Coherency Stresses Research Articles

Effect of microstructure rafting on deformation behaviour and crack mechanism during high-temperature low-cycle fatigue of a Ni-based single crystal superalloy

The low cycle fatigue behaviours of a microstructure rafting Ni-based single crystal superalloy have been experimentally investigated at 980 ℃. Deformation of γ/γ’ phases and the corresponding dislocation configurations were investigated, highlighting rafting γ/γ’ morphology that contributes to crack initiation and propagation, as well as macro-scale accumulated plastic strain. Unlike the discrete slip lines of a virgin superalloy, intense slips developed along the parallel {111} slip plane result in crossed slip bands in the rafting superalloy. The decreased resistance of widened γ channels to dislocation movement, along with the prevention of dislocation cutting through γ’ precipitates in pre-existing dense dislocation networks, facilitates crack propagation in the γ channel in the slightly rafting superalloy. As the rafting state increases, the dislocation network loses its protective effect by reducing coherency stress and acting as a superdislocation source, which facilitates crack propagation along the γ/γ’ interface. Finally, a microstructure-based fatigue model is developed considering the reduction of deformation resistance induced by rafting. The fatigue loading control mode effect is introduced by a combination of resolved shear stress and tensile stress effects on crack initiation. The LCF life of rafting Ni-based superalloys significantly decreases under stress-controlled conditions compared to strain-controlled conditions due to the increase in cumulative plastic strain. However, the insignificant impact of the initial surface oxide layer on LCF life is revealed.

Investigation of coherent interface on relaxation behavior and reliability of Mg-doped BaTiO3 dielectric ceramics: Experiments and first-principle calculations

The addition of Mg generally enhances the high-temperature stability and reliability of BaTiO3-based multilayer ceramic capacitors (MLCCs). Herein, a series of Mg-doped BaTiO3-based ceramics and ultra-thin MLCCs were successfully fabricated, and the coherent and semi-coherent interface has been observed in samples. Based on the density functional theory (DFT) calculations, the improvement in temperature stability is due to changes in the coherent interface and electronic structure that promote the formation of polar nano-regions (PNRs) and induce relaxation behavior. Based on the atomic displacement, it is found that the excess substitution released the coherent stresses in the form of defects and formed semi-coherent interfaces. The reliability degradation of MLCCs is mainly due to the evolution of the semi-coherent interfaces. This work points out an avenue to obtain high-temperature stability and high reliability in BaTiO3-based MLCCs.

Atomistic Insights into Nucleation of Ferroelastic Domains in PbTiO3.

Understanding the nucleation mechanism of domains is essential for domain engineering of perovskite ferroelectric materials. We proposed and examined atomistic details for nucleating ferroelastic (FS) domains by integrating topological analysis and first-principles calculations. FS domains are crystallographically treated as deformation twins. The conventional shear-shuffle nucleation mechanism under simple shear deformation is ruled out because the 1-layer elementary twinning disconnection (TD) cannot nucleate and glide in a perfect matrix. Thus, the pure-shuffle nucleation mechanism under pure shear deformation is proposed due to kinetically favored atomic shuffling. The coherency stress associated with the coherent nucleus is relaxed via forming misfit dislocations, accompanied by formation and sharpening of diffused (110)m∥(110)d domain walls (DWs). The sharp DWs enable growth of the FS nucleus through successive nucleation and gliding of TDs. These findings enrich the knowledge of domain behavior in perovskite ferroelectric materials.

Elastic energy driven multivariant selection in martensites via quantum annealing

We demonstrate the use of quantum annealing for the selection of multiple martensite variants in a microstructure with long-range coherency stresses and external mechanical load. The general approach is illustrated for martensites with four different variants based on the minimization of the linear elastic energy. The equilibrium variant distribution is then analyzed under application of tensile and shear strains and for different values of the considered shear and tetragonal contributions of the different martensite variants. The interface orientations between different domains of variants can be explained using the perspective of the elastic energy anisotropy for regular stripe patterns. For random grain orientations, the response to an external elastic strain is weaker and variant changes can be interpreted based on the rotated eigenstrain tensor. Published by the American Physical Society 2024

