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DOE OSTI2021

T$ \overline{T} $ deformation in SCFTs and integrable supersymmetric theories

We calculate the $ \mathcal{S} $ -multiplets for two-dimensional Euclidean $ \mathcal{N} $ = (0 , 2) and $ \mathcal{N} $ = (2 , 2) superconformal field theories under the T $ \overline{T} $ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $ \mathcal{N} $ = (0 , 2) deformed multiplets, we calculate two- and three-point correlators. We show the $ \mathcal{N} $ = (0 , 2) chiral ring’s elements do not flow under the T $ \overline{T} $ deformation. Specializing to integrable supersymmetric seed theories, such as $ \mathcal{N} $ = (2 , 2) Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer’s folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers’ equation. Finally, we show that several indices independent of D -term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the T $ \overline{T} $ deformation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Water-Weakening and Time-Dependent Deformation of Organic-Rich Chalks

Abstract The Ghareb Formation is a shallowly buried porous chalk in southern Israel that is being considered as a host rock for a geologic nuclear waste repository. Setup and operation of a repository will induce significant mechanical, hydrological and chemical perturbations in the Ghareb. Developing a secure repository requires careful characterization of the rock behavior to different loads. To characterize hydromechanical behavior of the Ghareb, several short- and long-term deformation experiments were conducted. Hydrostatic loading tests were conducted both dry and water-saturated, using different setups to measure elastic properties, time-dependent behavior, and permeability. A set of triaxial tests were conducted to measure the elastic properties and rock strength under differential loading at dry and water-saturated conditions. The hydrostatic tests showed the Ghareb began to deform inelastically around 12–15 MPa, a relatively low effective pressure. Long-term permeability measurements demonstrated that permeability declined with increasing effective pressure and was permanently reduced by ~ 1 order of magnitude after unloading pressure. Triaxial tests showed that water saturation significantly degrades the rock properties of the Ghareb, indicating water-weakening is a significant risk during repository operation. Time-dependent deformation is observed during hold periods of both the hydrostatic and triaxial tests, with deformation being primarily visco-plastic. The rate of deformation and permeability loss is strongly controlled by the effective pressure as well. Additionally, during holds of both hydrostatic and triaxial tests, it is observed that when water-saturated, radial strain surpassed axial strain when above effective pressures of 13–20 MPa. Thus, deformation anisotropy may occur in situ during operations even if the stress conditions are hydrostatic when above this pressure range.

58 GEOSCIENCES↗

DOE OSTI2021

Interrogating the Effects of Hydrogen on the Behavior of Planar Deformation Bands in Austenitic Stainless Steel

The effects of internal hydrogen on the deformation microstructures of 304L austenitic stainless steel have been characterized using electron backscattered diffraction (EBSD), transmission Kikuchi diffraction (TKD), high-resolution scanning transmission electron microscopy (HRSTEM), and nanoprobe diffraction. Samples, both thermally precharged with hydrogen and without thermal precharging, were subjected to tensile deformation of 5 and 20 pct true strain followed by multiple microscopic interrogations. Internal hydrogen produced widespread stacking faults within the as-forged initially unstrained material. While planar deformation bands developed with tensile strain in both the hydrogen-precharged and non-precharged material, the character of these bands changed with the presence of internal hydrogen. As shown by nanobeam diffraction and HRSTEM observations, in the absence of internal hydrogen, the bands were predominantly composed of twins, whereas for samples deformed in the presence of internal hydrogen, ε -martensite became more pronounced and the density of deformation bands increased. For the 20 pct strain condition, α '-martensite was observed at the intersection of ε -martensite bands in hydrogen-precharged samples, whereas in non-precharged samples α '-martensite was only observed along grain boundaries. We hypothesize that the increased prevalence of α '-martensite is a secondary effect of increased ε -martensite and deformation band density due to internal hydrogen and is not a signature of internal hydrogen itself.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Influence of Fiber Orientation on Deformation of Additive Manufactured Composites

