Volume Fraction Of Second Phase Research Articles

A model for the initiation of dynamic recrystallization in two-phase materials

Abstract A material model is presented for the prediction of the initiation of dynamic recrystallization in two-phase materials in which the second phase does not deform. Initiation is based on the criterion of Poliak and Jonas in which both energy and kinetic conditions are considered. The criterion is generalized for multiaxial stress states, and coupled with elastic-viscoplastic constitutive equations for high-temperature rate-sensitive materials undergoing strain hardening, dynamic recovery and strain softening due to dynamic recrystallization. The model is embodied within a finite-deformation finiteelement code. Micromechanical finite-element cells are then developed to model two-phase materials, and the dependence of the initiation of dynamic recrystallization on the second-phase volume fraction, shape and distribution is investigated. Stress-state dependence is also examined. Increasing volume fraction of the second phase is found to lead to considerably enhanced hardening at low strains but. at higher strains, dynamic softening reduces the steady-state flow stress approximately to that of the corresponding single-phase material. The steady-state flow stress is predicted to be largely independent of second-phase volume fraction. This is in agreement with experiments. The model correctly predicts the experimental trend of earlier initiation of dynamic recrystallization with increasing second-phase volume fraction, together with the sites of initiation in two-phase materials. Particle-matrix interfaces can act as preferential sites for initiation but, in a material with a randomly distributed second phase, the initiation is favoured in areas of particle clustering and can occur close to, but not necessarily at, particle-matrix interfaces. It is shown that the model predictions are entirely consistent with Avrami kinetics. For a uniform distribution of second-phase particles in a two-phase material, an Avrami exponent of 3.29 is predicted. For a random distribution, the Avrami exponent is predicted to be 3.01. Particle shape was found to influence the initiation of dynamic recrystallization. In addition, initiation was found to be delayed as the macroscopic-level stress state changes from one of pure shear to uniaxial stress and to pure hydrostatic pressure.

A model for the initiation of dynamic recrystallization in two-phase materials

Abstract A material model is presented for the prediction of the initiation of dynamic recrystallization in two-phase materials in which the second phase does not deform. Initiation is based on the criterion of Poliak and Jonas in which both energy and kinetic conditions are considered. The criterion is generalized for multiaxial stress states, and coupled with elastic-viscoplastic constitutive equations for high-temperature rate-sensitive materials undergoing strain hardening, dynamic recovery and strain softening due to dynamic recrystallization. The model is embodied within a finite-deformation finiteelement code. Micromechanical finite-element cells are then developed to model two-phase materials, and the dependence of the initiation of dynamic recrystallization on the second-phase volume fraction, shape and distribution is investigated. Stress-state dependence is also examined. Increasing volume fraction of the second phase is found to lead to considerably enhanced hardening at low strains but. at hi...

Microstructure and tribological properties of alumina ceramic with laser-dispersed tungsten additions

The surface of slightly porous, commercially available alumina ceramic was laser-modified with tungsten and/or zirconia additions. The thickness of the resulting multiphase surface layers ranged from 300–800 μm depending on the chemical composition and the parameters of the laser process used. Microstructure and worn surfaces were analysed by scanning electron microscopy and energy- dispersive X-ray spectroscopy. Mechanical properties were characterized by using Vickers hardness and nanoindentor testing. Tribological tests were carried out on the surface-modified ceramics using a ball-on-block tribometer. All tests were conducted in unlubricated oscillating sliding contact against balls of alumina in laboratory air at room temperature, relative humidities varying between 3% and 80%, and in distilled water. The multiphase surface layers showed a total volume fraction of second phases up to 40 vol% embedded in the alumina matrix, whereas the average size of the alumina grains was substantially reduced compared with the substrate ceramic. Tungsten dispersoids were distributed homogenously in the ceramic matrix and eutectic Al2O3–ZrO2 phase occurred along the boundaries of the alumina crystallites. Mechanical and tribological properties varied as a function of the microstructure of the laser-modified ceramics, i.e. type and volume fraction of the second phases, and both friction and wear were substantially reduced compared with the commercially available monolithic alumina ceramic used for reference. Friction coefficient and amount of linear wear of the ceramics decreased with increasing relative humidity of the surrounding air. © 1998 Kluwer Academic Publishers

