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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

The NASA Materials Science Research Program: It's New Strategic Goals and Opportunities

In the past year, the NASA s Office of Biological and Physical Research (OBPR) has formulated a long term plan to perform strategical and fundamental research bringing together physics, chemistry, biology, and engineering to solve problems needed for current and future agency mission goals. Materials Science is one of basic disciplines within the Enterprise s Division of Physical Sciences Research. The Materials Science Program participates to utilize effective use of International Space Station (ISS) and various world class ground laboratory facilities to solve new scientific and technology questions and transfer these results for public and agency benefits. The program has recently targeted new investigative research in strategic areas necessary to expand NASA knowledge base for exploration of the universe and some of these experiments will need access to the microgravity of space. The program is implementing a wide variety of traditional ground and flight based research related types of fundamental science related to materials crystallization, fundamental processing, and properties characterization in order to obtain basic understanding of various phenomena effects and relationships to the structures, processing, and properties of materials. , In addition new initiatives in radiation protection, materials for propulsion and In-space fabrication and repair focus on research helping the agency solve problems needed for future transportation into the solar system. A summary of the types and sources for this research is presented including those experiments planned for a low gravity environment. Areas to help expand the science basis for NASA future missions are described. An overview of the program is given including the scope of the current and future NASA Research Announcements with emphasis on new materials science initiatives. A description of the planned flight experiments to be conducted on the International Space Station program along with the planned facility class Materials Science Research Rack (MSRR) and Microgravity Glovebox (MSG) type investigations. Some initial results from the first three materials experiments are given.

Schlagheck, Ronald A.↗
NASA NTRS2004

Crystal Growth of CdTe by Gradient Freeze in Universal Multizone Crystallizator (UMC)

In the case of unsealed melt growth of an array of II-VI compounds, namely, CdTe, CdZnTe and ZnSe, there is a tremendous amount of experimental data describing the correlations between melt conditions and crystal quality. The results imply that the crystallinity quality can be improved if the melt was markedly superheated or long-time held before growth. It is speculated that after high superheating the associated complex dissociate and the spontaneous nucleation is retarded. In this study, crystals of CdTe were grown from melts which have undergone different thermal history by the unseeded gradient freeze method using the Universal Multizone Crystallizator (UMC). The effects of melt conditions on the quality of grown crystal were studied by various characterization techniques, including Synchrotron White Beam X-ray Topography (SWSXT), infrared microscopy, chemical analysis by glow discharge mass spectroscopy (GDMS), electrical conductivity and Hall measurements.

Su, Ching-Hua↗
NASA NTRS2008

Marshall Space Flight Center's Impact Testing Facility Capabilities

Marshall Space Flight Center's (MSFC) Impact Testing Facility (ITF) serves as an important installation for space and missile related materials science research. The ITF was established and began its research in spacecraft debris shielding in the early 1960% then played a major role in the International Space Station debris shield development. As NASA became more interested in launch debris and in-flight impact concerns, the ITF grew to include research in a variety of impact genres. Collaborative partnerships with the DoD led to a wider range of impact capabilities being relocated to MSFC as a result of the closure of Particle Impact Facilities in Santa Barbara, California. The Particle Impact Facility had a 30 year history in providing evaluations of aerospace materials and components during flights through rain, ice, and solid particle environments at subsonic through hypersonic velocities. The facility's unique capabilities were deemed a "National Asset" by the DoD. The ITF now has capabilities including environmental, ballistic, and hypervelocity impact testing utilizing an array of air, powder, and two-stage light gas guns to accommodate a variety of projectile and target types and sizes. Relocated test equipment was dated and in need of upgrade. Numerous upgrades including new instrumentation, triggering circuitry, high speed photography, and optimized sabot designs have been implemented. Other recent research has included rain drop demise characterization tests to obtain data for inclusion in on-going model development. Future ITF improvements will be focused on continued instrumentation and performance enhancements. These enhancements will allow further, more in-depth, characterization of rain drop demise characterization and evaluation of ice crystal impact. Performance enhancements also include increasing the upper velocity limit of the current environmental guns to allow direct environmental simulation for missile components. The current and proposed ITF capabilities range from rain to micrometeoroids allowing the widest test parameter range possible for materials investigations in support of space, atmospheric, and ground environments. These test capabilities including hydrometeor, single/multi-particle, ballistic gas grins, exploding wire gun, and light gas guns combined with Smooth Particle Hydrodynamics Code (SPHC) simulations represent the widest range of impact test capabilities in the country.

