共格沉淀析出过程的模拟Ⅱ--外加应力场的影响

采用相场模型对外加应力场对共格沉淀析出过程的微观结构演化进行模拟研究,在外加应力场作用下,非均匀弹性模量系统沉淀相的析出过程发生重大的变化,粒子沿弹性软方向呈各向异性析出,这种各向异性生长与外加应力、点阵错配度的符号以及非均匀模量差的符号有关。采用双级时效模拟方式时,外加应力场对析出相的成核及生长阶段均有影响,只是影响程度与析出相自身的点阵错配度有关。对适当的体系采用应力时效的方式可能是实现除分子束外延技术之外的一种全新的制备超晶格微结构的方法。     

Three-dimensional model of precipitation of ordered intermetallics

The development of the two-phase (f.c.c.+L1₂) coherent microstructure in the prototype Ni–Al superalloy is studied by using the three-dimensional computer simulation technique. The dynamics and morphology of the microstructure evolution are described by our three-dimensional version of the stochastic time-dependent kinetic equation which explicitly includes the coherency strain, elastic anisotropy and L1₂ ordering of the preciptate phase. The input parameters, the crystal lattice misfit, elastic moduli, interfacial energy and equilibrium compositions of the coexisting phases are taken from the published independent measurements. The simulation results demonstrate that the strain accommodation in the microstructure evolution results in the cuboidal-like precipitates faceted by the {100} planes. The size of the precipitates obtained in the simulation is of the order of 50 nm. The important conclusion is that the precipitates are always single-domain particles with no antiphase boundaries. This effect is associated with the ordered structure of precipitates. It causes the slowing down of the coarsening kinetics since it excludes the agglomeration of the out-of-phase precipitates in one particle. As has been shown previously, the latter is a very important coarsening mode in an absence of ordering.     

Phase field modeling of channel dislocation activity and γ′ rafting in single crystal Ni–Al

Dislocation-precipitate interaction and directional coarsening (rafting) of γ′ precipitates in single crystal Ni–Al alloys under external load are investigated by three-dimensional computer simulations. The simulation technique is based on an integrated phase field model that characterizes simultaneously the spatiotemporal evolution of both precipitate microstructure and dislocations. The initial configurations consisting of cuboidal γ′ particles and dislocations in γ channels are constructed according to experimental observations and phase field simulations of the dislocation filling process in the γ channels. For a given state (sign and magnitude) of the lattice misfit and external load commensurate with experimental values, the predicted morphologies of the rafted γ′ precipitates and the rafting kinetics agree well with experimental observations. This indicates that plasticity plays a dominant role in the rafting process as compared to elastic modulus mismatch between γ and γ′ phases, which has been ignored in the present simulations. The spatial variation of chemical potential of solute atoms caused by the coupling between channel dislocations and misfit stress is evaluated from concentration and stress distributions, from which diffusion fluxes in the γ channels are analyzed.     

The effect of elastic misfit strain on the morphological evolution of γ’-precipitates in a model Ni-base superalloy

The morphological evolution of coherent γ’-precipitates in a Ni-23.4Co-4.7Cr-4Al-4.3Ti (wt%) alloy has been observed under systematically varying heat-treatment conditions. By deeply etching the matrix and observing under a scanning electron microscope, the precipitate morphologies are determined accurately. By quenching after solution treatment and aging isothermally, high initial precipitate density is obtained, and the cuboidal precipitates cluster and align to form regularly spaced arrays. The dimensionality of the aligned structure increases with increasing precipitate volume fraction as the aging temperature decreases. By directly cooling to an aging temperature after the solution treatment intermediate precipitate density is obtained. During the isothermal aging, the cuboidal precipitates split into octets and clusters of several pieces which disintegrate subsequently into aligned cuboids. Upon further aging the coherency is broken. When directly cooled to aging temperatures very close to the solvus temperature, the dispersed precipitates grow dendritically along the 〈111〉 directions. Various thermodynamic and kinetic theories for the elastic strain effect stemming from the lattice misfit agree quantitatively with the observed clustering, alignment, and splitting, but presently there is no complete theory which accurately describes the observed morphologies.     

