Evolution Of Volume Fraction Research Articles

A Fast-Acting Method for Simulating Precipitation During Heat Treatment of Superalloy 718

A fast-acting, mean-field method for simulating precipitation of the γ′′ and γ′ phases during aging of superalloy 718 following super-delta-solvus solution treatment was formulated and validated using observations in the literature. The approach assumed classical (homogeneous) nucleation and diffusion-controlled growth (N&G) of disk/ellipsoidal-shaped-γ′′ and spherical-γ′ particles. For the γ′′ precipitates in particular, the evolution equations for both nucleation and growth incorporated corrections for the non-spherical shape, assuming a fixed aspect ratio. In addition, special attention was paid to the choice of input material properties for simulations. These parameters included the bulk free energies of transformation, particle-matrix (misfit) elastic strain energy (for γ′′), effective diffusivities, and the γ′′–γ and γ′–γ interface energies. The applicability of the diffusivities and interface energies chosen for the N&G simulations was established by their consistency in replicating previously measured rate constants for the diffusion-controlled coarsening of both γ′′ and γ′. The N&G formulation was discretized to obtain numerical (spreadsheet) solutions via the Kampmann–Wagner approach. Simulation results for the temporal evolution of volume fraction and average size of the precipitates showed good agreement with experimental measurements. The sensitivity of model predictions to various input parameters was also quantified.

A phenomenological model of deformation twinning kinetics

Abstract Inspired by the classical Olson and Cohen model for martensitic phase transformations, a simple phenomenological model of the deformation twinning kinetics is proposed with account for twin-twin interactions. The model was validated for different materials using experimental data abundantly available in the literature for the evolution of the twin volume fraction with strain.

X-ray analysis of twin dominated deformation in an aged Mg-7Sn-3Zn-0.04Na alloy

In-situ transmission X-ray diffraction based compression deformation experiments are performed to study the twinning behaviour in as-extruded (non-aged) and peak-aged Mg-7Sn-3Zn-0.04Na alloy. The axial lattice strains were measured in the parent grains, twins and the precipitates as a function of applied stress. The critical shear stress for achieving 5% twinning was found to be increased by ∼26 MPa by the presence of 7% of Sn and by ∼50 MPa by the presence of the particles formed after 10 h of aging. The evolution of twin volume fraction with plastic strain is similar in both non-aged and aged conditions, indicating no change in the relative activities of slip and twin in the ideally oriented (10 1 ¯ 0) parent grains. Predictions made in previous studies of twin thickening stresses and twin bypass stresses agree reasonably well with the measured values, given the experimental error. Considerable relaxation was seen in the precipitate lattice reflections. This is attributed to relaxation effects continuing during X-ray data collection. Macroscopic flow curves confirm that precipitate hardening in the present system is particularly sensitive to relaxation effects. This is likely to be an important consideration for fatigue loading of precipitate hardened samples.

Dynamic constitutive model of frozen soil that considers the evolution of volume fraction of ice

A new constitutive model for frozen soils under high strain rate is developed. By taking the frozen soil as a composite material and considering the adiabatic temperature rise and interfacial debonding damage, the nonlinear dynamic response (NDR) of the frozen soil is predicted. At the same time, the relationship between instantaneous temperature and unfrozen water content is given, and an evolution rule of the volume fraction of ice particles is obtained. This relationship shows good agreement with experimental data. Using this new constitutive model, the stress–strain relationship of frozen soil under impact loading at temperatures of − 3 °C, − 8 °C, − 18 °C, and − 28 °C is calculated. There is good agreements between the results based on this new constitutive model and the data of dynamic impact.

A weakest link model for multiple mechanism brittle fracture — Model development and application

A multiple mechanism weakest link model for intergranular and transgranular brittle fracture is developed on the basis of experimental observations of a thermally aged low alloy steel. The model development is carried out in tandem with micro mechanical analysis of grain boundary cracking using crystal plasticity modeling of polycrystalline aggregates with the purpose to inform the weakest link model. The fracture modeling presented in this paper is carried out by using a non-local porous plastic Gurson model where the void volume fraction evolution is regularized over two separate length scales. The ductile crack growth preceding the final brittle fracture is well predicted using this type of modeling. When applied to the brittle fracture tests, the weakest link model predicts the fracture toughness distribution remarkably well, both in terms of the constraint and the size effect. Included in the study is also the analysis of a reference material.

