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Investigations have been carried out to establish the relationship between the friction force and the normal force in dry sliding with high normal pressure at low speeds when there is considerable plastic flow of material on the rubbing surfaces. The study was extended by limiting the area of contact and by providing a virgin surface. Conditions which influence seizure phenomena caused by high pressure and temperature and the extent to which it may affect the sliding characteristics are discussed. Damage due to sliding under extreme conditions has been studied to aid the better understanding of friction phenomena.

Solutions are obtained for the problem of an infinite elastic beam subjected to essentially constant velocity boundary conditions at one point of the beam. The effects of finite deflections, normal force, rotatory inertia and shear deformation are included. The equations of the problem are converted into non-dimensional form and a perturbation approach is used to obtain a consistent approximation. Numerical solutions are obtained for the bending moment, shear force and the normal force for different velocities of impact. It is shown that the solution to the problem depends on a combined geometrical and material parameter which does not vary significantly for compact sections and a loading parameter which determines the amplitude of the response. Finally the linear Timoshenko beam theory is shown to predict the bending moment and shear force extremely well even when the deflections are large enough to cause appreciable stretching of the centroidal axis.

In order to make clear the effects of the bulk plastic deformation on the frictional mechanism, a two-dimensional drawing-type friction testing machine has been designed and made. Using this Apparatus, it is possible to measure simultaneously and continuously the frictional and normal forces on both metal surfaces of the die side and the blank-holder side during the process. The apparent surface area of metal increases notably on the die side only, although the microscopic surface texture varies notably on both the sides. It has been confirmed by a calibration of the measuring devices that all the forces shown above can be precisely measured without mutual interference. Some preliminary experiments on aluminium and copper sheets have been carried out by this apparatus. As the result, it has been found that the frictional coefficients on the die surface are larger than those on the blank-holder surface.

The authors derive an expression for the force on a classical charge moving with arbitrary velocity v in the neighbourhood of a metal surface. A simple physical argument shows why the parallel component of the velocity-dependent force is half the normal component for a slowly moving charge.

It is shown that the normal forces set up by large shear deformations make sliding impossible when a critical compressive deformation, of the order of 10%, is imposed on a sliding block of highly-elastic material. When the compressive load is maintained constant, rather than the deformation, the way in which the compressive stress is distributed leads to sliding only by means of slip bands which originate at the leading edge of the block and then pass through the contact zone from front to back, as found by Schallamach1. Thus, a discontinuity is predicted in frictional sliding as the compressive stress is increased from zero, and this occurs at a critical value which depends upon the coefficient of friction, the shear modulus of the material, and the detailed shape of the contact zone. Corresponding changes in wear behavior are inferred.

This paper presents a classical elastostatic analysis of the following situation. A rigid circular disc of radius a is buried in an elastic soil at a depth h below a stress-free surface. The disc is subject to a normal force T resulting in uniform normal displacement of the disc of amount α. Two problems are solved. In the first, the elastic soil is assumed to adhere to the underside of the disc and a solution is obtained by perturbation methods for a h . For the second, the material on the underside of the disc is assumed to have broken away; here, an exact solution is found for the limiting case a h → 0 . The analysis is pertinent to the recently innovated civil engineering technique which utilizes ground anchors to support the retaining walls of excavations.

SummaryThe power spectral technique has been extended to show the effect of aerodynamic non-linearities on the normal acceleration response of a rigid aircraft in the cruise configuration. Non-linearities in the normal force and pitching moment variations with incidence have been considered. The resulting changes from the linear root-mean-square values of normal acceleration were only 3 to 5½% for a root-mean-square vertical gust velocity of 20 m/s.