On an elastically induced splitting instability

We show that a morphological instability driven by deviatoric applied stresses can generate elastically induced particle splitting during diffusional phase transformations. The splitting instability occurs when the elastic fields are above some critical value. For subcritical elastic fields, one observes a small perturbation of the particle shape consistent with splitting, but this perturbation is stabilized by surface tension. Both the onset of the splitting instability and the nonlinear evolution of the particle towards splitting depend on the precise form of the applied stress, the elastic constants of the precipitate and matrix, and the initial shape of the precipitate. We also investigate whether non-dilatational misfit strains can generate splitting instabilities in the absence of an applied stress.     

Phase-field simulations with inhomogeneous elasticity: Comparison with an atomic-scale method and application to superalloys

We present a 2D and 3D phase-field analysis of microstructure evolution in the presence of a lattice misfit and with inhomogeneous elastic constants. The method is first critically compared with a Monte Carlo modeling at the atomic scale. We then apply the phase-field model to the Ni–Al system under external load along a cubic axis. We find that the microstructure becomes anisotropic and that the situation qualitatively differs depending on the sign of the applied stress. The microstructure evolution operates mainly by shape changes and alignments of precipitates, but also by splitting of precipitates initially elongated along directions perpendicular to the stress-induced, elastically favorable directions. The final microstructure is finally qualitatively analyzed in terms of a mean field theory in which the elastic inhomogeneity is embedded into an effective eigenstrain. This analysis leads to a simple formulation which can be used to easily predict the coherent microstructural anisotropy induced by any external loading condition.     

Microstructure dependence of strength of Ir-base refractory superalloys

Precipitation hardening was investigated in Ir–Nb and Ir–Zr alloys with a two-phase structure consisting of the fcc matrix and L1₂ coherent precipitate phases, similar to that in Ni-base superalloys. Cuboidal L1₂ precipitates and plate-like L1₂ precipitates were formed with coherent interfaces in the fcc matrix in the Ir–Nb and Ir–Zr alloys, respectively. Effects of precipitate shape and coherency strains on precipitation hardening are discussed in terms of lattice misfit. Plate-like precipitates forming a 3-dimensional maze structure in the Ir–Zr alloys were profitable to precipitation hardening in both factors, that is precipitate shape and coherency strains.     

A simulation study of the shape of β′ precipitates in Mg–Y and Mg–Gd alloys

The metastable β′ phase is a key strengthening precipitate phase in a range of Mg–RE (RE: rare-earth elements) based alloys. The morphology of the β′ precipitates changes from a faceted and nearly equiaxed shape in Mg–Y alloys to a truncated lenticular shape in Mg–Gd alloys. In this work, we study effects of interfacial energy and coherency elastic strain energy on the morphology of β′ precipitates in binary Mg–Y and Mg–Gd alloys using a combination of first-principles calculations and phase-field simulations. Without any free-fitting parameters and using the first-principles calculations, CALPHAD databases and experimental characterizations as model inputs (lattice parameters of the β′ phase, elastic constants and chemical free energy of Mg matrix and interfacial energies of the coherent β′/Mg matrix interfaces), the phase-field simulations predict equilibrium shapes of β′ precipitates of different sizes that agree well with experimental observations. Factors causing the difference in the equilibrium shape of β′-Mg₇Y and β′-Mg₇Gd precipitates are identified, and possible approaches to increase the aspect ratio of the β′ precipitates and thus to enhance the strength of Mg–RE alloys are discussed.     

Phase field study of precipitate rafting under a uniaxial stress

We examine rafting of two-phase microstructures under a uniaxial applied stress, a process in which a mismatch in elastic moduli (elastic inhomogeneity) plays a central role. For this purpose, we have used a phase field model of an elastically inhomogeneous alloy; elastic stress and strain fields are calculated using a method adapted from the homogenization literature. We have characterized the efficiency of the resulting iterative algorithm based on Fourier transforms. Our simulations of rafting in two-dimensional systems show that rafting (unidirectionally elongated microstructures) is promoted when the precipitate phase is softer than the matrix and when the applied stress has the same sign as the eigenstrain. They also show that migration (for both hard and soft precipitates) and coalescence (for soft precipitates) have significant contributions to rafting.     

