Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

We propose a new approach to the experimental estimation of local strains at the tip of a concentrator. The approach is based on the measurement of displacement of certain points in the vicinity of the tip of a notch, which is further associated with the effective radius of the notch. Various concentrators in structures are simulated within a wide range of variation in radii of notches (ρ=0.1−6.5mm) and in the geometry of specimens. We establish the main dependences between the value of the range of local strains Δɛ^* and the periodN _i prior to the nucleation of a fatigue macrocrack. Thus, by using the experimental quantity Δɛ^*, we can estimate the periodN _i prior to the nucleation of a fatigue crack of lengtha _i=d^* for structural elements of a complicated geometry. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv. Vol. 34, No. 3, pp. 55–66, May–June, 1998.     

A Quantum-Chemical Model of Active Centers of Electrochemical Corrosion of Metals

On the atomic level, we consider a model of the formation of active centers on the surface of a metal, which control the course of corrosion and electrochemical processes. Our quantum-chemical computations demonstrate that a foreign tin atom in a Sn - Ni₈ - Ni cluster can favor the dissolution of nickel in an acid medium, and a zinc atom in a Zn - Ni₈ - Ni cluster induces its passivation. We also show that the introduction of an oxygen atom into a cluster favors the passivation of nickel.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 1, pp. 12–18, January–February, 2005.     

New aspect of low-temperature phase transitions of La-cuprates

The change in the microstructure on aging at 12 K below a low-temperature structural phase transition in La_1.5Sr_0.1Nd_0.4CuO₄ has been examined by transmission electron microscopy. From a seriesof 100 forbidden dark field images obtained inin situ observation, spotty-shape regions with a Pccn/LTT tilt of the CuO₆ octahedron were found to be nucleated and grow inside a LTO domain, accompanying the annihilation of some spotty-shape regions. In addition, there exists a tweed texture in fundamental dark field images, which is due to the macroscopic strain involved in the transition. Because a mapof the tweed texture is different from that of the spotty-shape region, the tilt of the octahedron is not always coupled to a proper spontaneous strain.     

Special features of heat transfer under conditions of heat protection of high-temperature firing walls of components of modern power-generating units by way of tangential injection

In order to more precisely define the characteristics of heat transfer under conditions of protection of firing wall by means of tangential injection in the case of its high temperature (in particular, higher-thanadiabatic temperature) and to assess the effect of degree of turbulence of the incoming gas flow on heat transfer, a numerical investigation is performed under conditions of parameters typical of combustors of gas-turbine plants (GTP) with high parameters of the working medium. In so doing, the heat flux distribution, the profiles of turbulence intensity, the distribution of turbulent viscosity in the injection zone region under study, and other characteristics are determined. The low-Reynolds k-ε model with wall functions and a new model of turbulent viscosity without wall functions are employed. It is found that a maximum of turbulent viscosity takes place behind the exit section of the injection slit with a shift to the main flow under conditions of tangential injection on an isothermal surface with a temperature much in excess of injection temperature (in a more general case, T _w > T _ad). This causes impairment of heat protection by injection, i.e., an increase in heat fluxes in the computational domain compared to heat fluxes calculated using integral methods.     

An explanation of the relation between the fraction of multinational publications and the fractional score of a country

Consider a country's national output, measured by counting the number of authors from countryc that collaborate in every paper in a bibliography. Depending on whether countryc appears at least once in every paper, we are able to deduce the corresponding relationship betweenc's fractional score and its fraction of multinational papers to whichc belongs. One of these models, a slowly decreasing concave function is similar to the relation observed byNederhof andMoed ¹ between the fractionated score of a countryc and its fraction of multinational papers. The proof of the models developed here uses a stochastic property of weighting schemes, namely that the average fractional score of a country equals its total score.     

The sensitivity of estimates of regression to the mean

Estimations of the effectiveness of remedial treatments in road safety analysis are frequently bedevilled by the problem of regression to the mean (RTM). The number of accidents x observed at a site in the “before” period is a “noisy” quantity: x is Poisson distributed about an (unknown) true mean m for that site, so that x = m + e. Sites selected for treatment tend to have a positive random error component e, which will on average be zero in the “after” period, even if no treatment is applied.Methods for estimating RTM usually require some assumption about the underlying (prior) between-site distribution of the true means f₀(m): for example, in the empirical Bayes method, a gamma distribution is assumed. The paper considers the impact of different assumptions for this distribution and, indeed, whether any distributional form needs to be assumed. Using Markov Chain Monte Carlo methods, a variety of distributional forms are assumed for f₀(m) and applied to each of a number of real data sets, including that from a major study on the effectiveness of speed cameras. It is shown that, in some cases, the size of the estimated RTM effect can be quite sensitive to the choice of distribution.     

