Evolution Of Volume Fraction Research Articles

Cu addition retards the static recrystallization of cold-deformed 316L biomedical stainless steel

In this work, the effect of copper (Cu) addition on the static recrystallization behavior of large deformed 316L austenitic stainless steel is investigated by analyzing the hardness, microstructure evolution and recrystallization activation energy. The results show that Cu addition can retard the annealing softening process of 316L stainless steel and increase recrystallization activation energy, which is consistent with the evolution of the recrystallization volume fraction. Transmission electron microscope (TEM) images show that the fine Cu-rich precipitates preferentially distributed at the interface between the recrystallized grain and deformation region after annealing at 800 °C for 30 min, which pinned the migration of grain boundaries and retarded the recrystallization process. With increasing annealing temperature, the effect of Cu on recrystallization gradually decreases, due to the weaker pinning effect by lower volume fraction of Cu-rich precipitate at high temperature.

A new set of physically-based unified viscoplastic constitutive equations for superplastic deformation of Al-Zn-Mg-Cu alloy

A new set of physically-based unified viscoplastic constitutive equations using internal state variable(ISV) method during the superplastic deformation of Al-Zn-Mg-Cu alloy at temperatures ranging from 480 to 530 ℃ and strain rates ranging from 3×10−4s−1 to 3×10−3s−1 has been proposed. The damage evolution equation in this set of constitutive equations takes into account the critical cavity nucleation strain. This set of constitutive equations can predict microstructure evolution and flow stress during superplastic deformation of the investigated Al-Zn-Mg-Cu alloy. The set of constitutive equations have been coupled into crystal plasticity finite element method for determining the evolution of grain size and cavity volume fraction and the lattice rotation field map. The Material parameters are determined by genetic algorithm. The influences of strain, strain rate and temperature on grain size evolution and cavitation behavior were analyzed. The predicted stress-strain behavior, grain size and damage evolution are in good agreements with the experimental results.

In-situ strain induced martensitic transformation measurement and consequences for the modeling of medium Mn stainless steels mechanical behavior

This work aims at studying the control of medium manganese austenitic stainless steels’ mechanical behavior and austenite to martensite transformation via chemical composition. Six grades of austenitic stainless steel were cast with chemical compositions variations small enough able to keep relatively constant the stacking fault energy (SFE) value, but high enough to change the martensitic start temperature Ms. These experiments allow the effect of the martensite transformation on the mechanical behavior in tension to be compared while the austenitic mechanical behavior is almost unchanged. Tensile tests were performed at room temperature and at a low strain rate (10−4 s−1). In-situ magnetic measurement is implemented to quantify the martensite volume fraction evolution with strain. Strain heterogeneities are detected by digital image correlation (DIC) analysis. For all grades, stress–strain curves exhibit Portevin–le-Châtelier (PLC) phenomenon related to localized martensite transformation within the deformation bands. For the two most unstable alloys, a Lüders plateau is detected at the yield stress. The martensite evolution is modeled using the Olson–Cohen approach, which confirms slower kinetics for the most stable grades. Moreover, it is shown that the martensite fraction evolves linearly with stress after a stress threshold function of the austenite stability represented by Ms. The martensite volume fraction vs stress slope is constant whatever the composition. This result leads to the development of a coupled metallurgical/mechanical model which depends on a single parameter Ms related to the chemical composition.

Modeling crystal plasticity with an enhanced twinning–detwinning model to simulate cyclic behavior of AZ31B magnesium alloy at various temperatures

In this study, a multiscale model within crystal plasticity finite element (CPFE) framework was developed to predict the cyclic loading behaviors of a wrought magnesium alloy, AZ31B, at various testing temperatures. The temperature dependency was systematically modeled by employing a modified strain-hardening model, implemented in the CPFE. The developed model was further extended to cyclic loading scenarios, under which abnormal mechanical responses were observed, using an enhanced twinning–detwinning model based on the well-known predominant twinning reorientation scheme. For the first time, the concept of variable residual twin fraction was introduced in the twinning–detwinning model as a criterion for the inactivation of detwinning. The newly developed model was employed to predict the mechanical responses under monotonic in-plane tension and compression at testing temperatures ranging from room temperature to 200°C. In addition, the mechanical behaviors of the alloy under cyclic loadings at these testing temperatures were also predicted using the CPFE model. These predictions were then compared with the experimentally measured data. The micromechanical responses, such as the evolution of twin volume fraction and activation of slip/twin/detwin systems, under various loading and temperature conditions were also predicted and compared with the reported data.

