Effect of crack shape,inclination angle,and friction coefficient in crack surface contact problems

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle =15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for =45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for =15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K _II, K _III are calculated with varying the crack shape b/a, inclination crack angle , and crack face friction coefficient . The calculations show that the present method is useful for the analysis for =15–30 deg with high accuracy. It is seen that the K _II-values when b/a0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K _II values under Hertzian contact load, the results of =15 deg are smaller than the ones of =45 deg by 23–34%. Regarding the amplitude of (K _{II max}–K _{II min}), the results of =15 deg are smaller than the ones of =45 deg by 4–24%. With increasing the value of friction coefficient for crack faces the value of K _II decreases significantly. When the crack is short and the inclination angle is small, the value of friction coefficient f for Hertzian contact load largely affect the K _II value.     

Precipitation hardening in an Al-Cu-Si-Mg alloy at 130 to 220° C

The variation of the hardness of a complex Al alloy, of the L70 type, (Al 4% Cu 0.8% Si 0.8% Mg 0.7% Mn 0.5% Fe) with ageing time at 130, 160 and 190° C was measured and correlated with transmission electron microscope observations of preciptate morphology. It was established that the peak hardness, after both 160 and 190° C ageing, was associated with coherent precipitate particles with a diameter of 700 Å and the subsequent limited overageing at these temperatures was controlled by the slow growth of particles. Measurements of particle coarsening at 220° C suggested that the process occurred by Ostwald ripening. In contrast, ageing at 130° C gave a series of hardness—time plateaus, which were ascribed to the sequential precipitation of zones,' and precipitates.     

Upper Critical Field Hc2 on c Axis of Ag/Bi-2223 Polycrystal Tape

The upper critical field H _c2, based on Ginzburg–Landau theory at medial magnetic fields, can be calculated from the relationship of the magnetization intensity M(H) versus magnetic field H if M is linear with ln₀ H. For Ag/Bi-2223 tapes, the measured M(H) was found to be linear with ln₀ H. In this case, the values of H _c2(T) may in principle be determined. To do this, we will meet another problem in that the obliquity of crystal planes is not equal for different grains in tapes, and values of grain-oblique angle will appear in the calculated H _c2. Obviously, for Ag/Bi-2223 tapes is an uncertain parameter and hard to determine. To avoid the effects of , we only study the H _c2 in the c axis direction and the projections of H onto the c axis is taken as the actual applied fields. Thus, the effects of grain-oblique angle may be counteracted when measuring critical current density J, if the external magnetic fields are applied to the tape along both the parallel to and perpendicular to the c axes directions (on the narrow surfaces of the tape). On medial fields (H = 0 – 3 T), the upper critical fields H _c2(T) on c axis for the Ag/Bi-2223 tape are obtained and fitted as ₀ H _c2(T) = 830 e ^–0.07T . The average slope d[₀ H _c2(T)]/dT – 8T/K is found to be as large as that of Bi-2212. On extrapolating the relation to T = 0 K, the value of ₀ H _c2(0) 800T. The coherence length _ab is determined from H _c2(c), and _ab (0) = 0.63 nm at T = 0 K.     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

Grain growth in the two-phase Al-Cu alloys

Grain and phase growth in the two-phase Al-Cu alloys containing 6, 11, 1 7, 24 and 33 wt % Cu were investigated by annealing at 535 °C for 0.5–100 h. The grain and phase sizes of the phase are seen to be larger than that of the phase. The size of phase decreases whereas the size of phase increases with increasing copper content in the alloy. As such, the phase- and grain-size distributions are broader than the phase- and grain-size distributions, but the size range depends on annealing time and alloy composition. The grain sizes of the ,d , and ,d , phases can be related to the volume fraction of the phase,f , according to the equationd = 0.497d /f .     

Si-C-N ceramics with a high microstructural stability elaborated from the pyrolysis of new polycarbosilazane precursors

Si-C-N model filaments almost free of oxygen have been prepared from a novel PCSZ precursor by melt-spinning, -ray curing and pyrolysis under pure nitrogen (or argon) at a temperature _p as high as 1600 °C. The organic-inorganic conversion of the precursor takes place at 450 < _p < 850 °C. It yields an amorphous filament whose composition is close to SiC_0.93N_0.46 (with less than 2 wt % O). No significant change in composition and microstructure occurs up to about 1400 °C. Beyond 1400 °C under argon, a decomposition process takes place starting from the filament surface whereas, under nitrogen, the only observed phenomena are the growth of a skin a few nanometres thick at the filament surface and the formation of tiny -SiC crystals within the amorphous Si-C-N material. As _p is raised, the Young's modulus at room temperature continuously increases to reach a value close to 220 GPa for _p=1600 °C whereas the tensile failure stress undergoes a broad maximum close to 2400 MPa for _p =1200 °C and is still higher than 2000 MPa after ageing at 1600 °C. Thus, Si-C-N filaments free of oxygen have improved stability at high temperatures with respect to Si-C-O filaments processed under similar conditions.     