Evans, Steve↗
NASA NTRS2008

Marshall Space Flight Center's Impact Testing Facility Capabilities

Marshall Space Flight Center's (MSFC) Impact Testing Facility (ITF) serves as an important installation for space and missile related materials science research. The ITF was established and began its research in spacecraft debris shielding in the early 1960s, then played a major role in the International Space Station debris shield development. As NASA became more interested in launch debris and in-flight impact concerns, the ITF grew to include research in a variety of impact genres. Collaborative partnerships with the DoD led to a wider range of impact capabilities being relocated to MSFC as a result of the closure of Particle Impact Facilities in Santa Barbara, California, The Particle Impact Facility had a 30 year history in providing evaluations of aerospace materials and components during flights through rain, ice, and solid particle environments at subsonic through hypersonic velocities. The facility's unique capabilities were deemed a 'National Asset' by the DoD, The ITF now has capabilities including environmental, ballistic, and hypervelocity impact testing utilizing an array of air, powder, and two-stage light gas guns to accommodate a variety of projectile and target types and sizes. Relocated test equipment was dated and in need of upgrade. Numerous upgrades including new instrumentation, triggering circuitry, high speed photography, and optimized sabot designs have been implemented. Other recent research has included rain drop demise characterization tests to obtain data for inclusion in on-going model development. Future ITF improvements will be focused on continued instrumentation and performance enhancements. These enhancements will allow further, more in-depth, characterization of rain drop demise characterization and evaluation of ice crystal impact. Performance enhancements also include increasing the upper velocity limit of the current environmental guns to allow direct environmental simulation for missile components. The current and proposed ITF capabilities range from rain to micrometeoroids allowing the widest test parameter range possible for materials investigations in support of space, atmospheric, and ground environments. These test capabilities including hydrometeor, single/multi-particle, ballistic gas guns, exploding wire gun, and light gas guns combined with Smooth Particle Hydrodynamics Code (SPHC) simulations represent the widest range of impact test capabilities in the country.

Evans, Steve↗
DOE OSTI2023

Synthesis, crystal and electronic structure of the Zintl phase Ba 16 Sb 11 . A case study uncovering greater structural complexity via monoclinic distortion of the tetragonal Ca 16 Sb 11 structure type

The binary Zintl phase Ba 16 Sb 11 has been synthesized and structurally characterized. Detailed studies via single-crystal X-ray diffraction methods indicate that although Ba 16 Sb 11 appears to crystallize in the tetragonal Ca 16 Sb 11 structure type (space group $P\bar{4}2_1$m with a=13.5647(9) Å, c=12.4124(12)Å, Z=2, R 1 = 3.14%; wR 2 = 4.77%), there exists an extensive structural disorder. Some Ba 16 Sb 11 crystals were found to be monoclinic and the structure was solved and refined in space group P2 1 (a=18.3929(12) Å, b=13.5233(8) Å, c=18.3978(12) Å, β=94.6600(10)°; Z=4, R 1 =5.84 %; wR 2 =9.58 %). The latter corresponds to a 2-fold superstructure of the tetragonal one, which provides a disorder-free structural model. In both descriptions, the disordered tetragonal and the ordered monoclinic superstructure, the basic building units that make up the structure of this Ba-rich compound are pairs of face-shared square antiprisms of Ba atoms, which are centered by Sb atoms. The dimerized antiprisms are linked into parallel chains via square prisms of Ba atoms, which are also centered by Sb atoms. The Zintl concept can be applied in a straightforward manner and as result, the structure of Ba 32 Sb 22 (=2×Ba 16 Sb 11 ) can be rationalized as (Ba 2+ ) 32 (Sb 3– ) 20 [Sb 2 ] 4– . Notably, the partitioning of the valence electrons is done taking into an account the homoatomic Sb–Sb contacts (d=3.01 Å), which can be clearly distinguished in the lower symmetry space group. Electronic structure calculations of Ba 16 Sb 11 are in good accordance with the Zintl rationalization and predict a semiconductor with a band gap of 0.77 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Chemical Preparation, Crystal Structure Reinvestigation and Vibrational Study of CoNa 3 P 3 O 10 ·12H 2 O and X-ray Characterization of the New Anhydrous Triphosphate CoNa 3 P 3 O 10

