Creep Of Copper Research Articles

Modeling of Tertiary Creep in Copper at 215 and 250 °C

AbstractFor a long time, only empirical models existed for creep curves in the tertiary stage. To understand the role of creep damage, including changes in the dislocation structure, cavitation, and necking, basic models that do not involve adjustable parameters have, however, recently been developed. These models were used to predict tertiary creep for copper at 75 °C. In the present paper, these models are applied to creep tests at higher temperatures (215 and 250 °C). These results demonstrate again that tertiary creep in copper is primarily controlled accelerated recovery of the dislocation structure and not by cavitation. The modeling results suggest that the role of cavitation is modest also in other creep exposed ductile alloys, which should be of importance to consider in the formulation of models for creep damage. Necking was only found to be of significance very close to rupture again in agreement with results at lower temperature.

The Role of Glide during Creep of Copper at Low Temperatures

Copper canister will be used in Scandinavia for final storage of spent nuclear fuel. The copper will be exposed to temperatures of up to 100 °C. The creep mechanism at near ambient temperatures has been assumed to be glide of dislocations, but this has never been verified for copper or other materials. In particular, no feasible mechanism for glide based static recovery has been proposed. To attack this classical problem, a glide mobility based on the assumption that it is controlled by the climb of the jogs on the dislocations is derived and shown that it is in agreement with observations. With dislocation dynamics (DD) simulations taking glide but not climb into account, it is demonstrated that creep based on glide alone can reach a quasi-stationary condition. This verifies that static recovery can occur just by glide. The DD simulations also show that the internal stress during creep in the loading direction is almost identical to the applied stress also directly after a load drop, which resolves further classical issues.

Basic modelling of tertiary creep of copper

Mechanisms that are associated with acceleration of the creep rate in the tertiary stage such as microstructure degradation, cavitation, necking instability and recovery have been known for a long time. Numerous empirical models for tertiary creep exist in the literature, not least to describe the development of creep damage, which is vital for understanding creep rupture. Unfortunately, these models almost invariably involve parameters that are not accurately known and have to be fitted to experimental data. Basic models that take all the relevant mechanisms into account which makes them predictive have been missing. Only recently, quantitative basic models have been developed for the recovery of the dislocation structure during tertiary creep and for the formation and growth of creep cavities. These models are employed in the present paper to compute the creep strain versus time curves for copper including tertiary creep without the use of any adjustable parameters. A satisfactory representation of observed tertiary creep has been achieved. In addition, the role of necking is analysed with both uniaxial and multiaxial methods.

Compression creep of copper under electric current studied by a spark plasma sintering (SPS) apparatus

A spark plasma sintering (SPS) apparatus was successfully employed to perform uniaxial compressive creep tests on pure copper under a stress of 30MPa in the 400–600°C temperature range. By utilizing two different configurations, the creep experiments were conducted without or with a low-density pulsed direct electric current (~ 6–7A/mm2) passing through the samples. It was found that under the influence of the applied electric current, the creep rate increased significantly, while the extent of the effect diminished with temperature. The apparent activation energy for creep with applied current decreased from 110 to 66kJ/mol. This was attributed to the effect of current on the thermally-activated process and dislocations motion. No distinct evidence that the electric current affects the microstructure was observed.

Formation of a dislocation back stress during creep of copper at low temperatures

Copper gives creep strain versus time curves at 75°C that look very similar to those recorded at much higher temperatures. Thus, for example, an extended secondary stage where the strain rate is constant is observed. Considering the high creep exponent that can be up to 75, one would expect a creep curve with rapidly increasing strain rate but that is not found. The difference to creep of pure metals at high temperatures is so large that we can talk about an entirely new material class with respect to creep. To explain the observations a recently developed dislocation model (Sandstrom, 2017) for cell structures is used. A new creep model is presented where a back stress based on the dislocations in the cell walls is introduced. Unbalanced sets of dislocations without matching dislocations of opposite signs are formed in the cell walls. Since the unbalanced content is not exposed to static recovery, it forms a stable back stress. It is shown that the computed back stress can fully explain the observations and reproduce both creep curves and results for slow strain rate tensile tests.

