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RESEARCH PAPERS

J. Eng. Gas Turbines Power. 1993;115(1):1-8. doi:10.1115/1.2906678.

Norton/TRW Ceramics (NTC) is developing ceramic components as part of the DOE-sponsored Advanced Turbine Technology Applications Project (ATTAP). NTC’s work is directed at developing manufacturing technologies for rotors, stators, vane-seat platforms, and scrolls. The first three components are being produced from a HIPed Si3 N4 , designated NT154. Scrolls were prepared from a series of siliconized silicon-carbide (Si-SiC) materials designated NT235 and NT230. Efforts during the first three years of this five-year program are reported. Developmental work has been conducted on all aspects of the fabrication process using Taguchi experimental design techniques. Appropriate materials and processing conditions were selected for power beneficiation, densification, and heat-treatment operations. Component forming has been conducted using thermal-plastic-based injection molding (IM), pressure slip-casting (PSC), and Quick-Set™ injection molding.1 An assessment of material properties for various components from each material and process were made. For NT154, characteristic room-temperature strengths and Weibull Moduli were found to range between ≈920 MPa to ≈1 GPa and ≈10 to ≈19, respectively. Process-induced inclusions proved to be the dominant strength-limiting defect regardless of the chosen forming method. Correction of the lower observed values is being addressed through equipment changes and upgrades. For the NT230 and NT235 Si-SiC, characteristic room-temperature strengths and Weibull Moduli ranged from ≈240 to ≈420 MPa, and 8 to 10, respectively. At 1370°C, strength values for both the HIPed Si3 N4 and the Si-SiC materials ranged from ≈480 MPa to ≈690 MPa. The durability of these materials as engine components is currently being evaluated.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):9-16. doi:10.1115/1.2906692.

Nissan has been developing and marketing ceramic turbocharger rotors for five years. This paper outlines the major theories and techniques used in ceramic fabrication, joining of ceramic and metal components, and machining of ceramics. It also presents a dynamic stress analysis using DYNA3D and describes techniques used in performing impact damage experiments, reliability evaluation, and lifetime preprediction.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):17-22. doi:10.1115/1.2906675.

Two types of silicon nitride ceramic rotor have been introduced into the Japanese market by Toyota Motor Corporation, named CT26 and CT12A, to improve engine acceleration response by the reduction in moment of inertia. In order to design a suitable blade shape for a ceramic rotor, the critical stress of the blade was determined by the results obtained experimentally from correlating the fracture origin over spintested rotors with centrifugal stress at fracture. A suitable blade shape has been determined for the CT26 turbocharger rotor type, which is identical to the metal rotor except for the disk diameter of hub back face and the blade thickness. The CT12A type is of similar design to the CT26 type; all dimensions could be reduced except for the inlet blade thickness, which is determined by foreign object damage (FOD) resistance.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):23-29. doi:10.1115/1.2906681.

A ceramic turbocharger rotor (CTR) for high-temperature use has been developed. The features of this rotor are the use of silicon nitride, which maintains high mechanical strength up to 1200°C, and a new joining technique between the ceramic rotor and its metal shaft. The CTR is expected to cope with stoichiometric mixture burning engines, which produce a higher exhaust gas temperature for fuel economy, and the impact resistance of the rotor against foreign object damage (FOD) has been markedly increased, over that of earlier rotors, resulting in higher reliability. This paper describes the development of ceramic turbocharger rotors for high-temperature use, focusing on the mechanical strength of silicon nitride and the joining of the ceramic rotor and its metal shaft.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):30-35. doi:10.1115/1.2906682.

A silicon nitride (Si3 N4 ) radial inflow turbine wheel was fabricated by injection molding at Toyota Central R&D Labs. The wheel was 142 mm in outer diameter and had 14 blades. The radial wheel was too bulky to manufacture as a homogeneous and defect-free body in one piece. It was divided into two pieces for injection molding and put together into one body by a cold isostatic pressing step after binder removal. Spin testing was executed at room temperature and the resulting photographs, taken from three directions, provided useful information about the fraction mode of the wheels. The maximum burst speed of the wheels at room temperature was 98,900 rpm, which corresponded to 145 percent of the design speed. In a hot rig test, one of the wheels survived 75,000 rpm for ten minutes at a turbine inlet temperature of 1050°C.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):36-41. doi:10.1115/1.2906683.

