Analysis of thermal fatigue behaviour of brittle structural materials

The effect of the level of maximum temperature (T _max), the temperature range (T) and the mode of convective heat transfer on the thermal fatigue resistance of brittle structural materials is analysed. Expressions are derived for the number of thermal cycles to failure in terms of the appropriate mechanical and thermal properties, crack growth parameter, T andT _max. For simultaneous changes inT _max and T commonly used in practice, the change in thermal fatigue life is governed by both the thermal stress intensity exponent (n) and the activation energy (Q) for subcritical crack growth, in contrast to the results of other studies. For constantT _max but variable T, thermal fatigue life is affected byn only, whereas, for constant T but variableT _max, the value ofQ alone governs changes in fatigue-life. Heat transfer by natural or forced convection will result in differences in thermal fatigue resistance. Recommendations are made for the design and analysis of thermal fatigue experiments. Figures-of-merit for the selection of materials with high thermal fatigue resistance are presented.     

Thermal shock resistance of laminated ceramic matrix composites

The thermal shock resistance capability of laminated ceramic matrix composites is investigated through the study of three-dimensional transient thermal stresses and laminate failure mechanisms. A (–45°/45°)_s SiC/borosilicate glass laminate is utilized as a reference composite system to demonstrate the analytical results. The maximum allowable temperature change, T _max, has been taken as a measure of the thermal shock resistance capability of composites. The effects of fibre orientation, volume fraction, thermal expansion coefficient. Young's modulus, and thermal conductivity on the thermal shock resistance capability, expressed in terms of the maximum allowable temperature change, T _max, have been assessed. Numerical computations are also performed for six composite systems.     

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

Interaction between a dislocation and various divalent impurity in KCl single crystals for the Fleischer's model taking account of the Friedel relation

The interaction between a dislocation and the impurity in KCl : Mg²⁺ (0.035 mol% in the melt), KCl : Ca²⁺ (0.035 and 0.065 mol% in the melt) and KCl : Ba²⁺ (0.050 and 0.065 mol% in the melt) was investigated from the strain-rate cycling test during the Blaha effect measurement. This was carried out at 77–254 K. As a result, it was found that the Fleischer's model taking account of the Friedel relation seems to be suitable for KCl : Ca²⁺ and KCl : Ba²⁺. However, it was not appropriate for KCl : Mg²⁺. Furthermore, the values of T _c, H(T _c) and G ₀ were obtained for the specimens. T _c is the critical temperature at which effective stress is zero. H(T _c) and G ₀ are the enthalpy and the Gibbs free energy of activation for the breakaway of the dislocation from the impurity, respectively. H(T _c) was almost the same for the specimens except KCl : Mg²⁺. G ₀ increased with increasing the divalent cation size. In addition, the tetragonality around the divalent ion-positive ion vacancy pair was estimated on the basis of G ₀ for the each specimen.     

An investigation of the micromechanisms of fatigue crack growth in structural gas turbine engine alloys

This paper presents an overview of fatigue fracture modes in selected structural alloys employed in gas turbine engines. These include the mechanisms of fatigue crack growth in the near-threshold, Paris and high-K regimes obtained from Ti-6Al-4V, Inconel 718 and PWA 1472 (a single crystal nickel-based superalloy of similar chemical composition to Inconel 718). Fatigue fracture modes in these materials are shown to be strong functions of the stress intensity factor range, K, and the maximum stress intensity factor, K _max. Fatigue mechanism maps are also presented to show the parametric ranges of K and K _max corresponding to the different fatigue fracture modes.     

Low-temperature heat capacity of urea

The heat capacity of urea was measured with an adiabatic calorimeter in the temperature range 15–310 K. The data were extrapolated to 0 K by a model function to derive some standard thermodynamic functions including the enthalpy increments ₀ ^T H, the entropy increments ₀ ^T S, and the Giauque function (= ₀ ^TS – ₀ ^T H/T). A simple model for the reproduction of the experimental heat capacities of urea, based on the Debye and Einstein functions, is described. The Debye characteristic temperature determined in this way was compared with those calculated from properties other than the heat capacity. Any positive evidence of a suggested phase transition in urea around 190 K was not observed in the present heat capacity measurements. Possible existence of a phase with a Gibbs energy lower than that realized in the present investigation is discussed briefly.     

