A generalized line tension model has been developed to estimate the critical resolved shear stress in precipitation hardened alloys. The model is based in previous line tension models for regular arrays of either impenetrable or shearable spherical precipitates that were expanded to take into account the effect of the elastic mismatch between the matrix and the precipitates. The model parameters are calibrated from dislocation dynamics simulations that covered a wide range of precipitate diameters and spacing as well as of the mismatch in elastic constants. This model is extended to deal with random arrays of monodisperse spherical precipitates by changing the geometrical parameters of the model by the averaged ones corresponding to the random distributions. The model predictions were in good agreement with the critical resolved shear stresses obtained from dislocation dynamics simulations of random spherical precipitates distributions for both impenetrable and shearable precipitates, providing a fast and accurate tool to predict precipitate strengthening in metallic alloys.
Effect of ballistic re-solution on the nucleation kinetics of precipitates in diluted binary alloys under irradiation. Part 2: Cr-rich alpha' precipitates in Fe-Cr alloys
Nuclear Safety Institute (IBRAE), Russian Academy of Sciences（俄罗斯科学院核安全研究所（IBRAE））
Effect of ballistic re-solution on the nucleation kinetics of precipitates in diluted binary alloys under irradiation. Part 1: Stoichiometric gamma' precipitates in Ni-Al alloys
Nuclear Safety Institute (IBRAE), Russian Academy of Sciences（俄罗斯科学院核安全研究所（IBRAE））
The mechanisms of dislocation/precipitate interaction as well as the critical resolved shear stress were determined as a function of temperature in a Mg-4 wt. % Zn alloy by means of micropillar compression tests. It was found that the mechanical properties were independent of the micropillar size when the cross-section was $>$ 3 x 3 $μ$m$^2$. Transmission electron microscopy showed that deformation involved a mixture of dislocation bowing around the precipitates and precipitate shearing. The initial yield strength was compatible with the predictions of the Orowan model for dislocation bowing a…
The mechanical properties of Mg-4wt.% Zn alloy single crystals along the [0001] orientation were measured through micropillar compression at 23C and 100C. Basal slip was dominant in the solution treated alloy, while pyramidal slip occurred in the precipitation hardened alloy. Pyramidal dislocations pass the precipitates by forming Orowan loops, leading to homogeneous deformation and to a strong hardening. The predictions of the yield stress based on the Orowan model were in reasonable agreement with the experimental data. The presence of rod-shape precipitates perpendicular to the basal plane …
The critical resolved shear stress of an Al 4 wt. \% Cu alloy containing a homogeneous distribution of $θ''$ precipitates was determined by means of dislocation dynamics simulations. The size distribution, shape, orientation and volume fraction of the precipitates in the alloy were obtained from transmission electron microscopy observations while the parameters controlling the dislocation/precipitate interactions (elastic mismatch, transformation strains, dislocation mobility and cross-slip probability, etc.) were calculated from atomistic simulations. The precipitates were assumed to be eithe…
A detailed study of the precipitation of the γ' (AlAg2) phase in undeformed aluminium-silver alloys has been conducted. Several previously unreported features were observed, including the formation of discrete three-dimensional assemblies comprised of 5-7 precipitates on faulted dislocation loops. The precipitates assemblies adopted a morphology approximating a tetrahedral bipyramidal assembly. The bounding defect of the stacking fault was found to control both the nucleation of additional precipitates which was responsible for the formation of the assembly structure and also the growth charac…