The bending strength of specimens of various sizes, some of which were cut from a turbine wheel, was compared with predictions using Weibull statistical theory. The stress distribution of a ceramic turbine wheel in spin testing was determined with finite elements and the results were used to analyze a wheel that was spun until it burst. The cause of the burst of the ceramic radial turbine wheel at elevated temperature is discussed and based on the tensile rupture data. A design methodology using the Larson-Miller parameter was found to be applicable to the ceramic components at elevated temperatures.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):42-50. doi:10.1115/1.2906684.

A seven-year program, designated “Research and Development of Automotive CGT,” commenced in June 1990 with the object of demonstrating the potential advantages of ceramic gas turbine engines for automotive use. This program has been conducted by the Petroleum Energy Center (PEC) with the support of the Ministry of International Trade and Industry. The engine demonstration project in this program is being handled by a team from Japan Automobile Research Institute, Inc. (JARI). This paper describes the activities of the first year of the seven-year program, and includes the project goals and objectives, the program schedule, and the first-stage design of an experimental automotive ceramic gas turbine (CGT) engine and its components. The basic engine is a 100 kW, single-shaft gas turbine engine having a turbine inlet temperature of 1350°C and a rotor speed of 110,000 rpm. The primary engine components including the turbine hot flow path components have been designed using monolithic ceramics and are scheduled to be produced during the second year of the program.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):51-57. doi:10.1115/1.2906685.

This paper gives an overview of the current status of Japan’s national industrial ceramic gas turbine (CGT) project. The goals are 42 percent and higher thermal efficiency at the turbine inlet temperature (TIT) of 1350°C, and the emission from the exhaust gas should meet the regulatory values (for example, 70 ppm for NOx ). Also, ceramic material properties have the goals of 400 MPa for the minimum guaranteed strength at 1500°C, and 15 MPam for the fracture toughness. Currently, the basic metal gas turbine of TIT 900°C with all metallic components has already been fabricated and is running under some test conditions. The design of the basic ceramic gas turbine of TIT 1200°C has been completed and its manufacture is in progress. Research is addressing the production of large, complicated ceramic parts, and parts with less deformation and fewer defects can now be produced.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):58-63. doi:10.1115/1.2906686.

Hot gas path components of current generation, liquid fuel rocket engine turbopumps (T/P) are exposed to severe thermal shock, extremely high heat fluxes, corrosive atmospheres, and erosive flows. These conditions, combined with high operating stresses, are severely degrading to conventional materials. Advanced turbomachinery (T/M) applications will impose harsher demands on the turbine materials. These demands include higher turbine inlet temperature for improved performance and efficiency, lower density for improved thrust-to-weight ratio, and longer life for reduced maintenance of re-usable engines. Conventional materials are not expected to meet these demands, and fiber-reinforced ceramic matrix composites (FRCMC) have been identified as candidate materials for these applications. This paper summarizes rocket engine T/M needs, reviews the properties and capabilities of FRCMC, identifies candidate FRCMC materials and assesses their potential benefits, and summarizes the status of FRCMC component development with respect to advanced liquid fuel rocket engine T/M applications.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):64-69. doi:10.1115/1.2906687.

A program to establish the potential for introducing fiber-reinforced ceramic matrix composites (FRCMC) in future rocket engine turbopumps was instituted in 1988. A brief summary of the overall program (both contract and in-house research) is presented. Tests at NASA Lewis include thermal upshocks in a hydrogen/oxygen test rig capable of generating heating rates up to 2500°C/s. Post-thermal upshock exposure evaluation includes the measurement of residual strength and failure analysis. Test results for monolithic ceramics and several FRCMCs are presented. Hydrogen compatibility was assessed by isothermal exposure of monolithic ceramics in high-temperature gaseous hydrogen plus water vapor.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):70-75. doi:10.1115/1.2906688.

At the Institute for Thermal Turbomachinery, University of Karlsruhe (ITS), theoretical and experimental investigations of ceramic gas turbine components are performed. For the reliability analysis by finite element calculations the computer code CERITS has been developed. This code is used to determine the fast fracture reliability of ceramic components subjected to polyaxial stress states with reference to volumetric flaws and was presented at the 1990 IGTI Gas Turbine Conference. CERITS-L now includes subcritical crack growth. With the new code CERITS-L, failure probabilities of ceramic components can be calculated under given load situations versus time. In comparing these time-dependent failure probabilities with a given permissible failure probability, the maximum operation time of a component can be determined. The considerable influence of the subcritical crack growth upon the lifetime of ceramic components is demonstrated at the flame tube segments of the ITS ceramic combustor.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):76-82. doi:10.1115/1.2906689.