Anisotropy caused by flow-induced fiber orientation of discontinuous fibers within the extrudate in the Extrusion Deposition Additive Manufacturing (EDAM) process gives rise to anisotropic shrinkage in printed parts and thereby, final part deformations. Three fiber orientation states, described by the second-order orientation tensor, were investigated to determine their influence upon final geometry. Two material systems were investigated including a short glass fiber-reinforced polyamide and a short carbon fiber-reinforced polyamide. A curvilinear geometry was modeled and printed virtually in the thermo-mechanical simulation, ADDITIVE3D©. The scale of the printed geometry was in the range of 300–400 mm and contained three semicircular geometry regions connected to linear regions, thereby inducing significant magnification of the spring-in deformation. The predicted deformation of the printed geometry for the three fiber orientation states and two material systems were compared. The deformation predicted for glass fiber-filled polyamide and carbon fiber-filled polyamide of the same fiber orientation states showed comparable deformations. In conclusion, the largest residual deformation was shown to correspond to the orientation tensor with the greatest degree of anisotropy.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Microstructural and material property changes in severely deformed Eurofer-97

Severe plastic deformation changes the microstructure and properties of steels, which may be favourable for their use in structural components of nuclear reactors. In this study, high-pressure torsion (HPT) was used to refine the grain structure of Eurofer-97, a ferritic/martensitic steel. Electron microscopy and X-ray diffraction were used to characterise the microstructural changes. Following HPT at room temperature to a maximum shear strain of 230, the average grain size reduced by a factor of ~30, with a marked increase in high-angle grain boundaries. Dislocation density also increased by more than one order of magnitude. The thermal stability of the deformed material was investigated via in-situ annealing during synchrotron X-ray diffraction. This revealed substantial recovery between 450 K – 800 K. Irradiation with 20 MeV Fe-ions to ~0.1 dpa caused a 20% reduction in dislocation density compared to the as-deformed material. However, HPT deformation prior to irradiation only had a minor effect in mitigating the irradiation-induced reductions in thermal diffusivity and surface acoustic wave velocity of the material. Microstructural and material property changes are dominated by deformation compared to irradiation. In light of this, the benefits of using HPT to improve the irradiation resistance of Eurofer-97 are limited. These results provide a multi-faceted view of the changes in ferritic/martensitic steels due to severe plastic deformation, and how these changes can be used to alter material properties.

ion-irradiation↗

DOE OSTI2021

Autonomous extraction of millimeter-scale deformation in InSAR time series using deep learning

Systematically characterizing slip behaviours on active faults is key to unraveling the physics of tectonic faulting and the interplay between slow and fast earthquakes. Interferometric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformation at a global scale every few days, may hold the key to those interactions. However, atmospheric propagation delays often exceed ground deformation of interest despite state-of-the art processing, and thus InSAR analysis requires expert interpretation and a priori knowledge of fault systems, precluding global investigations of deformation dynamics. Here, we show that a deep auto-encoder architecture tailored to untangle ground deformation from noise in InSAR time series autonomously extracts deformation signals, without prior knowledge of a fault’s location or slip behaviour. Applied to InSAR data over the North Anatolian Fault, our method reaches 2 mm detection, revealing a slow earthquake twice as extensive as previously recognized. We further explore the generalization of our approach to inflation/deflation-induced deformation, applying the same methodology to the geothermal field of Coso, California.

58 GEOSCIENCES↗

DOE OSTI2024

Alloying effects on deformation induced microstructure evolution in copper

In this work, we investigated the effects of alloying elements on plastic deformation and microstructure evolution in polycrystalline copper (Cu) and Cu alloyed with 1 wt. % lead (Cu-1 %Pb). These materials were selected due to the size mismatch between Cu and Pb, with the latter forming precipitates at grain boundaries. Multi-modal characterization techniques, including neutron diffraction, electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM), along with finite element simulations were employed to study the deformation behavior across multiple length scales. While both Cu and Cu-1%Pb exhibited similar macroscale response and final deformation textures, both dislocation line profile analysis and TEM revealed increased dislocation density in deformed Cu-1%Pb specimens. The presence of lead precipitates also significantly affected local plastic deformation during compression, with their influence diminishing with increasing strain. These results demonstrate the complex relationships between alloying elements, plastic deformation, microstructural evolution, and material behavior under load. The insights gained from this multi-scale and multi-technique approach contribute to the fundamental understanding of microstructural evolution in immiscible alloys and are valuable for tailoring the properties of structural materials for specific engineering applications.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Pressure–strain interaction. I. On compression, deformation, and implications for Pi-D