The Effects of Post-processing in Additively Manufactured 316L Stainless Steels

This paper provides a systematic examination of microstructure and corrosion behavior of additively manufactured 316L stainless steel after post-processing by surface finishing, isothermal heat treating, or hot isostatic pressing. The effects of isothermal heat treatments from 500 °C to 1300 °C and hot isostatic press processing from 1000 °C to 1200 °C were correlated to the evolution of microstructure, pore morphology and volume fraction, microhardness measurements, and corrosion behavior to reveal the different post-processing temperature regimes and their corresponding characteristics. In particular, this study found that the AM 316L microstructures and properties are stable up to nearly 800 °C. Higher temperatures eliminate the fine solidification structure, causing a drop in microhardness and corrosion resistance. Corrosion was primarily driven by the porosity content of the exposed surface and near-surface regions, which is unaffected by isothermal or HIP post-processing, and the corrosion was not significantly affected by recrystallization, which begins around 1050 °C and is nearly complete by 1200 °C. The amount of porosity was not markedly affected by isothermal post-processing, but could be significantly reduced by HIP processing.

Incomplete carbon partitioning during quenching and partitioning of Fe–C–Mn–Si steels: Modeling and experimental validations

Carbon trapping at dislocations and carbide precipitation in martensite could significantly reduce the amount of carbon partitioning into austenite, e.g. incomplete carbon partitioning phenomenon, which would alter austenite decomposition behavior and austenite stability during the Quenching and Partitioning (Q&P) process. In this study, an integrated model is developed to clarify the mechanism of incomplete carbon partitioning and quantify its effects on austenite stabilization in the low-alloy medium-carbon Fe–C–Mn–Si steels. The fraction of carbon consumed by Cottrell atmospheres around dislocations is described using a semi-empiric equation. Then, the kinetic competition among carbide precipitation, carbon partitioning and austenite decomposition during the partitioning step is simulated by coupling the Deschamps–Bréchet model and quenching and partitioning-local equilibrium (QP-LE) model. It is found that transition carbide precipitation in martensite and carbon partitioning into austenite are kinetically coupled at the very early stage of the partitioning step and subsequently promotes austenite decomposition. Taking the synergy effects of incomplete carbon partitioning and austenite decomposition into account, our model is capable of predicting the evolution of volume fraction of austenite and its carbon content during partitioning.

Influence of heat treatments on plastic flow of laser deposited Inconel 718: Testing and microstructural based constitutive modeling

This work focuses on the experimental investigation into the heat-treatment influence on the plastic flow behavior of the laser metal deposited (LMD) Nickel-base superalloy Inconel 718 and the microstructural based constitutive modeling. The uniaxial compressive mechanical response of the LMD Inconel 718 superalloy was tested over wide ranges of temperature (298–1273 K) and strain rate (500 - ~12000/s). The tested samples were in three different heat-treatment conditions: as-deposited, direct-aged and aged after homogenization & solution (referred to as homogenized STA). Experimental results show that the differences of plastic flow behavior among these three samples were reflected in the amplitude of flow stress, strain hardening exponent, and the dependence on the temperature and strain rate. Based on micro observation, these differences were attributed to the evolution of grain geometry and volume fraction and size of γ" precipitates during heat treatments. A microstructural based constitutive model was developed. The thermal activated interaction between the moving dislocations and the precipitates was firstly proposed and embedded into the constitutive law. The influence of the heat treatments on the dynamic strain aging effect was attributed to the transition of interaction mechanism between dislocations and precipitates with the increasing precipitate size. This model was proved to be able to reproduce the plastic flow response of the LMD Inconel 718 alloy in different heat-treatment conditions over wide ranges of temperature and strain rate.

Study on Microstructure Transformation of High Strength Hot Rolled Steel by Using Finite Element Simulation

Advanced High-strength steels (AHSS) has widely application in automotive due to their high tensile strength and remarkable ductility. These good mechanical performances are strongly influenced by the processing and final microstructure. This paper performed Deformation Dilatometer and finite element simulation to study the effect of hot rolling parameters such as strain, cooling rate, and holding time at constant temperature on the microstructure formation of Nb-V low carbon microalloyed steel grade. It found that increasing deformation degree increased the volume fraction of ferrite, both of deformation dilatometer and finite element simulation give a similar trend of effects of hot rolling parameters on evolution of volume fraction of ferrite. These results give an insight for industrial application.