The problems of high-temperature oxidation and corrosion of Si3 N4 and SiC are discussed. Other ceramics usually do not meet the requirements of structural applications at high temperatures. If the application has to meet very defined limits of size change, it is necessary to specify the exact material composition, as well as the atmosphere composition and physical environment to be able to specify the limits. This is in any case true for extremely reducing conditions or very high temperatures. Under oxidizing conditions, the region between ≈850 and 1100°C should be avoided when salty, sulfurous, and wet fuel conditions are expected. High temperature limits for long-time applications of Si3 N4 in oxidizing environments are between 1200 and 1400°C, corresponding to eutectic temperatures of the glass phase. The ultimate limit for long-time use of SiC is likely to be between 1700 and 1800°C, where bubble formation and spallation may become inevitable.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):83-90. doi:10.1115/1.2906690.

Garrett Auxiliary Power Division of Allied-Signal Aerospace Company is developing methods to design ceramic turbine components with improved impact resistance. In an ongoing research effort under the DOE/NASA-funded Advanced Turbine Technology Applications Project (ATTAP), two different modes of impact damage have been identified and characterized: local damage and structural damage. Local impact damage to Si3 N4 impacted by spherical projectiles usually takes the form of ring and/or radial cracks in the vicinity of the impact point. Baseline data from Si3 N4 test bars impacted by 1.588-mm (0.0625-in.) diameter NC-132 projectiles indicates the critical velocity at which the probability of detecting surface cracks is 50 percent equalled 130 m/s (426 ft/sec). A microphysics-based model that assumes damage to be in the form of microcracks has been developed to predict local impact damage. Local stress and strain determine microcrack nucleation and propagation, which in turn alter local stress and strain through modulus degradation. Material damage is quantified by a “damage parameter” related to the volume fraction of microcracks. The entire computation has been incorporated into the EPIC computer code. Model capability is being demonstrated by simulating instrumented plate impact and particle impact tests. Structural impact damage usually occurs in the form of fast fracture caused by bending stresses that exceed the material strength. The EPIC code has been successfully used to predict radial and axial blade failures from impacts by various size particles. This method is also being used in conjunction with Taguchi experimental methods to investigate the effects of design parameters on turbine blade impact resistance. It has been shown that significant improvement in impact resistance can be achieved by using the configuration recommended by Taguchi methods.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):91-102. doi:10.1115/1.2906691.

The mechanical behavior of continuous fiber-reinforced SiC/RBSN composites with various fiber contents is evaluated. Both catastrophic and noncatastrophic failures are observed in tensile specimens. Damage and failure mechanisms are identified via in-situ monitoring using NDE techniques throughout the loading history. Effects of fiber/matrix interface debonding (splitting) parallel to the fibers are discussed. Statistical failure behavior of fibers is also observed, especially when the interface is weak. Micromechanical models incorporating residual stresses to calculate the critical matrix cracking strength, ultimate strength, and work of pull-out are reviewed and used to predict composite response. For selected test problems, experimental measurements are compared to analytic predictions.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):103-108. doi:10.1115/1.2906663.

For laminated ceramic matrix composite (CMC) materials to realize their full potential in aerospace applications design, methods and protocols are a necessity. This paper focuses on the time-independent failure response of these materials and presents a reliability analysis associated with the initiation of matrix cracking. It highlights a public domain computer algorithm that has been coupled with the laminate analysis of a finite element code and which serves as a design aid to analyze structural components made from laminated CMC materials. Issues relevant to the effect of the size of the component are discussed, and a parameter estimation procedure is presented. The estimation procedure allows three parameters to be calculated from a failure population that has an underlying Weibull distribution.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):109-116. doi:10.1115/1.2906664.

This paper describes nonlinear regression estimators for the three-parameter Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):117-121. doi:10.1115/1.2906665.

At a macroscopic level, a composite lamina may be considered as a homogeneous orthotropic solid whose directional strengths are random variables. Incorporation of these random variable strengths into failure models, either interactive or noninteractive, allows for the evaluation of the lamina reliability under a given stress state. Using a noninteractive criterion for demonstration purposes, laminate reliabilities are calculated assuming previously established load sharing rules for the redistribution of load as the failure of laminae occurs. The matrix cracking predicted by ACK theory is modeled to allow a loss of stiffness in the fiber direction. The subsequent failure in the fiber direction is controlled by a modified bundle theory. Results using this modified bundle model are compared with previous models, which did not permit separate consideration of matrix cracking, as well as to results obtained from experimental data.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):122-126. doi:10.1115/1.2906666.

