Evolution Of Volume Fraction Research Articles

Effects of strain rate on the microstructure evolution and mechanical response of magnesium alloy AZ31

The effects of strain rate on the mechanical behaviour and microstructure evolution of extruded Mg AZ31 alloy are investigated here for strain rates ranging from 0.0001s−1 to 4000s−1. High strain rate compression testing was performed using a split Hopkinson pressure bar apparatus. The microstructure and texture evolution were characterised by using electron backscatter diffraction (EBSD) and neutron diffraction. The results show that the yield strength increases by roughly 55% from the quasi-static to the high strain rate regime while the plateau stress increases by roughly 35%. After compression along the extrusion direction, the deformed textures of both quasi-static and high strain rate loading samples are similar, showing that a large portion of grains have been reoriented through the activation of tensile twinning. However, a detail EBSD analysis suggests that there is a higher fraction of secondary compressive twins in high strain rate deformed specimens at 16% strain. A visco-plastic self-consistent (VPSC) model, which incorporates the composite grain scheme to account for twinning, is employed to model the mechanical response and texture evolution, and to elucidate the collaborative nature of the slip-twinning deformation. Using only a single set of parameters, the VPSC model successfully reproduces the stress-strain curves at all tested strain rates, and more importantly, captures the texture and twin volume fraction evolutions. The simulation results suggest that under quasi-static and high strain rate loadings, the dominant slip systems are different in both untwinned grains and tensile twins. The results also suggest that twins are formed at a lower strain at high strain rates when compared to quasi-static loading.

In-situ TOF neutron diffraction studies of cyclic softening in superelasticity of a NiFeGaCo shape memory alloy

Real-time in-situ neutron diffraction was conducted during uniaxial cycling compression of a Ni49.3Fe18Ga27Co5.7 shape memory alloy to explore the mechanism on its superelasticity at room temperature, which was manifested by the almost recoverable large strains and the apparent cyclic softening. Based on the Rietveld refinements, the real-time evolution of volume fraction of martensite was in-situ monitored, indicating the incremental amount of residual martensite with increasing load cycles. Real-time changes in intensities and lattice strains of {hkl} reflections for individual phase were obtained through fitting individual peaks, which reveal the quantitative information on phase transformation kinetics as a function of grain orientation and stress/strain partitioning. Moreover, a large compressive residual stress was evidenced in the parent phase, which should be balanced by the residual martensite after the second unloading cycle. The large compressive residual stress found in the parent austenite phase may account for the cyclic effect on critical stress required for triggering the martensitic transformation in the subsequent loading.

Phase Equilibrium and Austenite Decomposition in Advanced High-Strength Medium-Mn Bainitic Steels

The work addresses the phase equilibrium analysis and austenite decomposition of two Nb-microalloyed medium-Mn steels containing 3% and 5% Mn. The pseudobinary Fe-C diagrams of the steels were calculated using Thermo-Calc. Thermodynamic calculations of the volume fraction evolution of microstructural constituents vs. temperature were carried out. The study comprised the determination of the time-temperature-transformation (TTT) diagrams and continuous cooling transformation (CCT) diagrams of the investigated steels. The diagrams were used to determine continuous and isothermal cooling paths suitable for production of bainite-based steels. It was found that the various Mn content strongly influences the hardenability of the steels and hence the austenite decomposition during cooling. The knowledge of CCT diagrams and the analysis of experimental dilatometric curves enabled to produce bainite-austenite mixtures in the thermomechanical simulator. Light microscopy (LM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were used to assess the effect of heat treatment on morphological details of produced multiphase microstructures.

Crystal Plasticity Constitutive Model for Multiphase Advanced High Strength Steels to Account for Phase Transformation and Yield Point Elongation

A constitutive law was developed based on a rate-independent crystal plasticity to account for the mechanical behavior of multiphase advanced high strength steels. Martensitic phase transformation induced by the plastic deformation of the retained austenite was represented by considering the lattice invariant shear deformation and the orientation relationship between parent austenite and transformed martensite. The stress dependent transformation kinetics were represented by adopting the stress state dependent volume fraction evolution law. The plastic deformation of the austenite was determined to have the minimum- energy associated with the work during the phase transformation. In addition to the martensitic phase transformation, yield point elongation and subsequent hardening along with inhomogeneous plastic deformation were also represented by developing a hardening stagnation model induced by the delayed dislocation density evolution.

