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RESEARCH PAPERS

J. Basic Eng. 1972;94(1):1-6. doi:10.1115/1.3425365.

In this paper a method is presented for correlating the creep and rupture strengths of a wide variety of commercial alloys. The ultimate aim of this correlation is to predict design creep properties from rupture data alone. This is of considerable interest because rupture parameter or isothermal rupture curves are frequently the only data available since relatively little creep data is taken today. It is demonstrated in this work that reasonable predictions, useful in design, can be made. The alloys studied range from aluminum base through low alloy and stainless steels and include iron-nickel, nickel, and cobalt-base superalloys. Very long time data for single heats of each of the alloy types has been taken from either the literature or sources willing to make such data available. The construction is simple, and common techniques for determining scatter in the correlation are developed. The predictions include scatter bands of strain-time data developed from the 15 data sets encompassing all the alloys. It is suggested that some refinement might be gained by studying numerous heats of a single specification material where such data is available. A complicating problem of structural instability arises and is discussed in the paper.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):7-12. doi:10.1115/1.3425391.

A total of 31 stress-rupture data sets for 28 different nickel-base alloys, including 1153 individual test results, have been treated by graphical methods and computer programs to allow determinations of the relative abilities of Larson-Miller, Manson-Haferd, Sherby-Dorn, Goldhoff-Sherby, Manson-Succop, Conrad and Korchynsky parameters to correlate and extrapolate data. For the correlation of all data the Goldhoff-Sherby and Manson-Haferd methods are attractive, while for extrapolation to longer times some superiority of the Manson-Haferd and Manson-Succop parameters is demonstrated. Overall use of a third order polynomial approximation to Manson-Haferd master curves is recommended, as is the avoidance of external extrapolation. Results are primarily based on modified and original computer programs and standard statistical treatments of data.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):13-21. doi:10.1115/1.3425343.

Time-dependent notch sensitivity of Waspaloy was observed at test temperatures from 1000 to 1300 deg F. Its occurrence in this range was dependent on the heat treatment. “Overaging” eliminated the notch sensitivity. Optimum combination of smooth and notched specimen strengths for material solution treated at 1975 deg F were obtained by aging 24 hr at 1550 deg F. Necessary conditions for time-dependent notch sensitivity were (i) the notch specimen loads had to be below the approximate 0.2 percent off set yield strength; and (ii) test data from smooth specimens had to indicate that small amounts of creep used up large fractions of creep-rupture life. No reasons were evident why these criteria will not prove applicable to other alloys.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):22-26. doi:10.1115/1.3425373.

The time micro and macroscales are computed from measured energy spectra in the fully developed region of a submerged circular water jet. The corresponding longitudinal scales are approximated using Taylor’s frozen turbulence hypothesis. The microscale is found essentially constant whereas the macroscale, although increasing linearly along the axis, does not show similarity in the total field.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):27-32. doi:10.1115/1.3425381.

A computer-oriented solution is given for the flow described in the title of the paper. The boundary shape is represented by specification of the coordinates of N points on the boundary; the initial velocity is represented by specification of L values of the velocity in the cross section at time zero; the arbitrary time-varying pressure gradient is implemented by use of Duhamel’s Theorem. In the solution method presented, boundary and initial conditions are satisfied in the least squares sense. The Gram determinant is used to determine eigenvalues and the Gram-Schmidt orthonormalizing procedure is used to construct a set of functions appropriate for a finite series solution. Computer programs are referenced which have been used to investigate the correctness of the solution and the accuracy obtainable with reasonable digital computational time.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):33-38. doi:10.1115/1.3425382.

