Measurement of grain size and size distribution in engineering materials

Abstract

Methods to characterise grain size distribution in engineering materials are evaluated, and compared with measurements on two representative materials, an equiaxed aluminium alloy and a heterogeneous nickel alloy. Computer simulations from a model tetrakaidecahedron structure have also been obtained using a personal computer program to rotate and section the model randomly, generating distribution data on section area and intercept lengths. Comparisons have been made between the model distribution data and intercept distribution data from the material microstructures.

It is recommended that size distributions of area plotted against size (intercept) or normalised size provide an effective method for discriminating between different grain size distributions. An estimate of area can be used indirectly by squaring intercept values rather than making direct measurements of grain areas.     

Plane section and spatial characteristics of equiaxed β-brass grains

Abstract

A study was undertaken to define better the concept of the statistical grain. A cube having edges of 52·1 mm was cut from a slowly cooled β-brass ingot which had equiaxed grains. The distributions of sizes and shapes of grain sections on the faces of the cube were determined. The grains were then separated in a solution of mercurous nitrate and nitric acid. Observations were made of the relationship between grain diameter and the number and shapes of faces. For the 941 separated whole grains, the frequency of distribution of grain diameters obeyed the log–normal law. A plane distribution curve was derived for the statistical grain which enables spatial distributions to be calculated from measurements made on a plane section.

MST/825     

Effect of cooling rate on grain size of ferrite in a carbon steel

Abstract

Ferrite grain refinement by accelerated cooling has been studied in a carbon steel. The size of ferrite grains d_α formed by continuous cooling transformation from polygonal austenite has been measured as a function of cooling rate and austenite grain size d_γ. In the cooling rate range studied (q= 0·05–5 K s^?1), d_α was found to be proportional to q^?0·26d_γ^0·46. The mechanism of grain refinement by accelerated cooling is discussed, and it is shown that this occurs in the transformation where the ratio of nucleation to growth rate increases with a decrease in temperature. The austenite grain size dependence of ferrite grain size is shown to become progressively large as the nucleation mode changes from homogeneous to grain surface to edge to corner. A theoretical estimation of ferrite grain size formed by continuous cooling transformation was attempted on the basis of nucleation and growth rates. In the alloy studied, ferrite grain size was theoretically estimated to be proportional to q^?0·17d_γ^0·33. This was in close agreement with the dependence obtained in the present experiment.

MST/466     

Statistical aspects of cleavage resistance of high strength microalloyed structural steels

Abstract

The statistical distribution of the cleavage fracture stress σ_cf was determinedfor two modern high strength microalloyed structural steels through a series of 30, four point bending tests at a temperature of 77 K. A parallel investigation of the distribution of the largest ferrite grain diameter d_max observable by optical microscopy in regions of approximately the same size as the cleavage process zone, was carried out using 120 datafor each steel. A calculated distribution of σ_max was then constructed by means of a theoretical formula developed in a previous work, which gives σ_cf as a power function of d_max. The comparison with the experimental distribution of σ_cf demonstrates that the statistical scatter of the cleavage fracture stress for the investigated steels can be explained as entirely due to the statistical scatter of d_max. Thus more evidence for the validity of the theoretical equation was obtained and, in addition, it was shown that the exponent of d_max was the same for both steels in spite of their different chemical composition.     

Computer model of a porous medium

A computer model has been set up to represent a porous medium. The basis for this model is a two-dimensional square network (100×100) of channels that have randomly assigned widths between the value of zero (closed) and the value of one (open, unrestricted flow). The channel width assignments have been made by a random selection from five different distributions:f(q)=q, f(q)=sinq, f(q)=erf(q),f(q)=1–sinq, andf(q)=1 –erf(q). Diffusion of particles in the network has been studied by a random-walk procedure for each realization of the channel width assignments. The diffusivity is quite sensitive to the distribution of channel widths. The percolation properties of the networks obtained from the three most restrictive distributions have been investigated and the independent, linked clusters within the network have been determined. For cluster sizes that are less than the full width of the network, the network does not percolate and either the flow is not diffusive or the diffusivity is severely reduced. An approximate value for the percolation threshold has been determined in each case and the fractal dimension has been calculated also.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