The triphosphate dodecahydrate of cobalt and sodium CoNa 3 P 3 O 10 ·12H 2 O was prepared by the ion exchange resin process. Its structure was studied by X-ray diffraction and determined in the monoclinic space group P12 1 /c1 with the unit-cell parameters a = 14.6650(5) Å, b=9.1916(3) Å, c = 15.0239(5) Å,β =90.2210(10)°, Z = 4 and V = 2025.13(12) Å 3 . The thermal dehydration of this compound was performed, leading to an anhydrous new form, CoNa 3 P 3 O 10 , which was characterized by X-ray diffraction. The obtained CoNa 3 P 3 O 10 crystallized in monoclinic space group P21/n with the unit-cell parameters a=15,3774 Å, b=7,6988 A°, c=14,2832A°, β=92,9115°. The characteristic IR wavenumbers of the P 3 O 10 5- ions observed in the vibrational spectra were calculated using isotopic substitutions, which confirms the existence of these groups in the studied compound. A comparison between the IR and Raman wavenumbers of CoNa 3 P 3 O 10 ·12H 2 O, CoNa 3 P 3 O 10 and Na 5 P 3 O 10 ·12H 2 was performed. A kinetic study was also made for CoNa 3 P 3 O 10 ·12H 2 O.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1998

Intrinsic Kinetics Fluctuations as Cause of Growth Inhomogeneity in Protein Crystals

Intrinsic kinetics instabilities in the form of growth step bunching during the crystallization of the protein lysozyme from solution were characterized by in situ high-resolution optical interferometry. Compositional variations (striations) in the crystal, which potentially decrease its utility, e.g., for molecular structure studies by diffraction methods, were visualized by polarized light reflection microscopy. A spatiotemporal correlation was established between the sequence of moving step bunches and the striations.

Vekilov, Peter G.↗
DOE OSTI2022

Crystal response measurement of the x-ray transmission crystals used by the Imaging Spectroscopy Snout at the National Ignition Facility

The Imaging Spectroscopy Snout (ISS) used at the National Ignition Facility is able to simultaneously collect neutron pinhole images, 1D spatially resolved x-ray spectra, and time resolved x-ray pinhole images. To measure the x-ray spectra, the ISS can be equipped with up to four different transmission crystals, each offering different energy ranges from ∼7.5 to ∼12 keV and different resolutions. Characterizing and calibrating such instruments is of paramount importance in order to extract meaningful results from experiments. More specifically, we characterized different ISS transmission-type alpha-Quartz crystals by measuring their responses as a function of photon energy, from which we inferred the angle-integrated reflectivity for each crystal’s working reflections. These measurements were made at the Lawrence Livermore National Laboratory calibration station dedicated to the characterization of x-ray spectrometers. The sources used covered a wide x-ray range—from a few to 30 keV; the source diameter was ∼0.6 mm. The experimental results are discussed alongside theoretical calculations using the pyTTE model.

Dozieres, M. (ORCID:0000000286401459)↗
DOE OSTI2020

Synthesis, Structural Characterization and Chemical Bonding of Sr 7 Li 6 Sn 12 and its Quaternary Derivatives with Eu and Alkaline Earth Metal (Mg, Ca, Ba) Substitutions. A Tale of Seven Li‐Containing Stannides and Two Complex Crystal Structures

In this paper, we discuss the synthesis and the structural characterization of the new ternary compound Sr 7 Li 6 Sn 12 and its six quaternary derivatives, where alkaline earth metals (Ca, Mg, Ba) and the rare earth metal Eu are substituted, yielding crystalline phases of monoclinic or orthorhombic symmetry. The title compounds were synthesized via high‐temperature solid‐state reactions of the corresponding elements. The crystal structures were determined by single‐crystal X‐ray diffraction methods. The (Sr,Ca) 7 Li 6 Sn 12 and Eu 7 (Mg,Li) 6 Sn 12 phases represent a new structure type (space group P 2/ m , No. 10) while Sr 7 Li 6 Sn 12 and the rest of the title phases crystallize in the orthorhombic base‐centered space group Cmmm (No. 65) which is similar to the Eu 7 Li 8– x Sn 10+ x ( x ≈ 2.0) phase with the Ce 7 Li 8 Ge 10 structure type (Pearson code oC 50). Careful examination of the resulting structures shows intricate disordering between Li and Sn atoms, which is governed by the total number of valence electrons. The discussion of experimental results is also supported by DFT electronic structure calculations.