This work describes a multidisciplinary research methodology for quantifying the size distribution of nanoscale precipitates in polycrystalline alloys. Complementary transmission electron microscopy (TEM) and small-angle x-ray scattering (SAXS) are employed in a study of precipitate growth in an isothermally aged Mg-Zn alloy. TEM is used to identify the precipitate phases as rod-shaped β' particles and to determine their radii and aspect ratio. Subsequently, SAXS data obtained from bulk quantities of the alloy is interpreted via a novel Monte-Carlo method to obtain accurate, form-free size dis…
Two different precipitate hardening aluminium alloys processed by friction stir welding were investigated. The microstructure and the hardness of the as delivered materials were compared to that of the weld nugget. Transmission electron microscopy observations combined with three-dimensional atom probe analyses clearly show that β;" precipitates dissolved in the nugget of the Al-Mg-Si giving rise to some supersaturated solid solution. It is shown that the dramatic softening of the weld could be partly recovered by post-welding ageing treatments. In the Al-Mg-Sc alloy, Al3Sc precipitate size an…
The precipitation microstructure of the γ' (AlAg2) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-0.90at.%Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ' phase formed as aggregates with a two-dimensional open assemblies. Each such assembly contained two variants of the γ' phase alternately arranged to form a faceted elliptical unit. The θ' (Al2Cu) phase formed on these assemblies after further …
The interaction between edge basal dislocations and $β$-Mg$_{17}$Al$_{12}$ precipitates was studied using atomistic simulations. A strategy was developed to insert a lozenge-shaped Mg$_{17}$Al$_{12}$ precipitate with Burgers orientation relationship within the Mg matrix in an atomistic model ensuring that the matrix/precipitate interfaces were close to minimum energy configurations. It was found that the dislocation bypassed the precipitate by the formation of an Orowan loop, that entered the precipitate. Within the precipitate, the dislocation was not able to progress further until more dislo…
Microstructural analysis of a Mg-Zn alloy deformed at room temperature by high-pressure torsion (HPT) indicates that fine-scale precipitation occurs even without post-deformation heat treatment. Small-angle X-ray scattering detects precipitates with radii between 2.5-20 nm after one rotation, with little increase in particle size or volume fraction after 20 rotations. High resolution electron micrographs identify grain boundary precipitates of monoclinic Mg$_4$Zn$_7$ phase after three rotations and MgZn$_2$ after 20 rotations.
The mechanisms of dislocation/precipitate interaction were studied by means of discrete dislocation dynamics within a multiscale approach. Simulations were carried out using the discrete continuous method in combination with a fast Fourier transform solver to compute the mechanical fields. The original simulation strategy was modified to include straight dislocation segments by means of the field dislocation mechanics method and was applied to simulate the interaction of an edge dislocation with a $θ'$ precipitate in an Al-Cu alloy. It was found that the elastic mismatch has a negligible influ…
The composition and site occupancy of Mg within ordered δ precipitates in a model Al Mg Li alloy have been characterized by atom probe microscopy and first-principles simulations. The concentration in the precipitates is found to be almost the same as that of the matrix, however, we show evidence that Mg partitions to the sites normally occupied by Li in the L12 structure. Density functional calculations demonstrate that this partition is energetically favorable, in agreement with experimental results.
The model of homogeneous semicoherent interphase boundary describes the processes of absorption and thermoactivated migration of irradiation-produced inequilibrium point defects at a semicoherent boundary between a heterophase precipitate and a substitution solid solution. Within this model the kinetics of evolution of the sizes of precipitates of constant chemical composition under irradiation is investigated. The results obtained are compared to the experimental data [I. Monnet et al., J. Nucl. Mater. 335 (2004) 311] for the ferritic ODS steel EM10+MgO under electron irradiation.
