A Nonlinear Shell Theory Compared with the Classical Three-dimensional Theory of Elasticity
Nonlinear theory for equilibrium deformation of shells compared with classical three-dimensional theory of elasticity
ELASTICITY↗
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FAST-1.0 Software Acceptance Testing Report
The purpose of this document is to detail the software testing of FAST-1.0 through unit, integration, and assessment tests. More than 400 tests were designed to provide coverage of the requirements for FAST-1.0. These requirements were developed in the NRC Statement of Work (SOW) for NRC Agreement Number NRC-HQ-25-14-D-001 and are transcribed to this document as part of the Software Quality Assurance Plan for the FAST Code System, PNNL-28767. FAST 1.0 represents the merger of the FRAPCON and FRAPTRAN codes and as such FAST-1.0 performs steady state and transient fuel performance calculations described below. FAST-1.0 calculates the steady state response of light-water reactor fuel rods during long-term burnup. The code calculates temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include: 1) heat conduction through fuel and cladding to the coolant; 2) cladding elastic and plastic deformation; 3) fuel-cladding mechanical interaction; 4) fission gas release from the fuel and rod internal pressure; and 5) cladding oxidation. FAST is used to perform independent calculations for regulatory evaluations of fuel performance under normal operation and anticipated operational occurrences (AOOs). FAST calculates the temperature and deformation history of a fuel rod as a function of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by FAST include: 1) heat conduction; 2) heat transfer from cladding to coolant; 3) elastic-plastic fuel and cladding deformation; 4) cladding oxidation; 5) fission gas release; and 6) fuel rod gas pressure. FAST code assessment, development and maintenance drive a significant portion of the NRC fuel research activities and the tools are used in a substantial number of regulatory products. Given the centrality of the FAST code to the effectiveness of fuel research, it is critical to assess, develop and maintain this tool.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Formulation and evaluation of an analytical model for composite box-beams
A direct method for determining the effective elastic stiffnesses and deformation behavior of composite box-beam (BB) structures is developed analytically, validated, and demonstrated. The BB walls are modeled as orthotropic-ply laminated plates, so that the elastic properties vary both through the thickness and around the BB contour; deformation is described in terms of extension, bending, twisting, shearing, and torsion-related out-of-plane warping. Numerical results for several BB configurations are presented in tables and graphs and compared with experimental data and FEM computations (Stemple and Lee, 1989): good general agreement is obtained for cross-ply, antisymmetric, and symmetric layups, except for symmetric layups with ply orientation angles theta greater than 30 deg. Both out-of-plane warping and transverse shear coupling are found to have significant effects on BB elastic response.
Smith, Edward C.↗
Friction, deformation and fracture of single-crystal silicon carbide
Friction experiments were conducted with hemispherical and conical diamond riders sliding on the basal plane of silicon carbide. The results indicate that, when deformation is primarily elastic, the friction does not depend on crystallographic orientation and there is no detectable fracture or cracking. When, however, plastic deformation occurs, silicon carbide exhibits anisotropic friction and deformation behavior. Surface fracture crack patterns surrounding wear tracks are observed to be of three types. The crack-geometries of two types are generally independent of orientation, the third crack, however, depends on the orientation. All surface cracks extend into subsurface. Anisotropic friction, deformation and fracture on the basal plane are primarily controlled by the slip system and cleavage.
Miyoshi, K.↗
Friction, deformation and fracture of single-crystal silicon carbide
An investigation was conducted to determine the nature of the deformation and fracture of silicon carbide and its effects on friction properties. Friction experiments were conducted with hemispherical and conical diamond riders sliding on the basal plane of silicon carbide. The results indicate that, when deformation is primarily elastic, the friction does not depend on crystallographic orientation and there is no detectable fracture or cracking. When, however, plastic deformation occurs, silicon carbide exhibits anisotropic friction and deformation behavior. Surface fracture crack patterns surrounding wear tracks are observed to be of three types. The crack-geometries of two types are generally independent of orientation, the third crack, however, depends on the orientation. All surface cracks extend into subsurface.