Effects of pre-strain and stress level on stress relaxation ageing behaviour of 2195 Al–Li alloy: Experimental and constitutive modelling

In the present work, the stress relaxation behaviour, mechanical properties and microstructural evolution of 2195 Al–Li alloy with different pre-strains (0%, 2% and 4%) have been experimentally investigated under different initial stress levels at 180 °C for 16 h. It is found that pre-strain can extend the duration of the first stress relaxation stage and significantly promote the stress reduction. Meanwhile, a new “multi-step stage” stress relaxation feature, containing a particular linear relaxation stage, is observed for the 2195 Al–Li alloy during stress relaxation ageing (SRA) process. In addition, the tensile strength of the alloy increases with the increase of pre-strains and initial stresses, while the corresponding elongation is opposite. The evolution of precipitates, including G.P. Zones, θ″, θ′ and T1 phases, have been characterized by transmission electron microscope (TEM). The number of T1 phases increases with the increase of the pre-strains and initial stresses, while the number of θ′ phases gradually decreases. Based on precipitation kinetics, stress relaxation mechanism and dislocation theory, a physically-based SRA constitutive model considering the evolution of dislocation density and relative volume fraction of T1 and θ′ precipitates is established. The results calculated by the constitutive model are in good agreement with the experimental data.

Phase transformation and grain growth behaviors of superalloy IN718 during heat treatment

The morphology of phase and grain of superalloy IN718 are important for the properties of final components as well as the forming process with repeated heating. Phase transformation and grain growth behaviors of IN718 at 920℃-1080℃ were studied by XRD and SEM. A model of volume fraction and size evolution of phases δ, γ′ and γ″ was established and used to predict the effect of phase transformation on the concentration of solute elements in the matrix. Based on the phase transformation model, a grain growth model of IN718 was established with consideration of solute drag and phase pinning effects. It was found that the drag effect of Mo and Nb is greater than that of the phase δ due to the 1.7 % phase δ content in the as-received alloy. The effect of phase δ content on grain growth was then studied by increasing the volume fraction of phase δ without change of grains. It was found that the needle-like phase δ has greater hindrance than short rod-like phase δ on grain growth and needs a correction coefficient for it in the grain growth model. The research provides a good understanding and develops a reliable method to design heat treatment process.

Numerical characterization of transient two-phase flow of nozzle under the impact of diesel fuel temperature and injector backpressure

The inner fluid flow within the micro-sac injector is investigated numerically via AVL-Fire CFD code particularly in a microscale dimension of nozzle hole is carried out in the present work. The structural parameters of the injector are left unchanged, while the physical properties of the fluid such as pressure gradient and fluid temperature are taken into account to survey their influence on vapor volume fraction evolution, vapor mass flow rate, cavitation inception, and discharge coefficient. The reliability of modeling results is confirmed by comparing obtained data with experimental one and numerical results of Payri et al. and a close match served as an indication for the accuracy of the methodology. The multiphase modality is activated for the two-fluid model application in the nozzle segment, while the interfacial source term accounts for the momentum exchange of phases in the cavitation drag model. According to results, increasing the fuel temperature is a factor for increasing turbulent kinetic energy; meanwhile, vapor volume fraction at different times shows a different trend. Concerning the discharge coefficient, it seems that increasing the fluid temperature reduces this parameter. In contrast, increasing the pressure gradient leads to a considerable increase in the discharge coefficient.

A three dimensional coupled VOF and Level set (VOSET) method with and without phase change on general curvilinear grids

A 3D coupled VOF and LS method (VOSET) on general curvilinear grids is developed for two-phase flow simulations in complex domains. The evolution of volume fraction with time is updated by calculating fluid volume fraction flux polyhedron passing through each face with geometrical approaches. The level set function is obtained by an iterative geometric operation. The level set based continuum surface tension model is derived to compute surface tension. Subsequently the model and the proposed coupled interfacial tracking method are incorporated into IDEAL, an incompressible Navier-Stokes solver. Finally, several benchmark problems including static bubble, sphere deformation, 3D Taylor instability growth, single bubble rising, two bubble merge and microchannel flow boiling are tested on irregular regions to validate the accuracy and robustness of the proposed method. The results show good agreement with previous literature results, indicating the present method is able to accurately simulate incompressible 3D two-phase flows in complex domains.

