Orowan Stress Research Articles

A new model for the description of creep behaviour of aluminium-based composites reinforced with nanosized particles

A basic model developed to describe the creep response of fcc metals has been used to obtain a new constitutive equation valid for alloys and composites reinforced with a dispersion of nanosized particles. The new model gives an excellent description of the minimum strain rate dependence of applied stress and temperature, and gives reason for the reduced creep rate observed in these composites when compared with conventional alloys. The reason for the different behaviour is that the dislocation mean free path becomes equivalent to the distance between nanosized particles. The volume fraction and size of the nanosized particulate thus assumes a key-role in determining the creep response of these materials. In addition, the strengthening effect due to the interaction between particles and dislocation has been described by introducing a back stress, which is in general proportional to the Orowan stress and has the nature of a true threshold stress.

Evolution of the microstructure in aged G115 steels with the different concentration of tungsten

The microstructural evolution and certain mechanical properties of three G115 steels, 9 Cr-(2.3, 2.6, 3.0) W-3 Co (wt%), were investigated after thermal aging at 675 °C for different times using optical microscopy, field emission transmission electron microscopy, X-ray diffraction, post-aged tensile tests and impact tests, focusing on martensitic lath, dislocations and precipitates. The results show that the coarsening rates of the lath and Laves phase particles increased with the increase in W concentration during thermal aging. The rates of the decreases in the dislocation and particle densities of the Laves phase particles increased with the increase in W concentration during thermal aging. Both the coarsening rates of the lath and precipitates (i.e., M23C6 and Laves phase particles) and reduction rate of the dislocation density are higher in the first 1000 h compared to those in the following 4000 h during the thermal aging process. As predicted using the Orowan stress formula, the 2.3W G115 steel revealed the best creep strength during service, among the three steels.

A phenomenological creep model for nickel-base single crystal superalloys at intermediate temperatures

For the purpose of good reproduction and prediction of creep deformation of nickel-base single crystal superalloys at intermediate temperatures, a phenomenological creep model is developed, which accounts for the typical γ/γ′ microstructure and the individual thermally activated elementary deformation processes in different phases. The internal stresses from γ/γ′ lattice mismatch and deformation heterogeneity are introduced through an efficient method. The strain hardening, the Orowan stress, the softening effect due to dislocation climb along γ/γ′ interfaces and the formation of dislocation ribbons, and the Kear–Wilsdorf-lock effect as key factors in the main flow rules are formulated properly. By taking the cube slip in slip systems and twinning mechanisms into account, the creep behavior for [110] and [111] loading directions are well captured. Without specific interaction and evolution of dislocations, the simulations of this model achieve a good agreement with experimental creep results and reproduce temperature, stress and crystallographic orientation dependences. It can also be used as the constitutive relation at material points in finite element calculations with complex boundary conditions in various components of superalloys to predict creep behavior and local stress distributions.

Modeling and Crystal Plasticity Analysis of Multiple Slip Deformation in the Microstructure of Particle Dispersed Alloy and Its Macroscopic Strain Hardening Characteristics

Multiple slip deformation in dispersion hardening steels are numerically analyzed by a crystal plasticity finite element technique and macroscopic strain hardening characteristics are discussed. The critical resolved shear stress (CRSS) for slip system is given by the extended expression of the Bailey-Hirsch type model which include contributions from lattice friction, Taylor hardening and also the Orowan stress to give a size effect from microstructure. Strain hardening of slip systems are estimated by the density of statistically stored dislocations (SSDs) through the Taylor term. Increment of the SSD density is evaluated by slip strain and the dislocation mean free path. Models for the CRSS and dislocation mean free path for the primary and secondary slip systems are discussed. Analysis results show that macroscopic yield stress agrees well with experimental one but strain hardening ratio is overestimated when the CRSS and dislocation mean free paths for secondary systems are given the same characteristics of scale dependency to that for the primary one. Some new models for the CRSS and mean free path for secondary systems are studied and analysis results with these models show to agree well not only for the yield stress but also for the strain hardening behavior.