The pressure–strain interaction describes the rate per unit volume that energy is converted between bulk flow and thermal energy in neutral fluids or plasmas. The term has been written as a sum of the pressure dilatation and the collisionless analog of viscous heating referred to as Pi–D , which isolates the power density due to compressible and incompressible effects, respectively. It has been shown that Pi–D can be negative, which makes its identification as collisionless viscous heating troubling. We argue that an alternate decomposition of pressure–strain interaction can be useful for interpreting the underlying physics. Since Pi–D contains both normal deformation and shear deformation, we propose grouping the normal deformation with the pressure dilatation to describe the power density due to converging/diverging flows, with the balance describing the power density purely due to shear deformation. We then develop a kinetic theory interpretation of compression, normal deformation, and shear deformation. We use the results to determine the physical mechanisms that can make Pi–D negative. We argue that both decompositions can be useful for the study of energy conversion in weakly collisional or collisionless fluids and plasmas, and implications are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Duality defect in a deformed transverse-field Ising model

Physical quantities with long lifetimes have both theoretical significance in the study of quantum many-body systems and practical implications for quantum technologies. In this manuscript, we investigate the roles played by topological defects in the construction of quasiconserved quantities, using as a prototypical example the Kramers-Wannier duality defect in a deformed one-dimensional quantum transverse-field Ising model. We construct the duality defect Hamiltonian in three different ways: half-chain Kramers-Wannier transformation, utilization of techniques in the Ising fusion category, and defect-modified weak integrability breaking deformation. The third method is also applicable for the study of generic integrable defects under weak integrability breaking deformations. We also work out the deformation of defect-modified higher charges in the model and study their slower decay behavior. Furthermore, we consider the corresponding duality defect twisted deformed Floquet transverse-field Ising model and investigate the stability of the isolated zero mode associated with the duality defect in the integrable Floquet Ising model, under such weak integrability breaking deformation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Role of quadrupole deformation and continuum effects in the “island of inversion” nuclei 28,29,31 F

The peculiar properties of nuclei in the so-called “island of inversion” around Z = 10 and N = 20 are the focus of current nuclear physics research. Recent studies showed that 28 F has a negative-parity ground state and thus lies within the southern shore of the island of inversion, and 29 F presents a halo structure in its ground state, but it is unclear which effects, such as deformation, shell evolution due to tensor forces, or couplings to the continuum, lead to this situation. Here, we investigate the role of quadrupole deformation and continuum effects on the single-particle structure of 28,29,31 F from a relativistic mean-field approach and show how both phenomena can lead to a negative-parity ground state in 28 F and halo structures in 29,31 F. We solve the Dirac equation in the complex-momentum (Berggren) representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field calculations using the NL3 interaction and calculate the continuum level densities using the Green’s function method. We extract single-particle energies and widths from the continuum level densities to construct the Nilsson diagrams of 28,29,31 F in the continuum and analyze the evolution of both the widths and occupation probabilities of relevant Nilsson orbitals in 28 F and find that some amount of prolate deformation must be present. In addition, we calculate the density distributions for bound Nilsson orbitals near the Fermi surface in 29,31 F and reveal that, for a quadrupole deformation 0.3 ≤ β 2 ≤ 0.45 (prolate), characteristic halo tails appear at large distances. Using the relativistic mean-field approach in the complex-momentum representation with the Green’s function method, we demonstrate that in neutron-rich fluorine isotopes, while in the spherical case the pf shells are already inverted and close to the neutron emission threshold, a small amount of quadrupole deformation can dramatically reduce the gap between positive- and negative-parity states and increase the role of continuum states, ultimately leading to the negative parity in the ground state of 28 F and the halo structures in 29,31 F.

