Volume Fraction Of Second Phase Research Articles

Unveiling the Microstructural Features during Compression of a High-Modulus Mg-15Gd-8Y-6Al-0.3Mn Alloy Reinforced by a Large Volume of Al2RE Phases

Magnesium alloys with a high volume fraction of secondary phases exhibit inferior formability. Therefore, investigating their thermal deformation characteristics is critical for optimizing thermal processing techniques. In this work, isothermal compression experiments were performed on a Mg-15Gd-8Y-6Al-0.3Mn alloy with an elastic modulus of 51.3 GPa with a substantial volume of aluminum-rare earth (Al2RE) phases. The rheological behavior and microstructural evolution of the material were systematically investigated at varying temperatures (350–500 °C) and strain rates (0.001–1.000 s−1). The calculated thermal processing diagram indicates that the unstable region gradually enlarges with increased strain, and all unstable regions appear within the high-strain-rate, low-temperature domain. The ideal thermal processing range of the alloy is 350–500 °C at strain rates ranging from 0.001 to 0.016 s−1. Particle-stimulated nucleation and discontinuous dynamic recrystallization are both verified to be responsible for the recrystallized microstructure of the alloy. The recrystallized grains exhibit a relatively random crystallographic orientation. As recrystallization proceeds, the texture gradually transitions from a typical [0001] texture in the compression direction to a random texture accompanied by decreased texture intensity. This work sheds new light on the thermo-mechanical processing of high-modulus Mg alloys, which could help design suitable processing techniques for related materials.

Microstructure and mechanical properties of 7075 aluminum alloy welds by gas tungsten arc welding with trailing ultrasonic rotating extrusion

In this investigation, gas tungsten arc welding (GTAW) and gas tungsten arc welding with trailing ultrasonic rotating extrusion (U-RE-GTAW) were applied to 7075 aluminum alloys. Qualitative comparisons and analyses were carried out to investigate the effects of the ultrasonic rotary extrusion-assisted technology on GTAW processes. The weld joints fabricated by GTAW and U-RE-GTAW were examined using X-ray diffraction (XRD), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM) techniques. Concurrently, the tensile strength and fatigue characteristics were assessed at ambient temperature. The experimental outcomes indicated that the U-RE-GTAW process mitigated porosity within the weld region and substantially augmented dislocation density, while concurrently achieving a notable reduction in grain size and an increase in the volume fraction of secondary phases due to the synergistic effects of ultrasonic oscillation and rotational extrusion. The enhancement in tensile and fatigue resistance of the welded joint was attributed to the strengthening mechanisms associated with these microstructural alterations. Specifically, the ultimate tensile strength exhibited a 20.4% increase, and the elongation at break was elevated by 46.3%. At stress amplitudes of 190 MPa, 160 MPa, and 100 MPa, the fatigue strength of the welded joints was enhanced by 67%, 55%, and 32%, respectively. A quantitative analysis was conducted to elucidate the impact of diverse strengthening mechanisms on the welded joints. It was concluded that dislocation strengthening is the predominant factor contributing to the superior performance of the U-RE-GTAW specimens.

Microstructure evolution and mechanical properties of a cast and heat-treated Al–Li–Cu–Mg alloy: Effect of cooling rate during casting

As a kind of cast aluminum alloy with high strength, Al–Li–Cu–Mg series alloys exhibit desirable stiffness and formability, while a limited investigation has discussed the influence of cooling rate on microstructure and mechanical properties of these alloys. In this work, the effect of cooling rate during casting on microstructure evolution and mechanical properties of cast Al–2Li–2Cu-0.5Mg-0.15Sc-0.1Zr-0.1Ti alloy was investigated using a step-like iron mold. The results showed that the increased cooling rate refined the grain size and augmented the volume fraction of second phase in the as-cast microstructure. In the aging process, the rapid cooling rate markedly promotes precipitation and suppresses coarsening of the δˊ(Al3Li), T1(Al2CuLi) and Sˊ(Al2CuMg) phases, which plays a vital role in enhancing strength of the peak-aged alloy. In addition to diffusion and vacancy mechanisms, a Li-rich zone offers a new precipitation pathway for T1 precipitates. Notably, the rapid cooling rate of 16.1 °C/s significantly facilitated the formation and inhomogeneous distribution of the cubic σ(Al6Cu5Mg2) phase, which competed with the T1 and Sˊ phases for Cu and Mg atoms. Finally, the formation mechanism of the σ phase under different cooling rates was discussed, and the strengthening and fracture mechanisms were quantified. The present work is expected to enlighten the understanding of the microstructure evolution of Al–Li alloys with varied cast cooling rates.

