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### Research Papers

J. Eng. Mater. Technol. 2009;131(3):031001-031001-7. doi:10.1115/1.3120385.

The coefficients of thermal expansion (CTEs) of fiber reinforced composites play an important role in the design and analysis of composite structures. Since the thermal expansion coefficients of polymer matrix materials are typically much higher than those of fibers, and the fiber often exhibits anisotropic thermal and mechanical properties, the stress induced in the composite due to temperature change is very complex. Large discrepancies exist among the analytical models for the transverse CTE of unidirectional composites. Hence, it is problematic when choosing a suitable model. With the development of computer technologies, finite element analysis (FEA) proved its effectiveness in calculating the effective CTE of composites. In this study, the transverse CTEs of unidirectional carbon fiber composites were calculated by finite element analysis using a representative unit cell. The analytical micromechanical models from literature were compared against the FEA data. It shows that Hashin’s concentric cylinder model is the best. However, it is inconvenient for practical applications due to the amount of computation. In this study, based on the FEA data, an engineering model for predicting the transverse CTE of unidirectional composites was developed by regression analysis. This model was validated against the FEA and experimental data. It shows that the developed model provides a simple and accurate approach to calculate the transverse CTE of unidirectional composites.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031002-031002-10. doi:10.1115/1.3120386.

In order to test new theories for residual stress measurement or to test the effects of residual stress on fatigue, fracture, and stress corrosion cracking, a known stress test specimen was designed and then fabricated, modeled, and experimentally validated. To provide a unique biaxial stress state, a 60 mm diameter 10 mm thick disk of 316L stainless steel was plastically compressed through the thickness with an opposing 15 mm diameter hard steel indenters in the center of the disk. For validation, the stresses in the specimen were first mapped using time-of-flight neutron diffraction and Rietveld full pattern analysis. Next, the hoop stresses were mapped on a cross section of two disks using the contour method. The contour results were very repeatable and agreed well with the neutron results. The indentation process was modeled using the finite element method. Because of a significant Bauschinger effect, accurate modeling required testing the cyclic behavior of the steel and then modeling it using a Chaboche-type combined hardening law. The model results agreed very well with the measurements. The duplicate contour measurements demonstrated stress repeatability better than 0.01% of the elastic modulus and allowed discussion of implications of measurements of parts with complicated geometries.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031003-031003-9. doi:10.1115/1.3120388.

In order to determine the mechanical properties of materials suitable for use as coatings on structural or gas turbine components, it is often necessary to conduct testing on coated specimens, with the properties of the coating then to be extracted from the response. A methodology for extracting material properties from comparisons of resonant frequencies and system loss factors for coated and uncoated beams, which is applicable even when the desired properties (storage and loss modulus) have a strong dependence on the amplitude of cyclic strain, is summarized and applied to the determination of the material properties of an air plasma sprayed alumina-titania blend ceramic to which a viscoelastic material has been added by vacuum infiltration. Tests were conducted at both room and elevated temperatures. Material properties obtained from specimens with three coating thicknesses are compared and show that values obtained for the stiffness (storage modulus) decrease with increasing coating thickness, but that values obtained for the measure of dissipative capacity (loss modulus) are essentially independent of thickness. Addition of the infiltrate was found to double the storage modulus and to increase the loss modulus at room temperature by factors of up to 3, depending on the amplitude of cyclic strain. The storage modulus of this infiltrated coating appears to diminish with increasing depth into the coating, suggesting dependence on the amount of infiltrate present. The loss modulus, however, appears to be comparatively insensitive to the amount of infiltrate present. Results from a limited investigation of the influence of increased temperature on the properties of the infiltrated coating show decreases in storage modulus with temperature, and a maximum in the loss modulus at a temperature determined by the temperature dependent properties of the specific viscoelastic material used as the infiltrate.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031004-031004-11. doi:10.1115/1.3078307.