20 ≤ A ≤ 38↗

DOE OSTI2025

Coulomb excitation of 80 Sr and the limits of the 𝑁 ≈ 𝑍 ≈ 40 island of deformation

The region of 𝑁 ≈ 𝑍 ≈ 40 has long been associated with strongly deformed nuclear configurations. The presence of this strong deformation was recently confirmed through lifetime measurements in 𝑁 ≈ 𝑍 Sr and Zr nuclei. Theoretically, however, these nuclei present a challenge due to the vast valence space required to incorporate all necessary orbitals. Recent state-of-the-art predictions indicate a near axial prolate deformation for 𝑁 = 𝑍 and 𝑁 = 𝑍+2 nuclei between 𝑁 = 𝑍 = 36 and 𝑁 = 𝑍 = 40. In this work we investigate the shores of this island of deformation through a sub-barrier Coulomb excitation study of the 𝑁 = 𝑍+4 nucleus, 80 Sr . Extracting a spectroscopic quadrupole moment of 𝑄 𝑠 ⁡($2^+_1$)= $0.5^{+0.8}_{−0.9}$𝑒⁢b, we find that 80 Sr is inconsistent with significant axial prolate deformation with a significance of 1.5⁢𝜎. This result, albeit with a large uncertainty, indicates that the predicted region of strong prolate deformation around 𝑁 = 𝑍 = 40 is tightly constrained to the quartet of nuclei: 76,78 Sr and 78,80 Zr .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Can changes in deformation regimes be inferred from crystallographic preferred orientations in polar ice?

Creep due to ice flow is generally thought to be the main cause for the formation of crystallographic preferred orientations (CPOs) in polycrystalline anisotropic ice. However, linking the development of CPOs to the ice flow history requires a proper understanding of the ice aggregate's microstructural response to flow transitions. In this contribution the influence of ice deformation history on the CPO development is investigated by means of full-field numerical simulations at the microscale. We simulate the CPO evolution of polycrystalline ice under combinations of two consecutive deformation events up to high strain, using the code VPFFT (visco-plastic fast Fourier transform algorithm) within ELLE. A volume of ice is first deformed under coaxial boundary conditions, which results in a CPO. The sample is then subjected to different boundary conditions (coaxial or non-coaxial) in order to observe how the deformation regime switch impacts the CPO. The model results indicate that the second flow event tends to destroy the first, inherited fabric with a range of transitional fabrics. However, the transition is slow when crystallographic axes are critically oriented with respect to the second imposed regime. Therefore, interpretations of past deformation events from observed CPOs must be carried out with caution, particularly in areas with complex deformation histories.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

Inelastic deformation of metal matrix composites: Plasticity and damage mechanisms, part 2

The inelastic deformation mechanisms for the SiC (SCS-6)/Ti-15-3 system were studied at 538 C (1000 F) using a combination of mechanical measurements and detailed microstructural examinations. The objectives were to evaluate the contributions of plasticity and damage to the overall MMC response, and to compare the room temperature and elevated temperature deformation behaviors. Four different laminates were studied: (0)8, (90)8,(+ or -45)2s, and (0/90)2s, with the primary emphasis on the unidirectional (0)8, and (90)8 systems. The elevated temperature responses were similar to those at room temperature, involving a two-stage elastic-plastic type of response for the (0)8 system, and a characteristic three-stage deformation response for the (90)8 and (+ or -45)2s systems. The primary effects of elevated temperatures included: (1) reduction in the 'yield' and failure strengths; (2) plasticity through diffused slip rather than concentrated planar slip (which occurred at room temperature); and (3) time-dependent deformation. The inelastic deformation mechanism for the (0)8 MMC was dominated by plasticity at both temperatures. For the (90)8 and (+ or -45)2s MMCs, a combination of damage and plasticity contributed to the deformation at both temperatures.