Osman, Hussien H.↗
DOE OSTI2020

Large Single Crystals of V 1– x Mo x O 2 from a Two-Step Chemical Vapor Transport Synthesis

This article details the synthesis of single crystals with the chemical formulas V 1-x Mo x O 2 ( 0 ≤ x ≤ 0.6) using the chemical vapor transport method at high temperatures (850 to 950 °C). These compounds are of interest due to the special relationship between their structure and electronic properties. Understanding this relationship will help guide future efforts in designing energy-saving devices. While some of these compounds have been synthesized before, this is the first time their synthesis has been reported for such a wide range of compounds in the form of bulk single crystals. The single crystal form is required for detailed characterization of the compounds. The materials were characterized chemically and structurally in order to validate the precise chemical compositions that were reported. Characterization methods included x-ray diffraction, inductively-coupled plasma atomic emission spectroscopy, and electron dispersive spectroscopy. The synthesis method is tunable, and the introduction of multiple steps both overcome the previous chemical challenges precluding synthesis of high molybdenum content crystals and allow for the creation of larger single crystals that were otherwise possible. The crystals synthesized this way are suitable for specialized measurements for determining the precise physical properties and atomic structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Synthesis of porous organic cage CC3 via solvent modulated evaporation

We demonstrate a Humidity Modulated Solvent Evaporation (HMSE) approach to promote the nucleation and growth of CC3 crystals. This approach relies on the gradual evaporation of dichloromethane (solvent) from a diluted concentration of CC3 precursors deposited on aluminum foil. The slow solvent evaporation allowed enough time for the organization and formation of CC3 porous organic cage. The solvent diffusion rate was modulated by the relative humidity in the system. The slow kinetics implied during the development of CC3 phase, allowed the formation of CC3 crystals. HRTEM, SAED, SEM, and XRD patterns were used as pivotal characterization techniques to follow and confirm the formation of CC3 crystals.

porous organic cages, modulated evaporation, cryst↗
DOE OSTI2020

Recent experimental explorations of non-classical nucleation

Nucleation, the early stage of crystallization, is a key step in producing functional materials, but nucleation processes have yet to be understood in detail. Recent advanced characterization techniques, especially atomic force microscopy, liquid-cell transmission electron microscopy (TEM) and cryo-TEM, enable scientists to observe previously inaccessible nucleation details at the nanoscale. In this review, we summarize newly suggested non-classical nucleation models with respect to mechanistic understanding from experimental views, which highlight multi-step nucleation mechanisms. Different intermediated phases such as clusters at the pre-nucleation stage, liquid-like precursors, amorphous phases and even oligomers have been revealed, which play vital roles in nucleation and structure control. Moreover, these intermediated phases practically contribute in general to the structural variances of materials for nanoscience and nanotechnology. Overall, these studies ultimately enable us to control nucleation processes for materials synthesis.