The mechanism of thin film lubrication of sliding point contacts of AISI 52100 steel has been studied as a function of load, sliding speed, composition and temperature of the lubricant. Below certain critical combinations of Hertzian pressure, speed and temperature the surfaces are kept apart by an elastohydrodynamic lubricant film. The load carrying capacity of this film depends primarily on the effective viscosity of the lubricant in the contact region which decreases with bulk oil temperature and with increasing sliding speed, because of friction induced thermal effects. After breakdown of the EHD film, boundary lubrication may still prevent severe adhesive wear. The transition from the boundary lubricated regime towards the regime of severe adhesive wear is a function of load (normal force), speed and bulk oil temperature and possibly depends on the conjunction temperature. Irrespective of the initial lubrication condition, oxidation of the steel surfaces leads to the (re)establishment of low friction, mild wear conditions.

The components of the friction force have been analysed at length from a physical point of view but no equivalent mechanical analysis has been formulated to date. In this study, elementary laws of statics are applied to a contact. The reasoning shows that, the friction term is composed of surface and shape effects but that these are not independent of each other and thus cannot be analysed separately. The argument is used to show under what conditions pure surface effects can be measured. Finally, the presence at the contact of conservative or dissipative materials is shown to influence greatly the contact shape, the normal tangential stress distribution and the friction force.

The plane strain problem of a half-plane crack in an unbounded elastic solid is considered. The faces of the crack are subjected to suddenly applied, equal but opposite concentrated normal forces which tend to separate the crack faces. The elastic wave propagation problem, which contains a characteristic length, is solved exactly by linear superposition over a fundamental solution arising from a particular problem in the dynamic theory of elastic dislocations. Attention is focused on the time-dependent stress intensity factor. For an applied load with step function time dependence, the stress intensity factor is negative from the time the first wave arrives at the crack tip until the arrival of the Rayleigh wave. At that instant, it takes on its appropriate static value, which is thereafter maintained. Generalizations are discussed for spatially distributed and/or time-varying normal impact loads.

The electrification of a system consisting of a metal and Teflon (polytetrafluoroethylene) has been investigated in vacuum under relative motion. A plane strip of Teflon was moved in relation to a metal electrode connected to an electrometer, which permitted the electrification charge to be continuously recorded. The electrification current was found to be closely proportional to the velocity, and it was practically independent of the radius of curvature of the tip of the electrode. The normal force was also varied, and the linear charge was found to be proportional to the square root of this force. Electrodes of Al, Au, Cu, Dural, Mg, Ni, and Pt were used, and the charge deposited was found to be linearly dependent on the metal work function, except for a large anomaly in the case of Cu. For a given metal the charge was shown to be closely proportional to the area swept out by the electrode on the insulator surface. The linear dependence of charge on metal work function and the short charging time (0.06 s) observed indicate that electrons from the metal fill empty surface states in the insulator up to a level corresponding to the Fermi level of the metal. The surface‐state density of Teflon was found to be 7×1010 eV−1 cm−2.

We consider the deformation of an elastic and incompressible cylindrical tube of circular cross-section into a cylinder of a given shape under the action of end forces, uniform external pressure and normal forces applied on the inside surface. The outside surface of the undeformed tube is reinforced by a two parameter family of inextensible helical cords. The only restriction imposed on the cross-section of the deformed inside surface is that it has a continuous curvature. The equations are given for the general strain-energy function. Subsequently, it is assumed that the thickness of the tube is small compared to its overall diameter and the solutions to the equations are obtained, to the second order, for a neo-Hookean solid. Since the deformations considered are plane, the analysis is also valid for a Mooney-Rivlin material. Applications to specific boundary value problems are also given.

In this paper, the waves propagated in an infinite medium has been considered by disturbances on the surface of a burried spherical source. The disturbances are produced by two types of forces viz. i) Transient normal force, ii) Transient twist applied on the surface of the source. The solutions are obtained in a very simple form. Graphical representations of some numerical solutions has been added at the end of each problem.