Influence of Different Soaking Times at 1050 °C on the UT Response Due to Microstructure Evolution of 2205 Duplex Stainless Steel

Under standard conditions, DSS (duplex stainless steel) features differing amounts of ferrite and austenite, essentially depending on the thermal treatment performed. This study is focused on the ultrasonic tests (UTs) response of DSS 2205, as a function of the microstructure, in terms of austenite volume fraction and austenitic grains evolution owing to different soaking times at 1050 °C. UTs were carried out on several samples. The samples underwent varying thermal treatments characterized by a constant maintenance temperature with different soaking times that allowed for microstructure evolution and modification of the structural constituents’ fraction. The UTs have highlighted an attenuation trend with the response mainly dependent upon the wave scattering and energy absorption caused by the grain features. In particular, the peak of sound attenuation was shown to correspond with the microstructure, which featured a major amount of austenite (in terms of volume fraction and the grain dimensions) and the disappearance of austenitic precipitates within the ferritic matrix. In order to obtain less UT attenuation, without affecting the mechanical and corrosion properties, the soaking should last as little time as possible.

Study of the combined effects of PTH treatment and mechanical loading in postmenopausal osteoporosis using a new mechanistic PK-PD model.

One of only a few approved and available anabolic treatments for severe osteoporosis is daily injections of PTH (1-34). This drug has a specific dual action which can act either anabolically or catabolically depending on the type of administration, i.e. intermittent or continuous, respectively. In this paper, we present a mechanistic pharmacokinetic-pharmacodynamic model of the action of PTH in postmenopausal osteoporosis. This model accounts for anabolic and catabolic activities in bone remodelling under intermittent and continuous administration of PTH. The model predicts evolution of common bone biomarkers and bone volume fraction (BV/TV) over time. We compared the relative changes in BV/TV resulting from a daily injection of 20 [Formula: see text]g of PTH with experimental data from the literature. Simulation results indicate a site-specific bone gain of 8.66[Formula: see text] (9.4 ± 1.13[Formula: see text]) at the lumbar spine and 3.14[Formula: see text] (2.82 ± 0.72[Formula: see text]) at the femoral neck. Bone gain depends nonlinearly on the administered dose, being, respectively, 0.68[Formula: see text], 3.4[Formula: see text] and 6.16[Formula: see text] for a 10, 20 and 40 [Formula: see text]g PTH dose at the FN over 2 years. Simulations were performed also taking into account a bone mechanical disuse to reproduce elderly frail subjects. The results show that mechanical disuse ablates the effects of PTH and leads to a 1.08% reduction of bone gain at the FN over a 2-year treatment period for the 20 [Formula: see text]g of PTH. The developed model can simulate a range of pathological conditions and treatments in bones including different PTH doses, different mechanical loading environments and combinations. Consequently, the model can be used for testing and generating hypotheses related to synergistic action between PTH treatment and physical activity.

Simulation of Cu precipitation in Fe-Cu dilute alloys with cluster mobility

Cu-rich precipitates formation is associated with the precipitation hardening of Fe-Cu based steels and the embrittlement of reactor pressure vessel steels under neutron irradiation. The accurate modeling of the time evolution of Cu-rich precipitates is therefore of fundamental importance for the design of Fe-Cu based steels and the prediction of the irradiation induced shift of the ductile to brittle transition temperature of reactor pressure vessels. This work applies cluster dynamics with mobile Cu monomers and clusters to model Cu precipitation in dilute Fe-Cu alloys at several temperatures. Optimized model parameters can be used to simulate the mean radius, number density, volume fraction, and matrix composition evolution during isothermal annealing with reasonable accuracy. The possible reduction of the mobility of Cu-rich clusters due to additional alloying elements in Fe-Cu based steels is discussed.

TRIP Steels: A Multiscale Computational Simulation and Experimental Study of Heat Treatment and Mechanical Behavior.