In the case of Kaplan turbines the consideration of the efficiency parameter is critical from the control strategy synthesis viewpoint. As it is not essential in hydrosystem analysis, explicit efficiency parameter relationships have not been deployed to date for linearized Kaplan mathematical models used in control design. The “efficiency transient control” concept is developed herein. Basically, this approach purports to optimize transient behavior by controlling so as to decrease efficiency during the early transient portion of load rejection and likewise maximizing efficiency for the load acceptance case. For each perturbation this method leads to minimal flow change and, therefore, minimal over or under-pressures. As applied to a dominant gate with blade follow-up control scheme, the efficiency transient control concept prescribes the appropriate delay to be employed for optimum performance within the constraint of a follow-up device. Where the early transient deviates from best efficiency operation, a return to steady-state or “cam” operation occurs as the follow-up. The standard equations describing Kaplan turbine operation in linearized form by partial derivatives have been revised to include the efficiency parameter explicitly and now present a comprehensive and intelligible approach to Kaplan turbine control synthesis. The effect of the efficiency transient control upon system stability is analyzed and recommendations are made for desirable deployment. Application to nonlinear system operation is discussed. The efficiency transient control is compared with present day control schemes to assess their effectiveness. It is determined that a delay imposed upon the blades for the load-on case is suboptimal performancewise. The one-to-one gate-to-blade control is optimal in that case.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):39-45. doi:10.1115/1.3425383.

The concept of a multiple-venturi system is applied to the design of a flow-rate meter. This meter type has the capability of offering a high signal-to-loss ratio over a broad flow range. Its internal fluid mechanics are discussed with a view toward design optimization. Experimental results are reported and analyzed for a three-element meter.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):46-52. doi:10.1115/1.3425384.

The heat transfer characteristics of yawed slender filaments have been generalized to include pairs of heated-film skin friction gages, as well as conventional hot wire probes, New sensor designs have been combined with a novel double-bridge electronic feedback system with accurate differential power capabilities for improved measurements in complex environments. Results of detailed calibration experiments illustrate the accuracy, simplicity, and utility of the probe designs and circuit techniques.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):53-60. doi:10.1115/1.3425385.

Motion pictures of launches of Titan III solid rocket motors were used, in conjunction with conservation equations and knowledge of rocket plume properties, to determine the initial temperature and mass of the large cloud that is generated during these launches. These initial conditions were applied to a mathematical model which accounted for buoyancy, drag and entrainment. The model predicted the radius, altitude, temperature and mass of the cloud as a function of time. The results showed fair agreement with size and altitude data extracted from the movies. This methodology was applied with limited success to smaller scale rocket clouds generated at test stands. The model was also used to predict the behavior of large exhaust clouds under various external temperature profiles. There is some experimental evidence that the model correctly accounts for unstable profiles, and the predictions of cloud rise during inversion conditions agree with what intuition would predict.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):61-64. doi:10.1115/1.3425386.

Punching of copper sheet at atmospheric pressure and under environmental pressures up to about 160,000 psi showed the following: The fraction of slug thickness that is burnished is essentially independent of the thickness of the metal specimen; finite pressures can be used for complete burnished punching (about 70,000 to 110,000 psi for the soft copper and about 70,000 to 120,000 psi for the hard copper); hard copper requires higher pressure to achieve the same fraction of burnished zone as soft copper at the lower pressures, but requires the same pressure at higher pressures; and, the effect of clearance is complex inasmuch as small clearance yields larger burnished zones at atmospheric pressure, but the reverse is true at the highest pressures, with a crossover in between at about 70,000 psi.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):65-66. doi:10.1115/1.3425387.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):67-70. doi:10.1115/1.3425388.

The four natural boundary conditions are derived for a newly observed symmetry in Bourdon tube action. The problem is described by an eighth-order system of pde’s for a Donnell-type shell theory. These, together with boundary conditions for the geometric symmetry and for the free end with rigid plug, comprise a well-posed mathematical problem. It requires only one-fourth the integration domain of the problem posed without symmetry, hence reduces storage requirements in computer calculations to one-sixteenth the number for the original problem.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):71-77. doi:10.1115/1.3425389.