Influence of cooling rate on the microstructure and mechanical properties of Al–Cu–Li–Mg–Zn alloy

This work investigated the influence of cooling rate (0.04, 0.87, 15.2 and 156.2 K/s) on the microstructure and compressive properties of Al–4Cu–3Li-0.7 Mg–1Zn alloys fabricated by several casting molds. The experiment results revealed that the microstructure cooled at low cooling rates of 0.04, 0.87 and 15.2 K/s is composed of α-Al, α(Al)+T2, θ (Al2Cu), T1 phases and core-shell configuration (Al13Fe4/Al7Cu2Fe phase). This core-shell structure is observed for the first time in an Al–Cu–Li alloy. However, T1 and core-shell configuration vanish at the high cooling rate of 156.2 K/s due to the insufficient diffusion time of Cu, Li and Fe elements. As the cooling rate increases, the average secondary dendrite arm spacing (SDAS) decreases significantly from 110.3 to 7.5 μm and the relationship between SDAS and cooling rate has been established. The average diameter/thickness of the α(Al)+T2, Al2Cu and Al13Fe4/Al7Cu2Fe phases decreases dramatically from 16.9 to 1.0 μm, 8.1 to 0.8 μm and 7.5 to 0.7 μm with the increase of cooling rate, respectively. Fine spherical Al13Fe4/Al7Cu2Fe and Al2Cu phases are beneficial to the improvement of comprehensive compressive properties. Additionally, the solute concentration in the matrix decreases, while the hot-tear resistance and volume fraction of secondary phases increase with increasing cooling rate. The empirical equations are established between (compressive properties, SDAS) and cooling rate. The fracture failure is responsible for the initial hot tearing at low cooling rates, the α(Al)+T2 or Al2Cu or Al13Fe4/Al7Cu2Fe phases at the moderate cooling rate, and the α(Al)+T2 phase at the high cooling rate.

Microstructure evolution and corrosion resistance of high-pressure rheo-cast Mg–Zn–Y alloy containing quasicrystal

The effects of high pressure applied during rheo-squeeze casting (RSC) process on the microstructure evolution and corrosion resistance of Mg90.8Zn8.6Y0.6 alloy were investigated. The results reveal that with the increase of pressure, both the average size of α-Mg grains and the lamellar spacing of in-situ formed quasicrystal phase (I–Mg3Zn6Y) are continuously decreased. Meanwhile, the high-pressure results in the increase in the supersaturation of Zn in matrix, the decrease in volume fraction of second phases and the disappearance of Mg7Zn3 phase. The high-pressure contributed to the improvement of corrosion resistance, and the corrosion process was changed from three stages (galvanic corrosion, filiform corrosion and pitting corrosion) to two stages (galvanic corrosion and pitting corrosion), which was mainly attributed to the supersaturation of Zn in matrix, the continuous distribution of finer I-phase and the disappearance of Mg7Zn3.