Majumdar, B. S.↗

NASA NTRS1993

Strength and deformation properties of basaltic lava flows on planetary surfaces

Basaltic rocks are thought to constitute a volumetrically significant rock type on the Moon, Mercury, Mars, and Venus, in addition to the Earth. Spacecraft images of surfaces with known or suspected basaltic composition on these bodies, particularly on Venus, indicate that these rocks have been deformed in the brittle regime to form faults and perhaps dilatant cracks, in addition to folding and more distributed types of deformation. Predictions of brittle fracture or other types of deformation are made by comparing calculated stresses from a tectonic model to some criterion for rock strength. Common strength criteria used in the planetary science literature for near-surface deformation include a Griffith tensile-strength criterion for intact rock, a Mohr envelope for intact basalt, and a brittle strength envelope based on Byerlee's law of rock frictional resistance. However, planetary terrains of basaltic composition consist of much more than just intact basaltic rock. The aggregate basaltic material, termed the 'rock mass,' consists of both the intact rock and the associated fracture, faults, lithologic contacts, and other discontinuous surfaces. A basaltic rock mass is the relevant material for which strength properties must be defined and calculated model stresses must be compared to in order to more accurately predict brittle deformation. For example, the various strengths of a rock mass are less than that of intact material of the same composition. This means that tectonic models which compare stresses to intact failure strengths overestimate the stresses required for fracture and so underestimate the extent and magnitude of brittle deformation predicted in these models. On the other hand, rock mass shear strength can be greater than that predicted from Byerlee's law. The concept of rock mass strength is central to many engineering design studies in which calculated stresses are used to predict brittle fracture, and this experience indicates that brittle strength envelopes which assume properties for intact rock (Griffith parabolas) or sliding along a single, continuous surface (Byerlee's law) inadequately characterize the tensile, compressive, and shear strengths of rock masses. The criterion adopted here to relate stresses to rock mass fracture is based on a Griffith-type curve for tensile normal stress and a concave downward curve for compressive normal stress. It is the only available criterion that explicitly considers the weakening effects of discontinuities within the rock mass on the stress state required for fracture.

Schultz, Richard A.↗

NASA NTRS1994

A spectral formalism for computing three-dimensional deformations due to surface loads. 1: Theory

We outline a complete spectral formalism for computing high spatial resolution three-dimensional deformations arising from the surface mass loading of a spherically symmetric planet. The main advantages of the formalism are that all surface mass loads are always described using a consistent mathematical representation and that calculations of deformation fields for various spatial resolutions can be performed by simpley altering the spherical harmonic degree truncation level of the procedure. The latter may be important when incorporating improved observational constraints on a particular surface mass load, when considering potential errors in the computed field associated with mass loading having a spatial scale unresolved by the observational constraints, or when treating a number of global surface mass loads constrained with different spatial resolutions. The advantages do not extend to traditional 'Green's function' approaches which involve surface element discretizations of the global mass loads. Another advantage of the spectral formalism, over the Green's function approach, is that a posteriori analyses of the computed deformation fields are easily performed. In developing the spectral formalism, we consider specific cases where the Earth's mantle is assumed to respond as an elastic, slightly anelastic, or linear viscoelastic medium. In the case of an elastic or slightly anelastic mantle rheology the spectral response equations incorporate frequency dependent Love numbers. The formalism can therefore be used, for example, to compute the potentially resonant deformational response associated with the free core nutation and Chandler wobble eigenfunctions. For completeness, the spectral response equations include both body forces, as arise from the gravitational attraction of the Sun and the Moon, and surface mass loads. In either case, and for both elastic and anelastic mantle rheologies, we outline a pseudo-spectral technique for computing the ocean adjustment associated with the total gravitational perturbation induced by the external forcing. Three-dimensional deformations computed using the usual Love number approach are generally referenced to an origin at the center of mass of the undeformed planet. We derive a spectral technique for transforming the results to an origin located at the center of mass of the deformed planet.

Mitrovica, J. X.↗

NASA NTRS1998

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Goldberg, Robert K.↗

NASA NTRS1996

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Wang, P. K. C.↗

NASA NTRS1999

Dynamic Deformation of ETNA Volcano Observed by GPS and SAR Interferometry

Synthetic aperture radar (SAR) interferometry and GPS have shown that during the quiescent period from 1993-1995 Mt. Etna volcano, Italy, inflated. Since the initiation of eruptive activity since late 1995 the deformation has been more contentious. We will explore the detailed deformation during the period from 1995-1996 spanning the late stages of inflation and the beginning of eruptive activity. We use SAR interferometry and GPS data to measure the volcano deformation. We invert the observed deformation for both simple point source. le crack elastic sources or if warranted for a spheroidal pressure So In particular, we will examine the evolution of the inflation and the transition to a lesser deflation observed at the end of 1995. We use ERS-1/2 SAR data from both ascending and descending passes to allow for dense temporal 'sampling of the deformation and to allow us to critically assess atmospheric noise. Preliminary results from interferometry suggest that the inflation rate accelerated prior to resumption of activity in 1995, while GPS data suggest a more steady inflation with some fluctuation following the start of activity. This study will compare and contrast the interferometric SAR and GPS results and will address the strengths and weaknesses of each technique towards volcano deformation studies.

Lundgren, P.↗