Results for “Normal forms” — Page 37

DOE OSTI2025

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel Jana Howard1,3, Guang Yang3, Haiyan Zhao1*, Patrick Warren4, Tiankai Yao3, Steven Cavazos4 Elizabeth Sooby Wood4*, Ching-heng Shiau2 1 University of Idaho, Environmental Science, Idaho Falls, Idaho, USA 2 Boise State University, Microscopy and Characterization Suite, Idaho Falls, Idaho, USA 3 Idaho National Laboratory, Idaho Falls, Idaho, USA 4 University of Texas San Antonio, Department of Physics and Astronomy, San Antonio, Texas, USA *Corresponding author: haiyanz@uidaho.edu; elizabeth.soobywood@utsa.edu Tri-structural Isotropic (TRISO) particle fuel is the preferred choice for the newest and next-generation high-temperature nuclear reactors due to its robust construction [1]. The fuel design effectively contains fission products inside the particle at extremely high temperatures [2]. However, the effect of transition metal fission products on fuel performance and structural integrity remains largely unknown, creating uncertainties in predicting fuel performance and potential failure mechanisms [2]. For example, palladium (Pd) has a strong tendency to form intermetallic phases with uranium (U). These new phases tend to be hard and brittle which could lead to fracture of fuel kernel during irradiation [3,4]. Pd is not normally produced in high concentrations in normal fission reactions however, driving the production of Pd into the locality of a Uranium Oxycarbide (UCO) nuclear fuel provides an opportunity to closely observe the diffusion and chemical interactions. This study focuses on detailed transmission electron microscopy characterization of the intermetallic phases formed by the interaction between a UCO kernel and a Pd bar after annealing at 1100 °C for 100 hours. Figure 1 provides an overview of the UCO kernel in contact with the Pd bar. The UCO-Pd sample surface was examined using a Focused Ion Beam (FIB) Quanta 3D FEG FEI in VCD detector mode at 10kV, 83pA to reveal surface features. Several key surface features in the interaction region were observed including: (1) a small area with dendritic microstructure, (2) color contrast near the UCO kernel and Pd boundary, and (3) darker and lighter regions throughout the sample surface. To analyze diffusion behavior, FIB was used to prepare lamellae from five different areas of the UCO-Pd sample, as well as one for the as-received sample. These lamellae were examined using a Scanning Transmission Electron Microscope ThermoFisher Spectra 300 (STEM-Spectra). Energy Dispersive Spectroscopy results confirmed the diffusion between the UCO fuel and Pd bar. Figure 2 shows the identified phases of UC, UO2, and Pd dispersed throughout the interaction region. It was also found that the Pd concentration decreases as the radial distance from the UCO-Pd interface increases. The Pd concentration was 36.93% atomic fraction 11µm from the interaction region then decreased to 7.51% atomic fraction at 257 µm away from the interaction region. Figure 3 shows how concentrations of U and Pd vary across the interaction zone, highlighting the extent of diffusion. This study confirms that Pd interacts with surrounding material to form U-Pd phase and diffusion zones. These diffusion zones vary in composition depending on its radial distance from the point of contact with the Pd bar. These findings contribute to a deeper understanding of the fission product behavior in high temperature nuclear fuels, aiding in the prediction and mitigation of potential fuel degradation mechanisms. A B C Fig. 1. SEM micrographs of UCO fuel kernel in contact with solid Pd bar and the lift out locations. Figure 1A shows UCO fuel kernel in contact with solid Pd bar. Figure 1B shows a higher magnification image of the UCO fuel-Pd interaction zone. Figure 1C shows lift out sites for the lamellae. A B C Fig 2. EDS maps reveal the distribution of U, O, and Pd in location 3. Figure 2A shows the distribution of uranium. Figure 2B shows the distribution of oxygen. Figure 2C shows the distribution of palladium. A B C Fig 3. Palladium and uranium concentration across interaction zone in location 2. Figure 3A shows EDS map of lift out number 2. Figure 3B shows a zoomed in EDS map taken from the interaction zone. Figure 3C shows a line graph of uranium and palladium concentrations across the interaction zone. References: 1. B.E. Wells, N.R. Phillips, K.J. Geelhood. Pacific West Laboratory. (2021). TRISO Fuel: Properties and Failure Modes. https://www.nrc.gov/docs/ML2117/ML21175A152.pdf (Accessed January 16, 2025). 2. American Nuclear Society. TRISO Fuel Development Progresses in INL, ORNL. https://www.gen-4.org/gif/upload/docs/application/pdf/2014-03/nov13nn_fuel_reprint.pdf (Accessed January 16, 2025) 3. Clark R.A., M.A. Con