On the equilibrium distribution of the impurity atoms in real crystals

This work discusses the equilibrium distribution of impurity atoms among different sinks and the matrix of a real crystal. A simple formula, interpolating the McLean formula is obtained. Impurity segregation in crystals, containing two types of sinks (e.g. grain boundaries and dislocations) is investigated. Impurity concentration on a weakly- binding sink (grain boundary) as a function of the temperature, T, may be represented by a curve, the shape of which depends on the ratio of the average impurity concentration and the relative volume of a strongly-binding sink (dislocation) and on the ratio of the binding energies of an impurity atom on different sinks. There are four possible shapes of the curve. Three of them are not monotonic and show a maximum at T=T _max. One of these three also exhibits a minimum at T=T _min < T _max. This may be used to diminish the content of a harmful impurity on the grain boundaries.     

A heat meter of finite thickness

The two-dimensional steady-state problem is solved for a heat meter of finite thickness. Corrections to the heat meter readings are estimated.Notation q_o unperturbed heat flux - q_H heat flux recorded by heat meter - heat-transfer coefficient - thermal conductivity - thickness of heat meter - R radius of heat meter - J_o, J₁ zero- and first-order Besael functions - T₁, T₂ temperature distributions of semi-infinite wall and heat meter - T_o temperature distribution of wall in the absence of heat meter Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 835–842, November, 1979.     

Static Ferromagnetic Modulation Revealed by Neutron Scattering in La1?xCaxMnO3

Mn perovskites La_1–x Ca _x MnO₃ (0x0.1) have been studied by small angle neutron scattering (SANS) and elastic neutron scattering (ESANS). At low temperature, both experiments reveal a broad modulation centered at the same q _m whatever the q direction. This scattering pattern is typical of a liquid-like distribution of similar magnetic droplets, or large magnetic polarons.     

Grain-size dependence of Snoek peaks in niobium

The effect of grain size on the oxygen and nitrogen Snoek peaks in niobium has been studied. It has been observed that the conversion factor K given by C = K _max, where C is the concentration of oxygen or nitrogen and _max the height of the corresponding Snoek peak, is concentration independent up to about 0.06 and 0.04 wt % oxygen and nitrogen respectively.The variation of K with grain size (d) obeys the relationship K = K ₀ + k_Kd^–1/2, where K ₀ represents the value of K for an aggregate of crystals without boundaries and k _K the grain size dependence of K.     

Heat transfer in nitrogen-methane mixtures under pressure with film boiling

Heat transfer from a horizontal cylinder into nitrogen-methane mixtures (0 to 100 molar per cent) was studied in the film boiling range at 0.2 and 2.8 MPa. At constant heat flux density ΔT decreases with increasing methane content.Heat transfer from a horizontal cylinder into nitrogen under pressure was studied in the bubble boiling region, in addition to the film boiling range, to provide a connexion between our experiments made on the horizontal surface, q_max at cylinder ~ 0.7 q_max at horizontal surface. For the relation $\text{q}\text{?}{}_{\mathrm{<mtext>max</mtext>}}\text{/}\text{q}\text{?}{}_{\mathrm{<mtext>min</mtext>}}$ at cylinder a value of ten was obtained at all pressures     

Radiative-convective heat transfer for high-temperature two-phase flow around bodies

Some methods for determining the basic parameters of high-temperature two-phase flows and the results of investigation of radiative—convective heat transfer with a flowing body in a flow are presented.Notation x=x/d, x distance from the plasmatron nozzle exit section - d diameter of the plasmatron nozzle - q=q_p/q₀, q_p heat flux in the vicinity of the critical point of the surface in a flow given the gas flow - q₀ neat flux in the absence of particles in the flow - _p mass concentration of particles in the flow - G_p mass flow rate of the condensed phase - G_g mass flow rate of the gas phase Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 300–303, March 1993.     

Heat source density and temperature distribution in a laser ruby crystal

The heat source density in a laser ruby is calculated by numerical integration of the pumping and absorption spectra. The heat source density can be represented approximately by the formula q(r) = =q₁ + q₂ I₀ (r/r₀), which can be used to determine the temperature distribution in the crystal for typical pumping and cooling conditions.     