MICROMECHANICS OF THE DAMAGE-INDUCED CELLULAR MICROSTRUCTURE IN SINGLE CRYSTAL Ni-BASED SUPERALLOYS

An analytical method to investigate the morphological evolution of the cellular microstructure is explored and proposed. The method is essentially based on the Eshelby‘s micromechanics theory, and it is extended so as to be applied for a material system containing inclusions with high volume fraction, by employing the average stress field approximation by Mori and Tanaka. The proposed method enables us to discuss a stable shape of precipitate in the material system, which must be influenced by many factors: e.g., volume fraction of precipitate; Young‘s modulus ratio and lattice misfit between matrix and precipitate; external stress field in multiaxial state; and heterogeneity of plastic strain between matrix and precipitate. A series of numerical calculations were summarized on stable shape maps. The application of the method to predict the γ‘ rafting in superaUoys during creep showed that the heterogeneity of plastic strain between matrix and precipitates may play a significant role in the shape stability of the precipitate. Furthermore, it was shown that the method was successfully applied to estimate the morphology of the cellular microstructure formed in CMSX-4 single crystal Ni-based superaUoy.     

Predicting equilibrium shape of precipitates as function of coherency state

A general approach is proposed to predict the equilibrium shapes of precipitates in crystalline solids as function of size and coherency state. The model incorporates effects of interfacial defects such as misfit dislocations and structural ledges on transformation strain and on interfacial energy. Using α precipitation in α/β titanium alloys as an example, various possible equilibrium shapes of precipitates having different defect contents at interfaces are obtained by phase-field simulations. The simulation results agree with experimental observations in terms of both precipitate habit plane orientation and defect content at the interface. In combination with crystallographic theories of interfaces and experimental characterization of habit plane of finite precipitates, this approach has the ability to predict the coherency state (i.e. defect structures at interfaces) and equilibrium shape of finite precipitates.     

Contributions from elastic inhomogeneity and from plasticity to γ′ rafting in single-crystal Ni–Al

Directional coarsening (rafting) of γ′ precipitates in single-crystal Ni–Al alloys under external load is investigated by three-dimensional computer simulations. Contributions from modulus mismatch between the precipitate and matrix phases and from channel plasticity are considered. The simulation technique is based on a phase field model that captures spatiotemporal evolution of precipitate microstructure in elastically anisotropic and inhomogeneous systems. Channel plasticity is incorporated in the model through the introduction of an effective plastic strain that is formulated based on dislocation contents in the γ channels. Experimental data on lattice misfit, elastic moduli, applied stress and dislocation density in γ channels are used as model inputs. The driving force for rafting is monitored continuously by tracking the change in chemical potential difference between different types of γ channels after an external stress is applied until rafting completes. Quantitative comparisons of the rafting driving force and rafting completion time obtained from the simulations confirm the dominant role of channel plasticity, indicating that the rafting direction is determined by channel plasticity rather than by modulus inhomogeneity. However, elastic inhomogeneity also makes a significant contribution to the driving force for rafting, especially during the first several hours after the external load is applied.     

共格沉淀析出过程的模拟Ⅰ--微观结构演化

采用相场模型对共格沉淀析出过程微观结构演化进行模拟研究.模拟结果表明,应力场的存在将会对相变过程中析出相形态产生显著的影响,通过界面能与弹性应变能的相互竞争析出相在不同阶段呈现不同的形态如模量结构、网格结构、三明治多畴结构、沉淀宏观点阵结构以及板条状等;此外,点阵错配度中等(2%～4%)时,粒子的粗化过程将出现应力诱导反向粗化现象,这种粗化现象取决于粒子的点阵错配度与体积分数.     

Some comments on the misfit and coherency loss of Al3Sc particles in Al–Sc alloys

An attempt of refining a recently reported calculation of the temperature dependent misfit between Al and Al₃Sc particles is given. Further, the impact of a temperature dependent misfit on the calculated diameter for coherency loss of Al₃Sc precipitates is demonstrated. The origin of misfit dislocations is also briefly discussed.     

