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An overview of engineering concepts and current design algorithms for probabilistic structural analysis

The article begins by examining the fundamentals of traditional deterministic design philosophy. The initial section outlines the concepts of failure criteria and limit state functions two traditional notions that are embedded in deterministic design philosophy. This is followed by a discussion regarding safety factors (a possible limit state function) and the common utilization of statistical concepts in deterministic engineering design approaches. Next the fundamental aspects of a probabilistic failure analysis are explored and it is shown that deterministic design concepts mentioned in the initial portion of the article are embedded in probabilistic design methods. For components fabricated from ceramic materials (and other similarly brittle materials) the probabilistic design approach yields the widely used Weibull analysis after suitable assumptions are incorporated. The authors point out that Weibull analysis provides the rare instance where closed form solutions are available for a probabilistic failure analysis. Since numerical methods are usually required to evaluate component reliabilities, a section on Monte Carlo methods is included to introduce the concept. The article concludes with a presentation of the technical aspects that support the numerical method known as fast probability integration (FPI). This includes a discussion of the Hasofer-Lind and Rackwitz-Fiessler approximations.

Duffy, S. F.↗

Accounting for Uncertainties in Strengths of SiC MEMS Parts

A methodology has been devised for accounting for uncertainties in the strengths of silicon carbide structural components of microelectromechanical systems (MEMS). The methodology enables prediction of the probabilistic strengths of complexly shaped MEMS parts using data from tests of simple specimens. This methodology is intended to serve as a part of a rational basis for designing SiC MEMS, supplementing methodologies that have been borrowed from the art of designing macroscopic brittle material structures. The need for this or a similar methodology arises as a consequence of the fundamental nature of MEMS and the brittle silicon-based materials of which they are typically fabricated. When tested to fracture, MEMS and structural components thereof show wide part-to-part scatter in strength. The methodology involves the use of the Ceramics Analysis and Reliability Evaluation of Structures Life (CARES/Life) software in conjunction with the ANSYS Probabilistic Design System (PDS) software to simulate or predict the strength responses of brittle material components while simultaneously accounting for the effects of variability of geometrical features on the strength responses. As such, the methodology involves the use of an extended version of the ANSYS/CARES/PDS software system described in Probabilistic Prediction of Lifetimes of Ceramic Parts (LEW-17682-1/4-1), Software Tech Briefs supplement to NASA Tech Briefs, Vol. 30, No. 9 (September 2006), page 10. The ANSYS PDS software enables the ANSYS finite-element-analysis program to account for uncertainty in the design-and analysis process. The ANSYS PDS software accounts for uncertainty in material properties, dimensions, and loading by assigning probabilistic distributions to user-specified model parameters and performing simulations using various sampling techniques.

Nemeth, Noel↗

"Ultra"-Fast Fracture Strength of Advanced Structural Ceramic Materials Studied at Elevated Temperatures

The accurate determination of inert strength is important in reliable life prediction of structural ceramic components. At ambient temperature, the inert strength of a brittle material is typically regarded as free of the effects of slow crack growth due to stress corrosion. Therefore, the inert strength can be determined either by eliminating active species, especially moisture, with an appropriate inert medium, or by using a very high test rate. However, at elevated temperatures, the concept or definition of the inert strength of brittle ceramic materials is not clear, since temperature itself is a degrading environment, resulting in strength degradation through slow crack growth and/or creep. Since the mechanism to control strength is rate-dependent viscous flow, the only conceivable way to determine the inert strength at elevated temperatures is to utilize a very fast test rate that either minimizes the time for or eliminates slow crack growth. Few experimental studies have measured the elevated-temperature, inert (or "ultra"-fast fracture) strength of advanced ceramics. At the NASA Lewis Research Center, an experimental study was initiated to better understand the "ultra"-fast fracture strength behavior of advanced ceramics at elevated temperatures. Fourteen advanced ceramics - one alumina, eleven silicon nitrides, and two silicon carbides - have been tested using constant stress-rate (dynamic fatigue) testing in flexure with a series of stress rates including the "ultra"-fast stress rate of 33 000 MPa/sec with digitally controlled test frames. The results for these 14 advanced ceramics indicate that, notwithstanding possible changes in flaw populations as well as flaw configurations because of elevated temperatures, the strength at 33 000 MPa/sec approached the room-temperature strength or reached a higher value than that determined at the conventional test rate of 30 MPa/sec. On the basis of the experimental data, it can be stated that the elevated-temperature, inert strength of an advanced ceramic material can be defined as the strength where no slow crack growth takes place at the temperature.