In view of the relatively low mean velocities which give optimum efficiency for pipelines transporting granular solids, it is important to study the conditions for which stationary deposits occur in pipes. The limit of deposition is the slip point, at which the force driving the bed exceeds the coefficient of friction times the total normal force exerted by the bed grains against the pipe wall. Although the state of intergranular stress in the deposit is generally indeterminate, it is shown that near the slip point it is a reasonable assumption that the granular pressure at the periphery of the bed follows a hydrostatic distribution. Experimental verification of this assumption was obtained from two types of tests, one involving flow conditions in a recirculating system and the other the slipping of deposits in a tilting pipe. The relationship derived for the hydrostatic distribution of granular pressure shows that the pressure gradient at the slip point is directly proportional to the underwater weight per unit volume of bed, and increases with the angle subtended by the deposit.

Painleve [1] in his book Lectures on Friction showed that the addition of dry friction forces does not alter the stability of equilibrium states of mechanical systems, for which the potential energy at the equilibrium state has an isolated minimum. In [2] and [3] a problem of stability of stationary motions of some particular mechanical systems with dry friction has been investigated: Some properties of the system were determined such that the addtion of the dry friction forces not affect the stability of the motion, provided that the systems are stable when subjected to the action of potential forces only. In [2] and [3], however, only such frictional forces are considered which appear during the sliding of the surfaces and which result in constant moments ± B , independent from the normal forces (the forces are acting in the opposite direction to the relative sliding velocity). Such a model of dry friction, obviously, differs from the classical Coulomb model. It may, however, serve as a step toward the study of the problem in its classical formulation. The present paper is devoted to such a study.

A closed functional solution is formulated for the expression of the steady state frequencies of vibration of a simply supported plate stiffened by a grid. The grid properties are assumed to be different in orthogonal directions. The plate-grid interactions are assumed to consist of only normal forces at the node points.

The general form of the flow behind an infinitely long thin flat plate inclined at a large angle to a fluid stream of infinite extent has been known for many years past. The essential features of the motion are illustrated in the smoke photograph given in fig. 1, Plate 6. At the edges, thin bands of vorticity are generated, which separate the freely-moving fluid from the “dead-water” region at the back of the plate; and at some distance behind, these vortex bands on account of their lack of stability roll up and form what is now commonly known as a vortex street (see fig. 2). Various theories for calculating the resistance of the plate have also been advanced from time to time. One of the earliest is the theory of “discontinuous” motion due to Kirchhoff and Rayleigh, who obtained the expression π sin α/4 + π sin α ρV 0 2 b (see symbols) for the normal force per unit length of the plate. More recently Kármán has obtained a formula for the resistance of a plate normal to the general flow, in terms of the dimensions of the vortex system at some distance behind the plate. In spite, however, of these and other important investigations, much more remains to be discovered before it can be said that the phenomenon of the flow is completely understood. No attempt has hitherto been made, as far as the writers are aware, to determine experimentally, at incidences below 90°, the frequency and speed with which the vortices pass downstream; the dimensions of the vortex system; the average strength of the individual vortices; or the rate at which vorticity is leaving the edges of the plate. The present investigation has been undertaken to furnish information on these features of the flow.

Mr. A. W. Johns states in the T. I. N. A. of 1907 that stress induced by centrifugal force T originating in unbalance of propeller is greatest and gives the value of the maximum bending moment at that time, but in this paper, the value of the bending moment is scrutinized a little further, and farthermore, the value of the twisting moment, shearing force, and normal force is examind. If the various dimensions are taken as given in the annexed figures. In ordinary ships l2 is severa times or more than l1 or 1, and L is several times or more larger than a. Furthermore, granting that conditions is between about 50 degrees and 90 degrees are generally substantiated, at such times, the stress due to twisting moment, shearing force, and normal force are negligibly small in comparnson to the stress due to bending moment. When T indicates certain direction the bending moment enlarges at the barrel part, but when the direction a changes it enlarges at the root. However its maximum value is induced in the barrel edge of the bracket, and its value, MI, is determined by the following formula;MI=-Tlc1cosα/(1+Kc2c)sinθwhereK=E0I0L/EI1lc1=3ll12+6ll22+12ll1l2+4l12l2+3l1l22/2ll2(4l1+3l2)c2=6l(l1+2l2)/l2(4l1+3l2)c=1/8sin2θ{5cos2(0-α)-6cosα×cos(θ-α)+5cos2α}E0 & I0…Young's modulus of shaft mNcos2α/sinα=1/sin(θ-α)whereN=2(3-5cosθ)/(8/Kc2+5sin2θ