Thermal stability of interface voids in Cu grain boundaries with molecular dynamic simulations

By means of molecular dynamic simulations, the stability of cylindrical voids is examined with respect to the diffusion bonding procedure. To do this, the effect of grain boundaries between the grains of different crystallographic orientations on the void closing time was studied at high temperatures from 0.7 up to 0.94 of the bulk melting temperature (). The diameter of the voids varied from 3.5 to 6.5 nm. A thermal instability occurring at high temperatures at the surface of the void placed in a grain boundary triggered the eventual closure of the void at all examined temperatures. The closing time has an exponential dependence on the examined temperature values. A model based on the defect diffusion theory is developed to predict the closing time for voids of macroscopic size. The diffusion coefficient within the grain boundaries is found to be overall higher than the diffusion coefficient in the region around the void surface. The activation energy for the diffusion in the grain boundary is calculated based on molecular dynamic simulations. This value agrees well with the experimental given in the Ashby maps for the creep in copper via Coble GB diffusion.

Regularities of varying the dislocation substructure of copper under creep in the magnetic field

The object of the study is polycrystalline copper of M006 brand. The dislocation substructure (DSS), which is formed in copper under the destruction in creep conditions in a magnetic field of 0.35 T, was studied by diffraction electron microscopy. The substructure of the initial state of copper is characterized by the presence of the following DSS types: chaotically distributed dislocations (56%), a cellular substructure of various degrees of perfection (36%), a netlike substructure (5%), a band substructure (3%), dislocation bundles (3%), and broken subboundaries (2%). It is established that the peculiarities in the quantitative ratio of DSS types manifest themselves under destruction in the magnetic field. Notably, the main DSS type near the destruction zone in copper deformed under creep conditions is the subgrain structure. The application of the magnetic field leads to a decrease in the relative content of the subgrain structure in copper by almost a factor of 2. It is shown that the magnetic-field effect retards the transformation rate of the dislocation substructure under creep of copper, which leads to an increase in strength characteristics.

Regularities of Varying the Dislocation Substructure of Copper during Creep in the Magnetic Field

The object of the study was polycrystalline copper of the M006 brand. The dislocation substructure (DSS), which is formed in copper during the destruction in creep conditions in the magnetic field of 0,35 T, is investigated by diffraction electron microscopy. The substructure of the starting state of copper is characterized by the presence of the following DSS types: chaotically distributed dislocations (56 %), cellular substructure of various degrees of perfection (36 %), net-like substructure (5 %), striated substructure (3 %), dislocation bundles (3 %), and torn subgrains (2 %). It is established that the features in the quantitative ratio of DSS types are revealed during the destruction in the magnetic field. Notably, a subgrain structure is the main DSS type near the destruction zone in copper deformed under creep conditions without the magnetic field. The imposition of the magnetic field leads to a decrease in the relative content of the subgrain structure by a factor of almost 2. It is shown that the effect of the magnetic field retards the reconstruction of the dislocation substructure under the creep of copper, which improves strength characteristics.

Effect of the surface charge density on the creep of copper

The creep of polycrystalline copper under the action of high and low electric potentials is studied. At potentials of ±4 kV and ±5 V, the steady-state creep rate decreases, and the effect in the former case is weaker than in the latter by a factor of 2.5. This difference is caused by the fact that the charge density in the sample-capacitor bank system at the high electric potentials is lower than at the low potentials.

Diffusional creep in Cu–Fe solid solutions

Abstract The activation energy of diffusional creep in copper–iron solid solutions was studied. Experiments were performed on foil samples in an atmosphere of dry hydrogen in a temperature range from about 1170–1340 K. The foils had a thickness of 1.8 × 10 −5 m and a length of about 0.15 m. The stress range was from 0 to 300 kPa. The method of the measurements was developed in our previous work and it was based on measuring the time dependence of stress on a sample. The viscosity of the solid solutions was higher than that for pure copper. It was shown that there is a gap on temperature dependences of viscosity. The temperature of the gap was about 1295 K. Our previous experiments on the Cu–Co system showed the same feature in the activation energies. As previously shown, two processes are required for describing the diffusional creep. They are the volume diffusion and generation/annihilation of the vacancies. The processes occur in sequence. We assume that only second type processes could lead to the appearance of the gap on the temperature dependence of viscosity in solid solutions.