The microstructural features and strengthening mechanisms of Mg-Al-Zn-Ca-(RE) extruded alloys having high-volume fractions of second-phase particles

The microstructures and tensile properties of Mg-4∼6Al-2∼4Zn-2∼3Ca-0∼1RE (in wt.%) extruded alloys have been investigated. C15 and C36 Laves phases, Ca2Mg6Zn3, Al2REZn2, and Al11RE3 phases were formed as networks during solidification in different alloys. After extrusion, coarse dendritic were significantly refined due to dynamic recrystallization, second phases were fragmented into pieces arranged as stripes, and typical basal fiber texture {0002} <10-10> with the extrusive direction paralleled to (0001) were formed in all studied alloys. Laves phase particles were prone to be crushed into nanoparticles, which appeared more easily to hinder the recrystallized grain growth and could bring about more than 30 vol % ultra-fine grains after extrusion. During extrusion, twinning-induced dynamic recrystallization occurred at first, and both discontinuous and continuous dynamic recrystallization dominated the microstructural evolution. The volume fraction of second phases had critical roles in recrystallization process, and a nearly complete recrystallization degree could be obtained in alloys containing more than 9 vol% second phases. The strengthening mechanisms were evaluated based on classic strengthening models, which agreed well with the experimental results. It was found that grain boundary strengthening, second phase strengthening, and texture strengthening contributed around 60%, 30%, and 10%, respectively, to yield strengthening, except for Mg-4Al-4Zn-2Ca alloy because of the high percentage of unrecrystallized region. Moreover, the overestimate of second phase strengthening happened in alloys having more than 9 vol% second phases, which revealed that too many second phases had limited influence on microstructures and the resulting mechanical properties.

The effect of Gd on the microstructure evolution and mechanical properties of Mg-4Zn-0.6Ca alloy

In this work, the effect of Gd on the microstructure evolution and mechanical properties of Mg–4Zn–0.6Ca–xGd (x = 0, 0.3, 0.6 and 1, wt%) alloys were investigated systematically. The results show that Mg-4Zn-0.6Ca alloy was composed of α-Mg, Mg7Zn3 and Ca2Mg6Zn3 phase. The W-phase (Mg3Zn3Gd2) was synthesized after addition of Gd. The dynamic recrystallization was restrained and the average grain size decreased after 0.6 wt% Gd addition, causing the increase of unrecrystallized region. In addition, the volume fraction of second phase increased with increasing Gd content up to 1 wt%, and the effect of particles stimulated nucleation (PSN) was enhanced, resulting in a decrease in unrecrystallized region. The addition of Gd promoted the occurrence of the overall texture split and TD-split texture component, causing decreased basal texture intensity. An optimal mechanical property of Mg–4Zn–0.6Ca–1Gd alloy, with the yield and ultimate tensile strength of 240 MPa and 297 MPa, respectively, was achieved. The values were increased by 82 MPa and 37 MPa, respectively, compared with that of Mg–4Zn–0.6Ca alloy. In initial deformation stage, strain-hardening rate of alloys decreased with increase of Gd content. Mg-4Zn-0.6Ca-0.6Gd alloy possessed the lowest strain-hardening rate because of fine grain size. However, strain-hardening rate was increased when Gd content was increased to 1 wt%, which may be related to decreased texture intensity and presence of many second phases. This work reveals the effect of co-addition of minor Ca and Gd on the microstructure evolution and mechanical properties of Mg-Zn alloys, which provides theoretical basis for the development of high strength Mg alloy.

Interfacial-dominated torque response in liquid–liquid Taylor–Couette flows

Immiscible and incompressible liquid–liquid flows are considered in a Taylor–Couette geometry and analysed by direct numerical simulations coupled with the volume-of-fluid method and a continuum surface force model. The system Reynolds number $Re \equiv r_i \omega _i d / \nu$ is fixed to $960$ , where the single-phase flow is in the steady Taylor vortex regime, whereas the secondary-phase volume fraction $\varphi$ and the system Weber number $We \equiv \rho r_i^2 \omega _i^2 d / \sigma$ are varied to study the interactions between the interface and the Taylor vortices. We show that different Weber numbers lead to two distinctive flow regimes, namely an advection-dominated regime and an interface-dominated regime. When $We$ is high, the interface is easily deformed because of its low surface tension. The flow patterns are then similar to the single-phase flow, and the system is dominated mainly by advection (advection-dominated regime). However, when $We$ is low, the surface tension is so large that stable interfacial structures with sizes comparable to the cylinder gap can exist. The background velocity field is modulated largely by these persistent structures, thus the overall flow dynamics is governed by the interface (interface-dominated regime). The effect of the interface on the global system response is assessed by evaluating the Nusselt number $Nu_{\omega }$ based on the non-dimensional angular velocity transport. It shows non-monotonic trends as functions of the volume fraction $\varphi$ for both low and high $We$ . We explain how these dependencies are closely linked to the velocity and interfacial structures.