Electrical conduction in thermoplastic elastomer matrix composites containing catalytic chemical vapour deposited carbon whisker

Electrical conduction in carbon whisker/thermoplastic elastomer (TPE) composites was found to be a thermally activated process. The carbon whiskers used were obtained by a catalytic chemical vapour deposition (CCVD) technique conducted at 500 °C and the TPE was a styrene-ethylene butylene-styrene (S-EB-S) block copolymer. The resistivity, (), versus 1/T curves of the composites exhibited two regions with distinct slopes with an inflection at the glass transition temperature,T _g, of the elastomer, EB; Region I <T _g and II >T _g. The thermally activated conduction mechanism of these composites is explained on the basis of electron transport in low-mobility solids with a large number of trap sites, Intra- and intermolecular motion of the polymer chains can result in the electron transport from such trap sites and were correlated to the observed activation energies. Intramolecular motion in region I, was related to the thermally assisted hopping with the activation energy, E _A, of 0.067 and 0.030 eV for 33% and 52% whisker volume fraction composites, respectively. Similarly, E _A due to the intermolecular segmental chain motions in region II for 33% and 52% whisker volume fraction composites was related to the equilibrium rate of trapping-detrapping of electrons from 0.240 and 0.138 eV deep traps.     

Enthalpy relaxation behaviour of Al-Si-Cr quasicrystalline and amorphous alloys upon annealing

Annealing-induced enthalpy relaxation behaviour was examined calorimetrically in quasicrystalline Al₆₂Si₁₉Cr₁₉ and amorphous Al₆₀Si₂₅Cr₁₅ alloys. When both alloys annealed at temperatures belowT _x are reheated, an excess endothermic reaction (enthalpy relaxation) occurs reversibly above the annealing temperature,T _a. The peak temperature of C _p,endo rises in a continuous manner with the logarithm of annealing time (t _a). The magnitudes of C _p,endo and H _endo of the amorphous alloy increase with increasingT _a while no appreciable change in C _p,endo and H _endo of the quasicrystal withT _a is seen. The activation energy,Q _m, for the enthalpy relaxation increases from 1.8 to 2.7 eV with the peak temperature of C _p T _m, for the amorphous alloy, whereas it remains constant (1.3 eV) for the quasicrystal. The endothermic reaction with smallO _m for the quasicrystal is thought to be attributable to the disappearance of short-range ordering of chromium and silicon atoms with stronger attractive interaction, which developed during annealing, i.e. the reversion phenomenon, in the unrelaxed localized regions with high free-energy isolately embedded in the more stable icosahedral structure. The similarity of the enthalpy relaxation behaviour between the quasicrystalline and amorphous phases allows us to infer that short-range atomic configuration is very similar between the quasicrystalline and amorphous phases.     

Growth and Characterization of YBCO Thin Films by Sequential Deposition and Annealing

A novel thin film growth procedure, sequential deposition and annealing (SDA), which contains the advantages of both in situ and ex situ procedures, was proposed. Y₁Ba₂Cu₃O_{7 – x} (YBCO) high temperature superconducting thin films were grown and characterized by the SDA procedure. Purely c-axis-oriented YBCO thin films with no foreign phases and other oriented grains were successfully prepared. The superconducting transition properties of SDA-grown YBCO thin films were measured by measurement of inductance and resistance. The inductance measurements gave a T _c ^onset of 85 K and a T _c of 5 K. The resistance measurements gave a T _c ^onset of 90 K and a T _c of 5 K. Atomic force microscopy studies showed that SDA-grown YBCO thin films had micrometer-size grains surrounded by many nanometer-size grains. The nanometer-size grains in SDA-grown YBCO thin films are responsible for degradation of superconducting transition properties.     

Testing procedures for fatigue crack propagation and the ΔKeffconcept

Two different procedures are available for the experimental determination of fatigue crack propagation (FCP) velocities da/dN as a function of the loading parameters K. The first procedure is the standardized method in accordance with ASTM E 647 [1] and the second procedure is the so-called K_max-constant method. Both procedures are equivalent, meaning that under the same loading conditions (K, K_max, R) the same FCP velocity (da/dN) is measured. But, the ASTM E 647 method emphasizes the effects of closure (contact of fracture surfaces) in the low K and low K_max regime. It is shown for Al 7075–T7351, the Ni-base alloy Nicrofer 5219 Nb (annealed), the Ti-alloys Ti 6Al 4V (annealed), and Ti 6Al 6V 2Sn that K_eff is the sole driving parameter for FCP.Published in Problemy Prochnosti, No. 7, pp. 13–30, July, 1995.     