The Al-Ag system is thought to be a well-understood model system used to study diffusional phase transformations in alloys. Here we report the existence of a new precipitate phase, zeta, in this classical system using scanning transmission electron microscopy (STEM). The zeta phase has a modulated structure composed of alternating bilayers enriched in Al or Ag. Our in situ annealing experiments reveal that the zeta phase is an intermediate precipitate phase between GP zones epsilon and gamma prime. First-principles calculations show that z is a local energy minimum state formed during Ag clust…
θ' (Al2Cu) precipitates in Al-Cu-Ag alloys were examined using high angle annular dark field scanning transmission electron microscopy (HAADF-STEM). The precipitates nucleated on dislocation loops on which assemblies of γ' (AlAg2) precipitates were present. These dislocation loops were enriched in silver prior to θ' precipitation. Coherent, planar interfaces between the aluminium matrix and θ' precipitates were decorated by a layer of silver of two atomic layers in thickness. It is proposed that this layer lowers the chemical component of the Al-θ' interfacial energy. The lateral growth of the…
The interaction between Mg edge basal dislocations and rod-shaped $β_1'$-MgZn$_2$ precipitates was studied by atomistic simulations using a new interatomic potential. The atomistic model was carefully built taking into account the experimental information about the orientation relationship between the matrix and the precipitate to ensure minimum energy interfaces. It was found that the dislocations initially overcame the precipitate by the formation of an Orowan loop that penetrated in the precipitate. The precipitate was finally sheared after several Orowan loops were piled-up. The number of …
We report on a quantitative investigation into the effect of size and distribution of rod-shaped β' precipitates on strength and ductility of a Mg-Zn alloy. Despite precipitation strengthening being crucial for the practical application of magnesium alloys this study represents the first systematic examination of the effect of controlled deformation on the precipitate size distribution and the resulting strength and ductility of a magnesium alloy. Pre-ageing deformation was used to obtain various distributions of rod-shaped β' precipitates through heterogeneous nucleation. Alloys were extruded…
A relative contribution to irradiation hardening caused by dislocation loops and solute-rich precipitates is established for RPV steels of WWER-440 and WWER-1000 reactors, based on TEM measurements and mechanical testing at reactor operating temperature of 563 K. The pinning strength factors evaluated for loops and precipitates are shown to be much lower than those obtained for model alloys based on the room temperature testing as well as those evaluated by means of atomistic simulations in the temperature range of 300 to 600 K. This discrepancy is explained in the framework of a model of ther…
Precipitation on deformation defects is essential for enhancing mechanical properties of age-hardenable alloys. {10-12} twinning is common in deformed alloys with hexagonal-close-packed structure. In this work, we revealed how {10-12} twin boundary (TB) influences beta-Mg17Al12 precipitation in Mg-9Al-1Zn alloy. The precipitates on the TB are rod-like, while others are lath-shape. The precipitates hold the Burgers orientation relationship (OR) only with twin or matrix, contrary to traditional wisdom in others alloys that precipitates on TB symmetrically keep an OR with both twin and matrix. Mo…
A multiscale approach based on the phase-field model is developed to simulate homogeneous and heterogeneous formation of θ' precipitates during high temperature ageing in Al-Cu alloys. The model parameters that determine the different energy contributions (chemical free energy, interfacial energy, lattice parameters, elastic constants) were obtained from either computational thermodynamics databases or from first-principles density functional theory and molecular statics simulations. From the information, the evolution and equilibrium morphology of the θ' precipitates is simulated in 3D using …
Precipitation hardening, which relies on a high density of intermetallic precipitates, is a commonly utilized technique for strengthening structural alloys. Structural alloys are commonly strengthened through a high density of small size intermetallic precipitates. At high temperatures, however, the precipitates coarsen to reduce the excess energy of the interface, resulting in a significant reduction in the strengthening provided by the precipitates. In certain ternary alloys, the secondary solute segregates to the interface and results in the formation of a high density of nanosize precipita…
This work presents a detailed investigation into the effect of a low Cu addition (0.01 at.%) on precipitation in an Al-0.80Mg-0.85Si alloy during ageing. The precipitate crystal structures were assessed by scanning transmission electron microscopy combined with a novel scanning precession electron diffraction approach, which includes machine learning. The combination of techniques enabled evaluation of the atomic arrangement within individual precipitates, as well as an improved estimate of precipitate phase fractions at each ageing condition, through analysis of a statistically significant nu…
A model for precipitation of the plate-shaped second-phase under applied stress is presented. The precipitates in the matrix-precipitate system are represented by their local volume fraction and an orientation parameter that defines the alignment of a precipitate platelet in a given direction. Kinetic equations, based on diffusion theory and classical nucleation theory, are used to describe the time evolution of these two parameters. The model is used to describe the stress orientation of hydrides in Zr-alloys in light of experiments.