Numerical Simulation of Zener Pinning with Growing Second‐Phase Particles

The Zener pinning effect with growing second‐phase particles in Al2O3‐ZrO2 composite systems were studied by two‐dimensional (2‐D) computer simulations using a diffuse‐interface field model. In these systems, all second‐phase particles are distributed at grain corners and boundaries. The second‐phase particles grow continuously, and the motion of grain boundaries of the matrix phase is pinned by the second‐phase particles which coarsen through the Ostwald ripening mechanism, i.e., long‐range diffusion. It is shown that both matrix grains and second‐phase particles grow following the power‐growth law, Rtm ‐ R0m = kt with m = 3. It is found that the mean size of the matrix phase (D) depends linearly on the mean size of the second‐phase particles (r) for all volume fractions of second phase from 10% to 40%, which agrees well with experimental results. It is shown that D/r is proportional to the volume fraction of the second phase (f) as f−1/2 for a volume fraction less than 30%, which agrees with Hillert and Srolovitz's predictions for 2‐D systems, while experimental results from 2‐D cross sections of three‐dimensional (3‐D) Al2O3‐rich systems showed that either a f−1/2 or a f−1/3 relation might be possible. It is also found that D/r is not proportional to f−1/3 and f−1 in 2‐D simulations, which suggests that the Zener pinning effect can be very different in 2‐D and 3‐D systems.

Examination of some high-strength, high-conductivity copper alloys for high-temperature applications

Copper alloys with high strength and high thermal and electrical conductivity have received a lot of attention over the last decades. Most of such efforts have concentrated on the development of alloys containing fine, dispersed particles, and using rapid solidification techniques to ensure a sufficient volume fraction and sufficient fineness of the dispersed phase. In a recent study, a Cu-8Cr-4Nb alloy was developed which shows relatively good strength up to 700 C, a result which was explained by the resistance to coarsening of the fine Cr{sub 2}Nb intermetallic particles in this materials. The amount of intermetallic Cr{sub 2}Nb second phase in this alloy was about 14vol% and it was claimed that the special compound-nature of the intermetallic phase was responsible for the good stability and retention of strength to high temperature. In order to examine the influence of the nature of the fine particles present and their stability against coarsening, as well as to examine the influence of volume fraction of second phase on tensile strength, three different alloys have been chosen for study: Cu-2Nb and Cu-4Cr for examining the role of second phase chemistry (Nb or Cr) on structural and property stability; and a Cu-14Cr alloy, for comparison with more » the Cu-4Cr alloy, to examine the role of volume fraction of the second phase. The stability of these alloys will then be compared with that reported for the Cu-8Cr-4Nb alloy. « less

Processing of MoSi2-based intermetallics

Abstract The influence of processing on the microstructure and properties of MoSi 2 and the adjacent hexagonal ternary compounds Mo(Si,Al) 2 and Mo 5 Si 3 C has been investigated. Since powder processing is clearly the preferred processing method for these compounds, it is important to realize that the oxides present on the starting powder surfaces (i.e. silica on the silicon and silicide powders) will be incorporated into the compacted samples unless special care is taken to remove them prior to and/or during consolidation. For binary MoSi 2 , the reduction of silica has been accomplished using carbon additions, to produce SiC and gaseous CO/CO 2 mixtures, or aluminum additions to produce alumina particles. For the Mo 5 Si 3 C studies, it is clear that the relatively large ternary phase field on previously published phase diagrams is in error and that this phase is closer to a line compound, making the production of single phase material difficult. In the case of the aluminum-modified MoSi 2 , aluminum additions beyond the solubility limit leads to the formation of the hexagonal C40 structure, which undergoes an unusual environmental degradation at near-ambient temperatures. In attempting to determine the mechanism of this degradation, it was noted that there are also significant inconsistencies in the published ternary Mo–Si–Al diagram. Finally, the relative importance of such variables as crystal structure, silica content, nature, size and volume fraction of second phase and matrix grain size on the high temperature properties of these silicides is described and compared with previous studies of MoSi 2 in order to clarify some of the confusion that has existed in the literature dealing with the mechanical behavior of MoSi 2 and its composites.