Miyoshi, K.↗
Nonaffine Strains Control Ductility of Metallic Glasses
The origin of limited plasticity in metallic glasses is elusive, with no apparent link to their atomic structure. In this study, we propose that the response of the glassy structure to applied stress, not the original structure itself, provides a gauge to predict the degree of plasticity. We carried out high-energy x-ray diffraction on various bulk metallic glasses (BMGs) under uniaxial compression within the elastic limit and evaluated the anisotropic pair distribution function. We show that the extent of local deviation from the affine (uniform) deformation in the elastic regime is strongly correlated with the plastic behavior of BMGs beyond yield, across chemical compositions and sample history. The results suggest that the propensity for collective local atomic rearrangements under stress promotes plasticity.
3-dimensional systems↗
A finite element formulation for deformation twinning induced strain localization in polycrystal magnesium alloys
Deformation twinning induces shear strain localization in hexagonal close-packed crystals and is critical for the material’s ductility and failure. Cracks often occur at twin-twin or twin-grain boundary intersections and propagate along twin bands. However, most crystal plasticity models for deformation twinning are based on a “pseudo-slip” approach and do not capture the localized deformation associated with the formation of each discrete twin band. The few exceptions are discrete twin models that involve very complex numerical algorithms and are often compromised in accuracy due to the numerical convergence. These factors make the discrete twin models hard to adopt. This paper proposes a modification to the conventional finite element weak form, to fully incorporate a twin-induced heterogeneous deformation that does not depend on the “pseudo-slip” assumption. The model starts by splitting the deformation gradient into elastic-slip-twinning components. The twin-induced deformation gradient component is computed separately by solving a microstructural evolution problem and then implemented into finite element weak form by constructing a global “twin-force” vector. The constitutive update (e.g., in the user-defined material subroutine, or UMAT, for ABAQUS) therefore avoids dealing with the twinning and recovers to the form of a regular slip-based crystal plasticity model. The results presented here indicate that the twin-induced strain localization and the associated stress-reversal phenomena near the twin band were naturally captured in the model, which was validated against an in-situ synchrotron X-ray micro-diffraction experiment.
36 MATERIALS SCIENCE↗
The contact of certain elastic shells with rigid flat surfaces Technical report no. 3
Stress and shear deformation analysis for simple symmetric elastic shells in contact with rigid flat surface
ELASTIC SHELL↗
Water Weakening of Calcium Oxide
Chemomechanical processes such as water weakening can control the permeability and deformation of rocks and manmade materials. Here, atomistic modeling and nanomechanical experiments were used to identify molecular origins of chemomechanical effects in calcium oxide (CaO) and its effect on observed elastic, plastic, and brittle deformation. Classical molecular dynamics simulations with the bond order-based reactive force-field ReaxFF were used to assess brittle fracture. In the presence of water, CaO fractured earlier and more often during quasi-static loading, with a calculated reduction in fracture toughness of ~80% associated with changes in the stress distribution around the crack tip. Experimentally, elastic and plastic deformation of CaO surfaces exposed to water was assessed experimentally using in situ liquid nanoindentation. Nanoindentation showed that following exposure to water, the contact hardness decreased by 1–2 orders of magnitude and decreased the modulus by 2–3 orders of magnitude due to surface hydroxylation. Furthermore, the strong chemomechanical effects on the mechanical processes in CaO suggests that minerals with similar structures may exhibit comparable effects, influencing the stability of cements and geomaterials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
New, unusual and nonclassical behavior of thin-walled composite structures
Examples are discussed which illustrated several new, unusual, and nonclassical effects that are present in thin-walled composite structures. Some of the unusual deformation characteristics occur naturally, such as the apparent increased flexibility of thin-walled beam structures due to bending-transverse shear and extension-transverse shear elastic couplings. Others are created intentionally, such as the exaggerated Poisson expansion in the tailored wing covers that produces elastic chordwise camber deformations.