A theory was developed to predict load-deflection curves for curved beams under loading conditions that produce finite strains. The theory assumed that the curved beam could be approximated by a number of truncated pie-shaped segments with circular arcs for the inner and outer boundaries. The cross section of each segment was assumed to have a plane of symmetry; the centroidal normal force and bending moment acting on the segment were assumed to lie in the plane of symmetry and to remain constant over the included angle of the segment. Using known tension and compression engineering stress-strain diagrams, internal values of centroidal normal force and moment could be calculated for assumed deformations of the segment. An iterative procedure was used to obtain the deformations which would make the internal values of centroidal normal force and moment equal to the applied values. The deformed shapes of the pie-shaped segments were reassembled to give the deformed shape of the curved beam. Good agreement was found between theory and experiment for nine mild steel curved beams and two commercially available crane hooks.

As far as the author's aware, the problem of the stresses in a semi-infinite strip under the forces applied at its end has scarcely been treated. Previously, however, the problem of a semi-infinite strip subjected to the normal compressive forces at its end was studied rather exhaustively by Prof. S. Higuchi. In this paper, we will treat a problem similar to the problem mentioned above taking shearing forces near the end of strip instead of the normal forces treated by Prof. Higuchi. Solution to this problem is obtained by using the stress function and from the results of numerical calculations of stresses characteristic properties with respect to the distribution of stress were pointed out and discussed.

A new method of instrumentation for normal-stress determinations was developed, making possible accurate unsteady state as well as steady state measurements, eliminating errors arising from fluid-filled pressure-tap holes, and permitting the determination of the complete stress state in a single cone-and-plate shearing-geometry experiment. Sensitive, nonflow semiconductor pressure transducers mounted at several radial positions with their pressuresensing diaphragms flush with the plate surface provide data for the normal-stress distribution. The normal-stress distribution, together with the total normal force from the single-geometry experiment, enables determination of the primary and secondary normal-stress differences by two independent methods of analysis while the transmitted torque enables determination of the viscosity, each as a function of shear rate. Only the normal-stress distribution is required if an independent check on the normal-stress determination is not desired. Similar advantages arise in the application of the instrumentation to a parallel-plate shearing geometry, The new instrumentation was used in the determination of the complete rheological stress state of three aqueous and two “Tetralin” solutions of polymers in a cone-and-plate shearing geometry shear rates of 0.02 to 450 s−1 on a Model R-17 Weissenberg Rheogoniometer. The normalstress differences computed by means of two methods of analysis are in surprisingly good agreement. The ratio of the secondary to the primary normal-stress difference was negative. The absolute values of this ratio decreased with increases in the shear rate, the maximum observed value being 0.4.

An apparatus for studying slip damping at rounded contacts for three different systems of forces is described. Experimental results for the constant normal force/varying tangential force problem when a Type 316 stainless-steel sphere is driven between two flat Type 316 stainless-steel plates are presented. They are in fair agreement with theoretical predictions by R. D. Mindlin,et al.

In a previous paper, the importance of lateral pressure in the tension and bending behaviour of yarns was discussed; a theoretical model, which included the effects of bending and torsional rigidities as well as the tensile, shear, and frictional forces, was proposed, and expressions for the lateral pressures were derived. In this sequel, the experimental verification of the previously derived expressions has been carried out on a very simple twisted structure, consisting of two rubber strands. The results obtained support the theoretical predictions of the lateral pressure for the experimental model and lead to the conclusion that, for filaments with significant torsional and bending rigidities, lateral pressures are obtained in the yarn even when there is no significant tension on the individual filaments. An approximate scheme for estimating the lateral pressures in an idealized, close-packed, multilayered continuous-filament yarn is proposed as an extension of the above results.