An elastoviscoplastic model for porous single crystals at finite strains and its assessment based on unit cell simulations

An elastoviscoplastic model is formulated at finite strains for porous single crystals. The model extends the yield function developed by Han et al. (2013) for porous single crystals at infinitesimal strains to finite strains, incorporating the evolution of void volume fraction and strain hardening of single crystal matrix. The model is assessed through three-dimensional unit cell finite element simulations based on periodic homogenisation and loading paths with prescribed constant stress triaxiality. The unit cell simulations are performed for face-centered cubic crystals with various crystallographic orientations, stress triaxialities and initial void volume fractions, showing the competitive influence of the stress triaxiality and the crystallographic orientation on the effective behaviour and the void volume evolution. The proposed model captures the hierarchy of porous single crystal responses with respect to crystal orientation and void volume fraction. It represents a remarkable compromise between description of unit cell behaviour and tractability in the computation of structural components.

Influence of Processing Parameters on the Solidification Behavior of Single-Crystal CMSX-4 Superalloy

The microstructural evolution of a superalloy, single-crystal CMSX-4 solidified at different withdrawal rates was investigated using a directional solidification quenching method. Analyses of the cross-sections within mushy zones generated the evolution of the solid volume fractions (fs) during the reduction in the temperature and the solidification sequences. At the withdrawal rate of 0.3 mm min−1, fs increases by about 81 pct within the first 23 pct of the solidification interval, whereas it increases by about 64 pct at the withdrawal rate of 0.7 mm min−1. The Bower–Brody–Flemings model can characterize the evolution tendency of fs curve at the lower withdrawal rate, while it can not only describe the changing tendency of fs, but also precisely predict the fs values at higher withdrawal rate. With increasing withdrawal rate, the solidification intervals of the γ dendrite and γ/γ′ eutectics are increased. In addition to this, the forming site of the γ/γ′ eutectic at the lower withdrawal rate lags behind that at the higher withdrawal rate. At both the withdrawal rates the solidification of the γ/γ′ eutectic islands commences with the γ/γ′ core formed on the surface of the γ dendrites, then progressed spatially and developed the coarse γ/γ′ structure.

Numerical modeling of the deformation of AISI 304L using a tangent additive Mori-Tanaka homogenization scheme: Application to sheet metal forming

The aim of this paper is to demonstrate the capability of the tangent additive Mori-Tanaka scheme to simulate complex processes like sheet metal forming. The strengths of such homogenization scheme are exemplified by performing numerical simulations on AISI 304L grade classified as TRIP (TRansformation Induced Plasticity) stainless steel. Some experiments are also performed to validate numerical results. The experimental data are obtained from tensile tests performed at different strain rates. During tensile tests, the evolution of the martensite volume fraction and of the temperature in the AISI 304L specimen are registered. Material parameters of the phase transformation constitutive model (which is coupled with the elastic-viscoplastic Mori-Tanaka homogenization approach) are identified using tensile experimental data. To validate the Mori-Tanaka homogenization scheme, a special focus is devoted to the comparison of the simulated responses to experimental data obtained via tensile tests. Overall stress-strain responses and volume fraction of martensite are accurately reproduced. In addition, local responses in each phase are provided. Numerical simulations of cup drawing process were also performed and a parametric study on material parameters, friction coefficient, holder force enabled to capture the evolution of the punch force and volume fraction of martensite in the blank. An isotropization strategy is also proposed which consists in using an isotropic instead of the anisotropic tangent stiffness modulus for the reference medium to evaluate the tangent polarization tensor present in the interaction law. Relevance of this isotropization is discussed.

In situ structural characterization of ageing kinetics in aluminum alloy 2024 across angstrom-to-micrometer length scales

The precipitate structure and precipitation kinetics in an AlCuMg alloy (AA2024) aged at 190 °C, 208 °C, and 226 °C have been studied using ex situ Transmission Electron Microscopy (TEM) and in situ synchrotron-based, combined ultra-small angle X-ray scattering, small angle X-ray scattering (SAXS), and wide angle X-ray scattering (WAXS) across a length scale from sub-Angstrom to several micrometers. TEM brings information concerning the nature, morphology, and size of the precipitates while SAXS and WAXS provide qualitative and quantitative information concerning the time-dependent size and volume fraction evolution of the precipitates at different stages of the precipitation sequence. Within the experimental time resolution, precipitation at these ageing temperatures involves dissolution of nanometer-sized small clusters and formation of the planar S phase precipitates. Using a three-parameter scattering model constructed on the basis of TEM results, we established the temperature-dependent kinetics for the cluster-dissolution and S-phase formation processes simultaneously. These two processes are shown to have different kinetic rates, with the cluster-dissolution rate approximately double the S-phase formation rate. We identified a dissolution activation energy at (149.5 ± 14.6) kJ mol−1, which translates to (1.55 ± 0.15) eV/atom, as well as an activation energy for the formation of S precipitates at (129.2 ± 5.4) kJ mol−1, i.e. (1.33 ± 0.06) eV/atom. Importantly, the SAXS/WAXS results show the absence of an intermediate Guinier-Preston Bagaryatsky 2 (GPB2)/S″ phase in the samples under the experimental ageing conditions. These results are further validated by precipitation simulations that are based on Langer-Schwartz theory and a Kampmann-Wagner numerical method.

Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

Multi-material flow generally describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. In order to model such flow situations in the context of geomechanics and geotechnical engineering, a theoretical framework is presented which introduces a possible two-phase coupled saturated granular material behavior among the different materials. This is achieved by extending the technique of local volume averaging to a hierarchy of three spatial scales, based on a product of two indicator functions. A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents. The closure relations are provided at the macroscale, including those describing granular behavior covering the full frictional-collisional flow regime and bulk material volume fraction evolution. The paper discusses the advantages and restrictions of the proposed mixture model and addresses its application and full-scale numerical implementation.

Microstructural characterization and recrystallization kinetics modeling of annealing cold-rolled vanadium microalloyed HSLA steels

In this study, we investigated the microstructural evolution and recrystallization kinetics during the annealing of cold-rolled Vanadium microalloyed HSLA (denoted as HSLA-V) steels using both experimental characterization techniques and theoretical model analysis method. Our experimental results indicate that the recrystallization kinetics can be quantified with the evolution of volume fraction of recrystallization as a function of annealing time, and is strongly dependent on the processing parameters (i.e., cold-rolling reduction and annealing temperature) of the HSLA-V steels. Validated by experimental data, our physics-based model analysis revealed that the recrystallization process in the HSLA-V steels consisted of an early stage with both nucleation and grain growth processes and a later stage with grain growth only. Moreover, the growth of the recrystallized grains was found to follow one dimensional preferential growth mechanism, owing to the dispersed V(C,N) precipitates, in the HSLA-V steels. Consequently, our new analysis model is demonstrated to be useful to gain insights into the recrystallization kinetics in the annealed cold-rolled HSLA-V and even other microalloyed steels.

Effect of multiaxial loading on evolution of [formula omitted] twinning in magnesium single crystals

We employ molecular dynamics (MD) simulations to investigate the evolution of {101¯2} twinning in magnesium single crystals with an initial crack. The focus is on discerning the effect of multi-axial loading (resulting in c-axis extension) on the evolution of variant twin volume fraction and number of twins. Both these quantities fully describe the evolution of the overall twin volume fraction. In all the five loading conditions considered here, the evolution of variant volume fraction clearly shows the signature of twin coalescence through discrete jumps, which coincide with decrease in the number of twins that belong to the variant pair. Interestingly, coalescence occurs between twins that belong to conjugate variants, in addition to coalescence between twins of the same variant. The activation of twin variants is consistent with the Schmid factor. However, variants with identical Schmid factors do not necessarily activate simultaneously. Further, active twin variants with identical Schmid factors do not evolve at the same rate and as a result they do not contribute equally to the overall twin volume fraction. The evolution of NT occurs a discontinuous manner through the competition of nucleation, coalescence and detwinning processes. Each of these processes is strongly influenced by the details of the loading states. A general rule is – the fewer the nucleation events of twins belonging to different variants, larger the overall volume fraction attained leading up to saturation (fsat). Incipient non-basal slip precedes twinning ahead of the crack tip. Significant dislocation plasticity evolves during and after twinning and it occurs on basal and prismatic 〈a〉 slip systems. Prior to the dominance of twin coalescence, f exhibits an exponentially decaying distribution with respect to NT at a given strain. We present expressions for the evolution of volume fraction and number of twins that qualitatively reproduce the observed features observed for the loading conditions investigated in this work. These should serve as a starting point for constructing improved models for modeling twinning evolution at continuum length scales.

Shape memory microactuation design by substrate's reinforcement layers

The use of a reinforcing non-transforming layer, deposited on one or on the other side of the substrate of shape memory-based microactuators, as an additional way to control the thermoelastic stress in the active material film is analyzed. A model developed in this view shows that, depending on the position of the reinforcing layer, a substantial change may result in the deflection vs. temperature relationship. Experimental data for cantilevers consisting of NiTi films deposited on Si substrates show a positive effect (an enhancement of the actuation) of a Ni reinforcing layer deposited on the opposite side of the substrate, compared to a reference NiTi bimorph actuator with the film of the same composition deposited on a non-reinforced Si substrate. On the contrary, when deposited as intermediate layer between the substrate and the NiTi shape memory alloy film, the same Ni layer only causes a limitation of the actuation potential. A model embedding the thermal evolution of the martensite volume fraction was proposed to describe or to predict the actuation (deflection) of such cantilevers.