Improving mechanical, degradation and biological behavior of biodegradable Mg–2Ag alloy: effects of Y addition and heat treatment

Biodegradable Mg–Ag alloys are promising implants for bone regeneration owing to their ability to decrease inflammation and infection after implantation by the presence of Ag. However, their bioperformance requires further enhancement. In this regard, the effects of 1 wt % Y addition and solid solution heat treatment (T4) on microstructure, biocorrosion behavior, mechanical properties and biological features of a cast Mg–2Ag alloy were studied. Corrosion tests indicated the remarkable role of T4 treatment in promoting corrosion resistance by increasing microstructure homogeneity, reduction of defects and volume fraction of secondary phases as well as eliminating the dendritic microstructure of as-cast Mg–2Ag alloy. The presence of a stable Y-rich corrosion film on the surface of heat-treated Mg–2Ag–1Y alloy could effectively improve the corrosion resistance by inhibiting corrosion propagation. The results of cell culture experiments proved the good cell attachment and proliferation of osteoblast-like cell line MG63 on Mg–2Ag and Mg–2Ag–1Y alloys. Furthermore, the cell attachment and viability were significantly enhanced by the incorporation of Y in the solution state of Mg–2Ag alloy due to the low volume of evolved hydrogen bubbles and superb corrosion resistance.

Controlling microstructure and mechanical properties of Ti-V-Cr-Nb-Ta refractory high entropy alloys through heat treatments

In this study, we have investigated the microstructure and mechanical properties of two refractory high entropy alloys (RHEAs), Ti-V-Cr5-Nb-Ta and Ti-V-Cr-Nb-Ta, in their as-cast and heat-treated conditions. Both alloys show almost single-phase BCC structure, while different size and volume fraction of secondary phases were formed after homogenisation heat treatment. The major secondary phase was indexed as a complex C15 Laves structure with a composition of (Ti, Ta)(V, Cr, Nb)2. The nanoindentation mapping indicates C15 Laves phase is very hard and brittle, performing a homogenisation heat treatment leads to an improved hardness in both alloys. The correlations between hardness changes and microstructural evolutions after homogenisation heat treatment are also discussed.

Solid state processing of the cantor derived alloy CoCrFeMnNi by oxide reduction

In recent years, high entropy alloys (HEAs), also known has Multi-Principal Element Alloys (MPEAs) have emerged as a new and exciting class of materials. One of the first (and most widely studied) HEA compositions is that of the so-called Cantor alloy, the equimolar CoCrFeNiMn composition. This paper reports on the synthesis of an HEA containing the same metallic elements via reduction of a mixture of the corresponding oxides. High purity precursor powders of Co(OH)2, Cr2O3, Fe2O3, MnO2, and NiO were milled and mixed using standard ceramic processing methods. The green pellets were subjected to a series of isothermal reduction anneals in flowing 3% H2–Ar (which is below the flammability limit), at temperatures ranging from 1000 to 1185 °C, with annealing times from 24 to 120 h. The microstructure and phase evolution of the samples were characterized using SEM, EDS analysis, and XRD. Reduction heat-treatment at 1185 °C resulted in samples developing a core-shell structure, with a dense outer metallic layer, and a core consisting of a mixture of metallic and ceramic phases. Using EPMA (electron microprobe analysis), the composition of the HEA shell was determined to be Co0·25Cr0·19Fe0·25Ni0·23Mn0.08. The hardness of the HEA was measured using Vickers micro-indentation. Examination of the individual indentation sites showed a strong positive correlation between the hardness value and the volume fraction of second phase particles (MnCr2O4, Cr2O3) within the indented area. A comparison between two sub-groups of indentation sites showed an 43% increase in average hardness (211.1 HV versus 148 HV) that was associated with a higher volume fraction of second phase (10.9% versus 2.9%). Consistent with thermodynamic considerations, experiments revealed that when a sample consisting solely of MnO2 was subjected to the same conditions, reduction to metallic Mn did not take place. A model is put forward whereby the free energy change related to the formation of the HEA solid solution provides an additional driving force for the reaction.