A three-dimensional structural analysis program (DANUTA), using newly developed subparametric finite elements, is described and applied to the analysis of turbo-machinery components. The hexahedron-shaped element has twelve generalized displacements concentrated at each of the eight corner nodes. The displacement components are represented by a complete third degree polynomial, with some selected terms of the fourth and fifth degree, while the geometry is described by a set of second order parametric interpolation functions. The derivation of the stiffness and consistent load matrices (surface and body forces) is outlined. Numerical results, for cases where a classical solution is available, illustrate the high accuracy of the element. Application of the program to the analysis of spherical valves, turbine runners and wicket gates, as well as machine requirements, automatic data generation and possible further developments are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):78-80. doi:10.1115/1.3425390.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):81-87. doi:10.1115/1.3425392.

A number of processes, such as pneumatic conveying of powdered materials through ducts, feed lines for powdered rocket fuels, or certain flow processes in air-augmented solid-propellant rockets, involve addition of a stream of solid particles to a gas flow. The present study deals with the analysis of gas flows from a constant-pressure and temperature reservoir through a pipe into which the particles are injected at some point, and the pipe is assumed long enough to allow equilibrium between the gas and the particles to be established. Ultimately, the mixture is discharged into another reservoir of constant pressure. The temperature of the injected particles may be different from the reservoir temperature of the gas, so that the effects of simultaneous particle and heat addition must be considered. Allowance is made in the flow equations for the volume fraction occupied by the particles, and the analysis may therefore be applied to arbitrarily high particle loadings. To demonstrate the influence of the various parameters involved, the flow equations are solved numerically with the aid of a digital computer. With increasing particle loading the gas flow is markedly reduced, and the temperature of the discharge closely approaches that of the injected particles as a result of the high heat capacity of the particle stream. If this temperature behavior is assumed to hold, simple relationships can be derived which yield results in good agreement with data obtained from the complete equations if the loading ratio equals about ten or more for typical gas-particle mixtures. Of special interest is the finding that the gas flow needed to transport particles at a prescribed rate can be significantly reduced by heating of the particles before injection. It is demonstrated that equivalent direct heating of the gas would not be practicable unless the particle loading is quite low.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):89-95. doi:10.1115/1.3425395.

The spherical expansion of vapor bubbles due to the application of either a thermal or a kinetic impulse is examined. There appears to be a wide range of initial and ambient conditions for which the vapor properties approach extremely close to ambient values at the end of the expansion, for both types of impulse. There is also a range of conditions for which the vapor is significantly subcooled at the end of the expansion for both types of impulse. It is postulated that such vapor conditions can cause a more vigorous motion in the subsequent collapse than would be expected for the prevailing ambient conditions.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):97-104. doi:10.1115/1.3425399.

The performance of two-dimensional jet-flap cascades is determined experimentally. Stream deflection angles are presented as a function of the ratio of jet to mainstream momentum flux at chord spacing ratios of 0.375 and 0.75. Results obtained with conventional jet-flap airfoils (normal blowing near trailing edge) are in good agreement with published theoretical results. Tangential blowing jet-flap airfoils (tangential blowing over a rounded trailing edge) are shown to approximately double the turning effectiveness of the cascade.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):105-119. doi:10.1115/1.3425334.

The pressure recovery performance of straight-wall, two-dimensional diffusers with air–water mixtures has been investigated, and their behavior as a function of gas volume flow ratio and diffuser geometry established within the limits of the experimental apparatus. The ranges of parameters investigated were: Gas volume flow ratio, β: 0 to 73 percent; area ratio, AR: 1.3 to 4; diffuser length to throat width ratio, N/W1 : 3, 6, and 18. Diffusers with air–water mixtures have the same general performance characteristics as diffusers with single-phase fluids, e.g., peak pressure recovery occurs near the onset of stall and decreases again for larger area ratios in the stalled flow regimes. In stalled flow regimes, appreciable pressure recovery may be achieved in a constant-area tailpipe downstream of the diffuser. The pressure recovery of diffusers with two-phase flow deteriorates with increasing air flow, especially after the two-phase flow regime changes from bubbly to churn-turbulent.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):122-129. doi:10.1115/1.3425337.