Deformation of microstructures containing a glassy phase

Viscous deformation of Si 3N 4 containing a variable amount of a Y 2O 3-SiO 2 glass was measured using a beam-bending viscometer. The viscosity of the glassy phase, which does not form a bulk glass and, thus, cannot be measured by conventional techniques, was estimated using the results of viscosity measurements on a model system. Viscosity measurements over a range of 10 8–10 11 Pa s on a model system, Corning 7761, a potassia borosilicate glass, with 0–50 vol.%, −325 mesh Al 2O 3 were also made. The addition of 50 vol.% Al 2O 3 increased the viscosity by a factor of 8000. The viscosity data were analyzed in terms of accepted models and empirical equations based upon power law and exponential functions of the volume fraction of second phase, . There was, however, no satisfactory agreement.

Advances in the development of silver sheathed (Bi,Pb)2223 composite conductors

Significant advances have been made in the critical current density of the technologically interesting (Bi,Pb)2223 composite conductors. Engineering current density, J/sub e/, of 9100 A/cm/sup 2/, corresponding to a filament current density, J/sub c/, of 32600 A/cm/sup 2/ (77 K, self-field) has been achieved by increasing the fraction of oxide in the conductor and improving the thermomechanical processing of the conductor. The filament microstructure may be further optimized by decreasing the volume fraction of secondary phases and porosity. The strain tolerance of the higher oxide fraction conductors remains adequate for applications by increasing the number of filaments in the conductors. Composite tapes with twisted filaments have been produced that have promising electrical properties in applied magnetic fields.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transient Ostwald ripening in systems with a concentration dependent diffusivity. II. Non-zero volume fractions

A particle growth rate is derived for coarsening systems with a small volume fraction of second phase in which the diffusion coefficient varies linearly with composition. With the growth rate incorporated into a previously published numerical code, the time evolution of the average particle radius, the number density of precipitates and the scaled particle size distribution has been monitored for various final volume fractions. The results suggest that the effects of a concentration dependent diffusivity are more pronounced at lower volume fractions.

The concept of effective hardness in the abrasion of coarse two-phase materials with hard second-phase particles

During the abrasion of a coarse two-phase material which contains hard second-phase particles, a brittleness mechanism can frequently coexist with plastic grooving. By taking R(X) as the abrasion resistance of given material with X as its second-phase volume fraction, the concept of effective hardness, Heff, gives rise to a modification of the linear rule of mixtures as R(X) ∫ (1-X)Hm + αXHs, where Hm and Hs are the hardness of pure matrix material and pure second phase, respectively. The parameter α decreases with increasing severity of the brittleness effect. By defining αc=Hm/Hs, dR/dX<0 provided that α<αc. The SiC abrasion data of a series of Al-Si alloys (with the volume fractions of pro-eutectic Si particles ranging from 0.023 to 0.219) can be rationalized by the above model since R(X) shows a nice linear fit with X. The αc value of the test alloys is close to zero. Therefore, as indicated from the wear surface, extensive brittle fracture can occur without deteriorating the abrasion resistance. For those with dR/dX<0, subsurface fracture is also pronounced.

Elastic Properties of Two‐Phase Composites

Simple expressions were derived to predict the elastic properties of two‐phase systems containing discontinuous reinforcements, on the basis of approximation of composite microstructure to a unit cell incorporating isostrain and isostress type elements, arranged in two different ways. The bounds on elastic modulus obtained in this manner have been shown to accurately describe the variation of elastic modulus as a function of volume fraction of one of the phases, for a wide variety of two‐phase composites. The present expressions offer predictions of elastic modulus that are much closer to experimental data than the commonly used Hashin and Shtrikman bounds, particularly for composites with constituents having large differences in elastic moduli. Similarly, it has been shown that the shear moduli and the Poisson's ratios of composites as a function of second‐phase volume fraction can also be predicted. the present unit‐cell‐based method of calculation presents a promising approach for the prediction of properties of multiphase materials. especially for those consisting of more than two dissimilar phases.