Effect of extrusion speed on microstructure and mechanical properties of Mg-Al-Ca-Sn alloy

Low-temperature and high-speed extrusion of wrought magnesium alloy is an urgent problem. Mg-2.5Al-2Ca-1Sn alloys were extruded at 260 °C with different ram speeds (2.0, 4.0 and 6.0 mm s)−1. The effects of extrusion speed on the microstructure and mechanical properties of the alloys were systematically investigated. It’s worth noting that all the three extruded alloys were fully dynamic recrystallized (DRXed). With the increase of extrusion speed from 2 mm s−1 to 6 mm s−1, the DRXed grain size are increased from 1.25 μm to 1.94 μm, average second phase particles are augmented from 0.79 μm to 0.89 μm and the volume fraction of second phase increases from 6.4% to 18.6%. All the three extruded samples show excellent comprehensive mechanical properties because of fine grain size, fully recrystallization and homogeneously dispersed second phase particles. The tensile yield strength (TYS) and ultimate tensile strength (UTS) decreased from 285 MPa, 304 MPa to 217 MPa, 264 MPa while the elongation increased from 11.4% to 20% when the ram speed rose from 2.0 mm s−1 to 6.0 mm s−1.

Variation of Microstructure and Mechanical Properties of ZW61 Magnesium Alloy Solidified under Different Pressures

There is little datum related to microstructure and properties of Mg alloys squeeze-casted with pressure over 200 MPa. In this study, the microstructure and properties of Mg-6Zn-1.4Y (ZW61) alloy solidified under 100MPa to 800MPa were investigated. The results show that a remarkable microstructure refinement and porosity reduction can be reached through solidification under high pressure. The average grain size and the volume fraction of second phase, i.e. quasicrystal I-phase, decrease continuously with the increase of applied pressure. The tensile properties, especially elongation, are obvious enhanced because of the microstructure refinement and castings densification under high pressure. The ultimate tensile strength and elongation of ZW61 alloy in as-cast state are 243 MPa and 18.7% when the applied pressure is 800 MPa, which are increased by 35% and 118% respectively, compared with that of the gravity castings.

The effect of vanadium and nickel on the microstructure and transformation temperatures of Ti50Pt50 alloy

Significant research has been done to produce shape memory alloys that have good shape memory properties and high martensitic transformation temperatures. The Ti50Pt50 alloys have been found to have high transformation temperature of around 1050℃ however, they exhibit negligible shape memory properties. The solid solution strengthening, and improved shape memory properties could be enhanced by ternary alloying. Therefore, this work investigates the effect of varying V and Ni contents, in the range of 6.25 to 12.5at%, on the austenitic and martensitic transformation temperatures, and hardness of the equi-atomic Ti50Pt50 alloy. Arc melting followed by casting and solution heat treatment was carried out to produce the alloys. As-produced alloys were characterized by using scanning electron microscopy, differential scanning calorimetry and hardness testing. The microstructures showed high volume fraction of second phases formed in the TiPtV alloy compared with Ti50Pt50 and TiPtNi alloys. The multiple phases formed in the TiPtV alloys could be the cause of high hardness values observed in these alloys as compared withTi50Pt50 and TiPtNi alloys. Thermal transformation studies revealed that TiPtV alloys exhibit transformation temperature close to Ti50Pt50 alloy, in contrast with TiPtNi alloys. TiPtNi alloys thermal behaviour was improved by solution heat treatment.

