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Deterministic and Probabilistic Creep and Creep Rupture Enhancement to CARES/Creep: Multiaxial Creep Life Prediction of Ceramic Structures Using Continuum Damage Mechanics and the Finite Element Method

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep ripture criterion However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of stress, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions This creep life prediction methodology was preliminarily added to the integrated design code CARES/Creep (Ceramics Analysis and Reliability Evaluation of Structures/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of this methodology and the CARES/Creep program.

Jadaan, Osama M.

Deterministic Multiaxial Creep and Creep Rupture Enhancements for CARES/Creep Integrated Design Code

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep rupture criterion. However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of sum, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions This creep life prediction methodology was preliminarily added to the integrated design code CARES/Creep (Ceramics Analysis and Reliability Evaluation of Structures/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of Ns methodology and the CARES/Creep program.

Jadaan, Osama M.

Endochronic theory of transient creep and creep recovery

Short time creep and creep recovery were investigated by means of the endochronic theory of viscoplasticity. It is shown that the constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation can all ber derived from the general constitutive equation by imposing appropriate constraints. In this unified approach, the effect of strain-hardening is naturally accounted for when describing creep and creep recovery. The theory predicts with reasonable accuracy the creep and creep recovery behaviors for Aluminum 1100-0 at 150 C. It was found that the strain-rate history at prestraining stage affects the subsequent creep. A critical stress was also established for creep recovery. The theory predicts a forward creep for creep recovery stress greater than the critical stress. For creep recovery stress less than the critical stress, the theory then predicts a normal strain recovery.

Wu, H. C.

Low Temperature Creep of Hot-Extruded Near-Stoichiometric NiTi Shape Memory Alloy: Isothermal Creep - Part I

This two-part paper is the first published report on the long term, low temperature creep of hot-extruded near-stoichiometric NiTi. Constant load tensile creep tests were conducted on hot-extruded near-stoichiometric NiTi at 300, 373 and 473 K under initial applied stresses varying between 200 and 350 MPa as long as 15 months. These temperatures corresponded to the martensitic, two-phase and austenitic phase regions, respectively. Normal primary creep lasting several months was observed under all conditions indicating dislocation activity. Although steady-state creep was not observed under these conditions, the estimated creep rates varied between 10(exp -10) and 10(exp -9)/s. The creep behavior of the two phases showed significant differences. The martensitic phase exhibited a large strain on loading followed by a primary creep region accumulating a small amount of strain over a period of several months. The loading strain was attributed to the detwinning of the martensitic phase whereas the subsequent strain accumulation was attributed to dislocation glide-controlled creep. An "incubation period" was observed before the occurrence of detwinning. In contrast, the austenitic phase exhibited a relatively smaller loading strain followed by a primary creep region, where the creep strain continued to increase over several months. It is concluded that the creep of the austenitic phase occurs by a dislocation glide-controlled creep mechanism as well as by the nucleation and growth of deformation twins.

Raj, S. V.

Prediction and verification of creep behavior in metallic materials and components, for the space shuttle thermal protection system. Volume 1, phase 1: Cyclic materials creep predictions

Cyclic creep response was investigated and design methods applicable to thermal protection system structures were developed. The steady-state (constant temperature and load) and cyclic creep response characteristics of four alloys were studied. Steady-state creep data were gathered through a literature survey to establish reference data bases. These data bases were used to develop empirical equations describing creep as a function of time, temperature, and stress and as a basis of comparison for test data. Steady-state creep tests and tensile cyclic tests were conducted. The following factors were investigated: material thickness and rolling direction; material cyclic creep response under varying loads and temperatures; constant stress and temperature cycles representing flight conditions; changing stresses present in a creeping beam as a result of stress redistribution; and complex stress and temperature profiles representative of space shuttle orbiter trajectories. A computer program was written, applying creep hardening theories and empirical equations for creep, to aid in analysis of test data. Results are considered applicable to a variety of structures which are cyclicly exposed to creep producing thermal environments.

Davis, J. W.

