Dislocation Creep Model Research Articles

A discrete dislocation dynamics model of creep in polycrystals

The dislocation creep represents high temperature plastic deformation of metallic materials. However, the subject is usually approached with constitutive and phenomenological formulations. The notable exceptions are the recent use of numerical modeling. For example, single-crystal discrete dislocation dynamics (DDD) has been adopted to involve dislocation glide and climb together with diffusion of vacancies. This naturally provides a physics-based framework for dislocation creep. However, the existing model(s) are limited to single crystals and hence are limited in scope. This study extended a single crystal dislocation creep model into polycrystalline ensemble. This was then used to simulate steady state creep rate (ε˙) with respect to creep stress (σ), temperature (T) and grain size (d) in polycrystalline aluminum. Our virtual experiments showed an Arrhenius relationship between ε˙ and T, and a power law scaling with σ. Further, our simulations also revealed a power law increase in ε˙ with d. This is striking, as available experimental data indicate both grain size dependence as well as independence. The answer to this apparent contradiction also emerged from our numerical simulations. It was shown that ε˙ is controlled by interactions of dislocations with static obstacles and grain boundaries. Dominance of static obstacles, in particular, significantly diminished the grain size effect. The role of dislocation mean free path on the pinning and dislocation creep behavior of polycrystalline metallic material was thus mechanistically established.

Application of a physically-based dislocation creep model to P92 for constructing TTR diagrams

ABSTRACT To raise the efficiency of thermal power plants, operation temperature and pressure must be increased by improving the creep performance of materials such as martensitic Cr-steels. To understand the underlying mechanisms of degradation, physical creep modelling provides a detailed and profound insight into microstructural processes. For such a physically based dislocation creep model, it is demonstrated that based on a parameter set found for one experimental creep curve, numerous creep curves on different stress levels can be simulated without any additional experimental data. These simulation results are then used for constructing a TTR diagram of P92. We succeeded in extrapolating rupture times for variations in both applied stress and temperature. In all cases, microstructural evolution of the simulated material is considered, including dislocation density, subgrain size and precipitates. The obtained rupture times in the simulated TTR diagram are compared to reference data, achieving good agreement.

Application of an advanced mean-field dislocation creep model to P91 for calculation of creep curves and time-to-rupture diagrams

This work deals with the development of a comprehensive mean-field dislocation creep model and its application to the martensitic 9% Cr-steel P91. Microstructural data from literature, EBSD measurements and results from precipitate kinetic simulations serve as input for the creep simulation in addition to material- and physical constants. The model has the capability for calculating creep curves depending on their initial microstructure, stress and temperature and is thus able to deduce time-to-rupture diagrams. Side-result is the microstructural evolution during creep exposure (different types of dislocation densities, subgrains and precipitates). The capability of the model is demonstrated in P91 within the stress range of 50-110 MPa at 650°C. Simulated results agree well with experimental data from sources such as NIMS, ASME, ECCC and industrial data.

Theoretical derivation of flow laws for quartz dislocation creep: Comparisons with experimental creep data and extrapolation to natural conditions using water fugacity corrections

AbstractWe theoretically derived flow laws for quartz dislocation creep using climb‐controlled dislocation creep models and compared them with available laboratory data for quartz plastic deformation. We assumed volume diffusion of oxygen‐bearing species along different crystallographic axes (//c, ⊥R, and ⊥c) of α‐quartz and β‐quartz, and pipe diffusion of H2O, to be the elementary processes of dislocation climb. The relationships between differential stress (σ) and strain rate ( ) are written as and for cases controlled by volume and pipe diffusion, respectively, where Dv and Dp are coefficients of diffusion for volume and pipe diffusion. In previous experimental work, there were up to ~1.5 orders of magnitude difference in the water fugacity values in experiments that used either gas‐pressure‐medium or solid‐pressure‐medium deformation apparatus. Therefore, in both the theories and flow laws, we included water fugacity effects as modified preexponential factors and water fugacity terms. Previous experimental data were obtained mainly in the β‐quartz field and are highly consistent with the volume‐diffusion‐controlled dislocation creep models of β‐quartz involving the water fugacity term. The theory also predicts significant effects for the transition of α‐β quartz under crustal conditions. Under experimental pressure and temperature conditions, the flow stress of pipe‐diffusion‐controlled dislocation creep is higher than that for volume‐diffusion‐controlled creep. Extrapolation of the flow laws to natural conditions indicates that the contributions of pipe diffusion may dominate over volume diffusion under low‐temperature conditions of the middle crust around the brittle‐plastic transition zone.