36 - MATERIALS SCIENCE↗

DOE OSTI2025

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel Jana Howard1,3, Guang Yang3, Haiyan Zhao1*, Patrick Warren4, Tiankai Yao3, Steven Cavazos4 Elizabeth Sooby Wood4*, Ching-heng Shiau2 1 University of Idaho, Environmental Science, Idaho Falls, Idaho, USA 2 Boise State University, Microscopy and Characterization Suite, Idaho Falls, Idaho, USA 3 Idaho National Laboratory, Idaho Falls, Idaho, USA 4 University of Texas San Antonio, Department of Physics and Astronomy, San Antonio, Texas, USA *Corresponding author: haiyanz@uidaho.edu; elizabeth.soobywood@utsa.edu Tri-structural Isotropic (TRISO) particle fuel is the preferred choice for the newest and next-generation high-temperature nuclear reactors due to its robust construction [1]. The fuel design effectively contains fission products inside the particle at extremely high temperatures [2]. However, the effect of transition metal fission products on fuel performance and structural integrity remains largely unknown, creating uncertainties in predicting fuel performance and potential failure mechanisms [2]. For example, palladium (Pd) has a strong tendency to form intermetallic phases with uranium (U). These new phases tend to be hard and brittle which could lead to fracture of fuel kernel during irradiation [3,4]. Pd is not normally produced in high concentrations in normal fission reactions however, driving the production of Pd into the locality of a Uranium Oxycarbide (UCO) nuclear fuel provides an opportunity to closely observe the diffusion and chemical interactions. This study focuses on detailed transmission electron microscopy characterization of the intermetallic phases formed by the interaction between a UCO kernel and a Pd bar after annealing at 1100 °C for 100 hours. Figure 1 provides an overview of the UCO kernel in contact with the Pd bar. The UCO-Pd sample surface was examined using a Focused Ion Beam (FIB) Quanta 3D FEG FEI in VCD detector mode at 10kV, 83pA to reveal surface features. Several key surface features in the interaction region were observed including: (1) a small area with dendritic microstructure, (2) color contrast near the UCO kernel and Pd boundary, and (3) darker and lighter regions throughout the sample surface. To analyze diffusion behavior, FIB was used to prepare lamellae from five different areas of the UCO-Pd sample, as well as one for the as-received sample. These lamellae were examined using a Scanning Transmission Electron Microscope ThermoFisher Spectra 300 (STEM-Spectra). Energy Dispersive Spectroscopy results confirmed the diffusion between the UCO fuel and Pd bar. Figure 2 shows the identified phases of UC, UO2, and Pd dispersed throughout the interaction region. It was also found that the Pd concentration decreases as the radial distance from the UCO-Pd interface increases. The Pd concentration was 36.93% atomic fraction 11µm from the interaction region then decreased to 7.51% atomic fraction at 257 µm away from the interaction region. Figure 3 shows how concentrations of U and Pd vary across the interaction zone, highlighting the extent of diffusion. This study confirms that Pd interacts with surrounding material to form U-Pd phase and diffusion zones. These diffusion zones vary in composition depending on its radial distance from the point of contact with the Pd bar. These findings contribute to a deeper understanding of the fission product behavior in high temperature nuclear fuels, aiding in the prediction and mitigation of potential fuel degradation mechanisms. A B C Fig. 1. SEM micrographs of UCO fuel kernel in contact with solid Pd bar and the lift out locations. Figure 1A shows UCO fuel kernel in contact with solid Pd bar. Figure 1B shows a higher magnification image of the UCO fuel-Pd interaction zone. Figure 1C shows lift out sites for the lamellae. A B C Fig 2. EDS maps reveal the distribution of U, O, and Pd in location 3. Figure 2A shows the distribution of uranium. Figure 2B shows the distribution of oxygen. Figure 2C shows the distribution of palladium. A B C Fig 3. Palladium and uranium concentration across interaction zone in location 2. Figure 3A shows EDS map of lift out number 2. Figure 3B shows a zoomed in EDS map taken from the interaction zone. Figure 3C shows a line graph of uranium and palladium concentrations across the interaction zone. References: 1. B.E. Wells, N.R. Phillips, K.J. Geelhood. Pacific West Laboratory. (2021). TRISO Fuel: Properties and Failure Modes. https://www.nrc.gov/docs/ML2117/ML21175A152.pdf (Accessed January 16, 2025). 2. American Nuclear Society. TRISO Fuel Development Progresses in INL, ORNL. https://www.gen-4.org/gif/upload/docs/application/pdf/2014-03/nov13nn_fuel_reprint.pdf (Accessed January 16, 2025) 3. Clark R.A., M.A. Con