Choi, Sung R.↗

A microstructure-based modeling approach to predict the mechanical properties of Zr alloy with hydride precipitates

In nuclear reactors, hydrides can form in fuel cladding due to hydrogen absorption in ZIrcaloy and cause embrittlement. This work presents a microstructure-based finite element model to predict the stress-strain response of Zircaloy containing hydrides. Quantitative microstructural details extracted from scanning electron microscopy (SEM) images were used to generate heterogeneous microstructures including the morphology and spatial distribution of hydrides. The constitutive material model for zircaloy in this study is based on crystal plasticity theory which considers the hexagonal close-packed (HCP) atomic structure of Zircaloy material. The hydrides were modeled as brittle material along with a damage model. Hydride formation inside the zircoloy matrix results in residual stress. This phenomenon is also captured in this model. A parametric study has been conducted to understand the effect of volume fraction, orientation, and lamellae thickness of the hydride phase on the mechanical properties of the overall material.

Kulkarni, Shank S.↗

Performance of multifunctional piezoelectric energy harvesting microgyroscopes with material degradation

Most microelectromechanical systems (MEMS) are made from brittle materials that are prone to cracking. Damage from the formation of cracks can occur anytime during the manufacturing process or due to mechanical loading of MEMS devices. Cracks can increase the structures flexibility and lead to changes in performance or total failure. Understanding the potential influences cracks in MEMS is necessary for the longevity of these systems. The energy harvesting microgyroscope studied in this work is susceptible to crack propagation in its silicon substrate and lead zirconate titanate piezoelectric patch. To this end, an electromechanical model is developed to capture the impacts of cracks on the performance of a damaged energy harvesting microgyroscope. Numerical methods are used to approximate the damage associated with distributed crack networks. Then, the static and dynamic responses of the damaged microgyroscope are analyzed for two possible multifunctional setups. Here, the current study revealed that cracks can significantly affect the static and dynamic behaviors of the microgyroscope energy harvester. Combinations of cracking and piezoelectric property degradation cause a decrease in the static pull-in voltage and shift the resonance frequencies of the system. Additionally, it is shown that the systems sensitivity to changes in the base rotation and energy harvesting capabilities vary widely depending on the severity of material degradation.

36 MATERIALS SCIENCE↗

Dynamic crack arrest in ceramics and ceramic composites

The results of past dynamic crack arrest experiments involving structural ceramics and ceramic composites are reviewed and analyzed. The lack of dynamic crack arrest in very brittle materials is discussed and contrasted with dynamic crack arrest in somewhat brittle metallic and polymeric materials. Numerical analyses show that the lack of crack arrest is due to reduced dynamic fracture resistance of the material and is not due to the kinetic energy.