An analysis of the effectiveness of fiber reinforcement in brittle matrix composites is presented. The analytical method allows consideration of discrete fiber distribution and examination of the development of crack growth parameters on the microscale. The problem associated with bridging zone development is addressed here; therefore, the bridging zone is considered to be smaller than the main pre-existing crack, and the small-scale approach is used. The mechanics of the reinforcement is accurately accounted for in the process zone of a growing crack. Closed-form solutions characterizing the initial failure process are presented for linear and nonlinear forcefiber pullout displacement relationships. The implicit exact solution for the extended bridging zone is presented as well.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):127-138. doi:10.1115/1.2906667.

The bridging of matrix cracks by fibers is an important toughening mechanism in fiber-reinforced brittle matrix composites. This paper presents the results of a nonlinear finite element analysis of the Mode I propagation of a bridged matrix crack in a finite size specimen. The composite is modeled as an orthotropic continuum and the bridging due to the fibers is modeled as a distribution of tractions that resist crack opening. A critical stress intensity factor criterion is employed for matrix crack propagation, while a critical crack opening condition is used for fiber failure. The structural response of the specimen (load-deflection curves) as well as the stress intensity factor of the propagating crack is calculated for various constituent properties and specimen configurations for both tensile and bending loading. By controlling the length of the bridged crack, results are obtained that highlight the transition from stable to unstable behavior of the propagating crack.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):139-147. doi:10.1115/1.2906668.

Silicon carbide is currently used as a structural material for heat exchanger tubes and related applications because of its excellent thermal properties and oxidation resistance. Silicon carbide suffers corrosion degradation, however, in the aggressive furnace environments of industrial processes for aluminum remelting, advanced glass melting, and waste incineration. Adherent ceramic oxide coatings developed at Solar Turbines Incorporated, with the support of the Gas Research Institute, have been shown to afford corrosion protection to silicon carbide in a simulated aluminum remelt furnace environment as well as in laboratory-type corrosion testing. The coatings are also protective to silicon carbide-based ceramic matrix composites.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):148-154. doi:10.1115/1.2906669.

This paper addresses an experimental investigation on the feasibility of using abrasive-waterjets (AWJs) for the precision drilling of small-diameter holes in advanced aircraft engine components. These components are sprayed with ceramic thermal barrier coating (TBC), and the required holes are typically 0.025 in. in diameter with a drilling angle of 25 deg. The parameters of the AWJ were varied to study their effects on both quantitative and qualitative hole drilling parameters. The unique techniques of assisting the abrasive feed process, ramping the waterjet pressure during drilling, and varying the jet dwell time after piercing were effectively implemented to control hole quality and size. The results of the experiments indicate the accuracy and repeatability of the AWJ technique in meeting the air flow and hole size requirements. Production parts were drilled for prototype engine testing.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):155-159. doi:10.1115/1.2906670.

This paper summarizes the key properties of GTD-222 (Wood and Haydon, 1989), a new cast nickel-base nozzle alloy developed by GE for use in land-based gas turbines. GTD-222 is being introduced as a replacement for FSX-414 in second and third-stage nozzles of certain machines. Presented in this paper are comparisons of the tensile, creep-rupture, and fatigue properties of GTD-222 versus FSX-414. In addition, the results of a long-term thermal stability study, high-temperature oxidation, and hot corrosion evaluation as well as weldability results will be discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):160-164. doi:10.1115/1.2906671.

HAYNES® alloy 242 is a promising new Ni-Mo-Cr alloy for high-strength, high-temperature aerospace fastener applications. Age-hardenable by virtue of a long-range-order strengthening mechanism, 242™ alloy is capable of developing very high strength, particularly in the cold-worked condition. A key difference from other fastener materials is its attendant good ductility. The relationship between the amount of cold work, aging temperature and time, and the properties of this alloy has not been previously explored in detail. In the present work, the nature of the interaction between cold work and aging will be examined, and the properties of the material relevant to aerospace fastener applications will be described.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):165-171. doi:10.1115/1.2906672.

The split-sleeve cold expansion process has been used successfully for over 20 years to extend the fatigue life of holes in aircraft structures. Cold expansion technology can also be applied to enhance engine low-cycle fatigue (LCF) performance in both production and repair applications. Specific test data are presented showing that fatigue life extension can be attained by cold expansion of holes in a wide range of situations (including nonround hole geometries and low edge margins), and in components subjected to high operating temperatures. A cold expanded bushing system is compared to standard shrink-fit bushing installations. Finally, two case studies are used to illustrate the application of cold expansion to full-scale engine components.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):172-176. doi:10.1115/1.2906673.