Dynamic recrystallization behavior and hot workability of AZ41M magnesium alloy during hot deformation

The dynamic recrystallization (DRX) behavior and hot workability of AZ41M magnesium alloy were studied via isothermal compression experiments. The tests were performed at 300–450 °C with strain rate of 0.005–1 s−1 on a Gleeble-1500D thermal-mechanical simulation machine. According to the experimental results, the flow stress curves show a quintessential single-peak dynamic recrystallization behavior. The characteristic points of the flow stress curves including the critical strain of DRX initiation (εc) and the strain for maximum softening rate (ε*) were determined by employing the method of strain hardening rate analysis. Then the DRX kinetic model of AZ41M magnesium alloy was established by Avrami equation to characterize the evolution of DRX volume fraction. Furthermore, the processing maps at different strains were developed and analyzed based on dynamic material model (DMM). According to the processing maps, the flow instability regions and stability regions were identified. And the optimum domain for hot working of AZ41M magnesium alloy is the temperature range of 390–450 °C and strain rate range of 0.005–0.015 s−1.

Phase transformation behavior and kinetics of high Nb–TiAl alloy during continuous cooling

Phase transformation behavior and kinetics of Ti–45Al–8.5Nb–0.2W–0.2B–0.02Y (at. %) alloy during continuous cooling under the cooling rates of 3 °C/min, 5 °C/min, 10 °C/min, 20 °C/min, 40 °C/min and water quenching (WQ) were investigated in this study. The phase composition and microstructure of the alloy were studied using X-ray diffraction (XRD) and optical microscopy (OM), respectively. The expansion and the volume fraction evolution of phases during continuous cooling were investigated by dilatometry (DIL), and the microhardness of the alloy suffered from cooling was also tested through micro-sclerometer. The results indicate that the phase transformation from parent α phase to γ and α2 take place during continuous cooling, the α→γ phase transformation occurs in the temperature range of 1150 °C–1310 °C while the α→α2 phase transformation takes place between 1100 °C and 1220 °C. The transformation temperature decreases with the cooling rate increasing, and the higher the cooling rate is, the higher the phase transformation rate is. The relative fraction of γ phase and α2 phase much depend on the cooling rate, and the lamellar colony sizes and interlamellar spacing of crystal structure decrease with the cooling rate increasing. The microhardness of high Nb–TiAl alloy increases with the cooling rate increasing due to the variations of phase composition and crystal structure.

On the slow decompressive response of volatile- and crystal-bearing magmas: An analogue experimental investigation

The degassing kinetics of ascending magma strongly affect eruption dynamics. The kinetics are in turn influenced by magma properties. The investigation of the relationship between magma properties and eruption dynamics is a key element in revealing the processes characterizing magmatic flows within the shallow conduit. To explore the effects of physical properties on degassing in basaltic eruptive systems, we have designed and carried out experiments on the slow decompressive response of analogue magmas, composed of silicone-oil-based suspensions, using a shock-tube apparatus. Four series of experiments were performed: 1) particle-free silicone oils with viscosity ranging from 1 to 1000 Pa s were used to constrain the liquid response; 2) silicone oils with variable proportion of suspended micrometric spherical particles were employed to assess the effect of different crystal fractions; 3) suspensions of elongated particles in silicone oils were used to investigate the role of crystal shape; 4) the effects of saturation time and pressure were examined. The rheology of both spherical- and elongated-particle-bearing suspensions were characterized by concentric cylinder rotational rheometry. The flow dynamics of the bubbly fluid, from the process of bubble nucleation up to the development of a permeable bubble network, were constrained using image analysis. Different fluid regimes were distinguished: (i) nucleation, (ii) foam build-up and (iii) foam oscillation. By comparing results obtained from the different series of experiments, we were able to assess the primary role played by the presence of particles on the evolution of the gas volume fraction within the samples. Particle fraction has a dominant role at high concentration, affecting the motion of the fluid. Finally, particle shape influences the long-term degassing efficiency of the fluid. Using scaling considerations, such observations are applied to mafic to intermediate systems. The results of our experimental investigation contribute to constraining vesiculation processes in magmas of various crystallinities at shallow depths.