γ-phase evolution in aged Co–Ni–Ga shape memory alloy

A synchrotron X-ray diffraction study of high-temperature (HT) shape memory alloy 49Co–21Ni–30Ga (in at. pct.) was performed. The volume fraction, cell parameter and temperature evolution of the different secondary phases were analyzed. This study reports reliable experimental data on these parameters to be used as a future reference to adjust the composition of the material.

Microstructure evolution and phase transformation in a nickel-based superalloy with varying Ti/Al ratios: Part 1 - Microstructure evolution

Nickel-based superalloy Waspaloy is a promising candidate material applied in power plant components for higher operation temperatures. Trial alloys based on Waspaloy with varying Ti/Al ratios (2.14, 1.44 and 0.74) were produced. The microstructure evolution, mainly focusing on strengthening phase γ’ and grain boundary carbides, were investigated and compared in these alloys during thermal exposure at 800 °C for up to 10,000 h. It is observed that lowering Ti/Al ratio leads to slight smaller average γ’ size and higher volume fraction of γ’. Moreover, γ’ in samples with low ratios kept spherical morphologies after long-term ageing compared to high ratio samples, which transformed to cuboidal shape in later ageing stage due to higher lattice misfit. A clear M23C6 carbides coarsening at grain boundary and growth toward grain interior in lower ratio samples were also observed during ageing process. The results showed higher thermal stability of lower ratio samples in terms of γ’ morphology and volume fraction evolution. This was reflected by the slightly higher hardness values in lower ratio samples in later ageing stages.

Flow and fracture of austenitic stainless steels at cryogenic temperatures

In this paper, we have characterized the microstructural evolution and the plastic flow and fracture behaviours of AISI 304L and AISI 316LN stainless steel grades at liquid nitrogen temperature (77K) and at liquid helium temperature (4K). Uninterrupted tensile experiments, where the sample is continuously deformed under quasi-static loading conditions until fracture, have been carried out with a Single-Section Sample to obtain the stress–strain characteristics of the two grades. Interrupted tensile experiments, in which the sample is unloaded before fracture, have been performed with a novel Double-Section Sample to later characterize the strain-induced martensitic transformation at different levels of deformation. The content of martensite has been determined post-mortem, using magnetic induction, electron backscatter diffraction and quantitative light optical micrography. The results obtained with the three methods show quantitative agreement, and reveal that the martensitic transformation in AISI 304L occurs faster and to a greater extent than in AISI 316LN both at 77K and at 4K. To the authors’ knowledge, in this paper we provide the first experimental results for the evolution of the content of strain-induced martensite in AISI 304L and AISI 316LN samples tested at liquid helium temperature. In addition, the experimental data for the evolution of the martensite volume fraction with the strain have been used to identify the temperature-dependent parameters of the martensitic transformation kinetic model proposed by Olson and Cohen (1975). Moreover, Mode I fracture tests with fatigue-precracked Compact Samples have been carried out to determine the fracture properties of the two investigated materials using the “resistance curve procedure” (ASTM-E1820-20a). The crack-growth resistance curves have been obtained with four different methods here referred to as ASTM Compliance Method, W–N Compliance Method, Modified W–N Compliance Method and ASTM Normalization Method, which is an original methodological contribution of this paper. While the four approaches yield similar results for the fracture toughness, only the W–N Compliance Method and the Modified W–N Compliance Method, the latter being proposed in this paper, fulfil all the requirements of the standard ASTM-E1820-20a so that the calculated fracture toughness can be accepted as a material property. The comparison of results for both materials and testing temperatures shows that AISI 316LN displays higher fracture toughness than AISI 304L. Moreover, post-mortem microstructural analysis of the Compact Samples near the fracture surface has revealed that the content of martensite is greater in AISI 304L than in AISI 316LN. Furthermore, for AISI 304L more martensite is formed in the sample tested at 77K because the plastic deformation near the crack is more than at 4K.