The mechanisms of dislocation/precipitate interactions were analyzed in an Al-Cu alloy containing a homogeneous dispersion of $θ'$ precipitates by means of discrete dislocation dynamics simulations. The simulations were carried out within the framework of the discrete-continuous method and the precipitates were assumed to be impenetrable by dislocations. The main parameters that determine the dislocation/precipitate interactions (elastic mismatch, stress-free transformation strains, dislocation mobility and cross-slip rate) were obtained from atomistic simulations, while the size, shape, spati…
Stress-induced martensitic transformations enable metastable alloys to exhibit enhanced strain hardening capacity, leading to improved formability and toughness. As is well-known from transformation-induced plasticity (TRIP) steels, however, the resulting martensite can limit ductility and fatigue life due to its intrinsic brittleness. In this work, we explore an alloy design strategy that utilizes stress-induced martensitic transformations but does not retain the martensite phase. This strategy is based on the introduction of superelastic nano-precipitates, which exhibit reverse transformatio…
The continuous miniaturization of modern electromechanical systems calls for a comprehensive understanding of the mechanical properties of metallic materials specific to micrometer and sub-micrometer scales. At these scales, the nature of dislocation-mediated plasticity changes radically: sub-micrometer metallic samples exhibit high yield strengths, however accompanied by detrimental intermittent strain fluctuations compromising forming processes and endangering structural stability. In this paper, we studied the effects of plate-like $θ^\prime$-Al$_2$Cu precipitates on the strength, plastic f…
Precipitation of the γ' (AlAg2) phase was investigated in Al-Ag(-Cu) alloys using high resolution transmission electron microscopy and scanning transmission electron microscopy. Precipitation commenced with segregation of silver to stacking faults, followed by thickening in steps corresponding to single unit cell ledges. In conjunction with gradual segregation of silver and aluminium into ordered layers this yielded γ' phase platelets with a thickness of either 2 or 3x the AlAg2 c-lattice parameter. Plates with a thickness of 2 c(AlAg2) would not achieve self-accommodation of the shape strain …
Kinetics of niobium and titanium carbide precipitates in iron has been simulated with cluster dynamics. The simulations, carried out in austenite and ferrite for niobium carbides, respectively in austenite for titanium carbide, were analyzed for dependency on temperature, solute concentration, and initial cluster distribution. The results are presented for different temperatures and solute concentrations and compared to available experimental data. They show little impact of initial cluster distribution beyond a certain relaxation time and that highly dilute alloys with only monomers present a…
One usual way to strengthen a metal is to add alloying elements and to control the size and the density of the precipitates obtained. However, precipitation in multicomponent alloys can take complex pathways depending on the relative diffusivity of solute atoms and on the relative driving forces involved. In Al-Zr-Sc alloys, atomic simulations based on first-principle calculations combined with various complementary experimental approaches working at different scales reveal a strongly inhomogeneous structure of the precipitates: owing to the much faster diffusivity of Sc compared with Zr in th…
Neutron irradiation tends to promote disorder in ordered alloys through the action of the thermal spikes that it generates, while simultaneously introducing point defects and defect clusters. As they migrate, these point defects will promote reordering of the alloys, acting against irradiation-induced disordering. In this study, classical molecular dynamics and a highly parallel accelerated sampling method are used to study the reordering kinetics of Ni$_3$Al under the diffusion of self-interstitial atoms (SIA). By monitoring the order parameter and potential energy from atomistic simulations,…
Age hardening induced by the formation of (semi)-coherent precipitate phases is crucial for the processing and final properties of the widely used Al-6000 alloys. Early stages of precipitation are particularly important from the fundamental and technological side, but are still far from being fully understood. Here, an analysis of the energetics of nanometric precipitates of the meta-stable $β''$ phases is performed, identifying the bulk, elastic strain and interface energies that contribute to the stability of a nucleating cluster. Results show that needle-shape precipitates are unstable to g…
