Evolution Of Volume Fraction Research Articles

Comparison of the properties of scutched flax and flax tow for composite material reinforcement

The industrial production of flax fibers yields two fibrous products: scutched fibers are valuable for their length, fineness and cleanness, while tows are entangled, impure and are low-priced. There is a need for technical data to compare these two kinds of fibers beyond the difference of appearance, and to assess their potential as composite material reinforcements. In this work, we have compared the properties of scutched flax and flax tows from the same batch. The morphology was first assessed by measuring the length, cleanness and fineness of fiber bundles. The tensile properties of single fibers and of unidirectionally reinforced epoxy composites were then measured. The results show that the morphology of flax tows is different from but close to the morphology of scutched flax. Tow bundles were 15% shorter than scutched flax bundles and tow bundles were 25% thicker than scutched flax bundles. The tensile properties of single fibers were in the same range. Tensile properties of the unidirectional composites show a similar evolution of properties versus fiber volume fraction. The use of scutched flax allowed volume fractions of 0.7 to be achieved while tow volume fraction was limited to 0.6. Despite the visual and morphological difference between tows and scutched flax both can be good candidates for composite reinforcement in high performance applications.

Two-step polarization reversal in biased ferroelectrics

Polarization reversal in polycrystalline ferroelectrics is shown to occur via two distinct and sequential domain reorientation steps. This reorientation sequence, which cannot be readily discriminated in the overall sample polarization, is made apparent using time-resolved high-energy x-ray diffraction. Upon application of electric fields opposite to the initial poling direction, two unique and significantly different time constants are observed. The first (faster time constant) is shown to be derived by the release of a residual stress due to initial electrical biasing and the second (slower time constant) due to the redevelopment of residual stress during further domain wall motion. A modified domain reorientation model is given that accurately describes the domain volume fraction evolution during the reversal process.

Solving seven-equation model for compressible two-phase flow using multiple GPUs

In this paper, the application of an HLLC-type approximate Riemann solver in conjunction with the third-order TVD Runge–Kutta method to the seven-equation compressible two-phase model on multiple Graphics Processing Units (GPUs) is presented. Based on the idea proposed by Abgrall et al. that “a multiphase flow, uniform in pressure and velocity at t=0, will remain uniform on the same variables during time evolution”, discretization schemes for the non-conservative terms and for the volume fraction evolution equation are derived in accordance with the HLLC solver used for the conservative terms. To attain high temporal accuracy, the third-order TVD Runge–Kutta method is implemented in conjunction with operator splitting technique, in which the sequence of operators is recorded in order to compute free surface problems robustly. For large scale simulations, the numerical method is implemented using MPI/Pthread-CUDA parallelization paradigm for multiple GPUs. Domain decomposition method is used to distribute data to different GPUs, parallel computation inside a GPU is accomplished using CUDA, and communication between GPUs is performed via MPI or Pthread. Efficient data structure and GPU memory usage are employed to maintain high memory bandwidth of the device, while a special procedure is designed to synchronize thread blocks so as to reduce frequencies of kernel launching. Numerical tests against several one- and two-dimensional compressible two-phase flow problems with high density and high pressure ratios demonstrate that the present method is accurate and robust. The timing tests show that the overall speedup of one NVIDIA Tesla C2075 GPU is 31× compared with one Intel Xeon Westmere 5675 CPU core, and nearly 70% parallel efficiency can be obtained when using 8 GPUs.

Dynamic recrystallization kinetics of a powder metallurgy Ti–22Al–25Nb alloy during hot compression

The flow behavior of a P/M Ti–22Al–25Nb alloy was evaluated by applying a series of compression tests to a height reduction of 50% performed within the temperature range of 950–1070°C using strain rate range of 0.001–1s−1. The dynamic recrystallization (DRX) behavior at elevated temperature was evaluated by the modified Avrami type equation based on stress–strain data. By means of conventional hyperbolic sine function, the activation energies for DRX were estimated to be 1053.06kJ/mol in the (α2+β/B2+O) phase region and 734.77kJ/mol in the (α2+B2) phase region, respectively. The critical strain (εc) for the onset of DRX, the strain for peak stress (εp) and the strain for maximum softening rate (ε⁎) under different deformation conditions were identified according to the strain hardening rate curves. The DRX kinetics model was proposed to characterize the evolution of DRX volume fraction, which revealed that the DRX exhibited the ‘slow-rapid-slow’ evolution with the increasing strain. It was also found that the process of DRX was promoted by decreasing strain rate and increasing deformation temperature. Moreover, the microstructure examination results indicated that the theoretical prediction results were shown to be in good agreement with the statistical results. Finally, the continuous dynamic recrystallization (CDRX) was identified to be the DRX mechanism by referring to a transmission electron microscope (TEM) observation.