Effect of external stress on γ nucleation and evolution in TiAl alloys

We have shown in a previous paper that twin boundary area fraction in lamellar γ-TiAl based alloys depends on collective or correlated nucleation induced by long-range elastic interactions among nucleating precipitates or between pre-existing and nucleating precipitates. In this study we investigate the effects of applied stresses on γ nucleation and evolution by elastic interaction energy calculations and phase field simulations. It is found that the elastic interaction energy reaches minimum when two variants are twin related because of their self-accommodation of the coherency strain. When external stresses are present, such autocatalysis during nucleation could be either enhanced or suppressed. Compression perpendicular or tension parallel to the basal plane of the α phase is found to enhance the internal elastic interactions between nucleating precipitates, promote twin variant selection and reduce the overall nucleation rate, while isostatic pressing, compression parallel, tension perpendicular to the basal plane does the opposite. Shear along the interface always reduce the twin boundary area fraction, regardless of the shear direction. These findings could shed light on optimizing processing routes to increase twin boundary area fraction in lamellar microstructures of γ-TiAl based alloys.     

Steady-State Creep Behavior of Super304H Austenitic Steel at Elevated Temperatures

Creep behavior of Super304 H austenitic steel has been investigated at elevated temperatures of 923-973 K and at applied stress of 190-210 MPa.The results show that the apparent stress exponent and activation energy in the creep deformation range from 16.2 to 27.4 and from 602.1 to 769.3 kJ/mol at different temperatures,respectively.These high values imply the presence of a threshold stress due to an interaction between the dislocations and Cu-rich precipitates during creep deformation.The creep mechanism is associated with the dislocation climbing governed by the matrix lattice diffusion.The origin of the threshold stress is mainly attributed to the coherency strain induced in the matrix by Cu-rich precipitates.The theoretically estimated threshold stresses from Cu-rich precipitates agree reasonably with the experimental results.     

Microstructure Evolution of a Single Crystal Nickel-Base Superalloy During Heat Treatment and Creep

Microstructure evolution of a single crystal nickel-base superalloy during heat treatment and tensile creep at 1010℃ and 248 MPa for 30h was observed and analyzed. Internal stresses because of lattice mismatch between γ and γ‘ phase provided the driving force for γ‘ shape evolution during heat treatment. More than 65 vol. % distorted cubic γ‘ phase keeping coherency with the γ matrix precipitated after solution at 1295℃ for 32h. The shape of γ‘ phase was perfectly cubic with increasing precipitate size during the two-step aging treatment. Due to the applied stress and intemal stress field the continuous γ-γ‘ lamellar structure perpendicutar to the apptied stress was fonmed after 30h tensile creep.     

Lattice misfit measurement in Inconel 706 containing coherent γ′ and γ″ precipitates

Lattice misfit is an important parameter in Ni–Fe based alloy IN706 as coherency strain influences the strength of the alloy and the stability of the microstructure. X-ray and synchrotron measurements were performed on bulk samples with precipitates in constrained lattice. Lattice parameters of different phases and the lattice misfit could be determined even though the peaks were completely overlapped.     

Changes in the misfit stresses in an Al/SiCp metal matrix composite under plastic strain

Results are presented from neutron diffraction measurement of the strains in each phase, matrix and reinforcement, of a metal matrix composite bar before and after deformation beyond the elastic limit by four-point bending. The strains in each phase have been converted to stress. A stress separation technique was then applied, and the contributing mechanisms separated and identified. In this way the changes in the different contributions owing to plastic deformation have been determined. It is found that, initially, the average phase stresses can be explained in terms of a combination of essentially hydrostatic phase average thermal misfit stresses in the matrix (tension) and particles (compression) combined with a parabolic macrostress from quenching. After plastic bending the change in axial macrostress is as expected for that for a monolithic bar, but unexpectedly the misfit stresses had relaxed to approximately zero in both the tensile and compressive plastically strained regions of the bar.     

Elastically driven morphology of coherent trigonal precipitates inside a close-packed hexagonal matrix

The influence of a crystallographic symmetry break on the morphology of precipitates during the coherent precipitation of a trigonal phase in a close-packed hexagonal matrix is analyzed. It is pointed out that in spite of the isotropy of the stress-free strain of the precipitate in the basal plane, the existence of an extra elastic constant in the precipitate (associated to the loss of symmetry) induces a morphological evolution from a shape having a symmetry of revolution around the threefold axis to a needle-like one oriented along the compact directions in the basal plane. These general considerations are applied to the case of zirconium hydrides, the crystallography of which has recently been identified to be coherent with that of the αZr matrix.