Jin, Biao↗
DOE OSTI2023

Axis dependent conduction polarity in the air-stable semiconductor, PdSe 2

Axis-dependent conduction polarity (ADCP) is a unique electronic phenomena in which the charge polarity of carrier conduction can differ from p-type to n-type depending on the direction of travel through the crystal. Most materials that exhibit ADCP are metals, and very few semiconducting materials exhibit this effect. Here, in this work, we establish that PdSe 2 , a ~0.5 eV band gap semiconductor that is air- and water-stable, exhibits ADCP, through the growth and characterization of the transport properties of crystals with extrinsic p- and n-type doping levels of Ir and Sb, respectively, in the 10 16 –10 18 cm –3 range. Electron doped PdSe 2 exhibits p-type conduction in the cross-plane direction and n-type conduction along the in-plane directions above an onset temperature of 100–200 K that varies with doping level. Lightly p-doped samples show p-type thermopower in all directions at low temperatures, but above ~360 K the in-plane thermopower turns negative. Density functional theory calculations indicate that the origin of ADCP arises from the complementary effective mass anisotropies in the valence and conduction bands in this material, which facilitate hole transport in the cross-plane direction, and electron transport along the in-plane directions. ADCP occurs at temperatures with sufficient thermal population of both carrier types to overcome the extrinsic doping levels to exploit the effective mass anisotropy. In total, the development of this stable semiconductor in which thermally or optically excited holes and electrons inherently migrate along different directions opens up numerous potential applications in a multitude of technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Time Domain Thermoreflectance (TDTR) Studies of Microstructural Characterization of as-Fabricated and/or Irradiated TPBAR Components

Paddock et al. demonstrated for the first-time the measurement of thermal diffusivity from thin metal films using picosecond transient thermoreflectance in 1986. This project attempted to use a similar experimental setup based on a femtosecond time domain thermoreflectance (TDTR) to measure the damage to the crystal lattice of LiAlO 2 from irradiation in the reactor and production of tritium and helium. The TDTR is based on a pump-probe laser configuration where the pump laser is used to heat the sample and the probe laser is used to follow the thermal evolution created by the pump laser. The goal for this project is to measure the differences in thermal diffusivity between LiAlO 2 and the irradiated Li AIO 2 sample in a reactor. Unfortunately, COVID-19 restricted laboratory research time and the availability of researchers capable to conduct TDTR work. In addition, the ultrafast laser (Astrella 35fs laser) required to conduct the work was inoperable making this particulate work impossible to conduct in FY20 and FY21. The purpose of the thermal diffusion measurements with a TDTR setup is to probe the damage and disorder to the crystal lattice of pristine and irradiated samples. Since TDTR was not available for this work, a different approach using Raman and luminescence spectroscopy was used to characterize the crystal lattice damage in LiAlO 2 from irradiation.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2020

Isolation and Structural Elucidation of 15–Nuclear Copper Dihydride Clusters: An Intermediate in the Formation of a Two–Electron Copper Superatom

Highly reactive copper-dihydride clusters, [Cu 15 (H) 2 (S 2 CNR 2 ) 6 (C 2 Ph) 6 ](PF 6 ) {R = n Bu (1 H ), n Pr (2 H ), i Bu (3 H )}, are isolated during the reaction of [Cu 28 H 15 {S 2 CN n Bu 2 } 12 ](PF 6 ) with ten equivalents of phenylacetylene. They are found to be intermediates in the formation of the earlier reported two-electron superatom [Cu 13 (S 2 CNR 2 ) 6 (C 2 Ph) 4 ] + . Better yields are obtained by reacting dithiocarbamate sodium salts, [Cu(CH 3 CN) 4 ](PF 6 ), BH 4 – and phenylacetylene. The presence of two hydrides in the isolated clusters is confirmed by the synthesis and characterization of its deuteride analogue [Cu 15 (D) 2 (S 2 CNR 2 ) 6 (C 2 Ph) 6 ] + , and a single-crystal neutron structure of 2 H . Structural characterization of 1 H reveals a new bicapped icosahedral copper(I) cage encapsulating a linear copper dihydride (CuH 2 ) – unit. In conclusion, reaction of 3 H with Au(I) salts yields a highly luminescent [AuCu 12 (S 2 CNiBu 2 ) 6 (C 2 Ph) 4 ] + cluster.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Fabrication of Advanced Nanocarbon-Metal Composites for Improved Energy Efficiency