A mechanism-based model for deformation twinning in polycrystalline FCC steel

Deformation twinning, a common and important plastic deformation mechanism, is the key contributor to the excellent combination of strength and ductility in twinning-induced plasticity (TWIP) steel. In the open literature, a significant amount of research has been reported on the microstructural characteristics of deformation twinning and its influence on the overall deformation behavior of TWIP steel. In this study, we examine the feasibility of a mechanism-based crystal plasticity model in simulating the microstructural level deformation characteristics of TWIP steel. To this end, a model considering both double-slip and double-twin is developed to investigate the stress–strain behavior and local microstructural features related to the formation and growth of micro-twins in low stacking fault energy (SFE) TWIP steel. The twin systems are described as pseudo-slips that can be activated when their resolved shear stress reaches the corresponding critical value. A hardening law that accounts for the interaction among the slip and twin systems is also developed. Numerical simulations for different mesh sizes and single crystal patch tests under different loading modes are carried out to verify the modeling procedure. Our simulation results reveal that, despite its simple nature, the double-slip/double-twin model can capture the key deformation features of TWIP steel, including twin volume fraction evolution, continuous strain hardening, and the final fracture in the form of strain localization.

A phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys

Shape memory alloys (SMAs) possess the distinctive ability to recover large mechanically-induced inelastic strains upon unloading, which is known as the pseudoelastic behavior. This paper deals with an extension of the phenomenological viscoplasticity theory, which has been developed by the author to depict the negative strain rate sensitivity, to model the macroscopic behavior of the phase transformation. Unlike most phenomenological models for the pseudoelasticity, the proposed model does not employ a kinetic law describing the evolution of the martensitic volume fraction and the transformation loading and unloading conditions but introduces two internal state variables concerned with the evolution of the elastic modulus and the back stress. The applicability of the constitutive model to SMAs is validated by comparing simulation results with experimental data on uniaxial and torsional loading reported in the literature. And then it is demonstrated that the same constitutive equations can be applied to model the highly nonlinear unloading behavior of solid polymer.

Quantitative description of the T1 formation kinetics in an Al–Cu–Li alloy using differential scanning calorimetry, small-angle X-ray scattering and transmission electron microscopy

The object of the present study is to design a methodology to follow the kinetics of T1 precipitation, in an AA2198 alloy, in terms of precipitate size, morphology (thickness, diameter) and volume fraction, during a two-temperature isothermal heat treatment. We used in situ small-angle X-ray scattering (SAXS) as a way to measure the evolution of the T1 mean thickness and diameter during the heat treatment. Transmission electron microscopy (TEM) was then performed in order to calibrate these evolutions. Furthermore, we demonstrate that the volume fraction evolution can be described successfully using a simple analysis of the differential scanning calorimetry (DSC) thermograms. The latter was calibrated by selected observations in high angular annular dark field scanning transmission electron microscopy (HAADF-STEM). Microstructure evolution during DSC heating ramps was analysed using in situ SAXS: the T1 phase transformation is found to consist in a two-step thickening process explained by two consecutive diffusion stages. The enthalpy of formation of the T1 phase is deduced from the DSC measurements.

Study of inhomogeneous distribution of Bi-2223 phase in Ag/Ni composite-sheathed tapes

Inhomogeneous distribution of Bi-2223 ceramics in Ag/Ni composite-sheathed superconducting tapes was studied systematically. Difference of volume fractions of Bi-2223 phase in different locations at the sheath–ceramic interface was reported first. The real local oxygen partial pressure (PO2) variance was identified as the reason leading to the phenomenon. Meanwhile, the volume fraction evolution of Bi-2223 phase in different locations of samples treated in various PO2 with sintering time extension was studied. It was concluded that a long-time sintering in a PO2 reduced atmosphere seemed to be good for decreasing inhomogeneous distribution of Bi-2223 ceramics. In addition, a combined heat treatment in the initial formation stage of Bi-2223 phase was designed to successfully eliminate the inhomogeneous distribution of Bi-2223 ceramics.