General equations in two-dimensional statical problems of piezoelectricity have been deduced by introducing the Airy stress function and the electric potential. Particular solutions for quartz plates have been obtained in two problems. The first problem is that of lateral bending by shearing forces at one edge while the second one is concerned with the deformation due to uniformly distributed normal forces.

Bei groser elastischer Verformung last sich der Spannungszustand mit einem linearen Spannungs-Dehnungs-Gesetz beschreiben, wenn die Spannung auf den wirklichen Querschnitt bezogen wird. Fur die dreiachsige Normalbeanspruchung sowie fur rotationssymmetrische Lastfalle werden die Spannungen ermittelt. At large elastic deformation the state of tension may still be represented by a linear stress-strain relation provided the tension of referred to the actual cross-section. The stresses are calculated for normal forces along the three axes and for loads of rotational symmetry.

The frictional properties of rigid and plasticized PVC have been measured as a function of temperature, speed of test, applied load, and plasticizer content. It was found that the data could be correlated by the simple equation F=F*[1−exp(−kf)], where F is the frictional force, F* is a limiting frictional force dependent upon temperature and composition, and f is the applied normal force. The constants F* and k could be correlated with the tensile strength and the bulk modulus, respectively. A mechanism of polymer frictional behavior is proposed.

The purpose of this paper is to investigate the metal removal mechanism of coated abrasive belts considering the wear of active grains. For this purpose, following assumptions are applied. (1) The new grain cutting edge is a conical shape and the worn one is the shape of a truncated cone. (2) Grinding force F is resolved into the normal grinding force FN and the tangential grinding force FT. FN is composed of FNC (cutting component of FN) which is the sum of normal forces acting upon rake faces of grain cutting edges and FNS (sliding component of FN) which is the sum of normal forces acting upon worn grain flats. Similarly, FT is composed of FTC and FTS. Under the above assumptions the relation among the percent wear flat area, grinding force and rate of stock removal is theoretically developed. By experiments, C (value of FTC/ FNC), KS (specific grinding force), e (exponent of the size effect), pm (average contact force intensity between wear flats of abrasive grains and workpiece) and μ (coefficient of friction between wear flats of abrasive grains and workpiece) are obtained and discussed. As the result, the metal removal mechanism of coated abrasive belts is considerably made clear.

The use of the Coulomb yield criterion to describe the compaction of granular material is proposed. Its use is demonstrated by the numerical solu tion of the stress and displacement equations de scribing the axisymmetric pressing of a cylindrical compact. The model is applied to the pressing of uranium dioxide pellets; to do so, the shear strength of the pellets is measured as a function of normal stress. These measurements showed an increase of shear strength with normal load and permitted assignment of values of cohesion and angle of internal friction to be used in the Coulomb failure condition. The computed re sults of die wall friction, normal force at the die wall, and stress distribution in the compact are compared with measured results.

