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J. Eng. Mater. Technol. 1992;114(4):339. doi:10.1115/1.2904182.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Eng. Mater. Technol. 1992;114(4):340-347. doi:10.1115/1.2904183.

A unified constitutive model incorporating internal state variables based upon the deformation phenomena that are observed to occur at the microstructural level has been developed and applied to René 95. Material hardening is modeled using dragstress and back-stress state variables, while the reduction in the material’s load-carrying capability is described by using a damage-accumulation state variable. Application of the model to the tensile, cyclic, and creep loadings of René 95 at 650°C demonstrated that the model is capable of capturing cyclic hardening, damage accumulation, and tertiary creep by using one inelastic flow equation in concert with the state-variable-evolution equations.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):348-353. doi:10.1115/1.2904184.

This paper presents an experimental study of the strain-rate and temperature dependence of the yield stress for three low carbon steels (percent c = 0.2, 0.3, and 0.4). Tension test results using notched specimens are reported for temperatures of −20°C, 0°C, and 25°C and strain rates from 10−4 s−1 to 200 s−1 . Two regions with different kinetics have been observed. The yield stress shows a low sensitivity to strain-rate at higher temperatures and lower strain rates (region I), but the rate sensitivity is high at lower temperatures and higher strain rates (region II). An approximately linear dependence of yield stress on log strain rate is displayed in both regions. The carbon content of the steel strongly affects strengthening in region I, but weakening appears as the strain rate increases in region II. Deformation in the two regions is analyzed according to standard formalisms. When the yield stress is separated into athermal and thermally activated components, the carbon concentration dependence is shown to isolate to the athermal stress component, which becomes rate controlling at high temperatures and low strain rates.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):354-361. doi:10.1115/1.2904185.

A viscoplastic constitutive model characterization is presented for the small strain, nonisothermal behavior of a 9Cr-1Mo-V-Nb pressure vessel steel between 25°C and 600°C. A framework based on previously proposed viscoplastic models is reviewed. The technique for including deformation softening is discussed and the procedure used to determine model constants and parameters is presented. Results of model integration are compared with various isothermal and nonisothermal, uniaxial test results.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):362-367. doi:10.1115/1.2904186.

This paper appraises the accuracy with which distortion and residual stress can be predicted in carburized and quenched gear steels. An experimental sample is heattreated such that a nonsymmetric carbon profile results. During quenching, the strip develops longitudinal transformation strains that result in amplified transverse deflections, similar to those of thin bimetallic strips. Deformations in carburized SAE 4023 and SAE 4620 alloys are compared with finite element predictions. The finite element procedure is based on an elastic-plastic yield surface which includes dependence on temperature. The analysis uses property data published and used by others. Some, but not all, of the predicted distortions agree with experiments; the study shows that distortions are quite sensitive to small variations in constitutive parameters. The paper includes recommendations for practitioners using finite element procedures for prediction of residual stress.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):368-377. doi:10.1115/1.2904187.

We study plane strain thermomechanical deformations of a square block made of steel, and model a material defect in it by a rigid non-heat-conducting ellipsoidal inclusion located at the center of the block. The boundaries of the block are presumed to be thermally insulated, and its top and bottom surfaces compressed vertically at a prescribed rate. The loading pulse is assumed to be made up of three parts; an initial segment in which the speed increases from zero to the steady value, the steady part, and the third part in which the speed decreases gradually to zero and is maintained at zero subsequently. In the undeformed state, the specimen is assumed to be fully annealed, isotropic, and its microstructure to be a mixture of coarse ferrite and cementite. A material point is presumed to start transforming into austenite once its temperature exceeds the transformation temperature; the rate of transformation is controlled by a simple kinetic equation. Proper account is taken of the latent heat required for the transformation, the associated volume change, and the variation in the thermophysicalproperties. The complete thermomechanical problem is analyzed during the loading and unloading phase till all of the body points have essentially come to rest, and the energy equation is solved subsequently. It is found that the austenite is quenched rapidly enough by the surrounding material for it to be converted into martensite rather than pearlite or a mixture of pearlite and martensite.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):378-383. doi:10.1115/1.2904188.

Constitutive equations based on a state variable modeling of the thermo-viscoplastic behavior of metals are discussed, and incorporated in an exact, long-wavelength analysis of the neck-growth process in uniaxial tension. The general formalism is specialized to the case of f.c.c. metals in the range of intragranular, diffusion controlled plastic flow. The model is shown to provide a consistent account of aluminum behavior both under constant strain-rate and creep. Calculated uniaxial tensile ductilities and rupture lives in creep are also compared with experiments.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):384-389. doi:10.1115/1.2904189.