A two‐scale model for sheared fault gouge: Competition between macroscopic disorder and local viscoplasticity

AbstractWe develop a model for sheared gouge layers that accounts for the local increase in temperature at the grain contacts during sliding. We use the shear transformation zone theory, a statistical thermodynamic theory, to describe irreversible macroscopic plastic deformations due to local rearrangements of the gouge particles. We track the temperature evolution at the grain contacts using a one‐dimensional heat diffusion equation. At low temperatures, the strength of the asperities is limited by the flow strength, as predicted by dislocation creep models. At high temperatures, some of the constituents of the grains may melt leading to the degradation of the asperity strength. Our model predicts a logarithmic rate dependence of the steady state shear stress in the quasistatic regime. In the dense flow regime the frictional strength decreases rapidly with increasing slip rate due to thermal softening at the granular interfaces. The transient response following a step in strain rate includes a direct effect and a following evolution effect, both of which depend on the magnitude and direction of the velocity step. In addition to frictional heat, the energy budget includes an additional energy sink representing the fraction of external work consumed in increasing local disorder. The model links low‐speed and high‐speed frictional response of gouge layers and provides an essential ingredient for multiscale modeling of earthquake ruptures with enhanced coseismic weakening.

Finite Element Modeling of Diamond Indentation Creep in MgO

The modified dislocation creep model and the power law breakdown creep model were proposed to be used in the indentation creep deformation analyses for single crystal MgO at low temperature varying from 293K to 873K. A FE indentation creep modeling procedure was proposed and implemented. The activation energy and the shear flow stress for low temperature creep in single crystal MgO were predicted based on the analytical indentation creep analyses.

Steady state creep behavior of zirconia dispersion strengthened platinum alloys in medium stress regime

► A ZrO 2 dispersion strengthened Pt alloy with highly elongated grain structure exhibits much higher creep strength compared with pure Pt. ► Attractive interaction is present between dislocations and ZrO 2 particles at high temperatures. ► Interfacial pinning was speculated to be the rate controlling mechanism of the ODS Pt alloy in the medium stress regime. ► The roles of ZrO 2 inclusions are impeding dislocation motion, refining subgrains, and suppressing grain growth. Microstructure and creep behavior of a commercial ZrO 2 dispersion-strengthened Pt alloy were investigated. Emphasis was placed on examining the correlation between the minimum creep rates and the applied stress in the temperature range of 1273–1773 K. The ODS Pt alloy exhibited a highly elongated grain structure that had developed by a thermo-mechanical processing. The interfaces between ZrO 2 particles and the Pt matrix were found to be incoherent. An attractive interaction appeared to be present between dislocations and ZrO 2 particles. The detachment controlled dislocation creep model was used to explain the steady state creep behavior. The presence of ZrO 2 inclusions was also beneficial for maintaining the grain structure and the subgrains, which then provides increased resistance to high temperature creep deformation.

Primary, secondary and anelastic creep of a high temperature near α-Ti alloy Ti6242Si

The creep behavior of the near α-Ti alloy Ti6242Si is investigated at 500°C using constant stress tensile creep testing. Emphasis is put on primary and anelastic creep and their dependencies on processed microstructure and applied stress. The results of steady state creep are also reported. It is shown that the primary creep strain depends strongly on microstructure. Its dependence on stress is linear in the low stress regime, whereas a weak dependence is observed for high applied stresses. Unloading experiments lead to a time-dependent strain recovery that is also dependent on microstructure and prior stress. Unloading in the primary creep regime results in the recovery of almost all of the creep strain. However, a substantial strain recovery was also obtained upon unloading from steady state. It is shown that primary and anelastic creep strains are intimately related, and depend on microstructure and stress. The results are discussed with respect to existing dislocation creep models and the observed dislocation structures.