Effect of martensitic phase transformation on the behavior of 304 austenitic stainless steel under tension

The present work integrates in-situ neutron diffraction, electron backscatter diffraction and crystal plasticity modeling to investigate the effect of martensitic phase transformation on the behavior of 304 stainless steel under uniaxial tension. The macroscopic stress strain response, evolution of the martensitic phase fraction, texture evolution of each individual phase, and internal elastic strains were measured at room temperature and at 75°C. Because no martensitic transformation was observed at 75°C, the experimental results at 75°C were used as a reference to quantify the effect of formed martensitic phase on the behavior of 304 stainless steel at room temperature. A crystallographic phase transformation model was implemented into an elastic–viscoplastic self-consistent framework. The phase transformation model captured the macroscopic stress strain response, plus the texture and volume fraction evolution of austenite and martensite. The model also predicts the internal elastic strain evolution with loading in the austenite, but not in the martensite. The results of this work highlight the mechanisms that control phase transformation and the sensitivity of modeling results to them, and point out to critical elements that still need to be incorporated into crystallographic phase transformation models to accurately describe the internal strain evolution during phase transformation.

Densification and Microstructural Evolution of Hierarchically Porous Ceramics During Sintering

Several technologically important ceramics are porous. One common approach to make high porosity ceramics is to use fugitive pore formers followed by partial densification. The resultant ceramic has hierarchical porosity: extrinsic large pores from the burnout of the pore former; and intrinsic small inter‐particle pores. In this study, the effect of sintering conditions and pore former on porosity and microstructure of hierarchically porous ceramics has been investigated. Pore size and pore volume fraction evolution of intrinsic and extrinsic pores were quantified as a function of sintering conditions. The effect of porosity and sintering conditions on average grain size is also investigated. It is shown that during sintering both the extrinsic and the intrinsic porosity decrease but along different trajectories. It is shown that the intrinsic pores control the grain growth. The results are discussed in terms of standard mechanisms and models available in the literature.

Simulation and Modelling of the Solid Electrolyte Interphase with Varying Porosity

We extend a popular approach in SEI modeling by refraining from using a single reaction interface. Instead we trace the time evolution of the SEI volume fraction in a spatially resolved way. In this study, we test how neutral lithium interstitial diffusion can explain the continuous growth of the SEI. We observe that transport of neutral lithium interstitials, as estimated by DFT calculation, is too slow to explain the growth of SEI layers with several tens of nanometer thickness. In future work, this spatially resolved transport and reaction framework will be used to study more realistic transport mechanisms.

Deformation Twinning in Zirconium: Direct Experimental Observations and Polycrystal Plasticity Predictions

Deformation twinning was directly observed in three commercial zirconium alloy samples during split channel die plane-strain compression. One pair of samples had similar starting texture but different grain size distributions, while another pair had similar grain size distribution but different starting textures. Extension twinning was found to be more sensitive to the starting texture than to the grain size distribution. Also, regions of intense deformation near grain boundaries were observed. A hierarchical binary tree-based polycrystal plasticity model, implementing the Chin-Hosford-Mendorf twinning criterion, captured the experimentally observed twinning grains’ lattice orientation distribution, and the twin volume fraction evolution, provided the critical resolved shear stress for extension twinning, $$ \tau_{0} , $$ was assumed much larger than any of the values reported in the literature, based on the viscoplastic self-consistent model. A comparison of the models suggests that $$ \tau_{0} $$ obtained using the present model and the viscoplastic self-consistent models physically correspond to the critical stress required for twin nucleation, and twin growth, respectively.

A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse.

We propose a multiscale mechanobiological model of bone remodelling to investigate the site-specific evolution of bone volume fraction across the midshaft of a femur. The model includes hormonal regulation and biochemical coupling of bone cell populations, the influence of the microstructure on bone turnover rate, and mechanical adaptation of the tissue. Both microscopic and tissue-scale stress/strain states of the tissue are calculated from macroscopic loads by a combination of beam theory and micromechanical homogenisation. This model is applied to simulate the spatio-temporal evolution of a human midshaft femur scan subjected to two deregulating circumstances: (i) osteoporosis and (ii) mechanical disuse. Both simulated deregulations led to endocortical bone loss, cortical wall thinning and expansion of the medullary cavity, in accordance with experimental findings. Our model suggests that these observations are attributable to a large extent to the influence of the microstructure on bone turnover rate. Mechanical adaptation is found to help preserve intracortical bone matrix near the periosteum. Moreover, it leads to non-uniform cortical wall thickness due to the asymmetry of macroscopic loads introduced by the bending moment. The effect of mechanical adaptation near the endosteum can be greatly affected by whether the mechanical stimulus includes stress concentration effects or not.