A detailed finite element analysis has been conducted of the thin-walled torsion specimen. This specimen, when properly gripped, provides an approximation to the simple shear deformation field. Variations through the thickness of the specimen are small for the shear stress but can be large for the axial normal stress. Plastic deformation extends into the shoulder region requiring a correction factor to be used when converting the applied twist at the grips to average shear strain across the gauge section. This correction factor can be numerically quantified and used in data reduction.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):390-398. doi:10.1115/1.2904190.

Low-cycle fatigue tests on Ti 6-4 (Ti-6Al-4V) have been carried out at 260°C under strain-controlled conditions with constant strain amplitude and increasing multistep strain levels. The results of constant strain amplitude tests were used to establish the fatigue diagram whereas the multistep tests were examined to assess the cyclic stress-strain behavior in comparison with the conventional stress-strain curve. Most of the tests were carried out under zero-to-tension conditions in the intermediatecycle range (Nf ≃ 3 x 103 to 105 cycles). The effect of prior strain cycling on the tensile properties was also investigated. The experimental data is discussed together with theoretical evaluations. In addition, microstructural examinations of the rupture surfaces have been made to show evidence on the type of crack initiation sites and on the crack propagation modes at different strain levels.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):399-405. doi:10.1115/1.2904191.

The shadow optical method of caustics has been applied to the measurement of the bulging out of the surface of aluminum alloy 7075-T6 in the vicinity of a blunt notch in a single edge notch tensile sample after a compression overload and during compression fatigue. The size and shape of the caustic were found to be sensitive functions of the amount of elastic and plastic strain in the vicinity of the notch. Examination of the caustic during application and after release of the overload shows the elastic zone to be larger and more circular than the plastic zone, as predicted. A crack was propagated through the plastic zone using only far-field cyclic compression loading: the crack was self-arresting at the edge of the elasticplastic boundary created by the initial compression overload. The size of the plastic zone as measured by the caustic was found to agree with the maximum length of the crack. The actual surface profile in the vicinity of the notch was measured and its shape was used along with geometrical arguments to develop a model for interpretation of the caustics results. These results indicate that the caustics technique can be used to detect the presence of a plastic zone at the tip of a notch after a compressive overload, and that the size of this zone as measured by caustics is approximately equal to the size as determined by subsequent fatigue crack propagation.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):406-408. doi:10.1115/1.2904192.

In certain biaxial fatigue problems, the stress components can be represented as a superposition of mean components, and proportionally applied alternating components. Such representation is the first step in applying some of the more popular methods for long-life fatigue analysis. It is commonly assumed, perhaps unwittingly, that the relative orientation of the mean and alternating principal stress axes does not influence fatigue behavior. It is explained how this assumption is inherent in several popular methods. It is pointed out that the validity of the assumption cannot be demonstrated by existing data.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):409-415. doi:10.1115/1.2904193.

A study was conducted to investigate the fatigue behavior of a cross-ply, [0/90]2s , laminate of silicon fiber reinforced titanium matrix composite, SCS-6/Ti-15-3 at an elevated temperature of 427°C. Two sets of tests, at frequencies 0.02 and 2 Hz, were run at different stress levels. Fatigue damage initiation and growth patterns were dependent on the specific test conditions of frequency and stress level. Microscopic analysis of the fatigued specimens revealed matrix failure mechanisms ranging from ductile failure to cleavage fracture. The results of this study showed that temperature and frequency, as well as stress levels, are important design considerations for this composite in fatigue loading applications.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):416-421. doi:10.1115/1.2904194.

In this study it is demonstrated that thermal conductivities of polymeric fiber-reinforced composite materials can be enhanced by using coated fibers and by adding thermally conductive microspheres to the resin. Two and three-dimensional finite element unit cell models are developed to predict the directional thermal conductivities. The analyses are based on the flash pulse method. It is found that the thermal conductivities in the longitudinal and the transverse directions are highly dependent on the fiber and microsphere volume fractions as well as on the thermal conductivities of fiber, microsphere, and coatings. It is shown that the 2-D analysis is a good approximation for the 3-D model. Close agreements among analytical, finite element and experimental results are obtained.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):422-431. doi:10.1115/1.2904195.

During fabrication of fiber reinforced metal-matrix composites by hot pressing, fiber breakage due to particles impingement during consolidation of fiber/particle system is very common. In studying the fiber breakage, one of the main issues is the interactions between fibers and particles during consolidation. In this study, we proposed to investigate the problem of fiber/particle interactions by examining a unit problem consisting of a deformable particle and a cylinder. A rather engineering model for axisymmetric deformation of a particle induced by a rigid sphere was developed first and then extended to the interactions between a deformable particle and a rigid cylinder. The calculations were compared with experiments on lead balls, good agreement was observed. The model was then applied to determining the maximum bending stress in fibers using the simple beam theory. A safe criterion for preventing fibers from breaking was found.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):432-438. doi:10.1115/1.2904196.