36 - MATERIALS SCIENCE↗

DOE OSTI2022

A liquid stratification model to predict failure in thermally damaged EBW detonators

In previous work, commercially available downward facing exploding bridgewire detonators (EBWs) were exposed to elevated temperatures. These detonators were then initiated using a firing set which discharged a high amplitude short duration electrical pulse into a thin gold bridgewire. Responses of the detonators were measured using photonic doppler velocimetry (PDV) and high-speed photography. A time delay of 4 μs between EBW initiation and first movement of an output flyer separated operable detonators from inoperable detonators or duds. Here, we propose a simple method to determine detonator operability from the calculated state of the detonator at the time the firing set is initiated. The failure criterion is based on the gap distance between the exploding bridgewire (EBW) and the adjacent initiating explosive within the detonator which is low-density pentaerythritol tetranitrate (PETN) that melts between 413-415 K (140-142 ºC). The gap forms as PETN melts and flows to the bottom of the input pellet. Melting of PETN is modeled thermodynamically as an energy sink using a normal distribution spread over a temperature range between the onset temperature of 413 K and the ending temperature of 415 K. The extent of the melt is determined from the average temperature of the PETN. The PETN liquid is assumed to occupy the interstitial gas volume in the lower part of the input pellet. The vacated volume from the relocated liquid forms the gap between the EBW and the PETN. The remaining sandwiched layer consists of solid PETN particles and gas filling interstitial volume. We predict that a threshold gap between 17-27 μm separates properly functioning detonators from duds.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

NASA NTRS1987

Nonlinear plants, factorizations and stable feedback systems

For nonlinear plants represented by causal maps defined over extended spaces, right factorization and normalized right-coprime factorization concepts are discussed in terms of well-posed stable feedback systems. This setup covers continuous-time, discrete-time, time-invariant or time-varying input-output maps. The nonlinear maps are factored in terms of causal bounded-input bounded-output stable maps. In factored form, all instabilities of the original map are represented by the inverse of a causal stable `denominator' map. The existence of maps with right factorizations and normalized right-coprime factorizations is shown using a well-posed stable unity-feedback system. In the case where one of the subsystems has a normalized right-coprime factorization, the stability of the feedback system is equivalent to the stability of the pseudostate map.

Desoer, Charles A.↗

DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Auxiliary function approach for determining symmetry energy at suprasaturation densities

Nuclear symmetry energy E sym (ρ) at density ρ is normally expanded or simply parameterized as a function of χ = (ρ – ρ 0 )/3ρ 0 in the form of Esym(ρ) ≈ S + Lχ + 2 –1 K sym χ 2 + 6 –1 J sym χ 3 + … using its magnitude S, slope L, curvature K sym and skewness J sym at the saturation density ρ0 of nuclear matter. Much progress has been made in recent years in constraining especially the S and L parameters using various terrestrial experiments and astrophysical observations. Furthermore, such kind of expansions/parameterizations do not converge at supra-saturation densities where χ is not small enough, hindering an accurate determination of high-density E sym (ρ) even if its characteristic parameters at ρ0 are all well determined by experiments/observations. By expanding the E sym (ρ) in terms of a properly chosen auxiliary function Π sym (χ,Θ sym ) with a parameter Θsym fixed accurately by an experimental E sym (ρ r ) value at a reference density ρr, we show that the shortcomings of the χ-expansion can be completely removed or significantly reduced in determining the high-density behavior of E sym (ρ). In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher χ-order contributions and converges to the same E sym (ρ) much faster than the conventional χ-expansion at densities ≲3ρ 0 . Several quantitative demonstrations using Monte Carlo simulations are given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