Rehfield, Lawrence W.↗
Robust tracking of a flexible spacecraft subject to induced disturbances and parametric uncertainties
A variable structure control technique combined with an operator spline for bilinear systems is implemented to a fast moving deformable structure for purposes of achieving robust tracking performance. The control torque applied to the structure is based on estimates of the structure parameters and on upper bounds of the model errors. For a rapid rotation of the deformable structure, the elastic response can be modeled by oscillators driven by angular acceleration, where stiffness and damping coefficients are also angular velocity and acceleration dependent. By transforming this 'slew-driven' elastic dynamics into a bilinear form, an operator spline can be constructed, that gives a low order estimate of the induced disturbance. An upper bound between the estimated deformation and the unknown exact deformation is also generated, which can be used where required in the sliding control correction.
Karray, Fakhreddine↗
Vibration of a flexible spacecraft with momentum exchange controllers
Floating reference frames were investigated in order to allow first order vibration analysis in the presence of large system rotations. When the deformations of an elastic continuum are expanded in terms of the free-free modes of an unconstrained system, the rigid body modes are found to be fixed relative to the Tisserand frame, with respect to which the relative momentum is zero. The proof presented for this is based on the orthogonality condition for modes with distinct natural frequencies. This result also guarantees the independence of coordinates for all modes with nonzero natural frequencies. A Modified Tisserand Constraint is introduced in order to define a floating reference frame with similar properties for an elastic body which contains a spinning rotor. Finite element equations of motion are derived for a completely flexible spacecraft with momentum exchange controllers, using a Modified Tisserand Frame. The deformable systems covered in this application are assumed to undergo only small rotations, and therefore the rotor torques must formally be small, although in engineering applications it may be possible to relax this constraint. A modal analysis is performed for the system and the resulting set of equations is reduced in number by a truncation procedure for more efficient system simulation.
Canavin, J. R.↗
Sliding control of pointing and tracking with operator spline estimation
It is shown how a variable structure control technique could be implemented to achieve precise pointing and good tracking of a deformable structure subject to fast slewing maneuvers. The correction torque that has to be applied to the structure is based on estimates of upper bounds on the model errors. For a rapid rotation of the deformable structure, the elastic response can be modeled by oscillators driven by angular acceleration, and where stiffness and damping coefficients are also angular velocity and acceleration dependent. By transforming this slew-driven elastic dynamics into bilinear form (be regarding the vector made up of the angular velocity, squared angular velocity and angular acceleration components, which appear in the coefficients as the input to the deformation dynamics), an operator spline can be constructed, that gives a low order estimate of the induced disturbance. Moreover, a worst case error bound between the estimated deformation and the unknown exact deformation is also generated, which can be used where required in the sliding control correction.
Dwyer, Thomas A. W., III↗
Dislocation drag and its influence on elastic precursor decay
Plastic deformation is mediated by the creation and movement of dislocations, and at high stress the latter is dominated by dislocation drag from phonon wind. Here, by simulating a 1-D shock impact problem we analyze the importance of accurately modeling dislocation drag and dislocation density evolution in the high stress regime. Dislocation drag is modeled according to a first-principles derivation as a function of stress and dislocation character, and its temperature and density dependence are approximated to the extent currently known. Much less is known about dislocation density evolution, leading to far greater uncertainty in these model parameters. In studying anisotropic fcc metals with character dependent dislocations, the present work generalizes similar earlier studies by other authors.
36 MATERIALS SCIENCE↗
Viscoelastic deformation near active plate boundaries
Model deformations near the active plate boundaries of Western North America using space-based geodetic measurements as constraints are discussed. The first six months of this project were spent gaining familarity with space-based measurements, accessing the Crustal Dynamics Data Information Computer, and building time independent deformation models. The initial goal was to see how well the simplest elastic models can reproduce very long base interferometry (VLBI) baseline data. From the Crustal Dynamics Data Information Service, a total of 18 VLBI baselines are available which have been surveyed on four or more occasions. These data were fed into weighted and unweighted inversions to obtain baseline closure rates. Four of the better quality lines are illustrated. The deformation model assumes that the observed baseline rates result from a combination of rigid plate tectonic motions plus a component resulting from elastic strain build up due to a failure of the plate boundary to slip at the full plate tectonic rate. The elastic deformation resulting from the locked plate boundary is meant to portray interseismic strain accumulation. During and shortly after a large interplate earthquake, these strains are largely released, and points near the fault which were previously retarded suddenly catch up to the positions predicted by rigid plate models. Researchers judge the quality of fit by the sum squares of weighted residuals, termed total variance. The observed baseline closures have a total variance of 99 (cm/y)squared. When the RM2 velocities are assumed to model the data, the total variance increases to 154 (cm/y)squared.