Kobayashi, A. S.↗

Tectonics of the Outer Planet Satellites

Tectonic features on the satellites of the outer planets range from the familiar, such as clearly recognizable graben on many satellites, to the bizarre, such as the ubiquitous double ridges on Europa, the twisting sets of ridges on Triton, or the isolated giant mountains rising from Io's surface. All of the large and middle-sized outer planet satellites except Io are dominated by water ice near their surfaces. Though ice is a brittle material at the cold temperatures found in the outer solar system, the amount of energy it takes to bring it close to its melting point is lower than for a rocky body. Therefore, some unique features of icy satellite tectonics may be influenced by a near-surface ductile layer beneath the brittle surface material, and several of the icy satellites may possess subsurface oceans. Sources of stress to drive tectonism are commonly dominated by the tides that deform these satellites as they orbit their primary giant planets. On several satellites, the observed tectonic features may be the result of changes in their tidal figures, or motions of their solid surfaces with respect to their tidal figures. Other driving mechanisms for tectonics include volume changes due to ice or water phase changes in the interior, thermoelastic stress, deformation of the surface above rising diapirs of warm ice, and motion of subsurface material toward large impact basins as they fill in and relax. Most satellites exhibit evidence for extensional deformation, and some exhibit strike-slip faulting, whereas contractional tectonism appears to be rare. Io s surface is unique, exhibiting huge isolated mountains that may be blocks of crust tilting and foundering into the rapidly emptying interior as the surface is constantly buried by deposits from hyperactive volcanoes. Of the satellites, diminutive Enceladus is spectacularly active; its south polar terrain is a site of young tectonism, copious heat flow, and tall plumes venting into space. Europa's surface is pervasively tectonized, covered with a diverse array of exotic and incompletely understood tectonic features. The paucity of impact craters on Europa suggests that its tectonic activity is ongoing. Geysers on Triton show that some degree of current activity, while tectonic features that cross sparsely cratered terrain indicate that it may also be tectonically active. Ganymede and Miranda both exhibit ancient terrains that have been pulled apart by normal faulting. On Ganymede these faults form a global network, while they are confined to regional provinces on Miranda. Ariel, Dione, Tethys, Rhea, and Titania all have systems of normal faults cutting across their surfaces, though the rifting is less pronounced than it is on Ganymede and Miranda. Iapetus exhibits a giant equatorial ridge that has defied simple explanation. The rest of the large and middle-sized satellites show very little evidence for tectonic features on their surfaces, though the exploration of Titan's surface has just begun.

McKinnon, W. B.↗

A cohesive zone treatment for the material point method involving problems of large deformation and damage

A new algorithm is described that permits the use of cohesive zones in the material point method for problems involving large deformation and fracture. In contrast to previous cohesive zone implementations, this method does not utilize massless surface-element particles. Instead, cohesive tractions are computed using the shape function mappings from a reference grid configuration in combination with explicitly defined particle surface normals and surface positions. These normals and relative surface positions are updated each time step according to particle deformation. The tractions are converted to cohesive forces using the nodal areas and mapped back to particles using the same reference shape function mappings. These forces are then remapped by conventional particle-to-grid interpolation as external forces using the current-configuration shape-function mappings. This allows highly compliant cohesive zones to function over jump displacements larger than a grid cell. Upon damage, these interfaces can revert to conventional multi-field contact surfaces. This approach is general and readily applies to two and three dimensions as well as being compatible with damage-field gradient partitioning offering exceptional computational flexibility. The framework for this method enables other capabilities, such as improved contact precision using explicitly defined surface normals and positions, and a method to mitigate spurious material damage at weak discontinuities between stiff brittle materials and soft or compliant materials.

Cohesive zone↗

Safe Life Propulsion Design Technologies (3rd Generation Propulsion Research and Technology)

The tasks outlined in this viewgraph presentation on safe life propulsion design technologies (third generation propulsion research and technology) include the following: (1) Ceramic matrix composite (CMC) life prediction methods; (2) Life prediction methods for ultra high temperature polymer matrix composites for reusable launch vehicle (RLV) airframe and engine application; (3) Enabling design and life prediction technology for cost effective large-scale utilization of MMCs and innovative metallic material concepts; (4) Probabilistic analysis methods for brittle materials and structures; (5) Damage assessment in CMC propulsion components using nondestructive characterization techniques; and (6) High temperature structural seals for RLV applications.

Ellis, Rod↗

NASA/CARES dual-use ceramic technology spinoff applications

NASA has developed software that enables American industry to establish the reliability and life of ceramic structures in a wide variety of 21st Century applications. Designing ceramic components to survive at higher temperatures than the capability of most metals and in severe loading environments involves the disciplines of statistics and fracture mechanics. Successful application of advanced ceramics material properties and the use of a probabilistic brittle material design methodology. The NASA program, known as CARES (Ceramics Analysis and Reliability Evaluation of Structures), is a comprehensive general purpose design tool that predicts the probability of failure of a ceramic component as a function of its time in service. The latest version of this software, CARESALIFE, is coupled to several commercially available finite element analysis programs (ANSYS, MSC/NASTRAN, ABAQUS, COSMOS/N4, MARC), resulting in an advanced integrated design tool which is adapted to the computing environment of the user. The NASA-developed CARES software has been successfully used by industrial, government, and academic organizations to design and optimize ceramic components for many demanding applications. Industrial sectors impacted by this program include aerospace, automotive, electronic, medical, and energy applications. Dual-use applications include engine components, graphite and ceramic high temperature valves, TV picture tubes, ceramic bearings, electronic chips, glass building panels, infrared windows, radiant heater tubes, heat exchangers, and artificial hips, knee caps, and teeth.