AGC 226178 and NGVS 3543: Two Deceptive Dwarfs toward Virgo

The two sources AGC 226178 and NGVS 3543, an extremely faint, clumpy, blue stellar system and a low surface brightness dwarf spheroidal, are adjacent systems in the direction of the Virgo cluster. Both have been studied in detail previously, with it being suggested that they are unrelated normal dwarf galaxies or that NGVS 3543 recently lost its gas through ram pressure stripping and AGC 226178 formed from this stripped gas. However, with Hubble Space Telescope Advanced Camera for Surveys imaging, we demonstrate that the stellar population of NGVS 3543 is inconsistent with being at the distance of the Virgo cluster and that it is likely a foreground object at approximately 10 Mpc, whereas the stellar population of AGC 226178 is consistent with it being a very young (10–100 Myr) object in the Virgo cluster. Through a reanalysis of the original ALFALFA H i detection, we show that AGC 226178 likely formed from gas stripped from the nearby dwarf galaxy VCC 2034, a hypothesis strengthened by the high metallicity measured with MUSE VLT observations. However, it is unclear whether ram pressure or a tidal interaction is responsible for stripping the gas. Object AGC 226178 is one of at least five similar objects now known toward Virgo. These objects are all young and unlikely to remain visible for over ~500 Myr, suggesting that they are continually produced in the cluster.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1974

An analytic method to account for drag in the Vinti Satellite theory

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Watson, J. S.↗

NASA NTRS1974

Reduction of blood serum cholesterol

By feeding a human subject as the sole source of sustenance a defined diet wherein the carbohydrate consists substantially entirely of glucose, maltose or a polysaccharide of glucose, the blood serum cholesterol level of the human subject is substantially reduced. If 25 percent of the carbohydrate is subsequently supplied in the form of sucrose, an immediate increase from the reduced level is observed. The remainder of the defined diet normally includes a source of amino acids, such as protein or a protein hydrolysate, vitamins, minerals and a source of essential fatty acid.

Winitz, M.↗

NASA NTRS1977

Crystal growth from solutions in low gravity

An experiment performed during the Apollo-Soyuz flight investigated a novel process for growing single crystals from solutions. In zero gravity, reactant solutions were allowed to diffuse slowly toward each other through a region of pure solvent in which they underwent a chemical reaction to form crystals of an insoluble material. The process is analogous to the growth of crystals in gels in normal gravity. The experiment was successful and yielded crystals of about the expected size, number, and quality. The results indicate that with further refinement the process should yield large, high quality crystals of a variety of materials.

Lind, M. D.↗

NASA NTRS1977

A survey of interstellar HI from L alpha absorption measurements 2

The Copernicus satellite surveyed the spectral region near L alpha to obtain column densities of interstellar HI toward 100 stars. The distance to 10 stars exceeds 2 kpc and 34 stars lie beyond 1 kpc. Stars with color excess E(B-V) up to 0.5 mag are observed. The value of the mean ratio of total neutral hydrogen to color excess was found to equal 5.8 x 10 to the 21st power atoms per (sq cm x mag). For stars with accurate E(B-V), the deviations from this mean are generally less than a factor of 1.5. A notable exception is the dark cloud star, rho Oph. A reduction in visual reddening efficiency for the grains that are larger than normal in the rho Oph dark cloud probably explains this result. The conversion of atomic hydrogen into molecular form in dense clouds was observed in the gas to E(B-V) correlation plots. The best estimate for the mean total gas density for clouds and the intercloud medium, as a whole, in the solar neighborhood and in the plane of the galaxy is 1.15 atoms per cu. cm; those for the atomic gas and molecular gas alone are 0.86 atoms per cu cm and 0.143 molecules per cu cm respectively. For the intercloud medium, where molecular hydrogen is a negligible fraction of the total gas, atomic gas density was found to equal 0.16 atoms per cu cm with a Gaussian scale height perpendicular to the plane of about 350 pc, as derived from high latitude stars.

Bohlin, R. C.↗

NASA NTRS1979

Studies of interstellar absorption lines with IUE

The paper deals with a survey of interstellar absorption lines in the wavelength region from 1150 to 3200 A toward 25 stars. The spectra of 10 of these stars show very strong narrow absorption lines of Si IV and C IV. Lines of N V appear in eight directions. The N V lines can arise in the same gas that is responsible for the ubiquitous interstellar lines of O VI, observed previously with a Copernicus spectrometer, but the lines of Si IV and C IV must be formed in a cooler gas. The measured lines of Si IV and C IV can be produced by normal H II regions photoionized by the observed stars.