An Analytical Approach to Investigate the Evolution of Bone Volume Fraction in Bone Remodeling Simulation at the Tissue and Cell Level

Simulation of bone remodeling at the bone cell level can predict changes in bone microarchitecture and density due to bone diseases and drug treatment. Their clinical application, however, is limited since bone microarchitecture can only be measured in the peripheral skeleton of patients and since the simulations are very time consuming. To overcome these issues, we have developed an analytical model to predict bone density adaptation at the organ level, in agreement with our earlier developed bone remodeling theory at the cellular level. Assuming a generalized geometrical model at the microlevel, the original theory was reformulated into an analytical equation that describes the evolution of bone density as a function of parameters that describe cell activity, mechanotransduction and mechanical loading. It was found that this analytical model can predict changes in bone density due to changes in these cell-level parameters that are in good agreement with those predicted by the earlier numerical model that implemented a detailed micro-finite element (FE) model to represent the bone architecture and loading, at only a fraction of the computational costs. The good agreement between analytical and numerical density evolutions indicates that the analytical model presented in this study can predict well bone functional adaptation and, eventually, provide an efficient tool for simulating patient-specific bone remodeling and for better prognosis of bone fracture risk.

Heat transfer in shape memory alloy thin films

The thermal response of periodic, shape memory alloy (SMA) island structures is addressed in this paper. Incorporated into the thermal modeling are several ingredients that are encountered at length scales typical to micron-sized thin films: (i) the microstructure may be heterogeneous, e.g., there may be a mix of an amorphous layer, a non-transforming crystalline layer and a crystalline layer that does undergo phase transformation; (ii) given the typical large surface-to-volume ratios and the attendant thermal losses to the environment, the strength of the heat source as well as its duration during a martensite to austenite transformation become very important. These issues, especially the latter, are investigated for a range of periodic structures with different spacings including the limiting structures of vanishing inter-island spacing on the one hand (infinitely extended thin film) and infinite inter-island spacing on the other (isolated islands). It is seen that a reduced inter-island spacing results in lower heat losses to the substrate, that a heterogeneous microstructure has a minimal effect on the thermal field, and that there appears to be a threshold in the strength of the heat source (represented by a current density, if the heat source is electrical in origin) above which the reduction in the heating time does not improve substantially. Interestingly, the evolution of martensite volume fraction with respect to time seems to be insensitive to the thickness of the film undergoing transformation to austenite.

Model for multiple stress affected martensitic transformations, microstructural entropy and consequences on scatter in properties

Building on previous work on stress affected martensitic transformations, a simple theory is presented to enable the calculation of the volume fractions of each martensite variant in an austenite grain, as a function of temperature. Polycrystalline austenite is dealt with by introducing specific textures, so that the orientation of the martensite in any region of the sample is defined. The calculations show that there is strong variant selection even with relatively small applied stresses, and the evolution of overall volume fraction is dominated by the favoured variants. The notion of microstructural entropy, which indicates the level of heterogeneity in the microstructure, is then used to indicate consequences on properties such as the scatter to be expected in toughness. These and further detailed consequences of stress affected transformation are described.

Cyclic Stress-Strain Response and Martensitic Transformation Behavior for Type 304 Stainless Steel

Stress-strain responses of type SUS304 stainless steel at large strain under uniaxial tension and cyclic loading were investigated with special reference to plastic strain induced martensitic transformation. From the experiment it was found that the martensitic transformation plays an important role for the workhardening of the material at large strain, and a new finding from the cyclic experiment is that the stagnation of martensitic transformation appears at an early stage of reverse deformation. The evolutions of martensite volume fraction during monotonic and cyclic deformations were calculated by Stringfellow model, and it was found that the model is accurate enough for predicting the martensite volume fraction vs. plastic strain curve under monotonic loading case. On the other hand, it significantly overestimates the evolution of martensite volume fraction in a cyclic deformation.