The constitutive equations for shallow shells of viscoelastic (Maxwell) material with elastic reinforcement are derived. With respect to reinforced concrete shells shrinkage is considered. (Constitutive equations here mean relations between stress resultants, as membrane forces, bending and twisting moments, and strains or distortions of the shell middle surface, and further, formulae for the determination of the stress resultants related to the elastic and to the viscoelastic part of the section, respectively.) Concerning strain geometry, the usual assumptions of the theory of elastic shells are made. The reinforcement shall be orthogonal, but may be unsymmetrical to the middle surface and locally variable. Influences of transverse contraction are not considered. The derivations are based on the tri-dimensional constitutive equations for viscoelastic media of the type of reinforced concrete as established by D. Hilliges, who proved, that such a medium behaves in a different manner under shearing stresses than under normal stresses. This characteristic behaviour is also expressed in the constitutive shell equations given in this paper. The elastic and inelastic strains of a compound shell uder bending moments and normal forces are much smaller than those of a corresponding shell without reinforcement, and there is a decrease of the stress resultants of the viscoelastic part of the section (relaxation) and a corresponding increase of the stress resultants of the elastic part, whereas under shearing and twisting loads the (elastic and inelastic) rigidity of a compound shell element is only slightly higher than that of an element without reinforcement, and there is no remarkable shift of the stresses from the viscoelastic to the elastic part of the section. Using the derived constitutive equations there are given the displacement equations of the orthotropic Maxwell shell. Exact solutions can only be found for some simple cases (i.e. for a simply supported rectangular plate). Therefore these equations are transformed in a way that perturbation calculation can be applied. Thus the solution is reduced to the solution of the corresponding elastic problem and to the finding of particular integrals. This method of analysis of orthotropic Maxwell shells is applied to the following examples: circular cylindrical shell, rectangular plate, and circular disk with locally variable reinforcement. It is found that partly the stress resultants are considerably different (more than 20%) from those of an elastic isotropic shell and after creeping even different from those of the corresponding orthotropic elastic shell. It may even occur, that the stress resultants in the viscoelastic component of the material act against the reinforcement stress resultants. The present work represents an extension and generalization of derivations by R. Trostel for the case of compound plates.

A comparison is made between Stone's and vSauer's methods of calculation of the supersonic flow about a slightly yawing cone. I t is shown that the neglect of vorticity, while having only a small effect on the ratio of shock yaw to cone yaw, may lead to erroneous values of the normal force coefficient.

The present paper relates to experimental researches on rudder performance utilizing a free running, self-propelled model.Hardover to hardover steering tests have been carried out on four different balance ratios including the optimum one estimated by turning tests, and it is known that the balance ratio must be selected so as to prevent the abnormally large positive torque which may occur when the rudder is steered from port to starboard.An interpretation for the complicated rudder performance during the turning tests have been tried using the results of behind tests and free model tests. As the results, the resonable values for normal force coefficients have been provided through considering the change of slip ratio of propeller and drift angle of ship, but it remains some problems to be investigated for the center of pressure.

A method is developed which accurately predicts for blunt-based bodies of revolution the normal force coefficient and the pitching moment coefficient for angles of attack far beyond the range of potential theory. It is based on the principle of superposition of the results of potential theory and the viscous force on a cylindrical body due to the transverse component of flow. In contrast to previously used methods, the viscous cross force is assumed not to be in a steady state, but in a transient development along the body. The method is compared with experimental data for both subsonic and supersonic flows and with both laminar and turbulent axial boundary layers. The method is also useful for extrapolation of small-yaw data to large yaws and to different Reynolds numbers. The results presented have been applied only in the range M = 0 to M = 2.87 and for a limited range of Reynolds numbers.

The hydrodynamic force experienced by a small solid sphere of radius ap resting on a solid plane wall in axisymmetric stagnation flow, ${\bf v}_{\infty} = \Omega(- z^2{\bf i}_z + z\tilde{\omega}{\bf i}_{\tilde{\omega}})$, or in planar stagnation flow, v∞ = Ω(−z2iz + 2zxix), is computed on the basis of Stokes’ creeping flow equations. In both cases, as well as for any flow whose z component of velocity is −Ωz2, this force is found to be Fz = − 60·87μΩap3, where μ is the viscosity of the fluid. The uniform flow parallel to the line of centres of two touching spheres of arbitrary radii is also solved.