Microstructural characterisation and mechanical properties of Ni–Ge alloys containing Ni3Ge

Six Ni–Ge alloys were prepared and equilibrated at 1000°C. The microstructures, compositions of phases, solubilities in various phases, volume fractions of phases, lattice parameters of Ni3 Ge, and microhardness values of phases were determined. Two alloys contained Ni3Ge and α, one alloy was single phase Ni3Ge, and three alloys contained Ni3Ge and Ni5Ge3. The volume fractions of second phase were 6 and 33%α and 37 and 54%Ni5Ge3. The amount of second phase in the third Ni3Ge–Ni5Ge3 alloy was too low to be determined accurately. The two phase alloys containing 6%α, 37%Ni5Ge3, or 54%Ni5Ge3 were tested in compression. A yield strength maximum was observed in the three alloys. The deformation behaviour of the alloy containing 6%α was similar to that of single phase Ni3Ge: crack formation along Ni3Ge grain boundaries and very low plastic strain were revealed. In alloys containing Ni3Ge and an appreciable percentage of Ni5Ge3, crack formation was not observed along Ni3Ge grain boundaries. Instead, at low temperatures, deformation and crack growth occurred within Ni5Ge3 grains and, at high temperatures, decohesion occurred along the Ni3Ge/Ni5Ge3 interphase. The plastic strain in the alloy containing 54%Ni5Ge3 increased to about 40%.MST/1724

On the actual contribution of crack deflection in toughening platelet-reinforced brittle-matrix composites

The effectiveness of crack deflection as a single toughening mechanism is evaluated in the case of brittle-matrix reinforced by high aspect-ratio platelets. Microstructural parameters characterizing size, morphology, orientation and distribution of the second phase including aspect ratio, volume fraction and interparticle distance, were experimentally obtained by means of image analysis techniques on a model composite. Introducing “true” microstructural parameters in the fracture mechanics formulation of the strain energy release rate for a deflected crack, it is demonstrated that no appreciable toughening can be obtained due to the geometrical local misalignment of the crack front even in the case of increasing aspect-ratio or volume fraction of second phase. It is concluded that crack deflection processes may play an important role only as precursors for other operative mechanisms, being, in the general case, the deflection of the crack path only phenomenologically related to toughening.

Computer Simulation of Microstructural Evolution in Thermomechanical Processing of Steel Plates.

The computer simulation model of microstructural evolution on the basis of chemical thermodynamics and classical nucleation and growth theory has been developed. The metallurgical phenomena in thermomechanical treatment of steel, such as austenite grain growth, recrystallization and growth, carbonitride precipitation and austenite to ferrite phase transformation can be predicted by the model. The influences of steel chemistry and thermomechanical condition on the transformed microstructure of 0.10C-1.5Mn-0.35Nb steel (high C-high Mn steel) and 0.06C-1.25Mn-0.035Nb steel (low C-low Mn steel) are evaluated by computer simulation. With the increase of C and/or Mn concentrations, the volume fraction of second phase increases and the ferrite grain size is refined C-high Mn steel, the transformed microstructure consists of ferrite and pearlite phases at lower cooling rates and/or larger effective austenite interfacial area per unit volume, SV. The volume fraction of second phase increases with the increase of cooling rate and/or the decrease of SV value. The second phase of the steel at higher cooling rates is bainite. The transformed microstructure of low C-low Mn steel consists of ferrite and bainite phases. The influences of the rolling condition and the cooling rate on the transformed microstructure are smaller in low C-low Mn steel. However, the transformed microstructures is apparently influenced by the start temperature of accelerated cooling.

Role of residual stress field interaction in strengthening of particulate-reinforced composites

A quantitative analysis was conducted on the effect of residual thermoelastic stress concentrations on the strength of particle-reinforced brittle matrix systems. The analysis is derived from the stress intensity factor for a periodic array of coplanar cracks emanating from the matrix-particle interface. It is shown that the major drop in strength occurs at smaller volume fractions of second phase where the residual stress field interaction effects are minimal. The effect of volume fraction on strength becomes important at larger volume fractions (normally above 10–15%). The theory is compared with experimental measurements of strength for glass and alumina matrix composites as a function of the particle volume fraction, its size, and thermal mismatch Δα.