A Gibbs‐energy‐barrier‐based computational micro‐sphere model for the simulation of martensitic phase‐transformations

SUMMARYWe introduce a material model for the simulation of polycrystalline materials undergoing solid‐to‐solid phase‐transformations. As a basis, we present a scalar‐valued phase‐transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The analysis of the related overall Gibbs energy density allows for the calculation of energy barriers. With these quantities at hand, we use a statistical‐physics‐based approach to determine the resulting evolution of volume fractions. Though the model facilitates to take into account an arbitrary number of solid phases of the underlying material, we restrict this work to the simulation of phase‐transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar model is embedded into a computational micro‐sphere formulation in view of the simulation of three‐dimensional boundary value problems. The final modelling approach necessary for macroscopic simulations is accomplished by a finite element formulation, where the local material behaviour at each integration point is governed by the response of the micro‐sphere model.Copyright © 2014 John Wiley & Sons, Ltd.

OS0111 HCP金属の結晶粒内における変形双晶域発展に関する定量的検討

The deformation twinning is an important deformation mechanism of magnesium and other HCP metals. This paper provides a framework of crystal plasticity model involving the effect of deformation twinning of HCP metals. The lattice rotation due to the deformation twinning is introduced into a conventional crystal plasticity framework, and the volume fraction of deformation twinning is considered. A numerical example is conducted to evaluate the evolution of volume fraction of twinned region in polycrystalline pure mangesium, and an evolution equation of volume fraction of twinning is quantitatively discussed.

Preventing Abnormal Grain Growth of Austenite in Low Alloy Steels

Abnormal grain growth (AGG) in austenitic state is studied in low alloy steel in relation with precipitation state. It is observed that initial austenite grain size and precipitation state plays more important role in defining the normal or abnormal grain growth condition than the final one obtained after a heat treatment. Precipitate volume fraction evolution with time-temperature having similar quantity at the end but different initial grain sizes, showed different grain growth phenomenon. Arguments are presented to rationalize the presented experience. A simplified AGG model is applied to understand the effects of initial mean austenite grain size and precipitate size distribution on the subsequent AGG occurrence.

Solvent Wrapped Metastable Colloidal Crystals: Highly Mutable Colloidal Assemblies Sensitive to Weak External Disturbance

Solvent wrapped "metastable" crystalline colloidal arrays (CCAs) have been prepared by supersaturation induced precipitation and self-assembly of monodisperse particles in polar/nonpolar organic solvents. These metastable CCAs possess ordered structures but with less stability comparing with traditionally fixed colloidal crystal systems. They are stabilized by the balance between long-range attraction and electrostatic repulsion of neighboring like-charged particles. Monitoring the reflection intensity during evaporation suggests that these crystals can exist for several hours at 90 °C and even longer at room temperature. Based on the evolution of particle volume fraction in whole suspension (φ(SiO2)), crystal phase (φ(crystal)), and liquid phase (φ(liquid)), the formation of metastable CCAs can be understood as a microscopic phase separation process, where the homogeneous dispersion will separate into a "crystal phase" with orderly stacked particles and a "liquid phase" with randomly dispersed particles. Further calculation of the volume fraction of crystal phase (V(crystal)/V(total)) and the ratio of particles in crystal phase (f(crystal)) shows that with the increase of designed Φ(SiO2), more particles precipitate to form colloidal crystals with larger sizes but the lattice spacing of the microcrystals remains constant. Unlike fixed or traditional responsive CCAs, these metastable CCAs can reversibly assemble and disassemble with great ease, because little energy is involved or required in this transformation. Therefore, they can sense weak external disturbances, including subtle motion and slight friction or shearing forces.

Interrupted Test of Advanced High Strength Steel with Tensile Split Hopkinson Bar Method

The phase fraction evolution in a material during quasi-static and dynamic tests can be studied by interrupting the test at predetermined elongation values. While it is straightforward to interrupt quasi-static tests at a predetermined level of elongation, this interruption presents difficulties at high strain rate conditions. In the present paper, an interruption mechanism has been developed to control the elongation of specimens at high strain rate using a modified split Hopkinson tensile bar. This interruption mechanism is based on the interaction between the test specimen and the external interruption device. The influence of the designed external device on the stress waves and also the ability of the system to support the interruption of the deformation process were considered in the numerical analysis and verified by the experimental results. Finally, the influences of strain and strain rates on the volume fraction evolution of the retained austenite in quenched & partitioned steel were reported.