Stress field and interaction forces between dislocations and precipitate distributions

AbstractA computational method is developed for calculation of the stress field and interaction forces between dislocations and precipitates of arbitrary shape and distribution. The internal stress generated by precipitates due to coherency strain is implemented within the discrete dislocation dynamics (DDD) framework. The s‐version finite element method (s‐FEM), which models a precipitate of arbitrary shape using a local mesh is used to calculate coherency stress fields. The method facilitates meshing precipitate volumes of arbitrary geometry, and multiple local meshes can be superimposed at various positions of the global mesh. Accuracy and convergence conditions of the method are established. For a single precipiate, the method is shown to be 3.5 times faster than a standard FEM calculation for the same accuracy, and the gain in speed increases with the number of precipitates. The CRSS of spherical precipitates is found to be higher than disk‐shaped precipitates of the same volume fraction.

A Comprehensive Stress Drop Map From Trench to Depth in the Northern Chilean Subduction Zone

AbstractWe compute stress drops for earthquakes in Northern Chile recorded between 2007 and 2021. By applying two analysis techniques, (a) the spectral ratio (SR) method and (b) the spectral decomposition (SDC) method, a stress drop map for the subduction zone consisting of 51,510 stress drop values is produced. We build an extended set of empirical Green’s functions (EGF) for the SR method by systematic template matching. Outputs are used to compare with results from the SDC approach, where we apply cell‐wise obtained global EGF's to compensate for the structural heterogeneity of the subduction zone. We find a good consistency of results of the two methods. The increased spatial coverage and quantity of stress drop estimates from the SDC method facilitate a consistent stress drop mapping of the different seismotectonic domains. Albeit only small differences of median stress drop, strike‐perpendicular depth sections clearly reveal systematic variations, with earthquakes at different seismotectonic locations exhibiting distinct values. In particular, interface seismicity is characterized by the lowest observed median value, whereas upper plate earthquakes show noticeably higher stress drop values. Intermediate depth earthquakes show comparatively high average stress drop and a rather strong depth‐dependent increase of median stress drop. Additionally, we observe spatio‐temporal variability of stress drops related to the occurrence of the two megathrust earthquakes in the study region. The presented study is the first coherent large scale 3D stress drop mapping of the Northern Chilean subduction zone. It provides an important component for further detailed analysis of the physics of earthquake ruptures.

Non-Equilibrium Turbulent Transport in Convective Plumes Obtained from Closure Theory

The non-equilibrium property of turbulence modifies the characteristics of turbulent transport. With the aid of response function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy (K) and its dissipation rate (ε) along the mean stream through the advective derivatives of K and ε. Applications of this effect to the turbulent convection with plumes are considered for the first time in this work. The non-equilibrium transport effects associated with plumes are addressed in two aspects. Firstly, the effect associated with a single plume is evaluated using data measured in the recent plume/jet experiments. The second argument is developed for the collective turbulent transport associated with multiple plumes mimicking the stellar convection zone. In this second case, for the purpose of capturing the plume motions into the advective derivatives, use has to be made of the time–space double-averaging procedure, where the turbulent fluctuations are divided into the coherent or dispersion component (which represents plume motions) and the incoherent or random component. With the aid of the transport equations of the coherent velocity stress and the incoherent counterpart, the interaction between the dispersion and random fluctuations are also discussed in the context of convective turbulent flows with plumes. It is shown from these analyses that the non-equilibrium effect associated with plume motions is of a great deal of relevance in the convective turbulence modeling.

Unraveling the superlattice effect for hexagonal transition metal diboride coatings

Superlattice structures enable the simultaneous enhancement in hardness (H) and fracture toughness (KIC) of ceramic-like coatings. While a deeper understanding of this effect has been gained for fcc-structured transition metal nitrides (TMN), hardly any knowledge is available for hexagonal diborides (TMB2). Here we show that superlattices can—similarly to nitrides—increase the hardness and toughness of diboride films. For this purpose, we deposited TiB2/WB2 and TiB2/ZrB2 superlattices with different bilayer periods (Λ) by non-reactive sputtering. Nanoindentation and in-situ microcantilever bending tests yield a distinct H peak for the TiB2/WB2 system (45.5 ± 1.3 GPa for Λ = 6 nm) but no increase in KIC related to a difference in shear moduli (112 GPa). Contrary, the TiB2/ZrB2 system shows no peak in H, but for KIC with 3.70 ± 0.26 MPa∙m1/2 at Λ = 4 nm originating from differences in lattice spacing (0.14 Å), hence causing coherent stresses retarding crack growth.