Hydrodynamic instability of a suspension of spherical particles through a branching network of circular tubes

A numerical method is presented for computing the unsteady flow of a monodisperse suspension of spherical particles through a branching network of circular tubes. The particle motion and interparticle spacing in each tube are computed by integrating in time a one-dimensional convection equation using a finite-difference method. The particle fraction entering a descendent tube at a divergent bifurcation is related to the local and instantaneous flow rates through a partitioning law proposed by Klitzman and Johnson involving a dimensionless exponent, q ≥ 1. When q = 1, the particle stream is divided in proportion to the flow rate; as q → ∞, the particles are channeled into the tube with the highest flow rate. The simulations reveal that when the network involves two or more generations, a supercritical Hopf bifurcation occurs at a critical value of q, yielding spontaneous, self-sustained oscillations in the segment flow rates, pressure drop across the network, and particle spacing in each tube. A phase diagram is presented to establish conditions for unsteady flow. As found recently for blood flow in a capillary network, oscillations can be induced for a given network tree order by decreasing the ratio of the tube diameter from one generation to the next or by decreasing the diameter of the terminal segments. The instability is more prominent for rigid than deformable particles, such as drops, bubbles, and cells, due to strong lubrication forces between the tightly fitting particles and tube walls. Variations in the local particle spacing, therefore, have a more significant effect on the effective viscosity of the suspension in each tube and pressure drop required to drive a specified flow rate.     

Aluminization of nickel-formation of intermetallic phases and Ni2Al3 coatings

The occurrence and growth mechanisms of the various intermetallic phases of the Al-Ni system formed during pack aluminization of unalloyed nickel have been investigated with respect to the aluminium activity in the pack. Several types of coatings were obtained: (1) a Ni₂Al₃ coating formed by inward aluminium diffusion in a high activity cement of pure aluminium; (2) a Ni-rich NiAl coating formed by outward nickel diffusion in a low activity pack constituted by an Al-Ni alloy; (3) a mixed type of coating exhibiting the phases Ni₂Al₃, Al-rich NiAl, Ni-rich NiAl and Ni₃Al in four superposed layers, formed in a pack containing an Al-Cr alloy; (4) a high temperature, high activity type of coating formed above 950° C with an outer layer exhibiting a hypereutectic structure of NiAl₃ grains in a eutectic matrix due to precipitation from the liquid state. The optimum cementation conditions, for the production of maximum thickness and quality Ni₂Al₃ coatings were determined. The influence of surface reactivity and pack activity on the coating quality parameters was investigated.     

Evaluation of the Field near a Cusp of a Caustic

The field in the neighbourhood of a cusp of a caustic can be expressed in terms of a function of two variables, P(X,Y), known as Pearcey's integral or the Pearcey function. In this paper we develop efficient algorithms for computing this function and its derivatives P/ X and P/ Y. They are based on a Taylor series expansion in a region close to the cusp at X = Y = 0, and on asymptotic approximations in regions far from the cusp. The asymptotic results are given in terms of contributions of isolated stationary points in regions far from the caustic, and in terms of the Airy integral function and its derivative in a region close to the caustic. Three terms in the asymptotic expansions are used, and they give an accuracy for P(X,Y) better than 0·006 in amplitude and 0·6° in phase at distances from the cusp greater than (X² +Y² )^1/2 = 4.     

Mechanism of carburization of high-temperature alloys

An investigation of the mechanism of gaseous carburization in a reducing environment was conducted for selected Fe- and Ni-base alloys. Carburization kinetics were measured as functions of temperature in the range 870–980 °C. Scanning electron microscopy, analytical electron microscopy and X-ray diffractometry were employed for microstructural characterization and microchemical analysis. Changes in mechanical strength produced by carburization were determined from microhardness and tensile property measurements. Kinetic studies indicated that the carburization reaction followed a parabolic rate law. Depending upon the nature of surface scale formed in the presence of a carburizing environment, the rate-determining step of the reaction varied from C diffusion into the alloy in the presence of a carbide scale to that in the presence of an oxide scale. Under reducing carburizing conditions, alloys inherently protected by Cr₂O₃-base scale were found to develop a surface carbide scale which allowed C to penetrate into the alloy with relative ease and, thus, the carburization kinetics was accelerated. In contrast, an alloy capable of forming Al₂O₃ developed and maintained a protective surface oxide scale which acted as an effective barrier to C diffusion into the alloy. Degradation of mechanical strength due to precipitation of carbides in the alloy was correlated with the rate of attack and consequently the nature of the surface scale.     

