Effect of martensitic transformation in Ti–15 at %V β-phase particles on lamellar boundary decohesion in γ-TiAl Part II Finite element analysis of crack-bridging phenomenon

The commercial finite element package ABAQUS has been used to analyse the crack bridging process by Ti-15 at%V -phase particles dispersed in -TiAl matrix in the presence of particle–matrix decohesion. Both the particle–matrix decohesion potential and the -phase materials constitutive relations are found to have a major effect on the ductility, fracture toughness and failure mode of the – two-phase material. The interface potential is found to primarily affect the distribution of the normal interface strength ahead of the advancing interfacial crack and the mode (gradual versus sudden) of decohesion. The -phase materials constitutive relations are found to influence the location of nucleation of the interfacial cracks and, in turn, the mode of decohesion. A metastable -phase that can plastically deform at low stress levels by undergoing a stress-assisted martensitic transformation, but experience a high rate of strain hardening is found to give rise to the largest levels of ductility and fracture toughness is the – two-phase material. © 1998 Kluwer Academic Publishers     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.     

The influence of ageing on the stability of β-γ/γ′ derived microstructures in Ni-Al-Cr-(Co) alloys

Multiphase Ni-Al-(Fe)-(Cr)-(Co)-based intermetallics with (B2)- (A1)/(L1₂), - or - microstructures can exhibit significant room-temperature tensile ductility. In the case of Ni-Al-Cr-based alloys, microstructural development is complicated by the precipitation of -Cr, which can supplant the -phase during ageing of three-phase -/ microstructures. An investigation of the stability, during ageing, of cast Ni-Al-Cr-(Co) alloys with microstructures derived from -/ is reported. In the as-cast condition, the materials investigated consisted of a dendritic matrix containing L1₀ type martensite and interdendritic /. Extensive intra- and interdendritic -Cr precipitation was also observed. The stability during ageing of the interdendritic / microstructure is also considered and transformation of the L1₀ martensite is examined.     

Precipitation phenomena in the Mg-31 at% Li-1 at% Al alloy

Precipitation phenomena produced in the -phase (b c c) of the Mg-31 at% Li-1 at%Al alloy subjected to different heat treatments have been studied by sensitive single-crystal X-ray diffraction techniques. The variation of the hardness values of specimens quenched and then aged was also examined. It was confirmed that AlLi is a stable phase at room temperature for the examined Al content; AlLi precipitation is only produced for very slow cooling rates from the -field. Phase reactions for specimens quenched and then aged can be summarized as follows: ++ after ageing at room temperature; + ++ AlLi after ageing at 473 K. A considerable increase of the hardness, which attains its maximum value after about 30 h ageing at room temperature, was observed. Neither the -phase nor the AlLi-phase precipitation can account for the observed hardening process. The presence of the -metastable phase when the hardness reaches its maximum value is verified.     

Specific heats of commercial titanium alloys at 50–1100°C

Specific-heat measurements are reported for nine titanium alloys with and + structures; the temperature of the transition has been revised by DTA. A generalized approximating formula for the specific heat has been derived for the temperature range in which the structural state is stable, which contains a dimensionless parameter that includes the temperature of the transformation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 4, pp. 593–598, April, 1980.     

Microstructure and room-temperature mechanical properties of Si3N4 with various α/β phase ratios

After polycrystalline silicon nitride samples with various / phase ratios were fabricated by uniaxial hot-pressing under vacuum, their microstructures, -to- transformations, and grain-growth mechanisms were then characterized by electron microscopy. Room-temperature fracture toughness (KIC) increased with increasing -phase content, and a value of 7.0 ± 0.5 MPa m1/2 was obtained for a sample that contained 60 vol% phase. The increase in KIC is the result of an increase in elongated-grain fractions with increasing content, which promotes energy absorption by crack deflection, as well as by grain debonding, pullout, and bridging mechanisms.     

Distribution of α-AlFeSi and β-AlFeSi particles in surface layer of AA6063 alloy billets after heat treatment

We developed the EPMA mapping method of small -AlFeSi(Al_8.3Fe₂Si) and -AlFeSi(Al_8.9Fe₂Si₂) particles in the billets of Al-Mg-Si alloys such as AA6063 alloys. To discriminate between -AlFeSi and -AlFeSi particles we used the relative X-ray intensities of Fe/Si ratio, the I _Fe/I _Si ratio, instead of the Fe/Si mass ratio. To obtain the I _Fe/I _Si ratio, we used a Monte Carlo method. In this study, using this method the mapping of -AlFeSi and -AlFeSi particles in the surface layer of AA6063 billets after the heat treatment (for 2 h at 580°C) was done. Namely, the distribution of -AlFeSi and -AlFeSi particles of zones from the billet surface to a depth of 800 m was measured. Results showed the zone from the surface to a depth of 200 m was occupied mainly by -AlFeSi particles and the zone from a depth of 200 m toward the center was occupied mainly by -AlFeSi particles. From these results, it was found that if we remove zones from the surface to a depth of 200 m, we can remove the majority of the -AlFeSi particles, and thus improve the quality of anodizing performance of Al-Mg-Si alloys extrusions.     