Powers, Lynn M.↗

Standardization Efforts for Mechanical Testing and Design of Advanced Ceramic Materials and Components

Advanced aerospace systems occasionally require the use of very brittle materials such as sapphire and ultra-high temperature ceramics. Although great progress has been made in the development of methods and standards for machining, testing and design of component from these materials, additional development and dissemination of standard practices is needed. ASTM Committee C28 on Advanced Ceramics and ISO TC 206 have taken a lead role in the standardization of testing for ceramics, and recent efforts and needs in standards development by Committee C28 on Advanced Ceramics will be summarized. In some cases, the engineers, etc. involved are unaware of the latest developments, and traditional approaches applicable to other material systems are applied. Two examples of flight hardware failures that might have been prevented via education and standardization will be presented.

Salem, Jonathan A.↗

Internal strain analysis of ceramics using scanning laser acoustic microscopy

Quantitative studies of material behavior characteristics are essential for predicting the functionality of a material under its operating conditions. A nonintrusive methodology for measuring the in situ strain of small dimeter (to 11 microns) ceramic fibers under uniaxial tensile loading and the local internal strains of ceramics and ceramic composites under flexural loading is introduced. The strain measurements and experimentally observed mechanical behavior are analyzed in terms of the microstructural development and fracture behavior of each test specimen evaluated. Measurement and analysis of Nicalon silicon carbide (SiC) fiber (15 microns diameter) indicate that the mean elastic modulus of the individual fiber is 185.3 GPa. Deviations observed in the experimentally determined elastic modulus values between specimens were attributed to microstructural variations which occur during processing. Corresponding variations in the fracture surface morphology were also observed. The observed local mechanical behavior of a lithium alumino-silicate (LAS) glass ceramic, a LAS/SiC monofilament composite, and a calcium alumino-silicate (CAS)/SiC fully reinforced composite exhibits nonlinearities and apparent hysteresis due to the subcritical mechanical loading. Local hysteresis in the LAS matrices coincided with the occurrence of multiple fracture initiation sites, localized microcracking, and secondary cracking. The observed microcracking phenomenon was attributed to stress relaxation of residual stresses developed during processing, and local interaction of the crack front with the microstructure. The relaxation strain and stress predicted on apparent mechanical hysteresis effects were defined and correlated with the magnitude of the measured fracture stress for each specimen studied. This quantitative correlation indicated a repeatable measure of the stress at which matrix microcracking occurred for stress relief of each material system. Stress relaxation occurred prior to the onset of steady state cracking conditions. The relaxation stress occurred at 18.5 percent of the fracture stress in LAS and 11.0 percent of the yield stress in CAS/SiC. The relaxation stress ratio was dependent upon the dominant fracture mode of the LAS/SiC specimens. Relaxation stress ratios greater than 0.30 were observed for specimens which fractured due to shear at the fiber matrix interface; specimens which fracture due to tensile cracking had relaxation stress ratios less than 0.30. The stress relaxation ratio appeared to be a specific characteristic of the glass ceramic material. The measured stress relaxation for LAS indicated a measure of the inherent residual stresses in the material due to processing and suggested localized toughening mechanisms for brittle material structures.

Kent, Renee M.↗

Real-Time Observation of Nanoscale Kink Band Mediated Plasticity in Ion-Irradiated Graphite: An In Situ TEM Study