Pore-pressure coefficients for unsaturated soils: generalized effective stress approach

Geotechnical problems with total stress changes occurring rapidly relative to the soil consolidation time can be conveniently addressed using an effective stress-based approach. For saturated states, analytical formulations of pore-pressure coefficients adopting coherent effective stress concepts exist. These formulations allow the induced pore water pressure variations and the corresponding effective stress changes to be determined. For unsaturated states, there are no analytical formulations of pore-pressure coefficients that adopt a suitable effective stress concept. This paper presents analytical derivations of pore-pressure coefficients for unsaturated elastic isotropic soils using the generalized effective stress (valid for saturated and unsaturated states) for different total stress changes. The model performance is described, and flowcharts to be adopted in engineering practice are provided. Compared with an existing approach that is not based on the effective stress, the proposed one requires fewer constitutive parameters (one of which, conveniently, is the soil bulk modulus), allows to analytically obtain the existing expressions for saturated states when the degree of saturation is 1 and to readily determine the retention curve under undrained conditions. Existing experimental data were analysed, and satisfactory interpretations and predictions of the experimental results were obtained. The proposed framework is a valuable tool for undrained mechanical analyses of unsaturated soils under different practical applications.

How Coherent and Semi‐Coherent Interfaces Govern Dislocation Nucleation in Lamellar TiAl Alloys

γ/γ interfaces drive plastic deformation in lamellar TiAl alloys. Due to the ordering and resulting tetragonal nature of γ phase, γ/γ twin interfaces exist as different variants, some of which exhibit coherency stresses or semicoherent interface structures. While geometric parameters, such as the lamella spacing and orientation, are explored extensively in experiments, the isolation of individual influence of different interfaces in a nanolamellar microstructure remains a challenge. Herein, the range of γ/γ interface states is modeled using bilayers of the coherent γ/γTrueTwin, and the coherent or semicoherent γ/γPseudoTwin, and their deformation behavior is compared. It is shown that residual coherency stresses arise due to misfit accommodation in coherent γ/γPT specimens, which causes early preferential nucleation in one γ layer. Similarly, semicoherent specimens show preferential nucleation from misfit dislocations at the interface, which obeys Schmid's rule. In contrast, coherent γ/γTT specimens show no preferential nucleation and therefore exhibit higher strength. Thus, it is demonstrated that the presence of rotational γ/γ interfaces with misfit is responsible for localized and early plasticity, that lowers the strength of a lamellar microstructure. The interface type, which considers the coherency state, is used as a criterion for alloy microstructure design in the future.

Relationship between coherent Reynolds shear stress and large-scale vortical structures

An equation that relates the principal derivative of the Reynolds shear stress and large-scale vorticity fluxes is developed and validated using experimental data in a cylinder near wake. When large-scale vortices prevail, the Reynolds shear stress associated with the coherent motion is a good approximation to the conventional Reynolds shear stress. The latter is essentially determined by the imbalance between the dynamic pressure arising from the streamwise non-homogeneity caused by large-scale vortical structures and the lateral coherent vorticity flux.