Phonon dispersion in He II at long wavelengths and low temperatures

Phonon dispersion in liquid He II at long wavelengths and low temperatures is calculated using a generalized polarization potential approach and shown to yield results in good agreement with both superthermal phonon propagation and neutron scattering experiments at pressures up to 24 bar. It is shown that the long-wavelength dispersion relation is of the form _q =s ₀ q(1+₂ q ²+₃ q ³+...) suggested by Feenberg and by Kemoklidze and Pitaevskii, but that the validity of such an expansion is restricted to wave vectorsq0.1Å ^–1. For larger values ofq, one can force a polynomial fit, containing only odd powers ofq, to the dispersion curve and other parameters of interest, but the number of terms which must be kept is so large as to render such an approach unwieldy.Work supported in part by the National Science Foundation Grant NSF DMR72-03026.     

Heat and mass transfer of a multiatomic gas in a cylindrical capillary with arbitrary Knudsen numbers

Processes of heat and mass transfer of a multiatomic gas in a cylindrical channel of circular cross section with arbitrary Knudsen numbers are considered on the basis of a model kinetic equation, taking account of the excitation of rotational and vibrational degrees of freedom of the molecules.Notation Kn Knudsen number - f, f^tr total and translational Eucken factors - R_o capillary radius - m molecular mass - k Boltzmann's constant - n, T numerical density and temperature of gas - v_i i-th component of the molecular velocity - h_ij perturbation function - E_i ^(r), e_j ^(v) energy of the i-th rotational and j-th vibrational levels - E_o ^(r), E_o ^(v) equilibrium values of the rotational and vibrational energy - P_i ^(r), P_i ^(v) probability of rotational and vibrational states of energy E _i ^r and E _j ^v - , logarithmic pressure and temperature gradients - T_o mean gas temperature - R rarefaction parameter of gas - C _V ^r , C _V ^v contributions of rotational and vibrational degrees of freedom of the molecule to the specific heat at constant volume - U macroscopic gas velocity - q^(t), q^(r), q^(v) components of the heat flux density due to translational, rotational, and vibrational degrees of freedom of the molecules - P, pressure and dynamic viscosity of the gas - l free path length of molecules - up velocity of Poiseuille flow - u_T rate of thermal creep - cross-sectional area of capillary - I_n, I_q numerical and heat fluxes averaged over the channel cross section - universal index characterizing the thermomolecular pressure difference - ^t, ^r, ^v thermal conductivities due to translational, rotational, and vibrational degrees of freedom of the molecules - mass density of the gas - D_rr, D_vv diffusion coefficients of rotationally and vibrationally excited molecules among the unexcited molecules - Z_r rotational collisional number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 71–82, July, 1984.     

Anisotropic mobility and carrier dynamics in the β-type BEDT-TTF salts as studied by inter-layer transverse magnetoresistance

Abstract

A new method to estimate an in-plane conduction anisotropy in a quasi-two-dimensional (q2D) layered conductor by measuring the inter-layer transverse magnetoresistance is proposed. We applied this method to layered organic conductors β-(BEDT-TTF)₂X (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene, C₁₀H₈S₈; X = IBr₂, I₂Br) by applying magnetic field rotating within the basal plane at 4.2 K. We found the anisotropic behaviour of carrier mobility μ. From this, anomalous distribution of carrier lifetime τ on the Fermi surface is derived, by the use of Fermi surface data reported for the materials. Calculations of the non-uniform susceptibility χ₀(q) suggest that carrier scattering is enhanced at specific k-points related to partial nesting of the Fermi surface. The present method is thus demonstrated to be an efficient experimental tool to elucidate anisotropic carrier dynamics in q2D conductors.     

Statistical basis for surface roughness assessment in oblique finish turning of steel components

The process variability with respect to surface roughness as measured by R_α and -R_max values in single point oblique finish turning of a carbon steel is systematically studied on a statistical basis throughout the life of the tool. Thus, firstly, the effect of tool wear on surface roughness is considered. Furthermore, cumulative distributions of R_α and -R_max values are presented to illustrate how well the observed data fits the theoretical. A x² statistical test of significance was applied to test the normality of these distributions. Normality was established for all distributions dealt with mostly at 5% significance level. Process variability, then, is quantitatively determined according to the experimental data analysed herein. Finally, application of the distributions modelled for setting control limits for sample means of surface roughness values is discussed.     

