Stephen F. Duffy

Reliability Analysis of Structural Ceramic Components Using a Three-Parameter Weibull Distribution

This paper describes nonlinear regression estimators for the three-parameter Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

Structural reliability analysis of laminated CMC components

For laminated ceramic matrix composite (CMC) materials to realize their full potential in aerospace applications, design methods and protocols are a necessity. This paper focuses on the time-independent failure response of these materials and presents a reliability analysis associated with the initiation of matrix cracking. It highlights a public domain computer algorithm that has been coupled with the laminate analysis of a finite element code and which serves as a design aid to analyze structural components made from laminated CMC materials. Issues relevant to the effect of the size of the component are discussed, and a parameter estimation procedure is presented. The estimation procedure allows three parameters to be calculated from a failure population that has an underlying Weibull distribution.

Noninteractive macroscopic reliability model for ceramic matrix composites with orthotropic material symmetry

A macroscopic noninteractive reliability model for ceramic matrix composites is presented. The model is multiaxial and applicable to composites that can be characterized as orthotropic. Tensorial invariant theory is used to create an integrity basis with invariants that correspond to physical mechanisms related to fracture. This integrity basis is then used to construct a failure function per unit volume (or area) of material. It is assumed that the overall strength of the composite is governed by weakest link theory. This leads to a Weibull-type model similar in nature to the principle of independent action (PIA) model for isotropic monolithic ceramics

A Viscoplastic Constitutive Theory for Monolithic Ceramics—I

This paper, which is the first of two in a series, provides an overview ofa viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics, the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

A unified inelastic constitutive theory for sintered powder metals

Abstract The inelastic behavior of powder metals is significantly influenced by hydrostatic stress. In this paper a unified theory is proposed that captures not only such time-dependent phenomena as creep, stress relaxation and rate sensitivity but also demonstrates a sensitivity to hydrostatic stress. The theory is developed from a dissipative potential function, which assures the inelastic boundary value problem is well posed with unique solutions.

Simulator Study of Primary and Precipitating Factors in Work Zone Crashes

Research with a driving simulator was conducted to determine the impact of various primary and precipitating factors on work zone crashes and associated driver performance. The primary factors included in the study were roadway type (undivided and divided), traffic density (low, moderate, and high), and work zone type (lane closure and shoulder closure). Precipitating factors included elements that caused the driver behavior or the environment to change and initiate the potential for a crash, near crash, or incident. Twelve precipitating factors were investigated; all could be described as involving either a stopped or slow vehicle in the travel lane or an object in the roadway. Forty-five participants were exposed to 24 different work zone configurations for which performance measures of crash frequency, speed, lane deviation, and deceleration data were collected. The performance measures were used to determine the most hazardous work zone configurations. Neither the level of traffic density for mean speed nor the type of roadway for lane deviation was found to be statistically different. The remaining statistical test rejected the null hypothesis that the performance measures were similar. Overall, the most hazardous work zone configurations entailed a divided roadway with a lane closure during low-density traffic conditions and a stopped or braking truck or car.

Trends in the Design and Analysis of Components Fabricated From CFCCs

Continuous fiber ceramic composite materials (CFCCs) are being considered for an increasing number of commercial applications. They provide the potential for lighter, stronger, more corrosion-resistant components that can perform at higher temperature for long periods of time. Global competitiveness demands a shortening of the time for CFCC commercialization. Thus, considerable effort has been expended to develop and improve the materials, and to a lesser extent, to develop component design methods and data bases of engineering properties. To shorten the time to commercialization, project efforts must be integrated, while balancing project resources between material development and engineering design. Currently a good balance does not exist for most materials development projects. To rectify this imbalance, improvements in engineering design and development technologies must be supported and accelerated, with a focus on component issues. This will require project managers to give increasing emphasis to component design needs in addition to their current locus on material development.

Noninteractive macroscopic reliability model for whisker-reinforced ceramic composites

Considerable research is underway in the field of material science focusing on incorporating silicon carbide whiskers into silicon nitride and alumina matrices. These composites show the requisite thermal stability and thermal shock resistance necessary for use as components in advanced gas turbines and heat exchangers. This paper presents a macroscopic noninteractive reliability model for whisker-reinforced ceramic composites. The theory is multiaxial and is applicable to composites that can be characterized as transversely isotropic. Enough processing data exists to suggest this idealization encom passes a significantly large class of fabricated components. A qualitative assessment of the model is made by presenting reliability surfaces in several different stress spaces and for different values of model parameters.

Strength of a Ceramic Sectored Flexural Test Specimen

A new test specimen, defined here as the “sectored flexural strength test specimen,” was developed to measure the strength of ceramic tubes specifically for circumstances when flaws located at the tube’s outer diameter are the strength-limiter when subjected to axial tension. The understanding of such strength-limitation is relevant when ceramic tubes are subjected to bending or when the internal temperature is hotter than the tube’s exterior (e.g., heat exchangers). The test specimen is both economically and statistically attractive because eight test specimens (eight in the case of this project—but the user is not necessarily limited to eight) were extracted out of each length of tube. An analytic expression for maximum (or failure) stress, and relationships portraying effective area and effective volume as a function of Weibull modulus were developed. Lastly, it was shown through the testing of two ceramics that the sectored flexural specimen was very effective; it produced failures caused by strength-limiting flaws located on the tube’s original outer diameter.

Weibull Analysis Effective Volume and Effective Area for a Ceramic C-Ring Test Specimen

C-ring specimen geometries are used to ascertain Weibull parameters for spatially distributed flaw populations in ceramic gun barrels. A review of previously published results used to compute effective areas and effective volumes for this test specimen geometry is presented along with deficiencies associated with these computations. In addition, the results of the numerical analyses presented utilizing finite-element analysis and component level reliability algorithms clearly indicate that geometric constraints called out in the current ASTM standard for C-ring testing must be revised.