The flow of a density-stratified fluid about symmetric towed bodies was investigated both experimentally and theoretically. A cylinder and a slender body were towed through a linearly stratified fluid at various depths and the resulting lee waves were observed and recorded photographically in such a manner as to show the flow tracers as streamlines of the flow. A theoretical investigation was made using an inverse method of solution in which the bodies are generated by distributions of doublets of varying strength and location within the flow field. This theoretical solution predicts that the flow field will be symmetric about the model, only if the model is at the midplane of the flow channel and will be non-symmetric at any other location of the model. This prediction is qualitatively verified by the experimental observations. Theoretical solutions corresponding to the experimental observations were generated. It was found that good agreement was obtained between the theory and experiment as long as the model was towed at a symmetric plane of the channel. At other planes of towing the quantitative agreement between theory and experiment was not good.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):131-138. doi:10.1115/1.3425340.

An explicit finite-difference scheme is formulated for calculating the development of the incompressible turbulent boundary layer on an infinite yawed cylinder. The governing partial differential equations are similar to those used by the author in a previous paper [1], and the empirical content is the same. In their general form the difference equations define a two-step scheme containing two disposable parameters, and numerical experiments have been conducted to determine the stability boundaries, and the boundaries of acceptable numerical precision, in terms of these parameters. By a particular choice of one of the parameters the system reduces to a one-step, staggered-mesh scheme, and it is in this form that the method finally emerges. With 15 collocation points through the boundary layer the method has a typical precision of 2 percent, and with 20 points, 0.5 percent.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):142-145. doi:10.1115/1.3425345.

The collapse of pure vapor bubbles in an infinite liquid initially perturbed from a spherical shape is simulated numerically for two cases. In Case A the bubble is initially close to a prolate ellipsoid, and in Case B it is initially close to an oblate ellipsoid. Nonlinear effects are determined by comparing the results with those predicted by the linearized theory of Plesset and Mitchell. These nonlinear effects are found to be important only in the final stages of collapse. In Case A a pair of inward moving jets develop and strike each other with a final speed which is roughly half that, predicted from the linear theory.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):147-151. doi:10.1115/1.3425348.

This paper reports the results of an analytical and experimental investigation whose object was to test the hypothesis that the flow of the gas phase controls critical and near critical two-phase flow for cases where the gas flow is essentially in separate streams. The results substantiate the hypothesis. The analytical results also indicate that one dimensional flow equations with reasonably accurate estimates for the droplet size and for the drag and heat transfer coefficients will adequately describe critical and near critical flow over a wide range of flow conditions.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):156-160. doi:10.1115/1.3425353.

The effect on the interfacial gravity wave between two fluids is studied when there is a temperature gradient in the fluids. It is found that the thermal effect is closely related to the phase transformation across the interface. The interfacial conditions with mass flow are first derived. Then the dispersion relation for the interfacial wave is obtained. It is found that the effect of evaporation is to damp the interfacial wave and to enhance the Rayleigh-Taylor instability. It is also found that the system will be stabilized or destabilized depending on whether the vapor is hotter or colder than the liquid.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):163-168. doi:10.1115/1.3425356.

A linearized theory for supercavitating flow through a cascade of cambered blades is developed. Numerical results illustrating various points of interest are presented.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):169-179. doi:10.1115/1.3425359.