Processing, microstructure, strength, and ductility relationships in ultrahigh carbon steel assessed by high strain rate torsion testing

The torsional ductility and strength of an unalloyed ultrahigh carbon steel containing 1·3%C (UHCS–1·3C) has been studied at high strain rates (0·2–26 s-1 ) and high temperatures (750–1200°C). The strength–strain rate relationships are in agreement with a diffusion controlled dislocation creep model, where power law creep is observed with a stress exponent n of ∼5. The results were compared with the high temperature ductility and strength of a medium carbon (0·3%C) high strength, low alloyed (HSLA) steel, 304 stainless steel, and an alloyed ultrahigh carbon steel (UHCS–1·8C–1·6Al–1·5Cr). It is shown that the UHCS–1·3C material is the most ductile of the four materials, and has the lowest stress for plastic flow. The results are explained by the high rate of iron lattice diffusion and by the high stacking fault energy in the UHCS–1·3C material. It is proposed that contemporary processing and manufacturing equipment can be used to make pearlitic structure ultrahigh carbon steels for high strength room temperature applications.

Steady state creep deformation behaviour of SiC particle reinforced 2618 aluminium alloy based composites

Tensile creep behaviour of 2618 aluminium alloy based composites reinforced with 15 vol.-%SiC particles (SiC p) of 3·5 and 10 μm at 423–673 K was investigated. The results showed that the composites reinforced with both small and large SiC particles exhibited apparent stress exponents of 7·1–10·2 and 8·3–25·2, and apparent activation energies of 314 kJ mol-1 and 344 kJ mol-1, respectively. Moreover, a critical stress was observed in the composite specimens, below which the creep resistance of the 2618 + SiCp (3·5 μm) composite was higher than that of the 2618 + SiCp (10 μm) composite. Above this value, the former was less creep resistant than the latter. Several established models were used to rationalise the creep data of these two composites at higher temperatures. The analyses revealed that the creep data for the 2618 + SiC (3p·5 μm) composite cannot be rationalised with a stress exponent of 8 or 5, while those for the 2618 + SiC (10 pμm) composite can be reasonably rationalised by a climb controlled dislocation creep model with a stress exponent of 5. On the other hand, the 2618 + SiCp (10 μm) composite crept at lower temperatures (below 0·51Tm , where Tm is the melting point of aluminium in Kelvin) exhibited stress exponents of 13·0 and 6·5 at 423 and 473 K, and activation energies of 85 and 182 kJ mol-1 in the vicinity of 423 and 473 K, respectively. The creep behaviour of the 2618 + SiCp (10 μm) composite at 423 K can be interpreted in terms of the dislocation pipe diffusion.

Steady state creep behaviour of an Al [sbnd]Al 2O 3 alloy

The Al Al 2O 3 alloy produced by powder metallurgy route has been tested under compression creep in the temperature range 573–723 K to evaluate the steady-state creep mechanisms. The steady state creep data covering almost five orders of magnitude in creep rate shows to distinct regimes of creep deformation at all the temperatures. In the high stress regime (region-II), the creep data shows high and variable apparent stress exponents, 25–30 and high apparent activation energy, 372 kJ/mol. However, in the low stress regime (region-I), the lower values of stress exponents, 7–11 and activation energy, 85 kJ/mol are observed. The TEM micrographs of the uncrept and crept specimens exhibit subgrains with Al 2O 3 particles lying on the subgrain boundaries. The high stress regime data was examined in terms of pipe-diffusion controlled constant substructure creep model and thermally activated detachment controlled dislocation creep model. The detachment controlled dislocation model can describe the present data more successfully. The low stress regime data was analyzed according to the thermally activated detachment controlled diffusional creep model and pipe-diffusion controlled stress dependent substructure model. Thermally activated detachment controlled diffusional creep mechanism appears to be more appropriate for the present data.