Recent research has demonstrated that the mechanical properties of metals are altered when an electrical current is passed through the material. These studies suggest that titanium alloys, due to their low formability and need for dramatic improvement, should be subjected to additional study. The research presented herein further investigates the use of electricity to aid in the bulk deformation of Ti–6Al–4V under tensile and compressive loads. Extensive testing is presented, which documents the changes that occur in the formability of titanium due to the presence of an electrical current at varying current densities. Using carefully designed experiments, this study also characterizes and isolates the effect of resistive heating from the overall effect due to the electrical flow. This study clearly indicates that electrical flow affects the material beyond that which can be explained through resistive heating. The results demonstrate that an applied electrical current within the material during mechanical loading can greatly decrease the force needed to deform the titanium while also dramatically enhancing the degree to which it can be worked without fracturing. Isothermal testing further demonstrates that the changes are significantly beyond that which can be accounted for due to increases in the titanium’s temperature. The results are also supported by data from tests using pulsed and discontinuously applied current. Furthermore, current densities are identified that cause an enhanced formability behavior to occur. Overall, this work fully demonstrates that an electrical current can be used to significantly improve the formability of Ti–6Al–4V and that these improvements far exceed that which can be explained by resistive heating.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031005-031005-9. doi:10.1115/1.3120390.

Experimental techniques were applied to study the heterogeneities of deformation of metals at the mesoscopic scale (typically $100 μm$ in the present case). The first are fiducial carbon grids that are transferred on to the surface of the test-pieces. Here, they were used on single and polycrystals deformed in channel-die compression. They prove efficient for strains above 1. They bring out the role of the corners of the samples, which trigger bands of deformation that grow in importance as the compression goes on. They put in evidence the mesoheterogeneities that appear in the mechanical behavior of a few highly symmetric orientations such as cube. The second technique is the use of microfocused X-rays, which give the crystallographic orientation at the same scale of $100 μm$ and can work in the presence of the carbon grids even when there is considerable strain hardening. The gradients found in the lattice rotations are far less pronounced than the sharp localizations in the displacement field. This highlights the importance of the rotations due to the activity of the slip systems.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031006-031006-6. doi:10.1115/1.3120391.

The instrumented indentation test, which measures indentation tensile properties, has attracted interest recently because this test can replace uniaxial tensile test. An international standard for instrumented indentation test has been recently legislated. However, the uncertainty of the indentation tensile properties has never been estimated. The indentation tensile properties cannot be obtained directly from experimental raw data as can the Brinell hardness, which makes estimation of the uncertainty difficult. The simplifying uncertainty estimation model for the indentation tensile properties proposed here overcomes this problem. Though the influence quantities are generally defined by experimental variances when estimating uncertainty, here they are obtained by calculation from indentation load-depth curves. This model was verified by round-robin test with several institutions. The average uncertainties were estimated as 18.9% and 9.8% for the indentation yield strength and indentation tensile strength, respectively. The values were independent of the materials’ mechanical properties but varied with environmental conditions such as experimental instruments and operators. The uncertainties for the indentation yield and tensile strengths were greater than those for the uniaxial tensile test. These larger uncertainties were caused by measuring local properties in the instrumented indentation test. The two tests had the same tendency to have smaller uncertainties for tensile strength than yield strength. These results suggest that the simplified model can be used to estimate the uncertainty in indentation tensile properties.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031007-031007-8. doi:10.1115/1.3120392.

A cold expansion process is used to prolong the fatigue life of a structure under cyclic loadings. The process produces a beneficial compressive residual stress zone in the hole vicinity, which retards the initiation and propagation of the crack at the hole edge. In this study, a three-dimensional finite element model of the split-sleeve cold expansion process was developed to predict the resulting residual stress field. A thin rectangular aluminum sheet with a centrally located hole was considered. A rigid mandrel and an elastic steel split sleeve were explicitly modeled with the appropriate contact elements at the interfaces between the mandrel, the sleeve, and the hole. Geometrical and material nonlinearities were included. The simulation results were compared with experimental measurements of the residual stress. The influence of friction and the prescribed boundary conditions for the sheet were studied. Differences between the split-sleeve- and the non-split-sleeve model solutions are discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031008-031008-10. doi:10.1115/1.3120393.