Effect of the as-built microstructure on the martensite to austenite transformation in a 18Ni maraging steel after laser-based powder bed fusion

During laser-based powder bed fusion, the non-equilibrium solidification conditions promote local elemental segregation, leading to a characteristic microstructure composed of cellular walls. These walls can display either low carbon BCC martensite or FCC retained austenite crystal structures, thus affecting the subsequent isochronal or isothermal martensite to austenite phase transformation mechanisms. In the present study, the effect of the non-homogeneous as-built microstructure on the martensite-to-austenite reversion phenomena was studied for a 18Ni maraging steel fabricated by laser-based powder bed fusion. In-situ synchrotron X-ray diffraction was used to retrieve the austenite volume fraction and lattice parameter evolution during the physical simulation of continuous heating cycles to the austenitic field; and during isothermal tempering cycles throughout the inter-critical tempered martensite + austenite (α’ + γ) field. The as-built microstructure resulted in the expansion of the inter-critical α’ + γ field during very slow heating rates. This was associated to the synergic effects of compositional segregations (anticipating reversion) and pre-existing retained austenite (delaying solubilization). During conventional inter-critical tempering, the as-built microstructure did not fundamentally alter the austenite reversion kinetics, resulting in similar high temperature microstructures at the end of the isothermal stage relative to the solution treated state.

Modeling and numerical investigation of mechanical twinning in β-HMX crystals subjected to shock loading

This manuscript establishes a crystal plasticity finite element (CPFE) model with large volumetric deformation for β-HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) energetic crystals with emphasis on the deformation twinning behavior under shock loading conditions. The CPFE model captures the nonlinear response of the monoclinic crystal through the application of large volumetric change under shock condition, dislocation slip at low and high moving speeds and mechanical twinning idealized by the twin volume fraction evolution. The twinning behavior is distinguished from dislocation slip through the decomposition of the plastic velocity gradient in which dislocation slip, twinning and slip in the twinned region are separately considered. Third-order Birch Murnaghan EOS is incorporated in the CPFE framework to describe the volumetric deformation under extreme pressure induced by explosion or impact. The results of the numerical investigations show that the twinning behavior exhibits strong orientation dependency, which becomes more evident at higher loading regime. Particle shape significantly affects the twin concentration. Peak twin volume fraction in HMX polycrystalline with regularized particle shapes is lower compared with mesostructure with realistic particle morphologies.

Optimization of volume fraction and microstructure evolution during thermal deformation of nano-SiCp/Al–7Si composites

Abstract This paper takes nano-SiCp/Al–7Si matrix composites prepared by powder metallurgy as the research object. With the help of advanced microstructure characterization techniques and performance analysis methods, the effect of nano-SiCp volume fraction on the microstructure and properties of composites is systematically studied. Based on optimizing the volume fraction of nano-SiCp, the thermal deformation behavior of the composites is investigated. It was found that with an increase of nano-SiCp content, the distribution uniformity of nano-SiCp decreases gradually. And because the surface of nano-SiCp is easy to adsorb gas and the aggregated distribution of nano-SiCp is not conducive to the sintering process, the density of the composites shows a gradually decreasing trend. The hardness of the composites tends increasing gradually, and the increase in amplitude gradually decreases. Due to the addition of nano-SiCp, there are many interfaces between SiCp and Al matrix, and cracks are prone to initiation and expansion at the interface. Therefore, as the volume fraction of nano-SiCp increases, the elongation of nano-SiCp/Al–7Si composites gradually decreases. When the volume fraction of nano-SiCp is 2%, the strength of the composites reaches the maximum value of 217 MPa. Compared with the Al–Si alloy without adding nano-SiCp, the results increased by 37.3%. In addition, with the decrease of strain rate and the increase of deformation temperature, the dislocation density in the composites gradually decreases, and the dynamic softening progresses more fully. The dynamic recrystallization nucleation mechanism mainly includes the subcrystal merging mechanism and the grain boundary bowing mechanism.