The fundamentals of laser beam interactions with materials are discussed briefly and unique laser processing capabilities are noted. Introduction of this processing capability to manufacturing is reviewed. Typical high-volume production application requirements are identified and representative performance and production experience are described. Specific multikilowatt laser welding, piercing, and hardfacing applications in aerospace production are described. The evolution of production processes is discussed against the background of required processing capability. Also discussed are the unique laser processing capabilities that resulted in selection of the laser for production. Production experience is reviewed and cost saving factors are noted.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):177-183. doi:10.1115/1.2906674.

Alpha-two titanium aluminides represent strong candidates for replacing many conventional titanium and nickel-base superalloys for intermediate temperature applications. One potential application of these alloys is turbine engine rings. Nonrotating rings of this type are typically manufactured by flash butt welding. The performance of welds in this alloy is known to be strongly affected by the weld microstructure. Welding processes that result in very slow cooling rates yield relatively coarse Widmanstatten-type microstructure(s), which generally yields acceptable weld performance. Processes that result in intermediate cooling rates, however, result in acicular alpha-two martensite microstructures. These microstructures have very little ductility and lead to reduced weld performance. Finally, for processes where the cooling rate is very rapid, the weld microstructure is a retained ordered beta phase, which apparently results in improved weld properties. In this paper, microstructures of some representative flash welds on T-14Al-21Nb were examined. In addition, flash welding conditions were varied to examine the effects of initial die opening and upset distance. In general, it appears that all the welds included in this study contain the ordered HCP martensite in the weld zone. However, both the scale of the microstructure and the weld hardness seem to depend heavily on the particular set of processing conditions used. These results were then used to estimate the relative cooling rates in these welds, and understand the effects of these processing conditions on the developing microstructures.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):184-192. doi:10.1115/1.2906676.

A finite element model of an elevated temperature upset welding process was developed to simulate the process and to study the role and sensitivity of the major process parameters. Particular attention was focused on the deformation characteristics by studying the displacement and stress fields generated for the purpose of obtaining a better understanding of this solidstate welding process. The paper describes the finite element formulation, the experiments used to validate the modeling, and a selected application for upset welding of a titanium alloy.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):193-199. doi:10.1115/1.2906677.

Recent developments in magnesium alloys, processing techniques, and corrosion protection schemes are reviewed. The casting alloy WE43 is detailed, data being presented showing that it compares favorably with aluminum-based casting alloys on a strength-to-weight basis. In addition its intrinsic corrosion characteristics are shown to be similar to those of aluminum-base alloys. A countergravity casting process, specifically designed to make higher quality, thin-walled magnesium alloy components, is described, together with property data indicating the improvements obtained. Also discussed are the ongoing developments in metal matrix composites and rapid solidification technologies, showing the benefits offered by these processing routes. Finally current corrosion protection schemes are reviewed and their overall cost effectiveness discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Gas Turbines Power. 1993;115(1):200-204. doi:10.1115/1.2906679.

When grinding carbon steels, creep-resistant materials, and other metals such a titanium, cubic boron nitride (CBN) has become recognized as the preferred choice over Al2 O3 and SiC. The succes or failure of the grinding process with CBN lies in the mechanical dressing of the wheel because mechanical dressing is accompanied by very large stresses that distort the grinding wheel and deflect the grinding machine. One recent approach is to true the CBN wheel mechanically and then dress the wheel during the actual grinding manufacturing process. This work observes the dressing of vitrified bonded CBN during the actual like cycle in the production process of steel bearings. Scanning electron micrographs of CBN wheel surfaces are related to surface topography measurements of both wheel and bearing using a Tallysurf machine. In addition, the compositions of the wheel surfaces were checked using the SEM x-ray spectrography facilities. In-process dressing was determined to comprise three distinct stages: the primary or initial dressing, the secondary occurring during steady-state grinding, and finally the tertiary stage after which dimensional tolerance is lost. It was found that the life characteristics of the CBN wheel are quite different than current theories predict. Instead of the limitation of grinding being due to work material loading of the wheel and subsequent dulling of the grains, it was found that the CBN grains remain unchanged and a wear process occurs in the matrix material until the grains fall out and the wheels lose their dimensional tolerance.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Eng. Gas Turbines Power. 1993;115(1):205-207. doi:10.1115/1.2906680.
Commentary by Dr. Valentin Fuster

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