Influence of Saffman's lift force on the motion of a particle in a Couette layer

The article is concerned with the study of the effect of E. S. Asmolov's corrections to Saffman's lift force for the wall vicinity and a nonzero ratio of Reynolds numbers. It is shown in what way these corrections change the particle paths in a Couette layer and the conditions of deposition.Notation x=X/D, y=Y/D dimensionless longitudinal and transverse coordinates - u=U _p /U , =V _p /U dimensionless projections of particle velocity on the longitudinal and transverse axes - =tU /D dimensionless time - U ²/(18D) Stokes number - = _g / _p , coefficient of the gas kinematic viscosity - particle diameter - /D - _g , _p densities of the gas and particle material - du/d - dv/d - P _s Saffman's force - C coefficient in the formula for Saffman's force - yRe _d ^1/2 - A v _r Re _d ^1/2 - 3.08 - Re V _r / - Re _k ²/)U _g /Y - A Re/Re _k ^1/2 - Re _d U D/ - V _r ((U _g –U _p )²+V _p ² )^1/2 Indices g refers to gas parameters - p refers to the parameters of particles - 0 at the time momentt=0 - S Saffman's force - k Reynolds number based on the velocity gradient - based on velocity - r relative velocity - x projection on thex axis     

Martensitic transformations in Ti-Mo alloys

A detailed investigation has been made of the structure of alloys of the Ti-Mo system containing up to 10wt% Mo, water-quenched from the-phase region. With increase in molybdenum content, the martensite structure changes from hexagonal () to orthorhombic () at 4 wt% Mo, and at 10 wt% Mo, the structure is completely retained . For alloy compositions <4 wt% Mo, there is a diffusional component in the transformation of the -phase at the quench rates employed. There is a transition, with increase in molybdenum content, in morphology (from massive to acicular) and in substructure (from dislocations to twins). However, the transitions in crystallography, morphology and sub-structure are not directly related to one another except for an abrupt loss of dislocation substructure at the/ transition. The to crystallographic transition has the characteristics of a second order transformation, and evidence has been obtained of the existence of a spinodal within the metastable orthorhombic system. The orthorhombic martensites of Ti-6 and 8 wt% Mo decompose during quenching producing a fine modulated structure within the martensite plates, consistent with a proposed spinodal mode of decomposition.     

Effect of crystalline phase, orientation and temperature on the dielectric properties of poly (vinylidene fluoride) (PVDF)

The effect of crystalline phase, uniaxial drawing and temperature on the real () and imaginary () parts of the relative complex permittivity of poly (vinylidene fluoride) (PVDF) was studied in the frequency range between 10² and 10⁶ Hz. Samples containing predominantly and phases, or a mixture of these, were obtained by crystallization from a DMF solution at different temperatures. phase samples were also obtained from melt crystallization and from commercial films supplied by Bemberg Folien. Different molecular orientations were obtained by uniaxial drawing of and phase samples. The results showed that the crystalline phase exerts strong influence on the values of and , indicating that the _a relaxation process, associated with the glass transition of PVDF, is not exclsively related to the amorphous region of the polymer. An interphase region, which maintains the conformational characteristics of the crystalline regions, should influence the process decisively. The molecular orientation increased the values of for both PVDF phases and modified its dependence with temperature over the whole frequency range studied. The influence of the crystallization and molecular orientation conditions on the dc electric conductivity (_dc) were also verified. The value of _dc was slightly higher for samples crystallized from solution at the lowest temperature and decreased with draw ratio.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu : Mg ratio alloys the main phases found were , , S and T₁, while fewer T₂ and Al₇Cu₂Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T₁ precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu : Mg ratio alloy the addition of 0.2 wt % Ag resulted in the precipitation of phase simultaneously with , , S and T₁ phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed.     

Effective Łojasiewicz inequalities in semialgebraic geometry

The main result of this paper can be stated as follows: letV ⁿ be a compact semialgebraic set given by a boolean combination of inequalities involving only polynomials whose number and degrees are bounded by someD > 1. LetF, G[X₁,, X_n] be polynomials with degF, degG D inducing onV continuous semialgebraic functionsf, g:VR. Assume that the zeros off are contained in the zeros ofg. Then the following effective ojasiewicz inequality is true: there exists an universal constantc ₁ and a positive constantc ₂ (depending onV, f,g) such that for allxV. This result is generalized to arbitrary given compact semialgebraic setsV and arbitrary continuous functionsf,g:V . An effective global ojasiewicz inequality on the minimal distance of solutions of polynomial inequalities systems and an effective Finiteness Theorem (with admissible complexity bounds) for open and closed semialgebraic sets are derived.     