Effect of strain on the frequency-independent parameters of the equivalent circuit of island gold films

This paper deals with the outcome of a follow-up of our earlier work on the effect of strain on the frequency-dependent resistance (r_p) of island gold films whose mass thicknesses in nm were 0.5, 1.2, 2.4, 3.5, 5 and 10. The frequency-independent parameters of the equivalent circuit of island metal films are R_b, R_g and C_g where R_b is the macroscopic resistance that associates the conduction within the interior (bulk) of islands, R_g is the macroscopic resistance that accompanies the conduction across the gaps among islands and C_g is the macroscopic capacitance of the film that results from the islands and gaps. We deduced the least-square values of R_b,R_g and C_g for our films by inserting the experimental values of r_p and the corresponding angular frequencies (ω) into the known equation that relates r_p to both of ω and the frequency independent parameters; this deduction was done via a computerized analysis. We found that: (1) For the tensional longitudinal strain, an increase in its magnitude is associated with an increase in R_g and a decrease in C_g. (2) For the compressional longitudinal strain, an increase in its value is accompanied by a decrease in R_g and an increase in C_g. (3) R_b is nearly invariant with strain. (4) The increase in the mass thickness of the island gold films is associated with: (i) a decrease in R_b,R_g and an increase in C_g. (ii) a decrease in the gauge factor of the studied films.     

Complex Model of the Efficiency of Rectification Plates. 4. Cross Motion of Phases

A model of mass transfer in the cross motion of phases is proposed in which the compositions of the flows on ideal and real plates at a certain distance h for a vapor and h ₁ for a liquid from the site of their injection are equal. The composition of the vapor after a plate is equal to the average value of the compositions of the vapor after the initial and final portions in the direction of liquid motion that, for an ideal plate, are in equilibrium with, respectively, the arriving and discharging liquid. Dependences of the efficiency in the vapor and liquid phases on the parameters of a real plate that are identical and confirm the equality of these efficiencies are derived. An analysis of particular cases of the model for h = h ₁ and h = h ₁ = 0.5 and for their boundary values when they are equal to zero or to unity is made. Corresponding relations of the efficiencies are obtained.     

Development of a structural model of deformation with hardening on the basis of distributed dislocations

We consider a problem of elastoplastic deformations with strengthening in the case where a “tooth” of yield is present in the (σ-∈) diagram. On simulation of the process of development of plastic deformations with hardening by using distributed screw dislocations, a conclusion on the existence of a structural parameter is drawn. Kherson Industrial Institute, Kherson. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 3, pp. 103–107, May–June, 1998.     

Determination of the size of the fatigue prefracture zone by the method of phase-shifting interferometry

We consider a new method for determining the size of the fatigue prefracture zone (a new structural-mechanical parameter d* of constructional materials) by the method of phase-shifting interferometry, based on the results of a comparative analysis of the surface profile of metallic specimens in the neighborhood of a constructional stress concentrator prior to and after a certain quantity of loading cycles. To obtain interferograms in laser light, we applied a Twyman–Green interferometer. Using these results, we determined the 3-D distribution of plastic strains near the concentrator vertex, which enabled us to establish that d* = 256–268 μm for low-carbon 08kp steel at a load ratio R = 0.1. The obtained value of this parameter is in good agreement with data obtained by other methods.     

Unified model of nucleation and growth of fatigue cracks. Part 1. Use of force parameters of fracture mechanics of materials in the stage of crack nucleation

According to the phenomenological model of nucleation of a fatigue macrocrack, the process is considered as a two-parameter process. The process is described by the local stress or strain range and a certain linear parameter of the material. We propose the corresponding parameters, namely, the local stress range Δσ _y ^* and the characteristic sized ^* of the prefracture zone. The formation of this zone is caused by the anomaly of the yield strength of the material in subsurface layers, the microstructure, the loading amplitude, the cyclic strain hardening, and the environment. The quantityd ^* is a constant of the material, which is independent of the geometry of notch and specimen. the boundary of the prefracture zone is considered as a macrobarrier that determines the growth of microstructurally short and physically small cracks. The moment when a physically small crack oversteps the boundary of the prefracture zone is defined by the quantitative criterion (a ₀=d ^*) of the initial sizea ₀ of a macrocrack in the material. The proposed dependences of (Δσ _y ^* ,N _i ),N _i ) and (d ^*,N _i ) can be regarded as a basis for the determination of characteristics of resistance of the material to the nucleation of a fatigue macrocrack. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 1, pp. 7–21, January–February, 1998.     