Effect of stress on the superconducting transition temperature of SrTiO3

The superconducting transition temperatures of several specimens of reduced SrTiO₃ and of Nb-doped SrTiO₃ have been investigated as functions of hydrostatic and uniaxial compressive stresses up to 1.8 kbars. Decreases inT _c as large as 0.12 K have been observed in specimens under hydrostatic pressure. Because of the lowT _c and small compressibility of SrTiO₃, (lnT _c)/P and (lnT _c)/(lnV) are orders of magnitude greater than the corresponding effects in elemental superconductors. The effect of uniaxial stress onT _c varied with the direction of stress. Compression along a [111] direction caused large decreases inT _c, while both small increases and small decreases inT _c have been observed for [100] compression. It is believed that the present results reveal the presence of a sensitive volume dependence in one or more of the parameters important to superconductivity in SrTiO₃, and that no significant electron-transfer effects occurred in the range of stresses of this experiment.     

Correlation between structural relaxation enthalpy and superconducting properties of amorphous Zr70Cu30 and Zr70Ni30 alloys

The anneal-induced change in the superconducting properties together with the irrecoverable relaxation enthalpy (H _i,exo) and recoverable relaxation enthalpy (H _r,endo) of amorphous Zr₇₀Cu₃₀ and Zr₇₀Ni₃₀ alloys was examined. The increase in _i,exo and the degradation ofT _c progress logarithmically with annealing timet _a in a temperature range of 373 to 523 K. The activation energy and the attempted frequency were respectively estimated to be 1.5eV and 6.6 × 10¹³ sec^–1 for the increase in H _i,exo and 1.5eV and 1.9×10¹⁴ sec^–1 for the degradation ofT _c. The recoverable structure relaxation exerts little effect onT _c. Based on the agreement between the kinetic parameters for the changes of H _i,exo andT _c, it appears that the degradation ofT _c on annealing is associated with the irrecoverable structural relaxation as a result of the annihilation of frozen-in defects and the topological and compositional atomic rearrangement. The values of the attempted frequency being of the order of Debye frequency suggest that the irrecoverable structural relaxation processes occur more or less independently from each other. The dressed density of electronic states at the Fermi level,N(E _f)(1+), determined from the measured values of _n and -(dH _c2/dT)_{T c} using GLAG (theory), was found to have a similar annealing dependence to that ofT _c. The degradation ofT _c by the irrecoverable relaxation was thus inferred as resulting from the decrease in due to the decrease inN(E _f) and the increases inM and . Furthermore, the irrecoverable structural relaxation resulted in a significant depression of fluxoid pinning force and was interpreted as due to an enhanced structural homogeneity on the scale of coherence length.     

The equilibrium humidity of dispersed solids at different temperatures

The use of the free energy of water vapor as a unique characteristic of saturated air permits the level of dehydration of dispersed solids to be determined unambiguously. The moist air diagram is computed for compensation of the moisture fluctuation of the surrounding air, corresponding to a change of the temperature of drying.Notation F₁ free energy of water vapor in air - F₂ free energy of bound water in dispersed solid - T₁ temperature of drying air, °C - T₂ temperature of dispersed solid, °C - T₃ temperature of air in laboratory, °C - P₁ water vapor pressure (absolute air humidity) - p_s saturated water vapor pressure at temperature T₁ - relative humidity of air, % - R gas constant - M molecular weight of water - W moisture content of dispersed solid - L₂ internal binding energy (thermal effect) of water in dispersed solid Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 5, pp. 787–791, May, 1971.     

On the driving force for fatigue crack formation from inclusions and voids in a cast A356 aluminum alloy

Monotonic and cyclic finite element simulations are conducted on linear-elastic inclusions and voids embedded in an elasto-plastic matrix material. The elasto-plastic material is modeled with both kinematic and isotropic hardening laws cast in a hardening minus recovery format. Three loading amplitudes (/2=0.10%, 0.15, 0.20%) and three load ratios (R=–1, 0, 0.5) are considered. From a continuum standpoint, the primary driving force for fatigue crack formation is assumed to be the local maximum plastic shear strain range, _max, with respect to all possible shear strain planes. For certain inhomogeneities, the _max was as high as ten times the far field strains. Bonded inclusions have _max values two orders of magnitude smaller than voids, cracked, or debonded inclusions. A cracked inclusion facilitates extremely large local stresses in the broken particle halves, which will invariably facilitate the debonding of a cracked particle. Based on these two observations, debonded inclusions and voids are asserted to be the critical inhomogeneities for fatigue crack formation. Furthermore, for voids and debonded inclusions, shape has a negligible effect on fatigue crack formation compared to other significant effects such as inhomogeneity size and reversed loading conditions (R ratio). Increasing the size of an inclusion by a factor of four increases _max by about a factor of two. At low R ratios (–1) equivalent sized voids and debonded inclusions have comparable _max values. At higher R ratios (0, 0.5) debonded inclusions have _max values twice that of voids.     