A simple apparatus has been developed to measure frictional forces of small magnitude. It provides a continuous recording of tangential forces ranging from below 0.01 dyne to about 50 dynes. Details of the stick-slip characteristics are thereby recorded. The small normal forces required are applied and controlled by passing a current through a meter movement. The basic element for sensing frictional forces is a d'Arsonval galvanometer system. The frictional force applied to a lever arm produces a torque about the axis of the galvanometer system. A dual photodiode-servo amplifier system provides a correcting current to the galvanometer so that the mechanically imposed torque is automatically balanced. The correcting current is directly proportional to the tangential force. This apparatus has been extensively used in friction studies of individual textile fibers and for fine wire samples. It has also been used for measurements of stylus friction on flat surfaces under small loads. This paper includes a deta...

SummarySemi-empirical methods are described for obtaining the normal forces and centre of pressure positions of isolated cone-cylinders and ogive cylinders with and without boat tails at supersonic speeds. The data for normal force slope and centre of pressure at zero incidence is, in general, accurate to better than 10 per cent and half calibre respectively. The data for high incidence must be considered speculative although reasonable agreement has been found with the very limited experimental data available.

The relation between the residual stress and the injury on the ground surface of hardened ball bearing steel was investigated. Ring specimens were hardened and tempered to Rockwell C62. The grinding of the internal surface was worked on a Heald constant force internal grinding machine under a series of severe operating conditions. The residual stresses were measured by the X-ray method, using a Geiger counter diffractometer with CrKα radiation.According as the normal force of grinding varied from 0.5 to 3.5kg/mm, the surface residual stress changed almost linearly from a compressive value of about 10kg/mm2 to a tensile value of 90kg/mm2. A marked decrease of the half-height breadth was also observed with increasing tensile stress. By macroetching with hot hydrochloric acid, etch cracks were developed on the surface where the tensile residual stress exceeded the value of 50kg/mm2.To ascertain whether the surface residual stress depends upon the cutting action or on the frictional heat, the rubbing experiment of steel was made with alumina ceramics and superfinishing stone. After rubbing 10sec. with alumina ceramics, the residual stress varied with increasing load from a compressive value of about 50kg/mm2 to a tensile value of 50kg/mm2, as in the case of constant force grinding. Decrease of the half-height breadth was also observed when the residual stress became tensile. On the other-hand, in the case of superfinishing stone, the compressive stresses of the order of 50kg/mm2 were always obtained. No decrease of the half-height breadth was observed in the range of the experiment.Since the cutting action is very poor in both cases, it is considered that the tensile residual stress is mainly due to the frictional heat. In case the frictional heat should be neglected, the compressive residual stress would be generated by the plastic deformation in very thin surface layers. In the case of superfinishing stone, as the abrasive grains are easily detached by a small frictional force, evolution of the frictional heat will not be enough to introduce the tensile residual stress.Tempering above 150°C decreases the tensile residual stresses and raises somewhat the critical stress of etch cracks.

Normal forces on rectangular flat plates in supersonic, rarefied flow were measured over the range 200 < Re < 2,400 and 3.7 < M < 4.1 at angles of attack up to eight degrees. In addition, the effect of aspect ratio on normal forces was determined with a series of models having an aspect ratio range from 1.0 to 2.0. The results were compared to linearized inviscid theory and indicated normal forces which were 33 per cent to 77 per cent greater than values predicted by theory, the experimental normal forces decreasing with increasing Reynolds Number. The decrease in normal force with decreasing aspect ratios was found to be from 3 to 7 per cent greater in magnitude than predicted by inviscid theory and substantially independent of Reynolds Number over the range tested. Weak interaction theory was used to derive a simple expression for the normal force and was found to predict the order of magnitude of the increased normal force as well as the trend of the normal force with Reynolds Number.

The deformation properties of glass-reinforced plastics are approximated by the relations for a homogeneous anisotropic material, only the shear creep strains being taken into account, since the normal forces, coinciding with the direction of the reinforcement, produce much less creep. Deflections commensurable with the thickness of the shell are considered (geometric nonlinearity), but the strain components are assumed small. The nonlinear relations obtained for this problem have been solved (for a particular case) on a computer. At loads less than the long-time critical value the growth of deflections in time is damped; at large loads the rate of growth of deflections increases.