Doping-Induced Pre-Transformation to Extend Solid-Solution Regimes in Li-Ion Batteries

In many intercalation electrodes of Li-ion batteries, lithiation induces distortive structural transformations with substantial implications for stress accumulation, capacity loss, and degraded rate performance. Here, we dope a phase-transforming electrode to stabilize a structure bearing considerable similarities to the initially lithiated phase. In this “pre-transformation” approach, demonstrated based on Mo-doping of V2O5, the thermodynamic penalty associated with the phase transformation is paid in part during materials’ synthesis rather than the charge/discharge of a battery. Mo-doping alters Li–V2O5 thermodynamics to unlock extended solid-solution lithiation regimes with modulated interplanar separations. Specifically, Mo-doping reduces structural distortions during charge/discharge processes, diminishes coherency stresses, and yields a substantially modified intercalation phase diagram. Operando synchrotron X-ray diffraction and chemical lithiation results in conjunction with phase-field modeling demonstrate the promise of doping-induced structural distortions to entirely alter phase evolution and improve electrochemistry–mechanics coupling in phase-transforming cathodes.

A mechanically strong and ductile soft magnet with extremely low coercivity

Soft magnetic materials (SMMs) serve in electrical applications and sustainable energy supply, allowing magnetic flux variation in response to changes in applied magnetic field, at low energy loss1. The electrification of transport, households and manufacturing leads to an increase in energy consumption owing to hysteresis losses2. Therefore, minimizing coercivity, which scales these losses, is crucial3. Yet meeting this target alone is not enough: SMMs in electrical engines must withstand severe mechanical loads; that is, the alloys need high strength and ductility4. This is a fundamental design challenge, as most methods that enhance strength introduce stress fields that can pin magnetic domains, thus increasing coercivity and hysteresis losses5. Here we introduce an approach to overcome this dilemma. We have designed a Fe–Co–Ni–Ta–Al multicomponent alloy (MCA) with ferromagnetic matrix and paramagnetic coherent nanoparticles (about 91 nm in size and around 55% volume fraction). They impede dislocation motion, enhancing strength and ductility. Their small size, low coherency stress and small magnetostatic energy create an interaction volume below the magnetic domain wall width, leading to minimal domain wall pinning, thus maintaining the soft magnetic properties. The alloy has a tensile strength of 1,336 MPa at 54% tensile elongation, extremely low coercivity of 78 A m−1 (less than 1 Oe), moderate saturation magnetization of 100 A m2 kg−1 and high electrical resistivity of 103 μΩ cm.

Modeling of precipitate strengthening with near-chemical accuracy: case study of Al-6xxx alloys

Many metal alloys are strengthened by controlling precipitation to achieve an optimal peak-aged condition where the strength-limiting processes of precipitate shearing and Orowan looping are thought to be comparable. Qualitative models have long captured the basic mechanisms but realistic predictions have been challenging due to both the lack of accurate material parameters and an inability to quantitatively validate the models. Here, dislocation/precipitate interaction mechanisms are studied in Al-6xxx Al–Mg–Si alloys using atomistic simulations in tandem with a near-chemically-accurate Al–Mg–Si neural network interatomic potentials. Results show that a given precipitate can exhibit shearing or looping depending on the relative orientation of the precipitate and dislocation, as influenced by the matrix and precipitate coherency stresses, direction-dependence of precipitate shearing energies, and dislocation line tension. Analytic models for shearing and calibrated discrete dislocation models of looping accurately capture the trends and magnitudes of strengthening in most cases. Good agreement with experiments is then approached by using the theories together with the more-accurate first-principles material properties. The combination of theories and simulations demonstrated here constitutes a path for understanding and predicting the role of chemistry and microstructure on alloy strength that can be applied in many different alloys.

Microplasticity in inhomogeneous alloys

We report on a preliminary modelling effort to understand the influence of compositional inhomogeneity on alloy microplasticity from a dislocation dynamics perspective. We tackle this problem by multiscale simulations in three steps: (1) analysis of the 3D composition morphology in alloys with tendency to undergo spinodal instability both thermally and under irradiation, with bcc FeCrAl alloys as a model system, (2) atomistic simulation of the dislocation mobility as a function of the local alloy composition, and (3) using dislocation dynamics simulations to understand the impact of composition inhomogeneity on microplasticity. The dislocation dynamics model takes into consideration the coherency stress associated with composition inhomogeneity when computing the forces driving the dislocation motion and on cross slip. Our preliminary investigation shows that the stress-strain response of the alloy and the dislocation density evolution depend on the wavelength of the composition fluctuations. Our investigation also shows that the alloy inhomogeneity may alter the cross-slip activity, which, in turn, influences the dislocation density evolution. The dependence of the dislocation mobility and coherency stress on local composition and its variation, as well as the altered cross slip rates, cause the dislocation microstructure to differ relative to that in the homogeneous alloy of the same average composition.