Damage fluctuations in creep deformed copper studied with synchrotron X-ray microtomography

AbstractDamage localization during power law creep of copper has been investigated in situ with synchrotron X-ray microtomography. The analysis of the area fraction of cavities corresponding to a given material slice has revealed that damage localization begins relatively early at half of the creep lifetime. The amplitude of the maximum fluctuation shows parabolic behavior as a function of mean void volume fraction. Existing models of damage evolution underpredict the amount of real damage and overpredict power-law creep life-time.

Grain boundary phase transformation in Cu–Co solid solutions

The present work examined the creep behavior of copper based solid solutions with cobalt at temperatures between 980°C and 1080°C and stresses lower than 0.2MPa. The samples were made from 18μm foil and were formed into cylinders. After the pre-annealing at 1000°C during about 30h the samples had a parquet structure. The experiments were performed in the hydrogen atmosphere. New equipment was designed for these measurements.The activation energy of pure copper creep was close to the activation energy of copper volume self-diffusion. Cu–Co solid solution creep rate was always lower than that of pure copper. It was shown that the creep activation energy in the relatively low temperature region was higher than in the high temperature region. The same behavior was typical for all studied solid solutions. The transition temperature was about 1030°C.It was proposed that such creep behavior was connected with grain boundary phase transformation and explanation was made in terms of interface controlled diffusional creep.

Basic model for primary and secondary creep in copper

A model for primary and secondary creep is established. The starting point is a combination of basic models for tensile stress–strain curves and for secondary creep. The derived model can describe experimental creep strain curves for Cu 50 p.p.m. P in the temperature interval 75–250 °C with the same precision as the variation in the experimental creep strain curves for identical conditions. No fitting parameters are involved in this representation. The model has also been applied successfully to creep specimens with round notches, where multiaxial stress states are present. One main aim of deriving a basic creep model is to improve the accuracy of extrapolation. That this is possible has been demonstrated for creep tests with estimated secondary creep rates down to 5 × 10 −22 s −1. In conventional creep rupture testing strain rates down to 1 × 10 −12 s −1 can be recorded. As a background, a summary of empirical methods for the extrapolation of creep strain data is given.

The influence of stacking fault energy on high temperature creep behaviour laws: The case of Cu and Cu-4Si

The influence of stacking fault energy during the secondary stage of the creep process is hard to grasp, both experimentally and theoretically. It is, however, well-known that such an effect is very important; indeed, a weak stacking fault energy is likely to produce a noticeable decreasing in creep rate and lead to a better heat resistance.The numerous attempts at grasping this complex phenomenon have in almost all cases been based on empirical laws which express the creep rate evolution as a function of temperature (T) and stacking fault energy (γ).The purpose of our study is to assess the influence of stacking fault energy on Cu (γ=55mJ/m2) and Cu-4Si (γ=25mJ/m2) high temperature creep. We try to show that the role of such an energy behaviour law is in accordance with the bibliography results.Several hypotheses have been examined in an attempt to account for the weakness of creep speed values in low stacking fault energies, such as copper and its alloys. On the whole, data analysis proves that copper creep is not controlled by bulk or pipe diffusion but is the result of a thermally actived slip, probably due to the cross - slip.In the case of Cu-4Si, the stacking fault energy represents half of that of Cu, the cross - slip proves to be harder and the creep could be controlled both by diffusion and cross - slip.