Influence of through-thickness crack shape on plasticity induced crack closure

In most of the previous three‐dimensional (3D) numerical studies of plasticity induced crack closure (PICC), ideal shapes have been assumed for the cracks. The aim of present paper is to study the effect of crack shape on PICC. With this objective a 3D numerical model was developed to predict PICC in middle‐tension (MT) specimens with different thicknesses and crack shapes. The radial size of crack tip elements and the stabilization of closure level were studied to ensure the quality of numerical predictions. Simultaneously, an independent numerical model was developed to predict crack shape evolution, stable crack shapes and corresponding K distributions. Crack closure was found to produce a significant tunnelling effect, with maximum values of ΔK and K_max at the surface. The curved crack presented significant plastic deformation near the free surface which has a high impact on the computation time, compared to the straight crack. The modification of ΔK and K_max with crack shape produced a variation of 38% in opening values at the interior positions, but relatively small variations at the surface. Considering the great influence of crack shape on PICC, it is fundamental to model realistic crack shapes.     

The flow of a fluid film entrained by a supersonic flow of gas

We have conducted an experimental study into the flow of a high-viscosity fluid directed through an orifice of small diameter onto the surface of a body contained within a supersonic flow of air.Notation M Mach number for the outlet cross section of the nozzle - Re_D Reynolds number calculated from the parameters of the unperturbed flow at the outlet section of the nozzle and from the diameter of model rounding - P₀ total pressure in the pressure chamber of the wind tunnel, Pa - T₀ deceleration temperature - sweepback angle of leading edge of plate (between the normal to the direction of the unperturbed flow and the generatrix of the leading edge), deg - d orifice diameter, mm - angle between direction of unperturbed flow and radius vector of orifice, deg - frictional stress at boundary separating fluid and gas, Pa - Q volumetric fluid flow rate, cm³/sec - kinematic viscosity of fluid, cSt - q /q_g ratio of the velocity head of the fluid at the outlet from the orifice to the local velocity head of the gas - thickness of fluid film, mm - b width of fluid film, mm - angle between tangents to the side boundaries of the fluid film, deg - s coordinate calculated from the center of the orifice along the midline of the film or along the axis of wedge symmetry, mm - z coordinate calculated along the normal to the axis, mm Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 2, pp. 181–186, August, 1990.     

Grain coarsening mechanism of Cu thin films by rapid annealing

Cu thin films have been produced by an electroplating method using nominal 9N anode and nominal 6N CuSO₄·5H₂O electrolyte. Film samples were heat-treated by two procedures: conventional isothermal annealing in hydrogen atmosphere (abbreviated as H₂ annealing) and rapid thermal annealing with an infrared lamp (abbreviated as RTA). After heat treatment, the average grain diameters and the grain orientation distributions were examined by electron backscattering pattern analysis. The RTA samples (400 °C for 5 min) have a larger average grain diameter, more uniform grain distribution and higher ratio of (111) orientation than H₂ annealed samples (400 °C for 30 min). This means that RTA can produce films with coarser and more uniformly distributed grains than H₂ annealing within a short time, i.e. only a few minutes. To clarify the grain coarsening mechanism, grain growth by RTA was simulated using the phase field method. The simulated grain diameter reaches its maximum at a heating rate which is the same order as that in the actual RTA experiment. The maximum grain diameter is larger than that obtained by H₂ annealing with the same annealing time at the isothermal stage as in RTA. The distribution of the misorientation was analyzed which led to a proposed grain growth model for the RTA method.     

Effect of the temperature dependence of thermal properties on the thermal shock tests of ceramics

Thermal stress generated during a thermal shock is closely related to the fracture of ceramics. An attempt has been made to obtain thermal stress in a specimen by numerical calculation. The temperature dependence of thermal conductivity and diffusivity were introduced to realize the practical thermal conditions. The maximum thermal stress, _max ^* , was recognized at the Fourier number, but differed from the temperature dependence. Correlative equations of _max ^* and _max ^* with the Biot number, _i, under cooling or heating tests, have been proposed. These equations resulted in the exact _max ^* and _max ^* compared with the previous equations, in which temperature dependence was ignored. The thermal shock resistance parameter was expressed by the correlative equations of _max ^* in order to suggest adequate experimental conditions and specimen size. A comparison of the measured and calculated time to failure of the specimen led to confirmation of the fracture criterion. The measured time disagreed with the calculated one, if the fracture by thermal shocking was not predominant. The correlative equations were also useful to select the kind of ceramics subjected to thermal shocking.