Fatigue and tensile deformation behaviors of laser powder bed fused 304L austenitic stainless steel

Unique microstructure equilibrium state induced by the laser powder bed fusion (LPBF) process endows the deposited metallic parts with excellent mechanical properties. However, the microstructure evolution of LPBF metallic materials during fatigue deformation and its influence on fatigue properties remain still unclear. This paper systematically investigated the microstructural evolution and deformation behavior of LPBF 304L austenitic stainless steel (ASS) during tensile and fatigue testing. Experimental results indicated that LPBF 304L ASS exhibited superior tensile and fatigue properties compared with its annealed counterparts, which could be attributed to different deformation mechanisms. The superior tensile properties were commonly attributed to the regulation of cell walls on the dislocation flow. Many fine α′-martensite particles were distributed in the γ-austenite matrix grains of fatigue-fractured LPBF 304L ASS, indicating the occurrence of martensitic transformation during cyclic deformation. The cell walls with strong chemical misfits and high coherent internal stress might provide the non-parallel lattice shear forces for α′-martensite nucleation during cyclic deformation. The martensitic transformation could inhibit the cyclic softening and postpone the strain localization, thus contributing to the remarkable prolongation of the steady stage and the significant improvement of fatigue lifetime. Collectively, this study established the microstructural evolution role in regulating the tensile and fatigue deformation of LPBF 304L ASS.

Mechanical properties and [formula omitted] interfacial misfit network evolution: A study towards the creep behavior of Ni-based single crystal superalloys

The aim of this study is to investigate the role of the temperature, stress, and rhenium (Re) on the γ/γ' interfacial misfit dislocation network and mechanical response of Ni-based single crystal superalloys. After aging at elevated temperatures, mismatch between the two phases results in an interfacial dislocation network to relieve the coherency stress. Molecular dynamics (MD) simulations have been performed to study the properties of the (100), (110), and (111) phase interface crystallographic directions. Increasing temperature disperses the atomic potential energy at the interface diminishing the strength and stability of the networks. In the case of loading, when a constant strain rate of 2×108(s−1) is applied at 0 K, the (100) and (111) phase interface models lose their co-coordinating role of maintaining the dynamic equilibrium. Dislocation propagation in the γ phase is the dominant deformation mechanism in these two interfacial models, resulting in dislocations pile-up in the damaged area, and the network is no longer able to fortify the interface. For the (110) phase interface model, the dominant deformational mechanism is precipitate shearing. As temperature increases, the elastic modulus, initial mismatch stress, and yield strength decrease. Also, the pinning effect of Re atoms is evaluated in the γ phase at 1600 K. The dislocation hampering property of Re is more perceptible when enough dislocations in the γ phase are moving at elevated temperatures. In addition, Re manages to relieve the interfacial stress field and does not affect the network morphology. Finally, an investigation of the creep behavior of the superalloy is provided. It is observed that the escalated damage to the interfacial network due to the increased temperature leads to the domination of the softening mechanisms (cross-slip and dislocation climb) on the deformation and shortens the steady-state creep. Moreover, Re atoms act as an extra hardening factor to improve the tertiary creep.

In Situ Investigation of TCP Phase Formation, Stress Relaxation and γ/γ′ Lattice Misfit Evolution in Fourth Generation Single Crystal Ni-Base Superalloys by X-Ray High Temperature Diffraction