Effect of scandium micro-alloying on the creep resistance properties of Al-0.7Fe alloy cables

The effect of Sc addition on creep resistance properties in the Al-0.7Fe-0.2Sc and Al-0.7Fe alloy has been studied. The microstructures before and after creep of Al-0.7Fe and Al-0.7Fe-0.2Sc alloy were investigated by optical microscopy, electron probe micro-analysis and transmission electron microscopy. In creep tests, the steady state creep rates of Al-0.7Fe-0.2Sc alloy were much lower than that of Al-0.7Fe alloy at 90–150°C/70MPa, it indicates that Sc addition significantly affected the creep resistance in Al-0.7Fe alloy cables. According to EPMA data and the known formation enthalpies of Al3Fe and Al3Sc phases, both of them are thermally stable. Additionally, TEM imaging showed that Al3Fe phases non-uniformly pinned on the subgrain boundary, and the average size of Al3Fe phase is approximately 0.4µm. The nanosized Al3Sc precipitates (25–40nm) both pinned on subgrain boundary and dislocation, making the pinned dislocations and subgrain boundary difficult to shift. The Orowan stress increment of ∆σOr in crept Al-0.7Fe-0.2Sc alloy is 61.3MPa, whereas the ∆σOr of crept Al-0.7Fe alloy is 30.1MPa, indicating that Al-0.7Fe-0.2Sc alloy cables possess higher creep resistance than Al-0.7Fe alloy cables.

A tensorial thermodynamic framework to account for the [formula omitted] rafting in nickel-based single crystal superalloys

A new model is developed in order to account for the effect of microstructural degradation (i.e. precipitate-directional-coarsening) on the viscoplastic behavior of single crystal superalloys under high temperature exposure. Microstructural changes are modeled by a tensorial description of γ channel width evolution and coupled to the Kelvin modes based viscoplasticity thanks to the Orowan stress. Such a coupling is performed within a thermodynamics framework. Isotropic and directional coarsening of the γ' hardening phase are modeled as well as its dissolution with temperature changes. Results are presented for isothermal creep of CMSX-4 alloy at 1050∘ C along <001> and <111> crystal directions but the formulation allows to account for anisothermal loadings, isotropization of the creep response at high temperature and misaligned loadings. This newly developed tensorial framework for rafting can also apply to single crystal superalloys having a positive misfit.

A Numerical Analysis of Deformation Processes in Oxide Dispersion-Strengthened Materials - Influence of Dislocation-Particle Interactions

A recently developed 3D discrete dislocation dynamics (DDD) model is employed to study kinetics of dislocation ensembles subjected to high temperature creep in microstructures of metal matrix composites. We particularly focus on a migration of low angle tilt boundaries in a field of rigid impenetrable particles. This type of dislocation boundaries represents a typical microstructural feature mediating plastic deformation during the high temperature loadings. The article compares results of numerical studies that considered distinct dislocation-particle in-teractions in order to describe the response of dislocation structure to the applied stress. The resultssuggest that, regardless the details related to the dislocation-particle interactions, a critical applied stress always exists, below which the boundary migration process ceases [1,2]. The existence of crit-ical threshold is confirmed by creep tests of ODS materials. This critical threshold, contrary to theclassical Orowan stress, is proportional to the dislocation density. The displacements of individual dislocation segments on the micro-scale level reflect the changes in the dislocation-particle interactions quite sensitively. Atthemacro-scale level, the overall strain rate, which averages out velocities of all the individual dislocation segments, is also significantly influenced by the changes in dislocation-particle interaction

Statistically motivated model of mechanisms controlling evolution of deformation band substructure

Deformation bands are interpreted as a spontaneously formed microstructure caused by anisotropy induced by the slip nature of plastic deformation. The gradient terms in the proposed constitutive equations have been derived by averaging the assembly of discrete dislocations. The rigid-plastic model points to the main constituents which control the fragmentation mechanism: anisotropy of the hardening matrix, anisotropic resistance of the boundaries to slip, and the bowing (Orowan) stress. For symmetric double slip compression, the model provides an explanation of the observed band orientation and band width, and of the significant change in structural morphology seen as the band reorientation occurs at large strains. The predictions are in favorable agreement with available observations.

硬質な球状微細粒子を含む二相合金の加工硬化に関する数理モデリング

Plastic deformation and dislocation accumulation in dispersion hardening alloys are numerically analyzed by a crystal plasticity finite element technique and work hardening characteristics are discussed. The critical resolved shear stress for slip system is given by the extended expression of the Bailey-Hirsch type model which include the Orowan stress as size effect of microstructure. Work hardening of slip system is estimated by statistically stored dislocation (SSD) density. Increment of the SSD density is evaluated by slip strain and the mean free path of dislocations (the Kocks-Mecking model). The mean free path depends on the average spacing of dispersed particles, which is also used to estimate the Orowan stress. The average spacing of dispersed particles is calculated from the volume fraction and average diameter of dispersed particles. As a result, flow stress level at the initial stage of deformation agreed very well with experimental result but work hardening rate was higher than that of experiment. From this fact, it is considered that the mean free path and the average spacing of dispersed particles are different spacing factors. When we assume that the mean free path is two to three times larger than the average spacing of dispersed particles, numerical result of the strain hardening agrees very well with experimental one.