Constitutive modeling of two-phase metallic composites with application to tungsten-based composite 93W–4.9Ni–2.1Fe

The two-phase metallic composites, composed by the metallic particulate reinforcing phase and the metallic matrix phase, have attracted a lot of attention in recent years for their excellent material properties. However, the constitutive modeling of two-phase metallic composites is still lacking currently. Most used models for them are basically oriented for single-phase homogeneous metallic materials, and have not considered the microstructural evolution of the components in the composite. This paper develops a new constitutive model for two-phase metallic composites based on the thermally activated dislocation motion mechanism and the volume fraction evolution. By establishing the relation between microscopic volume fraction and macroscopic state variables (strain, strain rate and temperature), the evolution law of volume fraction during the plastic deformation in two-phase composites is proposed for the first time and introduced into the new model. Then the new model is applied to a typical two-phase tungsten-based composite – 93W–4.9Ni–2.1Fe tungsten heavy alloy. It has been found that our model can effectively describe the plastic deformation behaviors of the tungsten-based composite, because of the introduction of volume fraction evolution and the connecting of macroscopic state variables and micromechanical characteristics in the constitutive model. The model's validation by experimental data indicates that our new model can provide a satisfactory prediction of flow stress for two-phase metallic composites, which is better than conventional single-phase homogeneous constitutive models including the Johnson–Cook (JC), Khan–Huang–Liang (KHL), Nemat-Nasser–Li (NNL), Zerilli–Armstrong (ZA) and Voyiadjis–Abed (VA) models.

Separation of nucleation and growth of voids during tensile deformation of a dual phase steel using synchrotron microtomography

The damage evolution in a DP980 dual phase steel is followed in situ by synchrotron microtomography during tensile deformation focusing on the effect that the triaxiality, induced by different sample geometries, exerts on damage formation and damage evolution. The growth of existing voids is separated from the voids nucleated between consecutive deformation steps using three-dimensional image analysis. The experimental results are correlated with those obtained by finite element analysis using a Gurson–Tvergaard–Needleman framework with a Chu and Needleman formulation to introduce the effect of nucleation of cavities. A relatively simple way to determine the nucleation parameters is proposed based on the volume of nucleated voids obtained from the tomographies. The evolution of the total volume fraction of cavities obtained from the calculations shows a good agreement with the experiments for the notched samples and reflects the effect of triaxiality on damage. Contrarily to experiments, the calculated accumulated volume fraction of nucleated voids does not reflect the effect of triaxiality suggesting the necessity to implement this parameter in the nucleation model.

Channelization of buoyant nonwetting fluids in saturated porous media

[1] We study the development of capillary instabilities during the invasion of a buoyant nonwetting phase in a saturated porous media. Capillary instabilities are generally attributed to heterogeneities in the porous medium resulting in the existence of fluid pathways opposing different resistance to the flow (“passive control”). We use a simple macroscale theoretical model based on the postulate that the nonwetting fluid will be distributed in the porous medium to minimize the resistance to transport. This theoretical argument is used to show that after their formation, some capillary instabilities can grow at the expense of others. The competitive growth between capillary channels arises because of pore-scale fluid interactions that occur even in a porous medium offering identical pathways at the pore scale. The evolution of the pore volume fraction of nonwetting fluid in capillary fingers is therefore dynamically controlled by fluctuations in the nonwetting phase saturation and its effect on the relative permeability (“active control”). The theoretical model predicts (1) the growth of heterogeneities in nonwetting fluid saturation among competing capillary channels if the second derivative of the invading phase relative permeability with respect to its saturation is positive, and (2) that the amplitude of the perturbation in nonwetting fluid content between competing fingers increases with the interfacial tension. We use a pore-scale multiphase flow numerical model to test the validity of the postulate for optimal transport of nonwetting fluids and the two ensuing predictions. We observe that the numerical calculations are in excellent agreement with the theoretical predictions.