Microstructure and corrosion properties of the AISI 904L weld cladding obtained by the electro slag process

The AISI 904L steel is a superaustenitic stainless steel, which presents a good combination of properties like high strength, weldability, and good corrosion resistance. Despite its wide use in several industrial segments, the literature reporting the performance of claddings deposited with this alloy to improve the corrosion performance of equipment is limited. Based on this scenario, this work evaluates the microstructure and corrosion properties of the AISI 904L steel weld cladding obtained by the electroslag welding (ESW) deposited on a carbon steel ASTM A516 Grade 70. Single layer cladding was deposited on 50 × 400 × 400 mm steel plates with average welding energy of 11.7 kJ/mm to obtain the minimum thickness required. After welding, metallographic examination and corrosion tests were performed on samples removed at 1 and 3 mm parallel to the fusion line. Metallographic characterization was performed by optical and scanning electron microscopy. Cyclic polarization tests in 3.5% NaCl solution were performed at the same positions as the metallographic examinations. The results showed that the austenitic microstructure presenting a low volume fraction of secondary phases provided suitable corrosion results for all conditions studied. It evidences that single layer weld overlays obtained with the AISI 904L steel deposited by the ESW process may be considered an adequate alternative for overlay welding with reduced thicknesses because good results were observed at only 1.0 mm from the fusion line, and this could represent a significant cost reduction.

Effects of Y content on microstructures and thermal expansion behavior of Mg-Al-Y alloys

Low thermal expansion alloys play an important role in the applications of high-precision instruments because of their excellent dimensional stability under thermal shock. Hence, the effect of Y content on coefficient of thermal expansion (CTE) of Mg-1Al-xY (x = 4, 6, 8, wt. %) alloys were systematically studied. The results showed that the volume fraction of second phase increased and the grain size of the Mg alloys decreased with the increases of Y content, resulting in the CTE of Mg-1Al-xY alloys decreased with the increases of Y content. The grain size of the Mg-1Al-6Y alloy was more suitable and the second phase distributed uniformly, which lead to the lowest CTE after multiple cycles. The experimental value and model predictions of CTE of alloys differ greatly at lower temperature and coincide well at high temperature. The XRD and EBSD results proved the existence of residual stress in the three alloys, which reduced the CTEs of the magnesium alloy. While the rotation of crystal grains reduces the residual stress in multiple thermal cycles, increasing the CTEs and stability of thermal cycling of Mg alloys. The pole diagram of Mg alloys revealed that number of thermal cycling has a great effect on the intensity of the texture.

Zn-Mg and Zn-Cu alloys for stenting applications: From nanoscale mechanical characterization to in vitro degradation and biocompatibility

In the recent decades, zinc (Zn) and its alloys have been drawing attention as promising candidates for bioresorbable cardiovascular stents due to its degradation rate more suitable than magnesium (Mg) and iron (Fe) alloys. However, its mechanical properties need to be improved in order to meet the criteria for vascular stents. This work investigates the mechanical properties, biodegradability and biocompatibility of Zn-Mg and Zn-Cu alloys in order to determine a proper alloy composition for optimal stent performance. Nanoindentation measurements are performed to characterize the mechanical properties at the nanoscale as a function of the Zn microstructure variations induced by alloying. The biodegradation mechanisms are discussed and correlated to microstructure, mechanical performance and bacterial/cell response. Addition of Mg or Cu alloying elements refined the microstructure of Zn and enhanced yield strength (YS) and ultimate tensile strength (UTS) proportional to the volume fraction of secondary phases. Zn-1Mg showed the higher YS and UTS and better performance in terms of degradation stability in Hanks’ solution. Zn-Cu alloys presented an antibacterial effect for S. aureus controlled by diffusion mechanisms and by contact. Biocompatibility was dependent on the degradation rate and the nature of the corrosion products.