We fabricated nanocarbon metal composites (NCMC) of Al alloys with a process called “electrocharging assisted process” (EAP). This method consists of the application of a high current to a mixture of liquid metal and carbon particles. We investigated aluminum alloys (6061 and 1350) and used activated carbon and graphite powder as the source of carbon. The high current induces the formation of carbon chains and ribbons in the liquid metal. Upon solidification of the metal an epitaxial relation between the carbon nanostructures and the metal lattice is produced. The purpose of the project was to find the parameters during the reaction that would give rise to a high density of nanoribbons extending throughout the metal such that the electrical conductivity and the mechanical strength of the composite increased and that the method could be extended to large scale manufacturing. For this purpose, we designed two reactors for the incorporation of nanocarbon ribbons in aluminum metal. The first reactor was designed to have more control of the region with the high current density. However, there were problems with getting good mixing of the carbon in small volumes. A second reactor was designed with a stirrer that allowed for better mixing of the carbon by the introduction of argon gas through the shaft of the stirrer. NCMC were fabricated with a series of parameters to understand the role of current, time of applied current, type and shape of the cathode electrode and stirring speed of the mixture. We analyzed the composites by Raman scattering to gain information on the crystallite size of the nanocarbon, XRD to obtain the crystal structure of the composite, SEM and TEM to characterize the grain size of the aluminum grains and the quality of the crystal structure. We also measured the electrical conductivity and mechanical properties of selected samples. The nanocomposites showed increase in crystallite size of the nanocarbon with a linear dependence of the crystallite size on the duration of the applied current. There is a minimum current density necessary for the crystallite size to increase compared to the ~ 10 nm size of the activated carbon source used in the fabrication. The electrical conductivity of the nanocomposites increased with crystallite size of the nanocarbon and with the concentration of converted carbon. The maximum increase in electrical conductivity was 5.7% above the baseline for samples with ~ 4 wt % nanocarbon with crystallite size larger than 30 nm. These samples presented a hardness ~ 8% higher than the baseline samples with no carbon.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1992

Study of FES/CAST/HGS

The microgravity materials processing program has been instrumental in providing the crystal growth community with an experimental environment to better understand the phenomena associated with the growing of crystals. In many applications one may pursue the growth of large single crystals which cannot be grown on earth due to convective driven flows. A microgravity environment is characterized by neither convection of buoyancy. Consequently superior crystals are able to be grown in space. On the other hand, since neither convection nor buoyancy dominates the fluid flow in a microgravity environment, then lesser dominating phenomena can affect crystal growth, such as surface driven flows or diffusion limited solidification. In the case of experiments that are to be flown in space using the Fluid Experiments System (FES), diffusion limited growth should be the dominating phenomenon. The use of holographic and Schlieren optical techniques for studying the concentration gradients in solidification processes has been used by several investigators over the years. The Holographic Ground System (HGS) facility at MSFC has been a primary resource in researching this capability. Consequently scientific personnel have been able to utilize these techniques in both ground based research and in space experiments. An important event in the scientific utilization of the HGS facilities was the TGS (triglycine sulfate) Crystal Growth and the Casting and Solidification Technology (CAST) experiments that were flown on the International Microgravity Lab (IML) mission in March of this year. The preparation and processing of these space observations are the primary experiments reported in this work. This project provides some ground-based studies to optimize on the holographic techniques used to acquire information about the crystal growth processes flown on IML. Since the ground-based studies will be compared with the space-based experimental results, it is necessary to conduct sufficient ground based studies to best determine how the experiment in space worked. The current capabilities in computer based systems for image processing and numerical computation have certainly assisted in those efforts. As anticipated, this study has certainly shown that these advanced computing capabilities are helpful in the data analysis of such experiments.

Workman, Gary L.↗
NASA NTRS1989

Fatigue behavior of a single-crystal superalloy

A single-crystal superalloy, PWA 1480 is under consideration as a replacement material for the turbine blades of the high pressure fuel turbopump (HPFTP) of the space shuttle main engine (SSME). Three separate experimental programs were conducted to characterize the fatigue behavior of this alloy. Fatigue tests were conducted at room temperature (in air) and at 1000 F (in vacuum) on smooth specimens machined from both cast bars and slabs. The data from all of these programs are consolidated to provide a broader characterization of the fatigue behavior of the single crystal PWA 1480. The zero-mean-stress fatigue relationships are expressed in terms of stress range versus cyclic life lines on log-log plots. Characterization of the fatigue behavior of (001) oriented PWA 1480 single crystal under conditions of tensile mean stress was performed by using the unified approach proposed by Heidmann. In this approach the fatigue life is modified by a mean stress parameter so that a single life relationship can be used to represent both zero and tensile mean stress data.

Kalluri, Sreeramesh↗