Shot peening is a commonly used surface treatment process that imparts compressive residual stresses into the surface of metal components. Compressive residual stresses retard initiation and growth of fatigue cracks. During the component loading history, the shot-peened residual stresses may change due to thermal exposure, creep, and cyclic loading. This paper describes a methodical approach for characterizing and modeling residual stress relaxation under elevated temperature loading, near and above the monotonic yield strength of nickel-base superalloy IN100. The model incorporates the dominant creep deformation mechanism, coupling between the creep and plasticity models, and effects of prior plastic strain. The initial room temperature residual stress and plastic strain profiles provide the initial conditions for relaxation predictions using the coupled creep-plasticity model. Model predictions correlate well with experimental results on shot-peened dogbone specimens subject to single cycle and creep loading conditions at elevated temperature. The predictions accurately capture both the shape and magnitude of the retained residual stress profile.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031009-031009-8. doi:10.1115/1.3078301.

An experimental study is presented to (1) quantify the rate-sensitive mechanical response and (2) examine the localized deformation behavior under an applied temperature gradient in the alloy AA 2024. Isothermal flow stresses are obtained at temperatures from $−100°C$ to $495°C$ and strain rates from $10−2/s$ to $10−5/s$ using routine compression tests and a novel cyclic test, which expedites the characterization. The material displays two distinct kinetic responses with both being amenable to localization phenomena. The lower temperature/high strain rate regime displays a rate-insensitive yield with Stage III/IV work hardening. At higher temperature/low strain rates, a rate-sensitive response with little work hardening is observed. In order to relate the material constitutive behavior to the development of localized deformation, a temperature gradient test is performed wherein temperature differences of approximately $30°C$ are enforced between the top and bottom surfaces of a cylindrical compression test specimen. Deformation heterogeneity developed in the two distinct regimes of material response is illustrative of warm and hot working conditions typical of industrial processes, such as rolling.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031010-031010-11. doi:10.1115/1.3120408.

Compressive post-buckling under thermal environments and thermal post-buckling due to uniform temperature field or heat conduction are presented for a shear deformable functionally graded cylindrical shell with piezoelectric fiber reinforced composite (PFRC) actuators. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and PFRC layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation shell theory that includes thermopiezoelectric effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine buckling loads (temperature) and post-buckling equilibrium paths. The numerical illustrations concern the compressive and thermal post-buckling behavior of perfect and imperfect FGM cylindrical shells with fully covered PFRC actuators under different sets of thermal and electric loading conditions, from which results for monolithic piezoelectric actuators are obtained as comparators. The results reveal that, in the compressive buckling case, the control voltage only has a small effect on the post-buckling load-deflection curves of the shell with PFRC actuators, whereas in the thermal buckling case, the effect of control voltage is more pronounced for the shell with PFRC actuators, compared with the results of the same shell with monolithic piezoelectric actuators.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031011-031011-16. doi:10.1115/1.3086334.

This paper describes the development of multiphase hybrid composites consisting of polyester reinforced with E-glass fiber and ceramic particulates. It further investigates the erosion wear response of these composites and presents a comparison of the influence of three different particulate fillers—fly ash, alumina $(Al2O3)$, and silicon carbide (SiC)—on the wear characteristics of glass-polyester composites. For this purpose, the erosion test schedule in an air jet type test rig is made, following design of experiments approach using Taguchi’s orthogonal arrays. The Taguchi approach enables us to determine optimal parameter settings that lead to minimization of the erosion rate. The results indicate that erodent size, filler content, impingement angle, and impact velocity influence the wear rate significantly. The experimental results are in good agreement with the values from the theoretical model. An artificial neural network approach is also applied to predict the wear rate of the composites and compared with the theoretical results. This study reveals that addition of hard particulate fillers such as fly ash, $Al2O3$, and SiC improves the erosion resistance of glass-polyester composites significantly. An industrial waste such as fly ash exhibits better filler characteristics compared with those of alumina and SiC. Finally, a popular evolutionary approach known as genetic algorithm is used to generalize the method of finding out optimal factor settings for minimum wear rate.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031012-031012-6. doi:10.1115/1.3086384.