A crystal plasticity model of a formation of a deformation band structure

The formation of deformation bands with the typically alternating sign of the misorientation across their boundaries is interpreted as spontaneous deformation instability caused by anisotropy of hardening. To analyse the nature of the fragmentation, a model of a rigid-plastic crystal domain deformed by symmetric double slip in a plane-strain compression is considered. The basic reason for the deformation band existence is that a local decrease in number of active slip systems in the bands is energetically less costly than a homogeneous deformation by multislip. However, such model of the bands predicts their extreme orientation and their width tends to zero. This trend is modified by hardening caused by a build up of the band boundaries and by a dislocation bowing (Orowan) stress. The model provides an explanation of observed orientation of the bands, their width and the significant change in the structural morphology seen as the band reorientation occurs at large strains. The predictions are in a favourable agreement with the available observations.

Constitutive modeling of creep behavior in single crystal superalloys: Effects of rafting at high temperatures

Rafting and creep modeling of single crystal superalloys at high temperatures are important for the safety assessment and life prediction in practice. In this research, a new model has been developed to describe the rafting evolution and incorporated into the Cailletaud single crystal plasticity model to simulate the creep behavior. The driving force of rafting is assumed to be the relaxation of the strain energy, and it is calculated with the local stress state, a superposition of the external and misfit stress tensors. In addition, the isotropic coarsening is introduced by the cube root dependence of the microstructure periodicity on creep time based on Ostwal ripening. Then the influence of rafting on creep deformation is taken into account as the Orowan stress in the single crystal plasticity model. The capability of the proposed model is validated with creep experiments of CMSX-4 at 950°C and 1050°C. It is able to predict the rafting direction at complex loading conditions and evaluate the channel width during rafting. For [001] tensile creep tests, good agreement has been shown between the model predictions and experimental results at different temperatures and stress levels. The creep acceleration can be captured with this model and is attributed to the microstructure degradation caused by the precipitate coarsening.

An assessment of creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb (ASME grade 92) steel

Creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb steel have been investigated at 873K, 923K and 973K over a stress range of 80–220MPa. The absence of clear primary creep regime and prolonged secondary stage of creep deformation have been noticed under lower stress level at 973K. The variation of minimum creep rate with applied stress obeyed Norton's power law of creep. The apparent stress exponents of 15.2, 12.3 and 5.8, and apparent activation energy of 619kJ/mole have been estimated for creep deformation of the steel. The apparent stress exponents and activation energy have been rationalised on the basis of threshold stress. The threshold stress values of 137.5MPa, 83.3MPa and 29.7MPa were obtained at 873K, 923K and 973K respectively. The threshold stress compensated true stress exponent of 4 and true activation energy of 244kJ/mole, and threshold stress normalised by Orowan stress confirms that the lattice diffusion assisted localised climb of dislocation is the rate controlling of creep deformation in the steel. The steel obeyed Monkman and modified Monkman–Grant relationships. Damage tolerance factor of 6 in the steel demonstrates that the microstructural degradation such as coarsening of precipitates and subgrain structure is the dominant creep damaging mechanism in the steel.

Development of nanoparticle-reinforced alumocomposites for rocket-space engineering

Some results of the development of a composite material based on sintered aluminum powder containing small additives of Al2O3 nanoparticles produced by the plasma-chemical method are described. The reasons for using small nanoparticle concentrations from the point of view of the role of interphase layer, Orowan hardening mechanism, etc., are given. Some properties and microstructure of produced alumocomposites with various contents of nanoparticles are demonstrated. According to the known laws, the Orowan stress is calculated for investigated composites as one of the possible contributions to an increase in material strength.

Paired Dislocations and Their Interactions with γ′ Particles in Polycrystalline Superalloy GH4037

The microstructural characteristics of nickel-based polycrystalline superalloy GH4037 turbine blades that have been in service for 1600 h have been studied by transmission electron microscopy. In particular, emphasis has been placed on paired dislocations and their interactions with γ′ precipitates. Paired dislocations are universal and coexist with Orowan loops occasionally. The attractive force due to anti-phase boundary energy and the repulsive force between two 1/2 dislocations act on paired dislocations simultaneously, causing different morphologies of edge dislocations. Since the shear stress required by paired dislocations to cut through γ/γ′ structure is much lower than Orowan stress of single matrix dislocation, the major formation mechanism is dislocation pairing. A large number of paired dislocations slipping on the same {111} plane can form slip band and can shear off γ′ particles, which may directly lead to the formation of microcracks.