In nickel-based superalloys, the lattice misfit between the γ and γ′ phases and the propensity to TCP phase formation at service temperatures critically influence the microstructural evolution that takes place and hence the resultant mechanical properties. In this work, the lattice misfits of a series of highly alloyed Ru-containing 4th generation Ni-base superalloys are investigated by in situ X-ray diffraction (XRD) at high temperature. While the lattice misfit values of all alloys range between − 0.3 and − 1.3 pct at room temperature, they show an atypical temperature dependence, becoming less negative above 900 °C. In situ XRD measurements at 1100 °C reveal that the majority of the internal coherency stresses are already relieved after two hours. This is particularly pronounced for the alloys that have both a lattice misfit larger than |0.6| pct at 1100 °C and are prone to TCP phase formation. However, throughout the relaxation of the internal coherency stresses the lattice misfit remains fairly constant. Due to the similar chemical compositions of the alloys studied, qualitative guidelines for an optimum lattice misfit magnitude are developed by comparing the lattice misfit values with previous creep experiments. Our results indicate that no universal optimal lattice misfit value exists for these alloys and the value strongly depends on the applied creep conditions.Graphical

Characteristics of Turbulence in the Downstream Region of a Vegetation Patch

In presence of vegetation patches in a channel bed, different flow–morphology interactions in the river will result. The investigation of the nature and intensity of these structures is a crucial part of the research works of river engineering. In this experimental study, the characteristics of turbulence in the non-developed region downstream of a vegetation patch suffering from a gradual fade have been investigated. The changes in turbulent structure were tracked in sequential patterns by reducing the patch size. The model vegetation was selected carefully to simulate the aquatic vegetation patches in natural rivers. Velocity profile, TKE (Turbulent Kinetic Energy), turbulent power spectra and quadrant analysis have been used to investigate the behavior and intensity of the turbulent structures. The results of the velocity profile and TKE indicate that there are three different flow layers in the region downstream of the vegetation patch, including the wake layer, mixing layer and shear layer. When the vegetation patch is wide enough (Dv/Dc > 0.5, termed as the patch width ratio, where Dv is the width of a vegetation patch and Dc is the width of the channel), highly intermittent anisotropic turbulent events appear in the mixing layer at the depth of z/Hv = 0.7~1.1 and distance of x/Hv = 8~12 (where x is streamwise distance from the patch edge, z is vertical distance from channel bed and Hv is the height of a vegetation patch). The results of quadrant analysis show that these structures are associated with the dominance of the outward interactions (Q1). Moreover, these structures accompany large coherent Reynolds shear stresses, anomalies in streamwise velocity, increases in the standard deviation of TKE and increases in intermittent Turbulent Kinetic Energy (TKEi). The intensity and extents of these structures fade with the decrease in the size of a vegetation patch. On the other hand, as the size of the vegetation patch decreases, von Karman vortexes appear in the wake layer and form the dominant flow structures in the downstream region of a vegetation patch.

An efficient algorithm of dislocation-precipitate interactions for single crystal nickel-based superalloys within discrete dislocation dynamics and its application

In this paper, the discrete dislocation dynamics (DDD) framework for single crystal nickel-based superalloys (SCNBSs) modeling is extended to simulate the superdislocation pairs shearing numerous precipitates more efficiently. An adaptive dislocation segment meshing scheme by specially treating the dislocation segments deposited on the γ/γ′ interfaces is also used to decrease the computational expense. In addition, the MPI parallel algorithm is also realized to increase the computational speed. Through this DDD framework, the size-related plastic response of SCNBSs microcrystal containing collections of precipitates is systematically investigated. Two types of SCNBSs microcrystal samples, one with intact precipitates and the other with partial precipitates truncated by free surfaces, are established for different sample sizes. The influence of the sample size, two types of boundary, and the coherency stress induced by lattice mismatch between the two phases are discussed. The results show that the influence of sample size on the yield strength and the dispersity of stress–strain curves are relatively weak when more than four precipitates across the cross section. And the effect of sample size on deformation mode and the dislocation density is still evident for all the considered sample sizes. For two types (intact and truncated precipitates) of SCNBSs microcrystal samples, the remarkable difference in their mechanical responses and dislocation evolution appears when there is only one precipitate across the cross section. In addition, the misfit stress can significantly change the dislocation distribution in different channels. However, it has less influence on the tensile stress–strain response for the considered tensile loading condition. Our results indicate that to properly characterize the global mechanical behavior of bulk SCNBSs by micro-test, the microcrystal sample should present more than sixteen whole precipitates across the cross section.