The performance of a condensing ejector depends on the interactions occurring between the liquid and vapor streams in the mixing section. Axial static and liquid-vapor stagnation pressure profiles were measured in a constant-area mixing section using steam and water over a limited range of inlet vapor conditions and a wide range of inlet liquid velocities. Three flow regimes were identified based on inlet liquid velocity. Complete vapor condensation due to a “condensation shock” occurred only in the High Inlet Liquid Velocity Regime. The presence of supersonic vapor flow was found to be a necessary but not a sufficient condition for the existence of the “condensation shock.” In addition, breakup of the liquid jet was found to play an important role in the mixing section processes. A quasi one-dimensional analytical model of the annular liquid-vapor flow patterns occurring in the upstream portion of the mixing section was formulated. Though it was not possible to predict sufficiently accurately the interfacial heat transfer rates from any currently available analyses or data, interfacial heat transfer coefficients of approximately 100 Btu/sec ft2 deg F were found to produce good agreement between the experimentally measured and computed analytical axial static pressure variations. These values compare favorably with other data on the heat transfer rates to turbulent water jets with condensation.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):181-186. doi:10.1115/1.3425362.

An analytical device for improving the accuracy of crack growth predictions in metal subjected to variable amplitude cyclic loading is presented. A modification to the linear cumulative growth idea is proposed which incorporates a consideration of prior load history by taking into account the yield zone ahead of the crack tip. Correlation between analysis and experimental results for six different cases shows that the scheme, even though only a first order improvement on the Miner idea, is sound and can be used with confidence for design and analysis.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):187-192. doi:10.1115/1.3425363.

An analytical and experimental study of isothermal bubble motion through a liguid which is itself in motion is presented. Both analytical and experimental results are reported for the velocities and trajectories of oxygen bubbles moving through a liquid annulus which is rotating at angular velocities ranging from 500 to 1500 rpm. Results are presented for both distilled water and glycerin. The analytical prediction of the trajectories and velocities showed good agreement with the experimental data. It was found that the bubbles, which were injected at the exterior of the liquid annulus, spiralled inward rapidly and, due to the large pressure gradient in the radial direction, did not reach a constant or terminal velocity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):193-199. doi:10.1115/1.3425364.

An attempt has been made in this paper to describe the velocity structure of a transpired turbulent boundary layer. The analysis makes use of a “wall-plus-wake” concept and derives a universal representation of the velocity structure of the turbulent boundary layer with uniform injection, “blow-off” or suction. The results of the analysis agree reasonably well with those obtained using an implicit finite difference technique advanced by Patankar and Spalding. The results also show a good correlation with the experimental data of Mickley, et al., and Simpson, et al. Predicted shear stress distributions compare well with the experimental data of Wooldridge, et al.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):200-204. doi:10.1115/1.3425366.

An analysis is presented which predicts the properties of an arbitrarily thick turbulent boundary layer for incompressible axial flow past a long cylinder. The approach makes use of a modified form of the law-of-the-wall, deduced by G. N. V. Rao, which properly accounts for transverse curvature effects. Using this law, the theory which follows is equivalent to an exact solution to the axisymmetric equations of continuity and momentum for zero pressure gradient. Numerical results show that curvature increases skin friction and overall drag and decreases the boundary layer thickness and the integral thicknesses. The velocity profile is flattened and the shape factor approaches unity at large curvature. Comparison with several sources of friction data show better overall agreement than previous theories, except for an unexplained discrepancy with data for moving nylon fibers at very small radius Reynolds numbers.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):207-212. doi:10.1115/1.3425369.

The effect of elastic strain rates ranging from 10−14 to 10 sec−1 and temperatures ranging from 200 K (−100 F) to 590 K (600 F) on the yield strength of several steels is reported. The steels utilized are a 1018 mild steel, 4340 steel, H-11 tool steel, and 300 grade maraging steel. The results are interpreted in terms of the Cottrell-Bilby yielding model based on release of dislocations from locking carbon atmospheres. The results for all of the materials except the maraging steel are consistent with this model if it is modified to account for relocking of dislocations by migration of carbon atoms. The maraging steel shows a constant strain rate sensitivity at a constant temperature, over the range of strain rates investigated. This rate sensitivity decreases with increasing temperature and at 590 K (600 F) a decreasing strength with increasing strain rate is found. This is attributed to stress aging effects.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):213-222. doi:10.1115/1.3425370.