Development of a reference strain approach for assessment of fracture response of reeled pipelines

As a result of recent increase in exploitation of hydrocarbon resources in harsher environments and also installation techniques which utilize the materials plastic deformation capacity, accurate assessment of fracture response of pipelines subject to large plastic strains (e.g., typical of reeled pipes) has attracted particular interest nowadays. In this paper, an approach, based on the evaluation of the J-integral, is developed for assessing the integrity of such pipelines, manifested in a model of a pipeline with a circumferential part-through crack subjected to plastic bending. The proposed approach is an extension of the reference strain method developed earlier by other researchers, and takes advantage of the displacement controlled loading nature in such pipes (thus being suitable for Strain Based Design methodologies), and the resulting high strain levels, which often cause fracture response of the material in the plastic regime. The developed formulation relates the fracture response of the pipe (in terms of the non-dimensionalized J-integral) as a linear function of the axial strain in the pipe at its uncracked state. A series of 300 3D nonlinear finite element models using the ABAQUS software were analyzed in preparation of the equation that could assess the fracture response of such pipes with great accuracy. The resulting equation, calibrated by the finite element results, can predict the fracture response of pipes with a maximum error of 2% for a practical uncracked material strain range of 1.5% ? ε_unc ? 4%.     

Development of a flow field structure in the vicinity of a circular cylinder in the presence of a laminar-turbulent transition

The Reynolds equations and the two-parameter differentialq-Ω model of turbulence are used to investigate a flow past a circular cylinder with an isothermal surface (temperature factorT _w0 = 0.5) at the Mach numberM _∞ = 5 in the range of Reynolds numbers Re = 10⁴-10⁸. It is demonstrated that the turbulization of flow leads to a shift of the separation point downstream, a reduction and stabilization of the separation zone length, a decrease in the maximum velocity in the separation zone, and an increase in the heat flux at the rear stagnation point compared with its value at the forward stagnation point.     

Prediction of welded joint thinning by the method of polarization resistance

The equivalent electric circuits for determiningR _p in electrolytic cells with two dissimilar electrodes are investigated. For welded joints, we suggest a relation for estimating the corrosion rate in terms ofR _p and describe the design of a solion for determining this rate in a local zone of a welded joint.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 5, pp. 94–96, September–October, 1993.     

Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.     

Effect of skin fracture on failure of a bilayer polymer structure

A thin skin of low tensile failure strain, if bonded to the tensile surface of an un-notched impact bend specimen of much tougher material, can change the global failure mode from ductile to brittle. A novel model of this well-known effect is developed and applied to results from impact tests on a tough core of polyamide-polyethylene blend, with a single skin of brittle EVOH. At a fixed crosshead speed, notched specimens of the blend become brittle at a relatively low temperature T _bt. Un-notched bilayer specimens continue to show skin fracture up to a considerably higher temperature T _fs; above this temperature they do not fail at all but below T _bt they too fail in a brittle manner. Within the temperature range from T _fs down to T _bt there is a transition from crack arrest, either at the skin/core interface or further into the core where a crack would not normally propagate, to brittle fracture. This brittle fracture temperature is predicted by modelling the process as a three-phase impact event. In the first phase, the striker bends the bilayer quasi-statically. The second phase begins with instantaneous fracture of the skin at its failure strain. The skin ends retract at finite speed, and a craze grows in the adjacent core material to accommodate the local strain singularity. The last phase is a striker-driven impact event similar to that in a notched bend specimen of the core material, except that the crack-tip craze already bears the adiabatic temperature distribution generated while it was driven open by skin retraction. The criterion for craze decohesion, and hence for a crack jump, is the same adiabatic decohesion criterion which accounts for the speed-dependence of impact fracture in notched monolayer specimens. Applied computationally, this model predicts whether a bilayer structure fails in a brittle way or whether cracks initiated in the skin are arrested, either temporarily or permanently, at the skin/core interface.