In this note the disturbances in an infinite viscoelastic medium ofViogt type with a spherical cavity have been considered. The problem has been solved separately for (1) transient radial forces and (2) transient twist acting on the inner spherical surface of the cavity. Exact solutions have been obtained in both cases.

Theories on normal force effect have been proposed by several workers since Weissenberg's first investigation. In experiments, however, data on this effect are not enough to verify these theories in generality.Two kinds of silicon oil were taken up as samples, one 104 centi stokes, the other 105 centi stokes. These samples were irradiated with a variety in radiation dose by γ ray from Co60. Normal force (σ11-σ22), steady flow viscosity over a range of shear rate from 10-2 to 102sec-1 and dynamic modulus and viscosity over a range of angular frequency between 5×10-2 and 3×10sec-1 were measured by a Weissenberg Rheogoniometer at 20°C. The variation of dynamic modulus and viscosity with the shear rate of superposed steady flow was also measured.Silicon oils with more radiation dose have larger viscosity and normal force. It is found that the normal force of more irradiated specimen was larger than that of less irradiated ones though their viscosities were in the same magnitude. This is considered to be due to cross linkages in the materials.Two kinds of molecular weight were determined: one according to the relation between molecular weight and viscosity which was treated as a linear molecule, the other according to the relation between molecular weight and radiation dose treated as cross linked materials.The recoverable shear s was calculated from the values of shearing stress σ12 and normal force σ11-σ22 in steady flow. It was found that these silicon oils follow “Hooke's low in shear” from the linearity of plots in s against σ12.The comparison of curves of dynamic viscosity against angular frequency and the steady flow viscosity against shear rate was made, and approximate equality of shear rate and angular frequency was seen.The elastic modulus G and relaxation time τ in the sense of Maxwell model were calculated from both steady flow and dynamic experiments, making use of the equality of shear rate and angular frequency. The values of G and τ agreed in the order of magnitude in the range where normal force experiments were done.

Experiments have been conducted in a normal atmosphere using a 0·25-in diameter mild-steel pin specimen sliding on a 10-in diameter mild-steel disc. The ranges of normal force and speed are 0·5–10·4 lbf and 20–190 ft/s respectively. Initially the coefficient of friction is comparatively large, and the wear is of the severe metallic form. However, frictional heating causes rapid oxidation of the surfaces and, if the sliding distance is sufficient, the eventual retention of an oxide layer causes a rapid decrease in the coefficient of friction and the wear rate decreases by 3–4 orders of magnitude. At speeds above about 75 ft/s and loads below about 5 lbf the formation, after several hours' sliding, of a continuous oxide layer on the track causes a further reduction in the pin wear rate. At higher loads and/or lower speeds this track condition is not attained. At speeds of 75 ft/s and above there exists a critical load (the magnitude of which depends on speed) above which periodic removals of the surface film(s) occur producing metallic wear and high friction. However, the subsequent increase in oxidation allows conditions of mild wear to be re-established generally within a few seconds. The steady-state coefficient of friction has been observed to be a function of load1/2 × speed, and periodic surface breakdowns found to occur when load1/2 × speed exceeds 170 lbf1/2 ft/s, the frequency decreasing with increasing load or speed.

Two steel balls, rolling on each other with low normal forces (10–60 g) are usually insulated by a layer of oxide. The probability for the occurrence of a breakdown, and in consequence the formation of a metallic contact, is proportional to the load. The frictional energy lost in disrupting these metallic contacts is, on average, 3–4 · 10−2 ergs for each contact. The energy necessary to form the contacts, i.e. to remove the oxide layers, is negligibly small compared with this. Energy losses by plastic deformation or elastic hysteresis are not detectable. Friction results in increased local oxidation. Wear of oxide particles and frictional oxidation after a certain period of time form a stationary equilibrium.