Strength of rotating discs
Influence of stress distribution and shape on deformation and strength of rotating disks
ROTATING DISK↗
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Results for “STRESS DISTRIBUTION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Stresses in a thick plate with axially symmetric loading.
Normal stress distribution on thick elastic plate with axially symmetric circular pressure loading
ELASTIC PLATE↗
A cracked sheet stiffened by several partially debonded intact or broken stringers
The effect of several stringers on the stress intensity factors at the tips of a crack is considered. The stringers which were continuously attached to the plate and placed perpendicular to the crack may be partially debonded due to high stress concentrations. Since the stringers may even break under excessive loading conditions, both intact and broken stringers are considered to investigate the effect of rupture. The continuity of displacements along the bond lines leads to an integral equation which is solved to give the shear stress distribution in the adhesive and the stress intensity factors at the crack tips.
Arin, K.↗
The effect of several intact or broken stringers of the stress intensity factor in a cracked sheet
The stringers which are continuously attached to the plate and placed perpendicular to the crack may be partially debonded due to high stress concentrations. Since the stringers may even break under excessive loading conditions, both intact and broken stringers are considered to investigate the effect of rupture. The continuity of displacements along the bond lines leads to an integral equation which is solved to give the shear stress distribution in the adhesive and the stress intensity factors at the crack tips.
Arin, K.↗
A study of defect structures with the field ion microscope Semiannual report, Sep. 1, 1966 - Feb. 28, 1967
Defect structures in ion emission images of metals and stress distributions under imaging conditions studied with field ion microscope
ION MICROSCOPE↗
Computational Modeling of Graphite Degradation due to Molten Salt Infiltration and Wear
Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet
The stress intensity factor is determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semiinfinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media. It is assumed they are in plane stress and the adhesive is in pure shear. From Green's functions and the complex variable theory of orthotropic elasticity developed by Lekhnitskiy, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations which is solved to obtain the shear stress distribution in the adhesive layer. With these stresses, equations for the stress intensity factors at both crack tips are found. A parametric study is conducted to determine the sensitivity of the system to material properties and specimen configuration. Unless the crack tip is very close to or under the stringer the stress intensity factor is approximately that of an unstiffened sheet. However, as the crack propagates beneath the stringer, the stress intensity factor decreases significantly. Increasing the stiffness of the stringer or the adhesive also results in a decrease in the stress intensity factor.
Bigelow, C. A.↗
Improvement of Reynolds-Stress and Triple-Product Lag Models
The Reynolds-stress and triple product Lag models were created with a normal stress distribution which was defined by the accepted 4:3:2 distribution of streamwise, spanwise and wall normal stresses, and a ratio of τ(sub w) = 0.3k in the log layer region of high Reynolds number flat plate flow, which implies R11(+) = 4/(9/2)∗.3 ≈ 2.96. More recent measurements show a more complex picture of the log layer region at high Reynolds numbers. The first cut at improving these models along with the direction for future refinements is described. Comparison with recent high Reynolds number data shows areas where further work is needed, but also shows inclusion of the modeled turbulent transport terms improve the prediction where they influence the solution. Additional work is needed to develop a model that better matches experiments, but there is significant improvement in many of the details of the log layer behavior.
Fluid dynamics↗
Improvement of Reynolds-Stress and Triple-Product Lag Models
The Reynolds-stress and triple product Lag models were created with a normal stress distribution which was defined by the accepted 4:3:2 distribution of streamwise, spanwise and wall normal stresses, and a ratio of τ(sub w) = 0.3k in the log layer region of high Reynolds number flat plate flow, which implies R11(+) = 4/(9/2)∗.3 ≈ 2.96. More recent measurements show a more complex picture of the log layer region at high Reynolds numbers. The first cut at improving these models along with the direction for future refinements is described. Comparison with recent high Reynolds number data shows areas where further work is needed, but also shows inclusion of the modeled turbulent transport terms improve the prediction where they influence the solution. Additional work is needed to develop a model that better matches experiments, but there is significant improvement in many of the details of the log layer behavior.