A multiscale investigation of the microstructure and the mechanical behavior of TRIP steels is presented. A multi-phase field model is employed to predict the microstructure of a low-alloy TRIP700 steel during a two-stage heat treatment. The resulting stability of retained austenite is examined through the temperature. The phase field results are experimentally validated and implemented into a model for the kinetics of retained austenite during strain-induced transformation. The kinetics model is calibrated by using experimental data for the evolution of the martensite volume fraction in uniaxial tension. The transformation kinetics model is used together with homogenization methods for non-linear composites to develop a constitutive model for the mechanical behavior of the TRIP steel. A methodology for the numerical integration of the constitutive equations is developed and the model is implemented in a general-purpose finite element program (ABAQUS). Necking of a bar in uniaxial tension is simulated and “forming limit diagrams” (FLDs) for sheets made of TRIP steels are calculated. The models developed provide an integrated simulation toolkit for the computer-assisted design of TRIP steels and can be used to translate mechanical property requirements into optimised microstructural characteristics and to identify the appropriate processing routes.

Strain hardening, twinning and texture evolution in magnesium alloy using the all twin variant polycrystal modelling approach

In this work, the viscoplastic self-consistent based All Twin Variant (ATV) polycrystal modelling was employed to decipher the deformation behaviour of Mg–3Al-0.3Mn Magnesium alloy that develops {101‾2}1‾011 - extension twins profoundly during ambient temperature compression. Twinning was considered by taking into account all the potential {101‾2}−twin variants, and hence called here as the ‘ATV’ approach. The model treats each twin variant as a grain with increasing volume fraction transferred from the respective parent grain according to its pseudo-slip shear-rate. The slip and twin-induced strain hardening were simulated by adopting a classical phenomenological hardening model while assigning a higher hardening coefficient for the twins relative to the parent matrix. The viscoplastic self-consistent polycrystal homogenisation scheme combined with the ATV approach permitted to reproduce with high precision the experimentally measured strain hardening behaviour, crystallographic texture and twin volume fraction evolution. Beyond these average measures, the activities of twin variants in individual grains could be predicted in good agreement with Electron Back-Scattered Diffraction measurements. The ATV approach permits also to examine the matrix and twin phases separately in terms of textures and misorientation distributions.

Liquid transport in scale space

When a liquid stream is injected into a gaseous atmosphere, it destabilizes and continuously passes through different states characterized by different morphologies. Throughout this process, the flow dynamics may be different depending on the region of the flow and the scales of the involved liquid structures. Exploring this multi-scale, multi-dimensional phenomenon requires some new theoretical tools, some of which need yet to be elaborated. Here, a new analytical framework is proposed on the basis of two-point statistical equations of the liquid volume fraction. This tool, which originates from single phase turbulence, allows us notably to decompose the fluxes of liquid in flow–position space and scale space. Direct numerical simulations of liquid–gas turbulence decaying in a triply periodic domain are then used to characterize the time and scale evolution of the liquid volume fraction. It is emphasized that two-point statistics of the liquid volume fraction depend explicitly on the geometrical properties of the liquid–gas interface and in particular its surface density. The stretch rate of the liquid–gas interface is further shown to be the equivalent for the liquid volume fraction (a non-diffusive scalar) of the scalar dissipation rate. Finally, a decomposition of the transport of liquid in scale space highlights that non-local interactions between non-adjacent scales play a significant role.

Calorimetric study of spinodal decomposition in β-Cu–Al–Mn

We report data obtained from the spinodal decomposition in samples of two compositions of intermetallic Cu–Al–Mn shape memory alloys. Detailed experimental information has been collected by means of differential scanning calorimetry (DSC). Spinodal decomposition was induced by isothermal treatments at different temperatures within the miscibility gap. To determine the precipitation kinetics, after each isothermal treatment particle dissolution curves were obtained by DSC. From the dissolution curves, various aspects of the precipitation process were determined, such as particles dissolution enthalpy; initial precipitate volume fraction evolution; non-isothermal dissolution characteristics; dissolution activation energy and particle distribution information. Regardless of the composition, the determined activation energy was 77 kJ mol−1. Diffusion of Mn atoms seems to be the fundamental factor that controls the studied processes.