The effect of pre-ageing deformation on the size and distribution of beta-prime precipitates and subsequently on the resulting strength and ductility have been measured in a Mg-3.0at.%Zn-0.5at.%Y alloy. The alloy was extruded and then subjected to a T8 heat treatment comprised of a solution-treatment, cold-work and artificial ageing. Extrusion was used to introduce texture, ensuring that deformation occurred via slip rather than twinning. Samples were subjected to controlled uniaxial deformation and then isothermally aged to peak hardness. Precipitate length, diameter and number density were m…
The Ni-based superalloy Alloy 718 is used in aircraft engines as high-pressure turbine discs and must endure challenging demands on high-temperature yield strength, creep-, and oxidation-resistance. Nanoscale $γ^{\prime}$- and $γ^{\prime \prime}$-precipitates commonly found in duplet and triplet co-precipitate morphologies provide high-temperature strength under these harsh operating conditions. Direct ageing of Alloy 718 is an attractive alternative manufacturing route known to increase the yield strength at 650 $^°$C by at least +10 $\%$, by both retaining high dislocation densities and chan…
Intermetallic precipitates formed in heat-treated and aged Mg-Zn and Mg-Zn-Y alloys have been investigated via electron microscopy. Coarse spheroidal precipitates formed on deformation twin boundaries contained domains belonging to either the MgZn2 hexagonal Laves phase or the monoclinic Mg4Zn7 phase. Both phases are structurally related to the quasi-crystalline phase formed in Mg-Zn-Y alloys, containing icosahedrally coordinated zinc atoms arranged as a series of broad rhombohedral units. This rhombohedral arrangement was also visible in intragranular precipitates where local regions with the…
An Al-11.3Li-0.11Sc (at. %) alloy was double-aged to induce first alpha'-Al3Sc and then delta'-Al3Li precipitates. Atom-probe tomography revealed both single-phase delta'-precipitates and core-shell alpha'/delta'-precipitates (with respective average radii of 16 and 27 nm, and respective volume fractions of 12 and 9%) conferring a high strength to the alloy. Although the delta'-shells contain little Sc (~0.027 at. %), the alpha'-cores have a high Li content, with an average composition of Al0.72(Sc0.17 Li0.11). The Li concentrations within the delta'-phase and the Li interfacial excess at the …
The microstructure of a CoNiAl FSMA was determined by conventional transmission electron microscopy, electron diffraction studies together with advanced microscopy techniques and in-situ Lorentz microscopy. 10 to 60 nm sized rod-like precipitates of hcp $ε$-Co were confirmed to be present by HRTEM. The orientation relationship between the precipitates and B2 matrix is described by the Burgers orientation relationship. The crystal structure of the martensite obtained after cooling is tetragonal L10 with a (1-11) twinning plane. The magnetic domain structure was determined during an in-situ cool…
The tensile creep performance of a polycrystalline Co/Ni-base superalloy with a multimodal gamma prime distribution has been examined at 800C and 300MPa. The rupture life of the alloy is comparable to that of RR1000 tested under similar conditions. Microstructural examination of the alloy after testing revealed the presence of continuous gamma prime precipitates and M23C6 carbides along the grain boundaries. Intragranularly, coarsening of the secondary gamma prime precipitates occurred at the expense of the fine tertiary gamma prime. Long planar deformation bands, free of gamma prime, were als…
We investigate, via three-dimensional atomistic computer simulations, phase separation in an alloy under external load. A regular two-dimensional array of cylindrical precipitates, forming a mesoscopic precipitate lattice, evolves in the case of applied tensile stress by the movement of mesoscopic lattice defects. A striking similarity to ordinary crystals is found in the movement of "meso-dislocations", but new mechanisms are also observed. Point defects such as "meso-vacancies" or "meso-interstitials" are created or annihilated locally by merging and splitting of precipitates. When the syste…