Creep and creep rupture of strongly reinforced metallic composites

A creep and creep damage theory is presented for metallic composites with strong fibers. Application is to reinforced structures in which the fiber orientation may vary throughout but a distinct fiber direction can be identified locally (local transverse isotropy). The creep deformation model follows earlier work and is based on a flow potential function that depends on invariants reflecting stress and the material symmetry. As the focus is on the interaction of creep and damage, primary creep is ignored. The creep rupture model is an extension of continuum damage mechanics and includes an isochronous damage function that depends on invariants specifying the local maximum transverse tension and the maximum longitudinal shear stress. It is posited that at high temperature and low stress, appropriate to engineering practice, these stress components damage the fiber/matrix interface through diffusion controlled void growth, eventually causing creep rupture. Experiments are outlined for characterizing a composite through creep rupture tests under transverse tension and longitudinal shear. Application is made to a thin-walled pressure vessel with reinforcing fibers at an arbitrary helical angle. The results illustrate the usefulness of the model as a means of achieving optimal designs of composite structures where creep and creep rupture are life limiting.

Robinson, D. N.

Tensile creep and creep-recovery behavior of a SiC-fiber-Si3N4-matrix composite

The tensile creep and creep-recovery behavior of a hot-pressed unidirectional SiC-fiber/Si3N4-matrix composite was investigated at 1200 C in air, in order to determine how various sustained and cyclic creep loading histories would influence the creep rate, accumulated creep strain, and the amount of strain recovered upon specimen unloading. The data accumulated indicate that the fundamental damage mode for sustained tensile creep at stresses of 200 and 250 MPa was periodic fiber fracture and that the creep life and the failure mode at 250 MPa were strongly influenced by the rate at which the initial creep stress was applied. Cyclic loading significantly lowered the duration of primary creep and the overall creep-strain accumulation. The implications of the results for microstructural and component design are discussed.

Holmes, John W.

Long-Term Creep and Creep Rupture Behavior of Woven Ceramic Matrix Composites

Tensile creep behavior of SiC/SiNC ceramic matrix composites at elevated temperatures and at various stress levels have been investigated for turbine engine applications. The objective of this research is to present creep behavior of SiC/SiCN composites at stress levels above and below the monotonic proportional limit strength and predict the life at creep rupture conditions. Tensile creep-rupture tests were performed on an Instron 8502 servohydraulic testing machine at constant load conditions up to a temperature limit of 1000 C. Individual creep curves indicate three stages such as primary, secondary, and tertiary. The creep rate increased linearly at an early stage and then gradually became exponential at higher strains. The stress exponent and activation energy were also obtained at 700 and 1000 C. The specimen lifetime was observed to be 55 hrs at 121 MPa and at 700 C. The life span reduced to 35 hrs at 143 MPa and at 1000 C. Scanning electron microscopy observations revealed significant changes in the crystalline phases and creep damage development. Creep failures were accompanied by extensive fiber pullout, matrix cracking, and debonding along with fiber fracture. The creep data was applied to Time-Temperature-Stress superposition model and the Manson-Haferd parametric model for long-time life prediction.

Haque, A.

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.

Creep-rupture behavior of 6 candidate stirling engine iron-base superalloys in high pressure hydrogen. Volume 1: Air creep-rupture behavior

Four wrought alloys (A-286, IN 800H, N-155, and 19-9DL) and two cast alloys (CRM-6D and XF-818) were tested to determine their creep-rupture behavior. The wrought alloys were used in the form of sheets of 0.89 mm (0.035 in.) average thickness. The cast alloy specimens were investment cast and machined to 6.35 mm (0.250 in.) gage diameter. All specimens were tested to rupture in air at different times up to 3000 h over the temperature range of 650 C to 925 C (1200 F to 1700 F). Rupture life, minimum creep rate, and time to 1% creep strain were statistically analyzed as a function of stress at different temperatures. Temperature-compensated analysis was also performed to obtain the activation energies for rupture life, time to 1% creep strain, and the minimum creep rate. Microstructural and fracture analyses were also performed. Based on statistical analyses, estimates were made for stress levels at different temperatures to obtain 3500 h rupture life and time to 1% creep strain. Test results are to be compared with similar data being obtained for these alloys under 15 MPa (2175 psi) hydrogen.

Bhattacharyya, S.