Turbulence↗
Plume-Surface Interaction Modeling for a Human-Scale Mars Lander
Landing vehicles impart thermal and strain energy onto the landing site from the retrorocket exhaust. Depending on the design of the vehicle, the energy may be great enough to cause spallation at the landing site. This damage may be minor and repairable in the case of landing on a terrestrial landing pad. For missions to other planetary bodies, the spallation may cause the landing site to become uneven and unstable, as well as damage. Simulating this phenomenon in a laboratory or computationally would require a significant amount of time and other resources. These resources typically are not available during the design phase of a mission. This paper presents a computationally-efficient model for the temperature and stress distributions that arise during landing. These quantities can be used along with existing failure criteria, such as the Hoek-Brown criterion for geological materials, to quickly determine whether spallation will occur. The stress and temperature distributions at the landing site are inherently 3D; however, there is a plane of symmetry and in that plane the distributions are 2D. Both quantities are modeled using series solutions to their governing partial differential equations (PDEs). The stress is modeled using the Airy stress potential function and its governing PDE is the biharmonic equation. The temperature is governed by Fourier's law. The models assume that stress due to gravity can be neglected, the points in the plane do not accelerate, and that the material properties are constant.
Hart, Kenneth↗
Computational modeling of graphite degradation in molten salt reactors: Role of infiltration
Molten salt reactors (MSRs) often employ graphite as a moderator and reflector. An important challenge for deploying graphite in these reactors is that, due to limited experimental data, our understanding of graphite’s structural integrity in molten salt environments remains incomplete. Here, this study addresses heat generation from fuel-bearing salt that has infiltrated open pores in the graphite, driven primarily by pressure differentials. This is one of multiple identified physical and chemical mechanisms through which molten salt could potentially degrade graphite. Thermally driven stresses are quantified using the Molten-Salt Reactor Experiment (MSRE) graphite moderator elements as a case study. Finite element simulations predict stress distributions at varying infiltration levels, indicating that thermal stresses increase with higher infiltration. Rare-event simulations using the parallel subset simulation framework identify the combinations and corresponding ranges of input parameters that lead to stresses above a specified threshold. In particular, combinations involving high infiltration amounts, high power density, and low thermal conductivity tend to induce the highest stresses. Under the inputs and assumptions considered in this work, the magnitudes of the thermally driven stresses are quite low, with a very low likelihood of causing failure due to exceeding the graphite’s tensile strength. Additionally, rare-event simulations were performed for two more scenarios: a scaled-up moderator geometry and a localized hotspot in the original geometry. Both cases resulted in increased susceptibility to failure, though not to a detrimental extent. Furthermore, the combined effects of irradiation and infiltration-induced thermal stresses were evaluated. The results showed that thermal stresses from infiltration were negligible compared to those caused by irradiation. The findings of such a study are inherently component-specific, but the methodology presented here could be used for similar assessments of salt-infiltration effects in other graphite components.
36 - MATERIALS SCIENCE↗
Longitudinal residual stresses in boron fibers
A method of measuring the longitudinal residual stress distribution in boron fibers is presented. The residual stresses in commercial CVD boron on tungsten fibers of 102, 142, and 203 microns (4, 5.6, and 8 mil) diameters were determined. Results for the three sizes show a compressive stress at the surface 800 to -1400 MN/sq m 120 to -200 ksi), changing monotonically to a region of tensile stress within the boron. At approximately 25 percent of the original radius, the stress reaches a maximum tensile 600 to 1000 MN/sq m(90 to 150 ksi) and then decreases to compressive near the tungsten boride core. The core itself is under a compressive stress of approximately -1300 MN/sq m (-190 ksi). The effects of surface removal on core residual stress and core-initiated fracture are discussed.