An improved velocity field based on the solution to an incompressible fluid flow is used to establish an upper bound approach for conical flows in metal forming. From a three parameter characterization of the equivalent stress-equivalent strain data on copper and aluminum, the effects of work hardening on forming stresses, maximum reduction ratios, optimum cone angles, and dead zone angles are studied for drawing, conventional, and hydrostatic extrusion. Results for a rigid-plastic material are obtained as a special case of the work hardening material. Experimental data are offered to show an excellent correlation with theory. A representation for the redundant work factor is developed that incorporates in it the effects of material properties and flow geometry. The existence of maximum pressure well inside the plastic region is pointed out and the possibility of introducing the forming fluid at some distance inside the die to facilitate better lubrication is examined.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):223-227. doi:10.1115/1.3425371.

Existing methods for evaluating spring steels in terms of load-loss resistance for automotive coil spring applications are very time-consuming and require special spring-making and spring-testing equipment. Over the years, the impracticalness of these methods has been an obstacle to the development of better spring steels. The present study shows how the torsional Bauschinger test can be used to predict the relative loadloss resistance of spring steels through correlations which were worked out during the laboratory investigation. Advantages of the torsional Bauschinger test are: (a) small, straight specimens are used, (b) the test takes only a few minutes, and (c) standard equipment is employed (a standard torsion tester). Results to date indicate that this test method will serve as a practical tool for providing the kind of information needed to develop improved spring steels.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):228-230. doi:10.1115/1.3425372.

A general yield criterion and flow rule based on invariance principles is applied to the case of an ideal strain hardening solid having principal axes of anisotropy and a significant Bauschinger effect.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):231-237. doi:10.1115/1.3425374.

An analysis is presented which shows how the theory of anisotropy based on a von Mises criterion of yielding first proposed by Hill may be extended to the plastic torsional straining of a hollow cylinder. Expressions are given for the anisotropic parameters, and the yield stresses along the anisotropic axes in terms of certain quantities, namely; the change in axial and tangential strain with shear strain, the principal yield shear stress, and the through thickness yield stress of the hollow cylinder. Experimental measurement of these quantities is made for the plastic torsional straining of hollow cylinders of A1-1100. Experimental data are analyzed using the previously derived expressions, and the anisotropic parameters, and yield stresses along the anisotropic axes determined. Finally, the results of the investigation are discussed, and conclusions drawn.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):238-242. doi:10.1115/1.3425375.

An experimental investigation of the stress-strain behavior of several rocks is described. The stress-strain response of the rocks tested is seen to be quite complicated, exhibiting a number of inelastic effects even in rocks considered brittle under pressure. The inelasticity is manifested in permanent set and hysteresis on unloading and volume changes produced by shearing stresses.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):243-247. doi:10.1115/1.3425376.

A fracture mechanics model is proposed to describe fatigue crack propagation in notched specimens. This model accounts for residual stresses which are present at the notch root after unloading from maximum compressive load. This is of particular interest for specimens subjected to compressive mean load. According to the model, cracks will stop growing at the boundary of the plastically deformed zone if the specimen is subjected to compressive load only. Validity of the model was verified with notched specimens of mild steel.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Basic Eng. 1972;94(1):248-249. doi:10.1115/1.3425377.
Abstract
Topics: Vapors , Bubbles
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):251-253. doi:10.1115/1.3425379.

The indentation of hard steel spheres into the plane surface of quasi elastic-perfectly-plastic metallic materials has been investigated experimentally. It is shown in the present note that uniform results are obtained when the experimental data corresponding to some materials are reduced to a common base. These results are in fairly good agreement with the predictions of a previous finite element analysis by the same authors.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(1):253-254. doi:10.1115/1.3425380.
Abstract
Commentary by Dr. Valentin Fuster

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