Deformation mechanism and microstructure evolution of medium-Mn AHSS under various loading conditions

Third-generation advanced high-strength steels possess an exceptional combination of high strength and ductility owing to their high work-hardening rate during deformation. In this study, the mechanical properties and microstructure/texture evolution of medium-Mn steel under various loading conditions (uniaxial tension, in-plane torsion, and equibiaxial tension) were investigated. Interrupted electron back-scattered diffraction and X-ray diffraction characterizations were carried out to track the microstructure and texture evolution of individual phases. Digital image correlation was employed for the in-situ measurement of formation and expansion of deformation bands, i.e., the Lüders and the Portevin-Le Châtelier (PLC) bands. The dynamic strain aging effect in terms of the formation of PLC bands and stress serrations was significantly affected by the loading conditions and stress level. Multiple types of stress serrations were observed in all tested specimens at different deformation stages. The texture evolution of the steel under various deformation modes was further tracked. Ferrite and fresh martensite exhibited the plain texture evolution like most body-centered cubic metals, whereas austenite showed a more complex texture evolution. The martensitic transformation notably decreased the RD||<001> intensity of the austenite; austenite debris was rotated with ferrite grains, while some intact austenite grains self-rotated to a stable orientation, which is unfavorable for martensitic transformation. The obvious intragranular orientation gradient observed in the austenite intact grains implies that considerable deformation occurred in the austenite. Finally, the experimental results indicate that equibiaxial tension primarily promoted the martensitic transformation, and the classical Olson–Cohen model was calibrated to capture the volume fraction evolution of austenite under various stress states.

Shape controlling and property optimization of TA32 titanium alloy thin-walled part prepared by hot forming

The hot flow behaviors, microstructure evolution and fractographs were studied to optimize the hot forming process of the TA32 titanium alloy thin-walled part. A set of microstructure-based constitutive equations were developed based on the experimental data, which described the relationships among the hot flow stresses and the evolution of phase volume fraction, dislocation density, grain size and damage. The constitutive model was imported into ABAQUS 6.14 to simulate the hot forming process for a typical thin-walled part. The effective strain, dislocation density and damage distribution as well as forming defects of formed parts under different process parameters were predicted. A qualified part without wrinkling and fracture defects was produced at a loading speed of 5 mm/s at 800 °C by the modified blank shape, where the maximum damage value was only 18.3%. The accuracy of constitutive model and finite element (FE) simulation was verified by the microhardness tests, which indicates that the FE model based on physical internal-state variables can well optimize the hot forming process of TA32 titanium alloy complex parts.

Numerical study of melting and heat transfer of PCM in a rectangular cavity with bilateral flow boundary conditions

The melting of phase change material (PCM) in a rectangular cavity with heat transfer fluids (HTFs) flowing at both sides from bottom up (bilateral flow boundary conditions) are numerically studied. A parametric study is performed by changing the Reynolds number (Re) of HTF in a range of 1 × 104, 3 × 104, 5 × 104, 7 × 104 and the Rayleigh number (Ra) in a range of 3 × 106, 4 × 106, 5 × 106, 6 × 106. The results show that the formation of natural convection is due to the impacts of non-uniform heat transfer of HTF and cooling between solid-liquid interface and liquid PCM. The asymmetric flow boundaries lead to various skew forms of the PCM melting process and effect the heat transfer and thermal energy storage. The melting process can be divided into three melting stages, the first two stages are mainly ruled by Re and the last stage by Ra. A set of introduced dimensionless parameters are analyzed to elaborate the heat transfer mechanism and the general rule of melting characteristics. The various dimensionless correlations are applied to describe the evolution of melting volume fraction, dimensionless average temperature and thermal energy storage fraction during the melting process.

Effects of ullage height on heat feedback and combustion emission mechanisms of heptane pool fires

This paper investigates the effects of ullage height (distance between the fuel surface and the pool upper rim) on heat feedback and combustion emission mechanisms of heptane pool fires. Results showed that ullage height significantly influences the flame structure and fuel mass loss rate. The incident radiative heat flux to the fuel surface and its heat feedback fraction first increase and then decrease with ullage height. Correspondingly, the convective heat feedback fraction presents a reverse trend. This attributes to flame base suspension effect and the evolution of soot volume fraction of the flame due to incomplete combustion. While for the conductive heat feedback fraction, it increases with ullage height and becomes the dominant heat feedback mode when the ullage height increases to a certain value. The profiles of the generation rate of the smoke particulates well explain the evolutions of the incident radiative heat flux. The combustion completeness is characterized by the ratio of CO/CO2. Furthermore, it is calculated that the maximum combustion completeness decreases by 18.4% and 14.3% for pool diameters of 10 cm and 15 cm, respectively. These findings will help to develop and establish more general heat transfer and heat release rate models for pool fires.