Behrendt, D. R.↗
Photo-orthotropic elasticity - A new technique for stress analysis of composites
This paper deals with the application of photoelastic methods to glass fiber reinforced plastics. The basic principles governing the photoelastic response in birefringent orthotropic composites are briefly reviewed. Then, three important aspects of photo-orthotropic elasticity, namely, photoelastic calibration, separation of principal stresses, and application to problems of engineering importance, are considered in detail. A new calibration specimen is proposed for determining the three independent photoelastic constants: an orthotropic half-plane subjected to a concentrated edge load. From the isochromatic response, the three stress-fringe values can be obtained by a least-squares procedure based on the theoretical stress distribution. Next, four methods of separating the principal stresses in birefringent composite models are proposed: the method of drilling small holes at the points of interest, the method of oblique incidence, the method of combining the transmitted photoelastic response with the reflected photoelastic response, and the method of birefringence dispersion.
Prabhakaran, R.↗
Parametric study of stress-intensity factors in bonded composite stringer panels
Stress-intensity factors are determined for an infinite cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semi-infinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media which are representative of many fiber-reinforced composite materials. The complex variable theory of elasticity was used to obtain a set of integral equations describing the problem. The integral equations are replaced by an equivalent sheet of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer. From these adhesive stresses, the stress-intensity factors are found. A parametric study is conducted to determine the sensitivity of the system to material properties and specimen configuration. Unless the crack tip is very close to or under the stringer, the stress-intensity factor is approximately that of the unstiffened sheet. However, as the crack propagates beneath the stringer, the stress-intensity factor decreases significantly. Increasing the stringer stiffness or the adhesive stiffness also decreases the stress-intensity factor.
Bigelow, C. A.↗
Impact ice stresses in rotating airfoils
Finite element analysis is used to study the tensile and shear stresses at the interface between impact ice adhering to a rotating airfoil and the metal airfoil surface. A simple rotating beam-ice structure is used to obtain basic understanding of stress distribution in the ice. Calculations show that shear stresses increase linearly with ice thickness and tensile stresses tend to zero for a fully bonded surface. When shear stresses exceed the ultimate strength, adhesive failure occurs and tensile stresses are developed in the unbonded ice, resulting in tensile failure of the impact ice. A second model is used to study the OH-58 tail rotor with a measured ice profile. Ice shedding predictions are compared to the resulting data using a statistical structural analysis.
Scavuzzo, R. J.↗
Skin Stresses in an Inflated Sphere During Impact
An analysis is made of the stresses in the skin of an inflated nonstretchable sphere during normal, nonrotating impact with a hard flat surface, assuming infinite modulus of elasticity in the skin and infinite propagation speed of stress waves. The analysis is further applied to the study of the inflated sphere landing vehicle containing a payload suspended at the center. Curves are presented showing the stress distributions during impact for cases corresponding to those calculated in previous reports in which the impact motion and payload landing performance capabilities of the landing vehicle have been studied. It is found, assuming the force from the payload-suspension cords to be distributed continuously on the skin, that is, neglecting stress concentrations,that the skin stresses along a meridian are reduced by the presence of the suspended payload during impact, but that the maximum values of skin stress normal to a meridian are little affected.
Martin, E. Dale↗
An experimental and analytical investigation of the rail shear-test method as applied to composite materials
This report presents the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test. The effects of non-uniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates are shown. A two-dimensional linearly elastic finite element model was used to analytically determine how various geometric parameters influenced the magnitude and distribution of inplane normal and shear stresses in a tensile rail shear specimen. Rail shear tests were conducted at room temperature and 589 K (600 F) on selected graphite-polyimide composite laminates using two titanium rail configurations. The analysis and test methods are discussed, and the results of the effects of the various parameters on shear modulus and ultimate strength are presented.
Garcia, R.↗
Moment distributions around holes in symmetric composite laminates subjected to bending moments
An analytical investigation of the effects of holes on the moment distribution of symmetric composite laminates subjected to bending moments is described. A general, closed-form solution for the moment distribution of an infinite anisotropic plate is derived, and this solution is used to determine stress distributions both on the hole boundary and throughout the plate. Results are presented for several composite laminates that have holes and are subjected to either pure bending or cylindrical bending. Laminates with a circular hole or with an elliptical hole are studied. Laminate moment distributions are discussed, and ply stresses are described.
Prasad, C. B.↗