Modeling the evolution of salt structures using nonlinear rocksalt flow laws

We analyzed the evolution of a single wavelength (λ = 13.4 km) salt structure of initial amplitude Ao = 100 m by means of a 2D finite-volume numerical model. The model incorporated two laboratory-derived rheological laws for rocksalt: a low-stress, dislocation-creep power law (ε˙ασ3.4) and a fluid-assisted diffusion creep law (ε˙ασ/Td3), in whichε˙is strain rate, σ is the equivalent stress, T the absolute temperature and d the grain size. Our model also accounts for salt thermal conductivity dependence on temperature. The models comprised 3.6 km of sediments overlying a 1.2-km-thick salt layer with a density difference between sediments and salt of 100 kg/m3 and sediments viscosity μ2 = 3.0 × 1019Pa s. We assumed that deformation is driven solely by buoyancy forces. Results predict that salt structures evolve faster (2- to 3.5-fold) in fluid-assisted models than in dislocation creep models. Equivalent stresses and viscosities predicted by the fluid-assisted law are lower than those predicted by the power law, by factors of 3, and 1 to 2 orders of magnitude, respectively, depending on the degree of structural maturity. In contrast, strain rates predicted by both rheological laws are nearly the same, near 10−14 s−1 for similar degrees of structural maturity. Temperature distribution in the model domain was controlled by the thermal conductivity contrast between salt and sediments, the shape of the salt structure and thermal conditions imposed at model boundaries. At the early stages of evolution, a positive thermal anomaly of +30°C developed at the top of the salt structure. At more advanced stages (e.g., diapiric stage), the thermal anomaly decreased, maintaining values between +5°C and +20°C.

High-temperature deformation of forsterite single crystals doped with vanadium

Creep experiments have been performed on samples from a single crystal of vanadium-doped forsterite under controlled\(p_{{\text{O}}_2 } \) conditions to investigate the effects of the addition of substitutional defects in the tetrahedral lattice sites. The addition of vanadium causes marked changes in the flow behavior of the forsterite, with a net increase in the creep rate at high\(p_{{\text{O}}_2 } \) and a new\(p_{{\text{O}}_2 } \) -dependent flow regime at low\(p_{{\text{O}}_2 } \) conditions. These observations can be interpreted as resulting from changes in the majority defect species that maintain the charge neutrality within the crystal. A climb-controlled dislocation creep model for the high-temperature deformation of vanadium-doped forsterite is proposed in which either (i) movement of uncharged jogs is rate-limited by the diffusion of silicon via a vacancy mechanism or (ii) movement of positively charged jogs is rate-limited by diffusion of oxygen via a vacancy mechanism.

Unification of Harper-Dorn and power law creep through consideration of internal stress

A single relation has been developed to describe the steady state creep behavior of coarse grained polycrystalline metals over a wide range of stress. The range of stress includes low stress Harper-Dorn (H-D) creep, intermediate stress power-law creep, and high stress power-law-breakdown creep. The unified creep relation is based on a diffusion-controlled dislocation creep model incorporating an internal stress which is visualized both to assist and inhibit the motion of dislocations. The internal stress arises from the presence of dislocations within subgrains. An extension of the unified creep relation is made by introduction of a structure dependent term based on the influence of subgrain size on the creep rate. It is proposed that the creep rate in the H-D regime can be decreased by subgrain size refinement and by a decrease in random dislocation density. The unified creep relations are shown to predict accurately the steady state creep rate of aluminum for over four orders of magnitude of stress in the temperature range of 0.21–0.99 T m In addition, good correlations are obtained for analysis of creep data for tin and lead, including the previously anomalous micro-creep tin data of Chalmers.

Dislocation Model of Low-Temperature Creep

A low-temperature dislocation creep model of the exhaustion type is proposed to account for the temperature independent activation energies which are found in recent experiments. Logarithmic creep can be obtained from the model if a Gaussian distribution function of Frank-Read sources is assumed. The theory is applicable under easy glide conditions but should not be used when extensive double glide occurs. The theory can be extended into the liquid helium temperature range with the aid of Glen-Mott quantum-mechanical dislocation tunneling.