The effects of various heat treatments on the microstructure and hardness of new Ni56Ti41Hf3 and Ni56Ti36Hf8 (atomic %) alloys were studied to evaluate the suitability of these materials for tribological applications. A solid-solution strengthening effect due to Hf atoms was observed for the solution annealed (SA) Ni56Ti36Hf8 alloy (716 HV), resulting in a comparable hardness to the Ni56Ti41Hf3 alloy containing 54 vol.% of Ni4Ti3 precipitates (707 HV). In the Ni56Ti41Hf3 alloy, the maximum hardness (752 HV), achieved after aging at 300C for 12 h, was attributed to dense, semi-coherent precipit…
The kinetic pathways resulting from the formation of coherent L12-ordered y'-precipitates in the g-matrix (f.c.c.) of Ni-7.5 Al-8.5 Cr at.% and Ni-5.2 Al-14.2 Cr at.% alloys, aged at 873 K, are investigated by atom-probe tomography (APT) over a range of aging times from 1/6 to 1024 hours; these alloys have approximately the same volume fraction of the y'-precipitate phase. Quantification of the phase decomposition within the framework of classical nucleation theory reveals that the y-matrix solid-solution solute supersaturations of both alloys provide the chemical driving force, which acts as …
Precipitate phase selection and grain boundary morphology in Cu-Ni-Si-Mn alloys: A machine-learning interatomic potential study
Korea Electrotechnology Research Institute (KERI)（韩国电工技术研究所）；Korea Institute of Materials Science (KIMS)（韩国材料科学研究所）；Seoul National University（首尔大学）；University of Science and Technology (UST)（科学技术联合大学院大学）；Korea Institute for Advanced Study（韩国高等研究院）
The influence of different types of precipitates (either Guinier-Preston zones, $θ''$ or $θ'$) on the critical resolved shear stress and strain hardening was determined by means of micropillar compression tests in an Al - 4 wt. \% Cu alloy. The size, shape and volume fraction of the precipitates were measured in each case. It was found that size effects were negligible for micropillars with diameter $\ge$ 5 $μ$m. Micropillars with Guinier-Preston zones showed strain localization due to precipitate shearing. The best mechanical properties were obtained with either a fine dispersion of the $θ''$…
Cobalt-based alloys with γ/γ' microstructures have the potential to become the next generation of superalloys, but alloy compositions and processing steps must be optimized to improve coarsening, creep, and rafting behavior. While these behaviors are different than in nickel-based superalloys, alloy development can be accelerated by understanding the thermodynamic factors influencing microstructure evolution. In this work, we develop a phase field model informed by first-principles density functional theory and experimental data to predict the equilibrium shapes of Co-Al-W γ' precipitates. Thr…
The recently developed refractory multi-principle element alloy (MPEA), AlMo$_{0.5}$NbTa$_{0.5}$TiZr, shows an interesting microstructure with cuboidal precipitates of a disordered phase ($β$, bcc) coherently embedded in an ordered phase ($β'$, B2) matrix, unlike the conventional Ni-based superalloys where the ordered phase ($γ'$, L12) is the precipitate phase and the disordered phase ($γ$, fcc) is the matrix phase. It becomes critical to understand the phase transformation pathway (PTP) leading to this microstructure in order to tailor the microstructure for specific engineering applications.…
Aiming at increasing the yield strength of transformation and twinning induced plasticity (TRIP and TWIP) titanium alloys, a dual-phase $α$/$β$ alloy is designed and studied. The composition Ti 7Cr 1.5Sn (wt.%) is proposed, based on an approach coupling Calphad calculations and classical Bo-Md design tool used in Ti-alloys. Its microstructure is made of 20% of $α$ precipitates in a $β$ matrix, the matrix having optimal Bo and Md parameters for deformation twinning and martensitic transformation. The alloy indeed displays a yield strength of 760 MPa, about 200 MPa above that of a Ti 8.5Cr 1.5Sn…
This work demonstrates the development of a strong and ductile medium entropy alloy by employing conventional alloying and thermomechanical processing to induce partial recrystallization (PR) and precipitation strengthening in the microstructure. The combined usage of electron microscopy and atom probe tomography reveals the sequence of microstructural evolution during the process. First, the cold working of homogenized alloy resulted in a highly deformed microstructure. On annealing at 700°C, B2 ordered precipitates heterogeneously nucleate on the highly misoriented sites. These B2 promotes p…
