low stresses: a review

In the present paper, some recent results on viscous creep in α-Fe and α-Zr are reviewed and some results of investigations of creep in a Cu14Al solid solution alloy at intermediate temperatures and low stresses are presented and discussed. The “low stresses” are specified as those causing steady state creep rates lower than 10 −10 s −1 at “intermediate temperatures” ranging from 0.4 T m to 0.6 T m ( T m is the melting temperature). It is shown that the creep in α-Fe and α-Zr results from stress-directed diffusional transport of matter via the grain boundaries (Coble creep) up to an intercept grain size of about 120 μm, while at the intercept grain sizes above this value Harper-Dorn creep controlled by dislocation core diffusion operates. In creep of a Cu14Al solid solution alloy, two flow processes act in parallel: (i) the viscous flow process identified with Coble creep and (ii) the non-viscous flow process characterized by a strain rate proportional to applied stress squared, inversely proportional to the intercept grain size cubed, and by the activation energy close to the activation enthalpy of grain boundary diffusion. The latter flow process was identified with the creep due to grain boundary sliding accommodated by slip in thin zones adjoining the sliding boundaries. In the solid solution alloy under consideration, Harper-Dorn creep does not take place up to an intercept grain size of 270 μm at least.

Harper-Dorn and power law creep in uranium dioxide

The creep behavior of uranium dioxide is reviewed based on the results of seven separate investigations. The data fall into two regimes: a power-law region at high stresses where the stress exponent, n, is about five and a Newtonian-viscous region at low stresses where the stress exponent is unity. It is shown that the data in the region where n = 1 cannot be explained by a Coble diffusional creep mechanism. This result negates the recent conclusion of Knorr, Cannon, and Coble who claim that “it is conclusively shown that Coble creep is the dominant mechanism” in the viscous region. It is demonstrated, rather, that Harper-Dorn creep describes the creep behavior of polycrystalline UO 2 above 0.6 T m and in single crystalline material in the region where n =1. Harper-Dorn creep in uranium dioxide is analyzed using an internal stress model developed to describe pure metal behavior. The value of the modulus-compensated internal stress, which is a measure of the random dislocation density, is shown to be higher for both polycrystalline and single crystalline uranium dioxide than it is for pure metals.

On the low stress creep in Cu-14Al alloy and α-zirconium at intermediate temperatures

Abstract It is shown that during creep in a Cu-14Al solid solution alloy at low stresses and intermediate temperatures, two flow processes act in parallel: (i) stress-directed diffusional transport of matter via the grain boundaries and (ii) grain boundary sliding accommodated by slip in thin zonesadjoining the sliding boundaries. However, creep in α-zirconium at low stresses and intermediate temperatures results from stress-directed diffusional transport of matter via the grain boundaries up to an intercept grain size of 120 μm, while for intercept grain sizes above this value, Harper-Dorn creep operates. An interpretation of the results of the investigations of creep in α-zirconium by Bernstein, Fiala and Cadek in terms of grain boundary sliding accommodated by slip as proposed by Ruano, Wadsworth and Sherby is shown to be incorrect.

Harper-dorn creep in class I solid solution alloys

Harper-dorn creep in class I solid solution alloys

In search of a systematics for the viscosity of perovskites: creep of potassium tantalate and niobate

Abstract With a view to gathering information on the high-temperature creep of crystals with perovskite structure, the creep behavior of single crystals of KTaO3 and KNbO3 has been investigated and the characteristic dislocation structures have been observed by transmission electron microscopy. At temperatures between 0.87 and 0.99 Tm, KTaO3 deforms by Newtonian Harper-Dorn creep (n = 1) with an activation energy Q = 292 ± 39 kJ mol−1, slip occurs mostly on {100} planes and the dislocations are mostly edge with Burgers vector 〈001〉, they easily expand in their climb planes and there probably is some pure climb strain. The results are compared with those previously obtained in the case of BaTiO3. It is found that perovskites do not constitute an isomechanical group and that the distortions of the lattice may be important in determining the dislocation core structures and the creep mechanisms.

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 10 8 m −2 or less and independent of stress and that for Harper-Dorn creep the density must be below a critical value of about 2×10 9 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.

The mechanism of Harper-Dorn creep

Existing theories of Harper-Dorn creep rely on the assumption that, under conditions where Harper-Dorn creep is observed, the dislocation density rapidly achieves a characteristic value which is independent of the method of preparation of the sample, of the applied stress, and of the extent of creep strain, but they do not attempt to justify this assumption. We perform a dimensional analysis in which it is assumed that the ratio of strain rate ϵ to applied stress σ, which is experimentally observed to be characteristic of the material and independent of the history of the material and of the applied stress, can depend only on the Burgers vector, the shear modulus μ, and the drag coefficients B c for dislocation climb and B g for dislocation glide. If we also accept the experimental observation that ϵ/σ has the activation energy of self-diffusion, the resulting relation indicates a value of ϵ/σ which is 10 11 times too large. The only other large number which can enter the theory is the ratio of μ to the Peierls stress σ p, and this indicates that the Peierls stress must play a significant role in the mechanism. We obtain a numerically reasonable theory by assuming that the equilibrium dislocation density is that at which the stress exerted by a dislocation on its neighbour is equal to the Peierls stress, while the motion of the resulting dislocation array under the applied stress is controlled by climb. The internal stresses in the Harper-Dorn régime are less than the applied stress.

An analysis of low stress creep data for coarse-grained pure lead

An analysis has been carried out of low stress creep data for pure lead at 298 to 323 K and grain sizes from 200 to 500 μm, as compiled by Gifkins and Snowden. The results suggest pipe-diffusion-controlled Harper-Dorn creep to be the dominant creep mechanism for the data considered. This finding is consistent with the theoretical predictions.

