Debunking Stress Rupture Theories Using Weibull Regression Plots
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Constituent-Based Life Models Being Developed for SiC/SiC Composites
For the successful utilization of ceramic matrix composites (CMC) as hot-section components in advanced aeropropulsion engines, the CMC constituents will need to be tailored and optimized to meet all the critical property demands of each component. Under the High-Speed Research (HSR) and Advanced High-Temperature Engine Materials Technology (HITEMP) Programs, the NASA Glenn Research Center at Lewis Field initiated research to develop mechanistic models for key CMC thermostructural properties. These models would describe the effects of different constituent factors (composition, geometry, and volume fraction) and of potential application conditions (stress, time, temperature, and environment) on these properties. Particular focus was placed on both analytical and numerical modeling of state-of-the-art SiC/SiC composites where the primary load-bearing constituents are stoichiometric SiC fibers in a complex multiphase SiC matrix produced by chemical vapor infiltration and melt infiltration. Recent studies have resulted in computer-based numerical models for the elastic modulus, thermal expansion, and thermal conductivity properties of the SiC/SiC system. Additional studies have generated analytical and empirical models for the time dependence of composite rupture strength at temperatures above 2200 F (1200 C), where CMC's have an important thermostructural advantage over current nickel-based superalloys. These life models utilize thermal activation theory and fiber stress-rupture results measured at Glenn to generate Larson-Miller (L M) plots of fiber rupture strength versus q, a single time- and temperature-dependent parameter. Assuming a worse case in which the SiC matrix is cracked, rupture is then controlled by the time-dependent fracture characteristics of the fiber bundles bridging the matrix cracks. With this as the controlling mechanism, one can then use simple composite theory and the fiber L M plots to predict CMC rupture strength versus the q parameter. The dashed line shows the predicted rupture strength of a SiC/SiC composite that is reinforced by a state-of-the-art stoichiometric SiC fiber. For the q parameter, time is in hours and temperature in degrees kelvin. To generate these predictions, a two-dimensional 0 /90 composite with approximately 16 percent fiber in the applied stress direction and an air test environment were assumed. As such, it is possible to compare the model predictions against limited stress-rupture data for this CMC as shown by the data points. The good agreement confirms the rupture model at least for the selected CMC and test conditions. Thus for this particular SiC/SiC composite, one can estimate a 1000-hr rupture strength of approximately 12 ksi at 2400 F (T = 1588 K and q = 39 700 K). At lower CMC application stresses, the SiC matrix is typically uncracked, so both the fiber and matrix constituents share the composite load. In this case, CMC rupture is controlled by the constituent with the longest rupture time based on the creep rate of the composite. Measured Monkman-Grant plots of rupture time versus creep rate for the two SiC constituents have been used to develop CMC life models for this important application condition. NASA and DOD are currently using this information to establish application and material goals for more advanced CMC's that can be used at even higher temperatures.
DiCarlo, James A.↗
Fracture Behavior in Nylon 6 Fibers
Electron paramagnetic resonance (EPR) techniques are used to determine the number of free radicals produced during deformation leading to fracture of nylon 6 fibers. A reaction rate molecular model is proposed to explain some of the deformation and bond rupture behavior leading to fracture. High-strength polymer fibers are assumed to consist of a sandwich structure of disordered and ordered regions along the fiber axis. In the disordered or critical flaw regions, tie chains connecting the ordered or crystalline block regions are assumed to have a statistical distribution in length. These chains are, therefore, subjected to different stresses. The effective length distribution was determined by EPR. The probability of bond rupture was assumed to be controlled by reaction-rate theory with a stress-aided activation energy and behavior of various loadings determined by numerical techniques. The model is successfully correlated with experimental stress, strain, and bond rupture results for creep, constant rate loadings, cyclic stress, stress relaxation and step strain tests at room temperature.
Lloyd, B. A.↗
Time-Dependent Stress Rupture Strength Degradation of Hi-Nicalon Fiber-Reinforced Silicon Carbide Composites at Intermediate Temperatures
The stress rupture strength of silicon carbide fiber-reinforced silicon carbide composites with a boron nitride fiber coating decreases with time within the intermediate temperature range of 700 to 950 degree Celsius. Various theories have been proposed to explain the cause of the time-dependent stress rupture strength. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of silicon carbide fiber-reinforced silicon carbide composites. This is achieved through the development of a numerically based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time-marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time-dependent behavior.