Black, J. H.↗

NASA NTRS1983

A standard description and costing methodology for the balance-of-plant items of a solar thermal electric power plant. Report of a multi-institutional working group

Standard descriptions for solar thermal power plants are established and uniform costing methodologies for nondevelopmental balance of plant (BOP) items are developed. The descriptions and methodologies developed are applicable to the major systems. These systems include the central receiver, parabolic dish, parabolic trough, hemispherical bowl, and solar pond. The standard plant is defined in terms of four categories comprising (1) solar energy collection, (2) power conversion, (3) energy storage, and (4) balance of plant. Each of these categories is described in terms of the type and function of components and/or subsystems within the category. A detailed description is given for the BOP category. BOP contains a number of nondevelopmental items that are common to all solar thermal systems. A standard methodology for determining the costs of these nondevelopmental BOP items is given. The methodology is presented in the form of cost equations involving cost factors such as unit costs. A set of baseline values for the normalized cost factors is also given.

Source record↗

NASA NTRS1986

The effects of gravity level during directional solidification on the microstructure of hypermonotectic Al-In-Sn alloys

Five hypermonotectic Al-In-Sn compositions were directionally solidified in a Bridgman-type furnace at normal gravity and during aircraft low-gravity maneuvers. The tendency of the Al-30In alloy to form an indium-rich band at the start of unidirectional growth (SUG) made it difficult to study the integration of L sub 2 into the solidification interface. Hypermonotectic compositions closer to monotectic slightly hypermonotectic caused only a partial band on L sub 2 to form at SUG and allowed the study of such variables as gravity, composition, and monotectic dome height on integration of excess L sub 2 into the solid plus L sub 2 interface. It was found that formation of aligned composite structures for the Al-In-Sn system is not only a function of G and R but also of the degree to which the composition varies from monotectic. Most of the aligned fibrous structures formed from hypermonotectic Al-In-Sn had spacings that were of the order of irregular fibrous structures reported for on monotectic Al-In-Sn. The spacings for the large fibers and aligned globules found for ground and low-gravity processed Al-In-18-Sn-22, respectively, were significantly larger than the others measured and were of the order expected for cell spacings under the growth conditions utilized. It was found that the integration into the solidification front of excess L sub 2 in low gravity was a function of the Sn composition of the alloy.

Curreri, P. A.↗

NASA NTRS1987

Coupled NASTRAN/boundary element formulation for acoustic scattering

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Everstine, Gordon C.↗

NASA NTRS1989

IRAS observations of optically selected galaxies. I - The properties of the UGC redshift sample

The FIR properties of more than 2400 optically selected galaxies in the Uppsala General Catalog are examined. The galaxies were detected by IRAS at 60 and 100 microns and have measured redshifts. A simple radiative transfer model is presented to study the nature of dust-heating sources. It is shown that for many normal disk galaxies, dust heated by old disk stars competes with dust heated by UV photons from newly formed stars. It is found that the 60-micron/100-micron flux density ratio may be used as an indicator of the dominant dust-heating source. Scaling relations with galaxy size and mass are presented which make it possible to estimate the contributions of any cirrus-like component to the total FIR luminosity.

Bothun, Gregory D.↗

NASA NTRS1991

Combined Backscatter Moessbauer Spectrometer and X Ray Fluorescence analyzer (BaMS/XRF) for planetary surface materials

A backscatter Moessbauer spectrometer (BaMS) with included x ray fluorescence (XRF) capability for the Mars Environment Survey (MESUR) Mission, which has been proposed by NASA for 1998, is being developed. The instrument will also be suitable for other planetary missions such as those to the Moon, asteroids, and other solid solar-system objects. The BaMS would be unique for MESUR in providing information about iron mineralogy in rocks, clays, and other surface materials, including relative proportions of iron-bearing minerals. It requires no sample preparation and can identify all the normal oxidation states of iron (3+, 2+, 0). Thus, BaMS is diagnostic for weathering and other soil-forming processes. Backscatter design allows the addition of XRF elemental analysis with little or no modification. The BaMS/XRF instrument complements the thermal analyzer with evolved gas analyzer (TA-EGA) and the alpha-proton x-ray spectrometer (APXS) proposed (along with BaMS) for geochemical analysis on MESUR.

Agresti, D. G.↗

NASA NTRS1999

A Phenomenological Description of Primary Creep in Class M Materials

Observations of creep microstructures in the primary creep region in class M materials show a remarkable similarity with those formed in the exponential creep regime. As a result, it is proposed that the constitutive creep law for normal primary creep is similar to that for the exponential creep regime. A phenomenological description is discussed to rationalize these microstructural observations in terms of a normalized strain rate vs. stress plot. The implications of this plot in describing different testing procedures, steady-state flow, and on the observed deviations from the universal creep law are discussed. The plot is also extended to explain the observed similarities in the transient creep behavior in pre-strained materials and in stress change experiments.

Raj, S. V.↗