Ward, S. N.↗
FAST-1.0 Software Release Document
The purpose of this document is to detail the release of FAST-1.0 and the documents that accompany the development and testing of FAST-1.0. Design requirements were for FAST-1.0 developed in the NRC Statement of Work (SOW) for NRC Agreement Number NRC-HQ-25-14-D-001 and are transcribed to this document as part of the Software Quality Assurance Plan for the FAST Code System, PNNL-28767. FAST 1.0 represents the merger of the FRAPCON and FRAPTRAN codes and as such FAST-1.0 performs steady state and transient fuel performance calculations described below. FAST-1.0 calculates the steady state response of light-water reactor fuel rods during long-term burnup. The code calculates temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include: 1) heat conduction through fuel and cladding to the coolant; 2) cladding elastic and plastic deformation; 3) fuel-cladding mechanical interaction; 4) fission gas release from the fuel and rod internal pressure; and 5) cladding oxidation. FAST is used to perform independent calculations for regulatory evaluations of fuel performance under normal operation and anticipated operational occurrences (AOOs).
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Revealing nanomechanical deformation at the interface and degradation in all-thin-film inorganic electrochromic devices
Recently, progress in electrochromic (EC) devices has been made in optimizing electrode and device configurations and performance. However, the ion insertion/de-insertion induced charge transfer (CT) nanomechanical effect has remained unexplored, i.e., repetitive electrode size changes at the nanoscale and stress/strain generated during electrochemical cycling, which is the focus of this work due to its intimate correlation with the elastic and plastic deformation at the interface. Considering the intervalence electrons, excellent electrochemical kinetics, and dramatic color changes, tungsten oxide (WO 3 ) and nickel oxide (NiO) films are configured as the EC cathode and anode materials, respectively, within a full device. Upon extended cycles (>10 000), the void generation and delamination that occurred at the interface account for performance decay. Encouraged by the findings, nanoindentation mechanical tests and electrical kelvin probe force microscopy were employed to investigate the CT induced effects at the interface. There is a dramatic increase of up to 45% in the elastic Young's modulus in colored/charged WO 3 at ~40 mC cm -2 . Here, the correlation between CT and synergistic mechanical effect is interpreted by the Lippman equation. Interestingly, despite the charged state (colored; lithiated) with a relatively flat morphology bringing an ~3.4 times higher electrostatic surface potential, the electrical work function unexpectedly decreases, arising from the dominant effect of the dipole layer potential over the chemical potential. The interatomic cohesive energy and equilibrium distance increase bury the seeds for mechanical deformation in the long run. This work provides fundamental insights into electro-chemo mechanics and interdisciplinary concerted interfacial effects at the nano/atomic level. The dependence of surface potential, stress, work function, and cohesive energy on electrochemical kinetics has been interpreted.
36 MATERIALS SCIENCE↗
Triboelectric nanogenerator for harvesting broadband kinetic impact energy
A triboelectric generator includes a first triboelectric member, which includes a first conductive layer and an insulating triboelectric material layer disposed on the first conductive layer. The triboelectric material layer includes a first material having a first position on a triboelectric series. An elastic member, disposed against the triboelectric material layer of the triboelectric member and includes a second conductive material, has an elasticity that results in the elastic member being deformed when compressed and returning to an original non-deformed shape after being compressed. The second conductive material has a second position on the triboelectric series. A first load is coupled to the first conductive layer and with the second conductive material so that when a force compresses the elastic member charges will flow between the first conductive layer and the second conductive layer through the load.
36 MATERIALS SCIENCE↗