Progressive Failure Analysis↗
A Numerical Solution Routine for Investigating Oxidation-Induced Strength Degradation Mechanisms in SiC/SiC Composites
The stress rupture strength of silicon carbide fiber-reinforced silicon carbide (SiCSiC) composites with a boron nitride (BN) fiber coating decreases with time within the intermediate temperature range of 700-950 C. Various theories have been proposed to explain the cause of the time dependent stress rupture strength. Some previous authors have suggested that the observed composite strength behavior is due to the inherent time dependent strength of the fibers, which is caused by the slow growth of flaws within the fibers. Flaw growth is supposedly enabled by oxidation of free carbon at the grain boundaries. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of SiCSiC composites. This is achieved through the development of a numerically-based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time dependent behavior.
degradation↗
A description of the mechanical behavior of composite solid propellants based on molecular theory
Both the investigation and the representation of the stress-strain response (including rupture) of gum and filled elastomers can be based on a simple functional statement. Internally consistent experiments are used to sort out the effects of time, temperature, strain and crosslink density on gum rubbers. All effects are readily correlated and shown to be essentially independent of the elastomer when considered in terms of non-dimensionalized stress, strain and time. A semiquantitative molecular theory is developed to explain this result. The introduction of fillers modifies the response, but, guided by the framework thus provided, their effects can be readily accounted for.
Landel, R. F.↗
Tensile Properties of Some Structural Sheet Materials Under Rapid-Heating Conditions
The results of the NACA tests to determine the tensile strength of some structural sheet materials heated to failure at temperature rates from 0.2 deg. F to 100 deg F per second under constant load conditions are reviewed . Yield and rupture stresses obtained under rapid-heating conditions are compared with the results of conventional elevated-temperature tensile tests. The relation between rapid-heating tests, short-time creep tests, and conventional creep tests is discussed . The application of a phenomenological theory for calculating rapid-heating curves is shown. Methods are given for predicting yield and rupture stresses and temperatures from master curves and temperature-rate parameters
Heimerl, George J.↗
Effects of cobalt in nickel-base superalloys
A study has been carried out to assess the role of cobalt in Udimet 700, a representative nickel-base superalloy containing 17 percent or more cobalt. The study spans the spectrum of microstructural, microchemical, and mechanical behavior aspects which together form a basis for superalloy performance in jet engines. The results suggest that cobalt affects the solubility of elements in the gamma matrix, which leads to enhanced gamma-prime volume fraction and to the stabilization of MC-type carbides and sigma phase. However, these microstructural and microchemical changes are too slight to significantly affect the strength and ductile properties. Depending on the heat treatment, the creep and stress rupture resistance can be cobalt-sensitive. In the coarse-grained, fully solutioned and aged condition, all of the alloy's 17 percent Co can be replaced by nickel without decreasing the creep and stress rupture resistance. These findings are discussed with reference to existing theories and experimental data obtained by other workers.
Tien, J. K.↗
Time/Temperature Dependent Tensile Strength of SiC and Al2O3-Based Fibers
In order to understand and model the thermomechanical behavior of fiber-reinforced composites, stress-rupture, fast-fracture, and warm-up rupture studies were conducted on various advanced SiC and Al2O3-based fibers in the,temperature range from 20 to 1400 C in air as well as in inert environments. The measured stress-rupture, fast fracture, and warm-up rupture strengths were correlated into a single master time/temperature-dependent strength plot for each fiber type using thermal activation and slow crack growth theories. It is shown that these plots are useful for comparing and selecting fibers for CMC and MMC reinforcement and that, in comparison to stress rupture tests, the fast-fracture and warm-up tests can be used for rapid generation of these plots.
Yun, Hee Mann↗
Creep and creep rupture of laminated graphite/epoxy composites
An incremental numerical procedure based on lamination theory is developed to predict creep and creep rupture of general laminates. Existing unidirectional creep compliance and delayed failure data is used to develop analytical models for lamina response. The compliance model is based on a procedure proposed by Findley which incorporates the power law for creep into a nonlinear constitutive relationship. The matrix octahedral shear stress is assumed to control the stress interaction effect. A modified superposition principle is used to account for the varying stress level effect on the creep strain. The lamina failure model is based on a modification of the Tsai-Hill theory which includes the time dependent creep rupture strength. A linear cumulative damage law is used to monitor the remaining lifetime in each ply.
Dillard, D. A.↗
Predicting Tensile Strengths of Boron/Aluminum Composites
To develop predictive theory to account for time/temperature effect of B/A1 composites, series of deformation and fracture studies was performed on commercial boron fibers over wide ranges of stress, stress application time, and temperature. By combining these single fiber results with fracture theory for metal matrix composites, design formulas were derived that describe B/A1 composite tensile and stress rupture strengths as function of time and temperature. Using derived formulas, calculated and experimental results agree to within 3 percent.