The plastic deformation induced surface roughening mechanism of aluminum sheets is experimentally investigated. Specimens used in the study have grain sizes varying from tens of microns to millimeters. The roughnesses of the specimens’ free surfaces are measured during plastic deformation by means of a mechanical stylus type profilometer with a tip radius of 5 microns. Observations show that plastic deformation roughens a free surface mainly by introducing slip bands within individual grains and relative rotation among grains. The average grain rotation and grain size are found to be the dominant contributor to the surface vertical characteristics such as the root-mean-square roughness. The surface horizontal characteristic such as the correlation length is found to be mainly determined by the average grain size. Based on the observations and some analysis, a model is advanced for the explanation of the phenomenon that the root-mean-square roughness is proportional to the magnitude of plastic deformation and average grain size.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):439-449. doi:10.1115/1.2904197.

A mathematical model has been developed in describing the temperature distribution, the flow of the molten fluid and the stress field in the solid during welding. In modeling the properties of the material during welding, the solid phase is assumed to behave as a thermoviscoplastic solid obeying Bodner-Partom/Walker type constitutive equation, whereas the fluid phase as a thermoviscous incompressible fluid. Three regions exist: pure solid, pure fluid, and the transition (solid-fluid mixture). In the formulation of the boundary value problem, the energy equation is coupled to the equation of motion through the terms of mechanical work and the latent heat of the phases, whereas the equations of motion of the solid and the fluid are decoupled. Appropriate thermal and traction boundary conditions are detailed in the text. Phase transformation activities during cooling are monitored by CCT diagram and Avrami equation. An arbitrary Lagrangian and Eulerian method is used to accommodate the kinematic description of both the solid and the fluid phases. A representative plane perpendicular to the moving heat source is analyzed. Results of sample calculations are presented to show the temperature and the stress evolution in time. Residual stress and microstructure patterns are presented.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):450-458. doi:10.1115/1.2904198.

Microstructure formation during the laser treatment of materials is discussed so as to enable one to design appropriate alloys and laser processing conditions which will produce a microstructure that has optimum properties. In order to predict microstructures for different laser processing conditions, the theoretical models for single phase and two-phase eutectic growth under a wide range of solidification rates have been developed. Specific emphasis is placed on the new physics that become important under rapid solidification conditions of laser processing. Based on these models, the selection of a specific microstructure under given laser processing conditions has been established. These results are then used to construct microstructure/ processing condition maps for the laser treatment of materials. These diagrams theoretically predict the variation in the microstructure along the depth of the solidified pool as a function of laser scanning velocity.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):459-464. doi:10.1115/1.2904199.

Tool-life tests are reported which show the relationship between the alloy composition of high-speed steel twist drills and performance. Tool-life is shown to depend primarily on the composition of the matrix consisting of tempered martensite and precipitated secondary carbides. The longest tool-life was obtained from alloys with high vanadium content and low tungsten or molybdenum content. This observation is consistent with the dispersion characteristics of vanadium carbide which precipitate during tempering.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 1992;114(4):465-471. doi:10.1115/1.2904200.

This paper presents a study of precision closed-die, isothermal, forgings via both experiments and computer simulation. The closed-die cross-section was an “H” shape and Tin/Lead eutectic solder was used for the billet material. Extensive statistical analysis of the axial force versus displacement history was conducted using replicated forging experiments. The purpose of the experiment was to obtain statistically significant data so that accuracy tests could be conducted on different FEM computer models, e.g., ALPID, EPIC2D, NIKE2D, and DYNA2D. Overall, the forging history exhibited complex behavior consisting of five distinct regions. The experimental results yield a 5.2 percent COV in the required forging force for a specific top-die displacement. A 6.5 percent COV in the “stiffness” of the first region (elastic behavior) of the forging history was also obtained. One set of simulations with one FEM computer model, ALPID Version 2.1 for rigid-thermoviscoplastic behavior, was conducted. The occurrence of all four viscoplasticflow regions was qualitatively predicted by the simulations. Quantitatively, the simulations are within the experimental bounds for the early viscoplastic regions, but out of bounds for the later regions. It appears that, for the eutectic tin/lead billet material, there is no combination of “power-law” material parameters that yield good agreement with the later stages of the forging force history.

Commentary by Dr. Valentin Fuster

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