Modification of nylon-6 with poly (m-phenylene isophthalamide) via MDI as a chain extender

Reinforcement of flexible nylon-6 by using poly (m-phenylene isophthalamide) PmIA (Nomex) using (MDI) 4,4-diphenylene methane diisocyanate as a chain extender was studied. Observation by scanning electron microscopy showed that the multiblock copolymer had a homogeneous texture. From the differential scanning calorimetry measurements, the multiblock copolymers were shown to have only one melting point, T _m, which is higher than that of nylon-6. The wide-angle X-ray diffraction pattern shows that nylon-6 has two diffraction peaks at 2=20° and 23.8°. However, the multiblock copolymer has only one peak at 2=20°, indicating a different crystal structure of multiblock copolymers. The copolymers appear to have a significant reinforcing effect on the mechanical properties.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Microstructural evolution in rapidly solidified Al-Cu-Si ternary alloys

Several Al-Cu-Si alloys were melt spun to produce stable, fine scale microstructures suitable for superplastic deformation and consolidation. Scanning electron microscopy of the ribbon cross-sections reveal two distinct alternating microstructural morphologies, suggesting transitions in solidification behavior. One structure consists of intimately interlocked -Al and (Al₂Cu) phases with dispersed spheroids of (Si). The other structure consists of equiaxed or cellular-dendritic -Al with interdendritic and (Si). The latter was found in the middle portion of the ribbon cross-section when cast at a low speed, and throughout the ribbon cross-section when cast at high speed. The dendritic structure appears to result from independent nucleation events in the undercooled liquid ahead of the solid-liquid interface. The solidification mechanism for the interlocked structure appears to involve multiple nucleation of the phase followed by its cooperative growth with the -Al phase. This cooperative growth is unlike that which forms a lamellar structure, as it results in a branched, randomly oriented network. We postulate that the (Si) phase is the first phase to form from the undercooled liquid, and it is uniformly dispersed throughout the undercooled melt. The (Si) spheroids provide nucleation sites for the phase because of its observed association with the phase. The -Al grain size varies from 1 m near the wheel side surface of the ribbon to 8 m with sub-grains near the free surface. The size of the and (Si) phases is on the order of a m and less. The microstructural size scale appears to be small enough for this material to exhibit superplastic behavior when deformed.     

On the nucleation ofθ′ and T1 on Al3Zr precipitates in Al-Li-Cu-Zr alloys

Two quaternary Al-Li-Cu-Zr alloys have been investigated using electron microscopy. Ageing at 190° C resulted in the nucleation of precipitates on the Al₃Zr/matrix interface in addition to heterogeneous nucleation on matrix dislocations. In the majority of cases, the broad, coherent face of the plans ms in contact with the Al₃Zr precipitates. Similar evidence showed that nucleation of T₁ precipitates occurred on the Al₃Zr, but to a lesser extent than. Solid-solid nucleation theory has been used to account for the Al₃Zr acting as a nucleation substrate.     

Anisotropy in the resistive superconducting transition under magnetic fields in single crystal Pb2Sr2Ho0.5Ca0.5Cu3O8

Anisotropie properties of the single crystal Pb₂Sr₂Ho_0.5Ca_0.5Cu₃O₈ have been investigated by measuring the electrical resistivity in theab-plane _ab (H, ,T), which depends on the angle between theab-plane and the magnetic-field direction, in various constant fieldsH perpendicular to the current direction. All the angle-dependent values of _ab (H, ,T) at a constant temperature are scaled to be on one curve as a function of reduced field. The anisotropic parameter (m _c ^* /m _ab ^* )^1/2 is estimated as 12–13, which is larger than that of YBa₂Cu₃O₇ and much smaller than that of Bi₂Sr₂CaCu₂O₈. It has been concluded that the anisotropy does not always depend on the thickness of the blocking layer but seems to depend on the overlap of the electronic wave functions along thec-axis. Anisotropy in the pinning potential has also been discussed from the resistive tail in the temperature dependence of _ab (H,,T).     

An exact calculation of Price's law for the law of Lotka

Price's law asserts — in its simpliest version — that authors produce half of the papers made by the total ofN authors. More generally: the topN (0<<1) authors produce a fraction (0<<1) of the papers made by the total ofN authors and the Price's law says that . In this paper — using Lotka's law — we prove a mathematical relationship of in function of and the parameter (the mean number of papers per author) and investigate when . More-over our reasoning uses the theory of the 80/20 rule as developed in: L. EGGHE, On the 80/20-rule,Scientometrics, 10 (1986) 55–68, thereby also showing the relation betwwen the 80/20-rules (being an arithmetical form of measuring elitarism) and Price's law (being a geometric form of measuring elitarism).     