An analysis of the transient stage in low stress viscous creep

Transient creep data recorded during low stress viscous creep of α-Ti, α-Zr, β-Co and zircaloy-2 are presented. The data are analysed in terms of the effect of stress, temperature and grain size on transient time as well as transient strain. Transient time is seen to be independent of stress in all four materials. Transient time decreases with increasing temperature and the variation can be described by an Arrhenius relation. Upto a grain size of nearly 100 μm, the transient time increases with increasing grain size. In the case of α-Ti and β-Co, beyond 100 μm and under conditions that facilitate Harper-Dorn creep to dominate flow, transient time exhibits grain size independent behaviour. Transient strain, normalised with elastic strain, appears generally to be independent of stress, temperature and grain size. Transient viscous creep data presented here, excluding those pertaining to coarse grained α-Ti and β-Co, can be satisfactorily rationalised following the grain boundary diffusion based model proposed by Raj. In regard to materials with grain size coarser than 100 μm, the data for α-Ti were more comprehensive and have been explained by a model proposed here, which is based on mutual annihilation of preexisting dislocations by volume diffusion controlled climb.

Harper-dorn creep in pure metals

Evidence is presented that Harper-Dora (H-D) viscous creep is a diffusion-controlled, dislocation creep process. The factors influencing H-D creep are the same as those influencing power-law creep, namely dislocation density, subgrain or grain size, stacking fault energy, and elastic modulus. H-D creep has been observed, and is analyzed, for seven different metals: Al, Pb, Sn, α-Zr, α-Ti, α-Fe, and β-Co. In addition, seven metals (α-Fe, Ni, Ag, β-Co, Cu, Mo, and Cr) which were originally believed to be controlled by diffusional (Nabarro-Herring) creep at low stresses, are shown to be controlled by Harper-Dorn creep. An internal stress assisted creep model is presented which correlates data in both the power-law and H-D creep regimes. The model predicts, quantitatively, the conditions under which H-D creep will dominate plastic flow.

On the grain size dependence of Harper-Dorn creep

The effect of grain size on the Harper-Dorn creep rate is re-examined through an analysis of the data on several metals and alloys. It is shown that the creep rate γ varies with the grain size d as γ ∂ (b/d) p where b is the Burgers vector and p is the grain size exponent, when the number of grains across the specimen thickness exceeds four. The magnitude of this exponent was estimated to be 1 ⩽ p ⩽2. However, the grain size effect is insignificant in multicrystals with a smaller number of grains across the cross-section, and the creep rate is similar to those for single crystals.

A dislocation network theory of Harper-Dorn creep—I. Steady state creep of monocrystalline Al

A recently developed dislocation network theory of high temperature creep is modified for consistency with the equally recent experimental observation that the dislocation link length distribution that develops during Harper-Dorn (H-D) creep of monocrystalline Al deformed in compression at 920 K contains no segments that are long enough to glide or climb freely. H-D creep is therefore a phenomenon in which all the plastic strain in the crystal is generated by the process of stress-assisted dislocation network coarsening, during which the glide and climb of dislocations is constrained by the requirement that the forces acting on individual links are balanced by the line tension of the links. It is not possible to test all the predictions of the theory because not all the required input information is available. In particular, the kinetic law governing the growth rate of individual links is not known. Nonetheless, using an established and well-known equation as a first guess, it is possible to simulate the experimentally observed distribution of dislocation link lengths with reasonable semiquantitative accuracy. In other respects, especially regarding the steady state creep rate, the theory is in excellent agreement with the experimental results.

Low stress high temperature creep in single crystal NaCl

Transient and steady-state creep of single crystal NaCl was measured in the temperature range 560–736°C and at stresses between 0.027 and 0.188 MPa. Samples were loaded parallel to the 〈100〉 direction and strain was measured using a capacitive transducer having a resolution of 10 −7. The non-recoverable portion of the transient response can be represented by a power law in time with an exponent of about 0.55. The activation energy for transient creep in previously deformed crystals is 0.20 MJ mol −1, the same as that for steady-state creep, while the activation energy for transient creep in annealed crystals is 0.16 MJ mol −1 which is approximately equal to the activation energy for core diffusion. Transient strain rates are linearly proportional to stress. Steady-state strain rates are proportional to σ 4 for stresses above 0.1 MPa, in agreement with previous studies. Below 0.1 MPa the strain rates have a linear dependence on stress. We interpret this behavior to be analogous to Harper-Dorn creep in metals, although higher dislocation densities and the observations of orthogonal slip bands suggest that a different micromechanism may control Newtonian flow in this non-metallic system.

Creep in zirconium at low stresses and temperatures from 748 to 973 K

The results of an investigation of creep in α-Zr at stresses ranging from 3.9 × 10−6 G to 1.2 × 10−4G at temperatures ranging from 748 to 973 K and with linear intercept grain sizes less than 120 μm are presented. It is shown that the steady state creep rate is inversely proportional to the third power of intercept grain size, increases with the stress linearly and is grain boundary diffusion controlled. For steady state creep a threshold stress is characteristic. The results are correlated with the model of non-uniform diffusional flow due to Ashby and Verrall. The measured threshold stress is accounted for on the assumption that it represents the stress opposing the motion of grain boundary dislocations.From the results of the present work together with those of previous work on power law creep and Harper-Dorn creep in α-Zr. creep mechanism maps were constructed.

On the importance of surface dislocation sources in Harper-Dorn creep

Etude theorique du fluage de Harper-Dorn en se basant sur les observations de Raman et Raj qui suggerent que l'importance des sources de dislocation a la surface ne peut pas etre surveillee quand le fluage par dislocation et diffusion contribue de facon insignifiante au fluage total