Creep behavior under isothermal and non-isothermal conditions of AM3 single crystal superalloy for different solutioning cooling rates

Isothermal and non-isothermal creep experiments are performed using AM3 Ni-based single crystal samples which were cooled from the solutioning temperature during heat treatment with different cooling rates. Cooling rates from the solution temperature influenced the precipitate size and distribution and influenced creep properties, with creep lifetimes increasing and secondary creep rates decreasing with faster cooling rates. Up to a cooling rate of about 100°C/min, the microstructure is very inhomogeneous and the γ׳-particles exhibit an irregular shape and are partially large in size. For the fastest cooling rate (300°C/min), the microstructure consists of ordered cubic γ׳-precipitates surrounded by narrow γ-channels. According to Orowan stress calculations, the investigated creep properties under both isothermal and non-isothermal conditions seem to be mainly controlled by the resistance to dislocation bowing in the γ-channels.

Physical interpretation of creep in single crystal René N4TM based on a phenomenological model

Creep and rafting in Ni-based single crystal René N4 is described using reported phenomenological models after modifying the creep model to represent the rafting induced hardening of the structure against creep and the greater propensity for shearing of γ′ as the structure rafts and dislocation density in the channels and γ/γ′ interface builds up. The proposed model can describe the creep strain evolution at 1144K over the stress range 241–413MPa. The rafting model is shown to provide an adequate representation of horizontal and vertical channel width evolution at 1144K and 1255K. The variation of the physical parameters in the creep model viz., back stress, dislocation density and shear rate is rationalized scientifically thereby substantiating the physical basis of the model. The development of back stress in the channels is explained mechanistically through the deposition of dislocation segments at γ/γ′ interface by the Orowan loops expanding in the channel and the recovery of the interfacial dislocation networks. The evolution in Orowan stress consequent to rafting and its effect on dislocation activity are elucidated. The evolution of the kinetics for dynamic and static recovery processes which accompany creep strain accumulation has also been explained mechanistically.

Phase-specific high temperature creep behaviour of a pre-rafted Ni-based superalloy studied by X-ray synchrotron diffraction

The phase-specific high temperature creep behaviours of the γ and γ′ phases of a rafted Ni-based single crystal superalloy were investigated by a combination of in situ creep experiments and diffraction of high-energy X-ray synchrotron radiation. In situ experiments were performed at constant temperatures in a 930–1125 °C temperature range and under variable applied stress in order to study the material’s response (plastic strain, load transfer) to stress jumps. Using three crystal diffractometry in transmission (Laue) geometry, it was possible to measure the average lattice parameters of both the matrix and the rafts in the [1 0 0] direction at intervals shorter than 300 s. The absolute precision on the measurement of the constrained transverse mismatch (in the rafts’ plane) is better than 10−5. Plastic strain occurs within the γ corridors as soon as the Von Mises stress exceeds the Orowan stress. The plasticity of the γ′ rafts apparently depends on the transverse stress (i.e. perpendicular to the tensile axis) exceeding a threshold value of 60 MPa.

Experimental characterization and mechanical modeling of creep induced rafting in superalloys

A constitutive model has been developed for the high temperature mechanical behavior of single crystal superalloys, including rafting and its consequences. The flow stress depends on the γ channel width via the Orowan stress. An evolution equation for channel widening during high temperature straining has been derived and calibrated with measurements. Therein, rafting is assumed to be driven by the relaxation of internal stresses. The model is able to represent the mechanical softening at high stresses consecutive to rafting. The model has been applied to simulate rafting during uniaxial creep in several crystal orientations, in notched specimens as well as in cyclically loaded specimens.

Atomistic-continuum modeling of dislocation interaction with Y2O3 particles in iron

Oxide dispersion strengthened (ODS) steels are promising candidates for applications in fusion and fission rectors. Y2O3 particles dispersed in an iron matrix drastically improve the strength without adverse effects on ductility. We investigate here details of the dislocation core structure in Y2O3 precipitates, and at the interface between the iron matrix and the Y2O3 precipitate. We also simulate dislocation interaction with nano-size Y2O3 precipitates. It is shown that the γ-surface energies on planes between oxygen atoms and metallic atoms are extremely high, and that dislocations in an iron matrix cannot penetrate into Y2O3 particles. Three-dimensional parametric dislocation dynamics simulations of the interaction between an edge dislocation and an Y2O3 particle are carried out. The results show that the critical resolved shear stress (CRSS) has a strong dependence on the lattice mismatch Y2O3 particles and the iron matrix, and that it is lower than analytically calculated values of the Orowan stress.

Effect of particles in promoting twin nucleation in a Mg–5 wt.% Zn alloy

The number of { 1 0 1 ¯ 2 } twins formed in a compressed Mg–5 wt.% Zn alloy increased when precipitate particles were present, reaching a maximum in the peak-aged condition. Particles were observed to promote twin nucleation, but inhibit twin growth. A simple model has been developed to show that in peak- and over-aged condition the increase in twin number is accurately predicted by assuming the additional stress driving twin nucleation equates to the Orowan stress inhibiting twin growth.