In the present work, a continuum damage mechanics model, based on Lemaitre’s concept of equivalent stress hypothesis (1986, “Local Approach to Fracture  ,” Eng. Fract. Mech., 25, pp. 523–537), has been applied to study the evolution of damage under monotonic loading condition in a near $α$ IMI-834 titanium alloy, used for aeroengine components in compressor module. The damage model parameters have been experimentally identified by in situ measurement of damage during monotonic deformation using alternating current potential drop technique. The damage model has been applied to predict damage evolution in an axisymmetrically notched specimen using finite element analysis. A reasonably good agreement has been observed between numerically simulated and experimentally measured damage behaviors. Damage micromechanisms operative in this alloy have also been identified which show multiple damage events.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031013-031013-7. doi:10.1115/1.3120410.

The purpose of this work is to explore nonuniform plastic flow at small length- and time-scales. Pure single crystal copper tensile specimens were pulled along the $[6¯ 5 6]$ crystal axis at three nominal strain-rates: 0.01%/s, 0.04%/s, and 0.10%/s. Simultaneously, the surface deformation was monitored with in situ digital image correlation over a length-scale of $∼100 μm$ and a time-scale of 0.07–0.2 s. Sequential digital image correlation strain-rate fields show compelling evidence of a wavelike plastic deformation that is proportional to the nominal strain-rate and decelerates with increasing strain hardening. While a mechanism responsible for the waves is not identified, a methodology correlating observations of multiple researchers is forwarded.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031014-031014-13. doi:10.1115/1.3086387.

Almost all of the available multiaxial high cycle fatigue (HCF) criteria are proposed based on definition of an equivalent stress expression that is a modified version of a static equivalent stress definition or a static yield function. All the equivalent stress expressions proposed so far in the fatigue analysis field have been expressed in semistationary forms wherein the global cyclic rather than the instantaneous changes are considered. In the present paper, a new technique for instantaneous fatigue equivalent stress definition is introduced based on new concepts of instantaneous (virtual) stress amplitude and instantaneous (virtual) mean stress. Then, new HCF criteria are proposed using two approaches: (1) polynomial approach and (2) integral approach, to overcome the shortcomings of the available criteria. A relevant fatigue life assessment algorithm is also proposed, and results of the available criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are evaluated for components with complicated geometries under proportional, nonproportional, and random nonproportional loadings. Results reveal that predictions of the proposed approaches are more accurate.

Topics: Fatigue , Stress , Polynomials
Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2009;131(3):031015-031015-14. doi:10.1115/1.3086405.

The effects of porosity architecture and volume fraction on the homogenized elastic moduli and elastic-plastic response of perforated thin metal sheets are investigated under three fundamental loading modes using an efficient homogenization theory. Steel and aluminum sheets weakened by circular, hexagonal, square, and slotted holes arranged in square and hexagonal arrays subjected to inplane normal and shear loading are considered with porosity volume fractions in the range 0.1–0.6. Substantial variations are observed in the homogenized elastic moduli with porosity shape and array type. The differences are rooted in the stress transfer mechanism around traction-free porosities whose shape and distribution play major roles in altering the local stress fields and thus the homogenized response in the elastic-plastic domain. This response is characterized by four parameters that define different stages of micro- and macrolevel yielding. The variations in these parameters due to porosity architecture and loading direction provide useful data for design purposes under monotonic and cyclic loading.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Eng. Mater. Technol. 2009;131(3):034501-034501-3. doi:10.1115/1.3120387.

High entropy alloys are usually defined as the kind of alloys with at least five principle components, each component has the equi-atomic ratio or near equi-atomic ratio, and the high entropy alloys can have very high entropy of mixing, forming simple solid solution rather than many complex intermediate phases. In this paper, the size effects on the microstructure and mechanical behaviors of a high entropy alloy of AlCoCrFeNi was studied by preparing as-cast rod samples with different diameters. The alloy independent of cast diameter samples has the same phase of body centered cubic solid solution. With decreasing casting diameter, both the strength and the plasticity are increased slightly.

Commentary by Dr. Valentin Fuster

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