Development of structure and porosity in cast Al5CuZr2 and Al66Mn9Zr25 intermetallic compounds

Arc melting and three various modifications of induction melting were used to fabricate Al5CuZr2 and Al66Mn9Zr25 (at. pct) intermetallic alloys. The alloys were also homogenized and hot isostatic pressed (hipped). Their microstructure, with special emphasis on changes in the volume fraction of porosity and second phase, was investigated by optical and scanning electron microscopy (SEM) and quantitative dispersive spectroscopy. In specimens induction melted by method 2, the porosity increase in Al5CuZr2 after homogenization is approximately proportional to the reduction in the volume fraction of second phase. This behavior is not observed in Al66Mn2Zr25 alloy. The increase in porosity after homogenization in Al66Mn9Zr25, induction melted by method 3, with stoichiometric matrix is only one third of that observed in the off-stoichiometric matrix alloy at the same homogenization time.

Effect of composition on critical (cold working) strain and recrystallised grain size of dilute Al–Fe alloys

Abstract Low strain cold deformation and annealing techniques have been applied to establish the effects of composition and heat treatment variables on the recrystallisation behaviour of Al–Fe alloys. The parameters controlling the critical strain required to initiate recrystallisation and the grain size produced by subsequent recrystallisation annealing have been established to be the volume fraction of secondary phases, the eutectic colony size in both as cast and processed material, matrix composition, the initial grain size preceding final cold deformation, the amount of deformation before annealing, and the final annealing temperature. The results derived from the application of the strain annealing test showed that increasing the volume fraction of secondary precipitate phases, the homogenisation and final annealing temperatures, or the eutectic colony size, decreases the critical strain and increases the maximum grain size produced after annealing, but increasing the initial grain size has opposite...

Effect of composition on critical (cold working) strain and recrystallised grain size of dilute Al–Fe alloys

Low strain cold deformation and annealing techniques have been applied to establish the effects of composition and heat treatment variables on the recrystallisation behaviour of Al–Fe alloys. The parameters controlling the critical strain required to initiate recrystallisation and the grain size produced by subsequent recrystallisation annealing have been established to be the volume fraction of secondary phases, the eutectic colony size in both as cast and processed material, matrix composition, the initial grain size preceding final cold deformation, the amount of deformation before annealing, and the final annealing temperature. The results derived from the application of the strain annealing test showed that increasing the volume fraction of secondary precipitate phases, the homogenisation and final annealing temperatures, or the eutectic colony size, decreases the critical strain and increases the maximum grain size produced after annealing, but increasing the initial grain size has opposite effects on these parameters.MST/1348

A new theoretical description for anomalous birefringence of phase-separated glasses

Theoretical relationships between anomalous birefringence and microstructure of phase-separated glasses are proposed based on light scattering by particles and self-consistent effective-medium theory. A phase-separated and stretched glass generally has positive anomalous birefringence because the positive birefringence produced by form anisotropy of the secondary phase particles is larger than the negative birefringence produced by the distribution anisotropy of the particles. A postpulling heat-treated glass has negative birefringence because the form anisotropy decays and the distribution anisotropy remains. The magnitude of the anomalous birefringence increasesin particle size, particle size distribution variance, volume fraction of secondary phase, and uniaxial load. Results obtained by the theoretical model are consistent with available experimental results.

Development of in-situ second phase pinning structure in niobium-titanium based superconducting alloys

A niobium-based superconducting alloy which has a rare-earth second phase that segregates between the matrix dendrites during solidification has been developed. The second phase can be refined by conventional deformation without heat treatment so as to form an in-situ fiber network. In such an alloy, one has independent control of the second-phase volume fraction as well as the matrix composition. The development of the in-situ alloy along with early microstructural and critical current results on the first wires are reported. The in-situ second phase was found to be about 2- mu m thick and 8- mu m apart in a conventionally solidified 35Nb-50Ti-15Y alloy. This size and spacing are suitable for producing a flux line lattice (FLL) pinning morphology in the strain available in conventional conductor processing. The properties of the test alloy are shown to be satisfactory with respect to easy melting, high ductility, and nondegraded superconducting properties.