Decarlo, J. A.↗
Lifetime Reliability Evaluation of Structural Ceramic Parts with the CARES/LIFE Computer Program
The computer program CARES/LIFE calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. This program is an extension of the CARES (Ceramics Analysis and Reliability Evaluation of Structures) computer program. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing the power law, Paris law, or Walker equation. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled using either the principle of independent action (PIA), Weibull's normal stress averaging method (NSA), or Batdorf's theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. Two example problems demonstrating cyclic fatigue parameter estimation and component reliability analysis with proof testing are included.
Nemeth, Noel N.↗
Time-dependent reliability analysis of ceramic engine components
The computer program CARES/LIFE calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. This program is an extension of the CARES (Ceramics Analysis and Reliability Evaluation of Structures) computer program. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing either the power or Paris law relations. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled using either the principle of independent action (PIA), the Weibull normal stress averaging method (NSA), or the Batdorf theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. Two example problems demonstrating proof testing and fatigue parameter estimation are given.
Nemeth, Noel N.↗
Durability evaluation of ceramic components using CARES/LIFE
The computer program CARES/LIFE calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. This program is an extension of the CARES (Ceramics Analysis and Reliability Evaluation of Structures) computer program. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing the power law, Paris law, or Walker equation. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled using either the principle of independent action (PIA), the Weibull normal stress averaging method (NSA), or the Batdorf theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. Application of this design methodology is demonstrated using experimental data from alumina bar and disk flexure specimens which exhibit SCG when exposed to water.
Nemeth, Noel N.↗
CARES/LIFE Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program
This manual describes the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction (CARES/LIFE) computer program. The program calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. CARES/LIFE is an extension of the CARES (Ceramic Analysis and Reliability Evaluation of Structures) computer program. The program uses results from MSC/NASTRAN, ABAQUS, and ANSYS finite element analysis programs to evaluate component reliability due to inherent surface and/or volume type flaws. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing the power law, Paris law, or Walker law. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled by using either the principle of independent action (PIA), the Weibull normal stress averaging method (NSA), or the Batdorf theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. The probabilistic time-dependent theories used in CARES/LIFE, along with the input and output for CARES/LIFE, are described. Example problems to demonstrate various features of the program are also included.
Nemeth, Noel N.↗
Determination of Stress-Rupture Parameters for Four Heat-Resisting Alloys
Stress-rupture data for four heat-resisting alloys are analyzed according to equations of the theory of rate processes. A method for determining the four parameters of structure and composition is demonstrated and the four parameters are determined for each of the alloys: forged S816, cast S816, cast S590, and cast Vitallium. It is concluded that parameters can be determined for an alloy provided sufficient reliable experimental data are available.
Lidman, William G.↗
Stress corrosion cracking in the earth
Two fundamental concepts of fracture mechanics are used to develop a theory of the earthquake mechanism which specifically predicts observed time-dependent rupture phenomena such as slow earthquakes, postseismic rupture growth and afterslip, multiple events, foreshocks, and aftershocks. The theory also predicts that there must be a nucleation stage prior to an earthquake, and suggests a physical mechanism by which one earthquake may trigger another. Investigations show that all earthquakes must be preceded by a quasi-static slip over a portion of the rupture surfaces, although it may be difficult to detect in practice, and a study of delayed multiple events characterizes the strength of some barriers in the earth as having a stress corrosion index of about 24.
Das, S.↗
Fracture Mechanisms For SiC Fibers And SiC/SiC Composites Under Stress-Rupture Conditions at High Temperatures
The successful application of SiC/SiC ceramic matrix composites as high-temperature structural materials depends strongly on maximizing the fracture or rupture life of the load-bearing fiber and matrix constituents. Using high-temperature data measured under stress-rupture test conditions, this study examines in a mechanistic manner the effects of various intrinsic and extrinsic factors on the creep and fracture behavior of a variety of SiC fiber types. It is shown that although some fiber types fracture during a large primary creep stage, the fiber creep rate just prior to fracture plays a key role in determining fiber rupture time (Monkman-Grant theory). If it is assumed that SiC matrices rupture in a similar manner as fibers with the same microstructures, one can develop simple mechanistic models to analyze and optimize the stress-rupture behavior of SiC/SiC composites for applied stresses that are initially below matrix cracking.
DiCarlo, James A.↗