Graphite IG-110 is a synthetic polycrystalline material used as a neutron moderator in reactors. Graphite is inherently brittle and is known to exhibit a further increase in brittleness due to radiation damage at room temperature. To understand the irradiation effects on pre-existing defects and their overall influence on external load, micropillar compression tests were performed using in situ nanoindentation in the Transmission Electron Microscopy (TEM) for both pristine and ion-irradiated samples. While pristine specimens showed brittle and subsequent catastrophic failure, the 2.8 MeV Au2+ ion (fluence of 4.378 × 1014 cm−2) irradiated specimens sustained extensive plasticity at room temperature without failure. In situ TEM characterization showed nucleation of nanoscale kink band structures at numerous sites, where the localized plasticity appeared to close the defects and cracks while allowing large average strain. We propose that compressive mechanical stress due to dimensional change during ion irradiation transforms buckled basal layers in graphite into kink bands. The externally applied load during the micropillar tests proliferates the nucleation and motion of kink bands to accommodate the large plastic strain. The inherent non-uniformity of graphite microstructure promotes such strain localization, making kink bands the predominant mechanism behind unprecedented toughness in an otherwise brittle material.

36 MATERIALS SCIENCE↗

Metallurgy and properties of plasma spray formed materials

Understanding the fundamental metallurgy of vacuum plasma spray formed materials is the key to enhancing and developing full material properties. Investigations have shown that the microstructure of plasma sprayed materials must evolve from a powder splat morphology to a recrystallized grain structure to assure high strength and ductility. A fully, or near fully, dense material that exhibits a powder splat morphology will perform as a brittle material compared to a recrystallized grain structure for the same amount of porosity. Metallurgy and material properties of nickel, iron, and copper base alloys will be presented and correlated to microstructure.

Mckechnie, T. N.↗

Composite Structural Materials

The development and application of filamentary composite materials, is considered. Such interest is based on the possibility of using relatively brittle materials with high modulus, high strength, but low density in composites with good durability and high tolerance to damage. Fiber reinforced composite materials of this kind offer substantially improved performance and potentially lower costs for aerospace hardware. Much progress has been made since the initial developments in the mid 1960's. There were only limited applied to the primary structure of operational vehicles, mainly as aircrafts.

Ansell, G. S.↗

Proof Test Diagrams for a Lithia-Alumina-Silica Glass-Ceramic

The glass-ceramic (Zerodur, Schott Glaswerke, Mainz, Germany) contains 70% to 78% by weight crystalline phase of high-quartz structure with a mean crystal size of 50-55 nm. The vitreous phase has a positive thermal expansion coefficient which is practically balanced by the negative coefficient of the crystalline phase. This results in a material which can maintain longitudinal stability during thermal cycling. This was one of the reasons for its choice as the material for the grazing incidence mirrors for the Chandra X-Ray Facility. Brittle materials such as glass and glass-ceramics which exhibit slow crack growth and subsequent fast fracture to failure exhibit a time dependence in strength. The decrease in strength for a constant applied load is known as static fatigue. In many cases, environment plays a major role in the material lifetime. It has been shown for silicate glasses that crack velocity will increase as the amount of water vapor in the environment surface finish and rate of loading. A rough surface finish leads to a lower tensile strength than for an optically polished surface. The strength of glass is observed in general to increase with increasing load rate. This phenomena is known as dynamic fatigue. This was observed for Zerodur by Tucker and Gent and Tucker in previous dynamic fatigue studies, in which lifetimes were obtained. All of the above named factors need to be considered when glass is to be used in load bearing applications.

Tucker, Dennis S.↗

Statistical Models of Fracture Relevant to Nuclear-Grade Graphite: Review and Recommendations

The nuclear-grade (low-impurity) graphite needed for the fuel element and moderator material for next-generation (Gen IV) reactors displays large scatter in strength and a nonlinear stress-strain response from damage accumulation. This response can be characterized as quasi-brittle. In this expanded review, relevant statistical failure models for various brittle and quasi-brittle material systems are discussed with regard to strength distribution, size effect, multiaxial strength, and damage accumulation. This includes descriptions of the Weibull, Batdorf, and Burchell models as well as models that describe the strength response of composite materials, which involves distributed damage. Results from lattice simulations are included for a physics-based description of material breakdown. Consideration is given to the predicted transition between brittle and quasi-brittle damage behavior versus the density of damage (level of disorder) within the material system. The literature indicates that weakest-link-based failure modeling approaches appear to be reasonably robust in that they can be applied to materials that display distributed damage, provided that the level of disorder in the material is not too large. The Weibull distribution is argued to be the most appropriate statistical distribution to model the stochastic-strength response of graphite.

Nemeth, Noel N.↗