Enthalpy relaxation behaviour of (Fe,Co, Ni)75Si10B15 amorphous alloys upon low temperature annealing

The effect of composition on the anneal-induced enthalpy relaxation for (Fe, Co, Ni)₇₅Si₁₀B₁₅ amorphous alloys was examined calorimetrically. Upon heating the sample annealed at temperatures well belowT _g (T _g<T _g–150 K), an excess endothermic reaction (enthalpy relaxation) occurs above the annealing temperature. The endothermic specific heat, C _p, evolves in a continuous manner with annealing time. The change in the magnitude of C _p withT _a is divided into two stages: a low-temperature stage which peaks at aboutT _g–150 K and a high-temperature peak just belowT _g. The activation energy,E _m, increases with the peak temperature of C _p,T _m, from 2.29 to 3.15 eV for the low-temperature peak and from 4.40 to 4.96 eV for the high-temperature peak. The low-temperature endothermic reaction is attributed to local and medium range atomic rearrangements and the high-temperature reaction to the long-range cooperative atomic regroupings. The magnitude of the low-temperature C _p is most pronounced for (Fe-Co)₇₅Si₁₀B₁₅, followed by (Fe-Ni)₇₅Si₁₀B₁₅, (Co-Ni)₇₅Si₁₀B₁₅, Fe₇₅Si₁₀B₁₅, Co₇₅Si₁₀B₁₅ and then Ni₇₅Si₁₀B₁₅. The reason for such a significant compositional effect of the enthalpy relaxation was investigated, based on the concept of distribution in relaxation time, which had been previously derived from the percolation theory, and was interpreted as due to the difference in the degree of local structure and compositional disorder in the as-quenched state; i.e. the higher the degree of short-range disorder (the larger the fraction of short relaxation time) the larger is the magnitude of the enthalpy relaxation (H _{, endo}). There existed a strong correlation between (H _{, endo}) or C _p and anneal-induced embrittlement tendency; the larger the (H _{, endo}) and C _p the larger is the embrittlement tendency. Such a strong correlation was interpreted based on the assumption that the internal strain which generated in the transition from as-quenched disordered state to a relaxed equilibrium state causes an enhancement of embrittlement tendency.     

Ideal Gas Thermodynamic Properties of Propyl tert-Butyl Ethers from Density Functional Theory Results Combined with Experimental Data

Ideal gas thermodynamic properties, S°(T), C _p°(, T), H°(T)–H°(0), _f H°(T), and _f G°(T), are obtained on the basis of density functional B3LYP/6-31G(d,p) and B3LYP/6-311 + G(3df,2p) calculations for two propyl tert-butyl ethers. All torsional motions about C–C and C–O bonds were treated as hindered internal rotations using the independent-rotor model. An empirical approximation was assumed to account for the effect of the coupling of rotor potentials. The correction for rotor–rotor coupling was found by fitting to entropy values determined from calorimetric measurements. Enthalpies of formation were calculated using isodesmic reactions.     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. II. Data analysis by the scaling-field method