The effect of dispersion hardening on the regularities and mechanisms of the creep of copper with submicron grain sizes

Regularities and mechanisms of the creep of submicrocrystalline copper and Cu-1.1 vol % Al2O3 dispersion-hardened powder composite in a temperature range of (0.2–0.35) T m Cu have been investigated. The role that the grain-boundary state and dispersion-hardening material with Al2O3 nanosized (10–40 nm) particles plays in the development of plastic deformation during creep is analyzed.

Work hardening during primary creep of copper

An analysis of primary creep curves in copper in the temperature range 423–573 K indicated results that were consistent with the view that hardening is due to athermal rather than thermally activated processes. It was assumed that the strain rate could be divided into a steady state component and primary creep deformation. By subtracting the steady state component, curves of primary creep rates against primary creep strains were plotted. Using a rate equation that has frequently been used to describe thermally activated glide controlled deformation, flow stresses were calculated from primary creep deformation rates. Curves of flow stress against primary creep strains were obtained. If initial strains accounting for plastic deformation during application of the steady loads were added to the strains, results could be superimposed to lie on a single curve, irrespective of creep load and temperature.

The effect of phosphorus on creep in copper

Pure copper with an addition of about 50 ppm phosphorus is the planned material for the outer part of the waste package for spent nuclear fuel in Sweden. Phosphorus is added to improve the creep ductility but it also strongly increases the creep strength. In the present paper the influence of phosphorus on the strength properties of copper is analysed. Using the Labusch–Nabarro model it is demonstrated that 50 ppm has a negligible influence on the yield strength in accordance with observations. For slow moving dislocations, the interaction energy between the P-atoms and the dislocations gives rise to an agglomeration and a locking. The computed break away stresses are in agreement with the difference in creep stress of copper with and without P-additions.

Effect of the intermediate action of hydrostatic pressure on the high-temperature creep and durability of copper

The intermediate action of hydrostatic pressure on the high-temperature creep of copper is studied at various creep stages. Tests performed at a constant tensile stress of 12.5 MPa at 773 K show that the application of a pressure at the creep third stage decreases the steady-state creep rate and extends the time to failure. At the steady-state stage of creep, the effect of the pressure may be ignored. At pressures of up to 1 GPa, this effect is found to be only related to healing of grain-boundary porosity. At higher pressures, the steady-state creep rate is governed by porosity healing and structural changes.

Cyclic creep of copper due to axial cyclic and tensile mean stresses

The behaviour of materials under axial stress-controlled cycling with tensile mean stress within the plastic region is governed by a superposition of cyclic creep and fatigue processes. Cyclic creep may dominate the damage process and cause distortional failure before the onset of fatigue cracking. The aim of this work was to investigate cyclic creep in copper under such loading conditions at room temperatures, and to derive an empirical relationship for cyclic creep in terms of imposed stress amplitude and mean stress, via a previously proposed exponential mean-stress function that accounts for the effect of mean stress on cyclic behaviour. It is found that cyclic creep behaviour at room temperatures could be described by a power-law relation similar to that of static creep at high temperatures.

Creep in ODS copper reinforced with alumina short fibres—DRS copper

Creep in copper dispersion strengthened with fine alumina particles (oxide dispersion strengthened (ODS) Cu) and reinforced with alumina short fibres—a DRS Cu composite—is investigated in two temperature intervals, namely 673–773 K, lower temperature interval (LTI) and 923–1023 K, higher temperature interval (HTI). It is shown that in both intervals creep is associated with true threshold stresses decreasing with increasing temperature more strongly than the shear modulus of copper. The true threshold stress in the composite is higher than that in the composite matrix (i.e. ODS copper) by a factor Λ, by which the flow stress in the matrix is reduced due to load transfer. The minimum creep strain rate is found to be dislocation core diffusion controlled in LTI and lattice diffusion controlled in HTI. High values of the apparent activation energies are fully explained in terms of the temperature dependence of the true threshold stress in LTI as well as in HTI. Also the values of the apparent stress exponents are explained in terms of the true threshold stresses. The true threshold stress is identified with the athermal detachment stress σ d =σ OB 1−k R 2 , and its nonproportionality to the Orowan stress σ OB is explained by the relaxation factor k R increasing with temperature.