Magnetic, electrical and mechanical properties of Fe40Mn40Co10Cr10 high entropy alloy

A prototypical, single-phase, and non-equiatomic high entropy alloy Fe40Mn40Co10Cr10 has been mechanically deformed at room and cryogenic temperatures. Plastic deformation was accommodated via crystallographic slip at room temperature while transformation induced plasticity (TRIP) has been observed in samples deformed at 77 K. The stress-induced martensitic transformation occurred from face-centered cubic (FCC) to hexagonal close-packed (HCP) structures. A detailed electron backscatter diffraction analysis was utilized to detect phase change and evaluate the evolution of the HCP phase volume fraction as a function of plastic strain. Physical properties of undeformed and deformed samples were measured to elucidate the effect of deformation-induced phase transitions on the magnetic and electrical properties of Fe40Mn40Co10Cr10 alloy. Relatively small magnetic moments along with non-saturating magnetic field dependencies suggest that the ground state in the considered material is ferrimagnetic ordering with coexisting antiferromagnetic phase. The temperature evolution of the coercive fields has been revealed for all samples. The magnitudes of the coercive fields place the considered system into the semi-hard magnetic alloys category. The temperature dependence of the zero-field cooled (ZFC) and field cooled (FC) magnetization was measured for all samples in the low field regime and the origin of irreversibility in ZFC/FC curves was discussed. Besides, the temperature dependence of the resistivity in all samples was measured and the possible conduction mechanisms were discussed.

Effect of Strain-Induced Precipitation on the Recrystallization Kinetics in a Model Alloy

The effects of Nb addition on the recrystallization kinetics and the recrystallized grain size distribution after cold deformation were investigated by using Fe-30Ni and Fe-30Ni-0.044 wt pct Nb steel with comparable starting grain size distributions. The samples were deformed to 0.3 strain at room temperature followed by annealing at 950 °C to 850 °C for various times; the microstructural evolution and the grain size distribution of non- and fully recrystallized samples were characterized, along with the strain-induced precipitates (SIPs) and their size and volume fraction evolution. It was found that Nb addition has little effect on recrystallized grain size distribution, whereas Nb precipitation kinetics (SIP size and number density) affects the recrystallization Avrami exponent depending on the annealing temperature. Faster precipitation coarsening rates at high temperature (950 °C to 900 °C) led to slower recrystallization kinetics but no change on Avrami exponent, despite precipitation occurring before recrystallization. Whereas a slower precipitation coarsening rate at 850 °C gave fine-sized strain-induced precipitates that were effective in reducing the recrystallization Avrami exponent after 50 pct of recrystallization. Both solute drag and precipitation pinning effects have been added onto the JMAK model to account the effect of Nb content on recrystallization Avrami exponent for samples with large grain size distributions.

In situ synchrotron diffraction and modeling of non-equilibrium solidification of a MnFeCoNiCu alloy

The solidification mechanism and segregation behavior of laser-melted Mn35Fe5Co20Ni20Cu20 was firstly investigated via in situ synchrotron x-ray diffraction at millisecond temporal resolution. The transient composition evolution of the random solid solution during sequential solidification of dendritic and interdendritic regions complicates the analysis of synchrotron diffraction data via any single conventional tool, such as Rietveld refinement. Therefore, a novel approach combining a hard-sphere approximation model, thermodynamic simulation, thermal expansion measurement and microstructural characterization was developed to assist in a fundamental understanding of the evolution of local composition, lattice parameter, and dendrite volume fraction corresponding to the diffraction data. This methodology yields self-consistent results across different methods. Via this approach, four distinct stages were identified, including: (I) FCC dendrite solidification, (II) solidification of FCC interdendritic region, (III) solid-state interdiffusion and (IV) final cooling with marginal diffusion. It was found out that in Stage I, Cu and Mn were rejected into liquid as Mn35Fe5Co20Ni20Cu20 solidified dendritically. During Stage II, the lattice parameter disparity between dendrite and interdendritic region escalated as Cu and Mn continued segregating into the interdendritic region. After complete solidification, during Stage III, the lattice parameter disparity gradually decreases, demonstrating a degree of composition homogenization. The volume fraction of dendrites slightly grew from 58.3 to 65.5%, based on the evolving composition profile across a dendrite/interdendritic interface in diffusion calculations. Postmortem metallography further confirmed that dendrites have a volume fraction of 64.7% ± 5.3% in the final microstructure.