Microstructural development in cast alloys based on the β-NiAl–β′-Ni2AlTi–γ′-Ni3Al–α-Cr system

An investigation of microstructural development in three arc-cast Ni–Al–Cr–Ti multiphase alloys derived from the B2 type -NiAl phase is presented. Detailed microstructural characterization of Ni–25 at % Al–20 at % Cr–15 at % Ti, Ni–26 at % Al–21 at % Cr–11 at % Ti and Ni–25 at % Al–24 at % Cr–15 at % Ti materials by transmission electron microscopy (TEM), is described. Microstructural development is examined in both the as-cast condition and after 140 h homogenization treatments at both 850 and 1100 °C. The formation of a eutectic between an L21-type phase (Heusler phase, with a nominal composition of Ni2AlTi) and elemental -Cr is examined. The precipitation of within () and vice versa, in both the inter- and intradendritic regions, is considered. The formation of L12-type (nominally Ni3Al) precipitates within the and -phases is discussed, as is the transformation of to two-phase / during ageing. © 1998 Chapman & Hall     

Complex microstructural changes in as-cast eutectoid Zn-Al alloy

Phase transformations and microstructural changes of an as-cast eutectoid Zn-Al alloy (ZnAl₂₂Cu₂) were investigated during isothermal holding. The typical dendritic structures consisted of _s phase as a core with the edge of decomposed _s phase and decomposed _s in the interdendritic regions. A series of complex phase transformations was observed. Both decompositions of _s and _s were determined at an early stage of ageing and a four-phase transformation, _f+T+, was observed at the boundaries of _f phase and the phase, instead of clearly observed at the boundaries of phase, in a solution-treated Zn-Al alloy during prolonged ageing.     

Propagation of Microscale Material Uncertainty in a Class of Hyperelastic Finite Deformation Stored Energy Functions

Whenever effective material responses are determined, there is a degree of microscale uncertainty. For example in the case of overall isotropic responses, we have uncertainties in the effective constitutive parameters, such as * + * and * + *. In this communication bounds on the resulting uncertainty in a class of polyconvex macroscale finite deformation stored energy functions, which employ the uncertain material parameters, are determined.     

Strength variations of reaction-sintered SiC heterogeneously containing fine-grained β-SiC

Strength variations of reaction-sintered SiC were examined to determine the effect of the volume fraction of fine-grained -SiC domain. The fracture strength significantly decreased with an increase in the volume fraction of the -SiC domain, and eventually fell to the strength of the -SiC domain alone. Furthermore, a substantial difference in the crack deflection was found between the indentation microfracture formed in a structure containing fine-grained -SiC and that in the typical structure of reaction-sintered SiC. This showed that the fracture toughness decreased on account of the -SiC layer.     

Factors affecting work of fracture of uPVC film

Essential work of fracture (EWF) approach was used to evaluate the fracture toughness of uPVC film. It was found that the specific essential work of fracture, (w_e) is independent of specimen width, specimen gauge length, loading rate and test temperature, but dependent on the geometry of the test specimens. Test temperature and geometry were the only testing parameters affecting the specific non-essential work of fracture (w_p) in a very significant way. The plastic zone shape factor () was found to be very sensitive to both the geometry and temperature. It was established that both w_e and w_p could be partitioned into components that are linked to yielding (i.e. w_e,y and _yw_p,y) and necking/tearing (i.e. w_e,nt and _ntw_p,nt) processes. The only testing parameter that affected w_e,y was test temperature, whereas w_e,nt was affected by test temperature as well as geometry. All testing parameters used in this study affected the values of _yw_p,y and _ntw_p,nt.     

Simulation of the Process of Water Freezing in a Round Pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof (Gr) and six Biot (Bi) numbers: Gr = 1.55 × 10⁶, Bi = 0.305 (0 < ), Bi = 0.044 ( < 2); Gr = 1.24 × 10⁷, Bi = 0.610 (0 < ), Bi = 0.087 ( < 2); Gr = 9.89 × 10⁷, Bi = 1.220 (0 < ), Bi = 0.174 ( < 2). The correctness of calculation of the problem disregarding free-convection flows is analyzed.     

Evidence for collective excitations in superconducting tin whiskers

Based on the assumption that a phase-slip center in a clean quasi-one-dimensional superconductor excites a collective oscillation, the time-averaged value of the electrochemical potential of quasiparticles is calculated. At larger distances from the phase-slip center, swings below (or above) the electrochemical potential _p of the Cooper pairs. This makes it possible to understand the unexpected results of previous measurements.