The scaling theory for tricritical phenomena by Riedel is applied to the analysis of thermodynamic properties of liquid³He-⁴He mixtures near the tricritical point. Within this theory experimental data for the phase diagram, the³He molar concentrationX, and the concentration susceptibility (X/) _T are discussed in terms of two scaling fields that are functions of the temperatureT and the difference = ₃ – ₄ of the chemical potentials of the two helium isotopes. The quantitiesX and (X/) _T in terms of thefields T and as independent variables are obtained for the intervals –0.1<T – T _t<0.53 K and –9< – _t <0.8 J/mole, from vapor pressure and calorimetric data described in a previous paper by Goellner, Behringer, and Meyer. The transformed data are analyzed to yield the tricritical exponents, amplitudes, scaling fields, and scaling functions. The values of the tricritical exponents are found to agree with those predicted by the renormalization-group theory of Riedel and Wegner. (Logarithmic corrections are beyond the precision of the present experiment.) Relations between amplitudes are derived and tested experimentally. The (linear) scaling fields are determined by using their relationship to geometrical features of the phase diagram. The data forX and (X/) _T are found to scale in terms of these generalized scaling variables. The sizes of the tricritical scaling regions in the normal and superfluid phases are estimated; the range of apparent tricritical scaling is found to be appreciably larger in the normal-fluid phase than in the superfluid phase. The tricritical scaling function for the concentration susceptibility is compared with the analogous scaling function for the compressibility of pure³He near thecritical gas—liquid phase transition. Finally, when the critical line near the tricritical point is approached along a path of constant < _t , the experimental data are found to exhibit the onset of the crossover from tricritical to critical behavior in qualitative agreement with crossover scaling.Work supported in part by the National Science Foundation through Grant No. GH-36882 and Grant No. GH-32007, and by a grant of the Army Research Office (Durham).     

Effect of annealing on the anomalous electrical resistivity of dilute copper-iron alloys at low temperatures

Electrical resistivity measurements in the temperature range 1.5–35 K on two copper alloys containing 115 and 380 atomic ppm iron are reported, in their unannealed state and also after annealing for 16 and 66 h in fore-vacuum at 530–550°C. Below the temperature of the resistivity minimum the impurity resistivity has the Kondo lnT behavior. However, in the liquid helium region the resistivity drops from its value atT=0, in proportion toT ², conforming to Nagaoka's theory forT<T _K/5. The Kondo temperatureT _K is evaluated from the versusT ² plots using Nagaoka's equation and is found to decrease with increasing concentration. Annealing is found to reduce the effective iron concentration and alsoT _K. The impurity resistivity per atomic percent in our samples can be expressed as a universal function ofT/T _K at the lowest temperatures underT _K/4.     

Quantum fluctuations in continuous superconducting films

Motivated by recent experiments on ultrathin continuous superconducting films, we study the dependence ofT _c and (for zero temperatures) on the film thicknessd. Using field-theoretical methods, we express the Coulomb interaction in terms of a fluctuating potential, and the fluctuation correction to the free energy (in one-loop approximation) is determined. Based on the standard dirty-limit expressions for the response functions, we findT _c and by a numerical investigation of the gap equation. Generally, we find that the decrease ofT _c and vs.d ^–1 is quite similar, but depends sensitively on both the large-wave-vector cut-off and the strength of the interaction. In particular, however, for a strong interaction (Coulomb interaction), the order parameter is more strongly suppressed than the critical temperature, which is due to long-wavelength fluctuations of the phase and the potential.     

Enthalpy relaxation behaviour of metal-metal (Zr-Cu) amorphous alloys upon annealing

Anneal-induced enthalpy relaxation behaviour was examined calorimetrically for Zr_50-70Cu_50-30, Zr₇₀(Cu-Fe)₃₀ and Zr₇₀(Cu-Ni)₃₀ amorphous alloys. When the alloys annealed at temperatures belowT _g are heated, an excess endothermic reaction (enthalpy relaxation) occurs above the annealing temperatureT _a. The peak temperature of C _p,endo, evolves in a continuous manner with lnt _a. The magnitudes of C _p,endo and H _endo for Zr-Cu binary alloys increase gradually with risingT _a and then rapidly at temperatures just belowT _g, while their changes as a function ofT _a for the ternary alloys show a distinct two-stage splitting; a low-temperature one which peaks at aboutT _g — 150 K and a high-temperature peak just belowT _g. From the result that the addition of iron or nickel causes the two stage splitting of the C _p,endo (T _a), it was proposed that the low-temperature endothermic peak is attributed to local and medium range rearrangments of copper and iron or nickel atoms with weak bonding nature and the high-temperature reaction to the long-range co-operative regroupings of zirconium and copper, iron or nickel atoms which are composed of the skeleton structure in the metal-metal amorphous alloys. The mechanism for the appearance of the two-stage enthalpy relaxation was investigated by the concept of two-stage distributions of relaxation times proposed previously, and the distinct two-stage splitting was interpreted as arising from the distinctly distinguishable difference in the ease of atomic rearrangements between Cu-(Fe or Ni) and Zr-(Cu, Fe or Ni).