Characteristic stepwise strain hardening behaviour induced by slip and twinning of large-deformed copper single crystals: crystal plasticity modelling and simulation

ABSTRACT The micromechanism-based stepwise strain hardening behaviour of copper single crystals significantly depends on the competition and collaboration between dislocation slip and deformation twinning. A crystal plasticity-based model of the strain hardening characteristics associated with slip and twinning interactions is proposed that focuses on modelling the stepwise strain hardening behaviour. An accumulated twin volume fraction is incorporated into the evolution of slip resistance to model slip–twinning (S-T) interactions at small strains. Then, the following stress fluctuation stage caused by the crystal reorientation is related to the twinning–twinning (T-T) interactions. Upon deformation to a large strain, a saturated hardening law including the slip–slip (S-S) interactions in the twinned region and the accumulated slip are presented. The effects of the initial crystal orientation and twinning on distinguished hardening stages are investigated. The stepwise strain hardening model reveals the dominating hardening mechanism at the initial hardening stage, which has been identified for orientation-dependent copper single crystals by investigating the slip and twinning increments. The stress fluctuation of a copper single crystal with a particular grain orientation can be described by introducing the evolution of the twin volume fraction and its saturation value, which allows an in-depth understanding of the evolution of large plastic deformation.

Shock structure for the seven-equation, two-phase continuum-mixture model

Continuum models of two-phase flow have been employed to investigate a wide variety of physical phenomena, ranging from bubbly-gas and solid-loaded liquid flows to detonation waves in granular explosives. The set of governing equations consists of mass, momentum and energy balance for each phase, and an equation for the evolution of volume fraction of either phase. The set is closed by providing an equation of state for each phase and by specifying the inter-phase interaction terms. Examination of the time scales associated with the interaction terms shows that in many regions of the flow, the pressures and velocities equilibrate rapidly, which has led to the development of a single-pressure and single-velocity reduced, 5-equation model. Such a reduction is incomplete in that it omits thin shock-like regions (inner layers) where pressure and velocity changes can remain. To regularise the reduced model, a number of studies have added dissipative terms which smoothen and thereby resolve these thin shock-like regions. However, the sensitivity of the solution to the choice of regularisation has not been investigated. Further, although the 5-equation model has been used extensively in the literature for numerical computations, its regularisation is often left to the numerical method employed. This study carries out a systematic analysis of the structure of this thin shock-like inner layer, with emphasis on the dependence of the structure of the layer and of the jumps across it on system parameters. The results are compared with those obtained via computations with the parent, 7-equation model.

Evolution of Shape and Volume Fraction of Superconducting Domains with Temperature and Anion Disorder in (TMTSF)2ClO4

In highly anisotropic organic superconductor (TMTSF)2ClO4, superconducting (SC) phase coexists with metallic and spin-density wave phases in the form of domains. Using the Maxwell-Garnett approximation (MGA), we calculate the volume ratio and estimate the shape of these embedded SC domains from resistivity data at various temperature and anion disorder, controlled by the cooling rate or annealing time of (TMTSF)2ClO4 samples. We found that the variation of cooling rate and of annealing time affect differently the shape of SC domains. In all cases the SC domains have oblate shape, being the shortest along the interlayer z-axis. This contradicts the widely assumed filamentary superconductivity along the z-axis, used to explain the anisotropic superconductivity onset. We show that anisotropic resistivity drop at the SC onset can be described by the analytical MGA theory with anisotropic background resistance, while the anisotropic Tc can be explained by considering a finite size and flat shape of the samples. Due to a flat/needle sample shape, the probability of percolation via SC domains is the highest along the shortest sample dimension (z-axis), and the lowest along the sample length (x-axis). Our theory can be applied to other heterogeneous superconductors, where the size d of SC domains is much larger than the SC coherence length ξ, e.g., cuprates, iron-based or organic superconductors. It is also applicable when the spin/charge-density wave domains are embedded inside a metallic background, or vice versa.