The formation of secondary phase in sub-rapid solidification process of Al-Mg-Si alloys

The formation of secondary phases (Mg2Si and (Si)) in Al-Mg-Si hypoeutectic alloys during the sub-rapid solidification was investigated via the CALPHAD-coupled pseudo-front tracking (PFT) model [Du Q, Jacot A. Acta Mater 2005; 53:3479–93] and V-shaped solidification experiment. The calculated and experimental results show that the amount of secondary phases initially increases and then decreases, as the cooling rate increases. We found from the calculated results that the local equilibrium at liquid-solid interface exhibits two different modes within the range of cooling rate of 0.2–300 K/s. It starts as the Scheil local equilibrium (Scheil-LE) and gradually transforms into a mode like the Non-partition Local Equilibrium (NPLE) encountered in solid-solid phase transformation. The NPLE-like mode at the solid/liquid interface can lead to the decrease of the volume fraction of secondary phases. At lower cooling rate, the solute diffusion in the liquid is more uniform, there is Scheil-LE mode without concentration peak at the front of solid/liquid interface, and the volume fraction of secondary phases increases with the increase of cooling rate. At higher cooling rate, the effect of NPLE-like is more significant and the volume fraction of secondary phases decreases with the increase of cooling rate. The results indicate that the finite diffusion of solute in the liquid plays a key role in solute distribution and formation of secondary phases during the solidification process.

Revisiting the Ostwald Ripening: A Discrete Model Based on Multiple Pairwise Interactions

A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions between precipitates with incoherent interfaces is presented. Although based on the mean field concept, it is a valid alternative to the classical LSW theory. The main differences with respect to the classical approach can be summarized as follows: i) Particles interact the one another; ii) The first Fick’s law is considered to evaluate the fluxes of matter instead of the quasi stationary solution of the concentration field around particles; iii) The rate of matter exchange depends on the average surface-to-surface interparticle distance, a characteristic feature of the system which naturally incorporates the effect of volume fraction of second phase; iv) The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. The model is in excellent agreement with the experimental data available in the literature. The shape of the quasi-stationary 3D particle size distribution of solid-solid and solid-liquid systems is well predicted from volume fractions of 0.07, 0.30, 0.52 and 0.74. Similarly, a very good prediction of the dependence of the kinetic constant of the coarsening process on the volume fraction of precipitates is obtained with reference to literature data on solid-liquid mixtures in the volume fraction range from 0.20 to about 0.75. For volume fractions below about 0.1 the model predicts broad and right-skewed stationary size distributions resembling a lognormal function. Above this value, a transition to sharper, more symmetrical but still right-skewed shapes occurs.

Mathematical Modeling of Plastic Deformation of a Tube from Dispersion-Hardened Aluminum Alloy in an Inhomogeneous Temperature Field

The effect of temperature distribution on a stress–strain state tube made of disperse-hardened aluminum alloy subjected to internal pressure was investigated. The mathematical model is based on equations of physical plasticity theory and principles of mechanics of deformable solids. The results of this investigation demonstrate that varying the outer wall temperature in the range of 200 K at a fixed temperature of the inner wall leads to a significant change in the plastic resistance limit (for the considered tube sizes, this change is approximately 15%). An increase of the tube wall temperature reduces the resistance to plastic deformation. For the same absolute temperature difference between the outer and inner walls, the plastic resistance limit is less for the higher temperature of the inner wall of the tube. A decrease of the distances between the hardening particles at the same volume fraction of second phase leads to a significant increase in the pressure required to achieve plastic deformation of the tube walls. An increase in tube wall temperature reduces the resistance to plastic deformation. For the same absolute temperature difference between the outer and inner walls, the plastic resistance limit is lower for the higher temperature of the inner tube wall. The decrease of the distance between the hardening particles at the same volume fraction of the second phase leads to a significant increase in the pressure required to achieve plastic deformation of the tube walls.