Comparative study of solubilities of hydrogen,nitrogen and carbon in α-iron

Solubility data of hydrogen, nitrogen and carbon in -iron are analysed on the basis of statistical thermodynamics. Present analysis appears to yield realistic values for the enthalpy term of the solutions of these interstitial elements into -Fe, while the entropy terms remain ambiguous. During the course of this analysis a parameter _x, which refers to the solubility limit of the specific interstitial element X (X=hydrogen, nitrogen or carbon), is also estimated; _H< _N< _C. This order of _X values appears to be in accord with the observation that, under normal conditions, the solubility of carbon is the highest and that of hydrogen the lowest in -Fe, while the atomic size increases with the order hydrogen相似文献   

Coupling behavior of Cu-O2 layers in oxygen-deficient YBCO films and ultrathin YBCO films

We have measured the resistivity as a function of temperature in a magnetic field at various field angles for oxygen-deficient YBCO films and ultrathin YBCO films; is the angle between the crystalc axis and the direction of the magnetic field. The angular dependence of the critical field,H _c2, shows a cusplike behaviour at =90° for the oxygen-deficient 60 K YBCO films indicating that the Cu-O₂ layers are two-dimensional in nature. BothT _c versus in a constant field andH _c2 as a function of show a plateau at =90° for 83 K (zero resistance) ultrathin YBCO films with a thickness of 20 units of the YBCO cell; these results indicate that there is a coupling between the Cu-O₂ layers. The dimensionality of the Cu-O₂ layers in oxygen-deficient YBCO films and ultrathin YBCO films is discussed in terms of the anisotropic Ginzburg-Landau model and the Tinkham thin-film model.     

Spin diffusion coefficient of the A and B phases of liquid3He

The spin diffusion coefficient tensors are calculated in the A and B phases of liquid ³ He in the _{L D} <1 regime by using the Kubo formula approach. The spin wave dispersions are also obtained in the presence of diffusive flow of the normal component. The results agree with Combescot's results qualitatively in the _{L D} <1 regime.     

The interdependence between the incidence angles associated with quasi-stable intersections during ion erosion

A general discussion, which is valid for any angular dependence of sputtering yieldS=S(), concerning the interdependence between the incidence angles _e and ₀, associated with quasi-stable intersections during ion erosion, is given. The object was firstly to establish the location of _e roots as a function of ₀ and secondly to identify the stationary points and general trend for the complex dependence _e= _e( ₀). The results obtained are applied to a quasi-stability analysis of some specific surface features during ion erosion. Various possible types of quasi-stable intersections (surface-surface, plane-surface, plane-plane) are reviewed from the point of view of their evolution caused by ion bombardment.     

Does Vortex Lattice of YBa2Cu3O6.94 in H⊥c Melt Below Intrinsic-Pinning Irreversibility Line?

Vortex lattice melting in the Hc configuration of an YBa ₂ Cu ₃ O _6.94 single crystal has been investigated by means of the ac susceptibility – i and the magnetic torque . The melting transition of vortex lattice occurs in Hc, too. Since the torque curve shows a sharp peak in the irreversible torque at _c 90° due to intrinsic pinning at lower temperatures, we can determine the irreversibility line for the intrinsic pinning. The melting transition in the Hc configuration appears at temperatures where the intrinsic-pinning peak is absent. We consider that the intrinsic pinning does not affect the nature of the vortex melting transition in the Hc configuration.     

Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source

Summary In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.

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Wärmespannungen in einer dünnen Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle

Zusammenfassung In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.

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Nomenclature r, polar coordinates - T temperature rise - ² ratio of conductivities - ² thermal diffusivity in -direction - J _n Bessel function ofn-th order - t time - p introduced in equation (2) - h heat transfer coefficient - a radius of circular disc - f(r, ) temperature distribution at initial state - r ₀, ₀ a point on the disc - T ₀ strength of point heat source - Dirac delta function - F stress function in two dimensions - ₁, ₂ coefficient of thermal expansion - a ₁₁,a ₁₂,a ₂₂,a ₆₆ elastic constants With 9 Figures     

Interfacial phenomena of plasma arc welding of mild steel and aluminium

The interfacial microstructures and intermetallic compounds produced by plasma arc butt fusion welding of aluminium to mild steel have been investigated. An intermetallic compound alloy layer formed at the interface region between mild steel and aluminium was determined using quantitative metallography and the mechanism of the intermetallic layer formation and growth was elucidated. The melt width and the alloy layer thickness decrease with increasing transfer-speed of the plasma torch. The intermetallic layers formed at the interface region between mild steel and aluminium are predominantly-phase (Fe₂Al₅) and-phase (FeAl₃). The-phase layer with columnar crystal grows rapidly as tongue-like structures in the direction of the mild steel substrate and the-phase layer with granular crystals projects slowly to the aluminium side in the course of solidification. As a result, many vacancies are produced in the-phase layer. The structures of the melted zone and the fusion boundary of the mild steel change into grain refinement, whereas the melted zone of the aluminium has a eutectic structure of aluminium and-phase.