Creep substructure formation in sodium chloride single crystals in the power law and exponential creep regimes

Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.

Raj, S. V.

Creep of Refractory Fibers and Modeling of Metal and Ceramic Matrix Composite Creep Behavior

Our concentration during this research was on the following subprograms. (1) Ultra high vacuum creep tests on 218, ST300 and WHfC tungsten and MoHfC molybdenum alloy wires, temperature range from 1100 K to 1500 K, creep time of 1 to 500 hours. (2) High temperature vacuum tensile tests on 218, ST300 and WHfC tungsten and MoHfC molybdenum alloy wires. (3) Air and vacuum tensile creep tests on polycrystalline and single crystal alumina fibers, such as alumina-mullite Nextel fiber, yttrium aluminum ganet (YAG) and Saphikon, temperature range from 1150 K to 1470 K, creep time of 2 to 200 hours. (4) Microstructural evaluation of crept fibers, TEM study on the crept metal wires, SEM study on the fracture surface of ceramic fibers. (5) Metal Matrix Composite creep models, based on the fiber creep properties and fiber-matrix interface zone formation.

Tewari, S.N.

Correlation of creep rate with microstructural changes during high temperature creep

The techniques of electron microscopy were used to examine the microstructural changes which occur during primary creep for two important types of engineering alloys: (1) alloys strengthened by solid-solution additions, and (2) dispersion-strengthened alloys. The metals chosen for study are unalloyed titanium, Ti-6Al-4V, and the cobalt-base alloy, Haynes 188. Results to date on NGR 47-004-108 show that development of prior dislocation substructure in Haynes 188 by 10% prestrain and annealing for one hour at 1800 F increases the time to reach 0.5% creep strain at 1600 F by more than an order of magnitude for creep stresses from 3 to 20 ksi. For creep at 1800 F, similar results were obtaind for stresses above 7 ksi, but the prior substructure decreases creep resistance below 7 ksi. This effect appears to be related to instability of grain structure at 1800 F in prestrained material.

Young, C. T.

Diffusional creep and creep-degradation in dispersion-strengthened Ni-Cr base alloys.

Dispersoid-free regions were observed in the dispersion-strengthened alloy TD-NiCr (Ni-20 Cr-2 ThO2) after slow strain rate testing (stress rupture, creep, and fatigue) in air from 1145 to 1590 K. Formation of the dispersoid-free regions appears to be the result of diffusional creep. The net effect of creep in TD-NiCr is the degradation of the alloy to a duplex microstructure. Creep degradation of TD-NiCr is further enhanced by the formation of voids and intergranular oxidation in the dispersoid-free bands. Void formation was observed after as little as 0.13% creep deformation at 1255 K. The dispersoid-free regions apparently provide sites for void formation and oxide growth since the strength and oxidation resistance of Ni-20 Cr-2 ThO2.

Whittenberger, J. D.

Prediction and verification of creep behavior in metallic materials and components for the space shuttle thermal protection system. Volume 2: Phase 2 subsize panel cyclic creep predictions

A method for predicting permanent cyclic creep deflections in stiffened panel structures was developed. The resulting computer program may be applied to either the time-hardening or strain-hardening theories of creep accumulation. Iterative techniques were used to determine structural rotations, creep strains, and stresses as a function of time. Deflections were determined by numerical integration of structural rotations along the panel length. The analytical approach was developed for analyzing thin-gage entry vehicle metallic-thermal-protection system panels subjected to cyclic bending loads at high temperatures, but may be applied to any panel subjected to bending loads. Predicted panel creep deflections were compared with results from cyclic tests of subsize corrugation and rib-stiffened panels. Empirical equations were developed for each material based on correlation with tensile cyclic creep data and both the subsize panels and tensile specimens were fabricated from the same sheet material. For Vol. 1, see N75-21431.

Cramer, B. A.

Diffusional creep and creep degradation in the dispersion-strengthened alloy TD-NiCr

Dispersoid-free regions were observed in TD-NiCr (Ni-20Cr-2ThO2) after slow strain rate testing in air from 1145 to 1590 K. Formation of the dispersoid-free regions appears to be the result of diffusional creep. The net effect of this creep is the degradation of TD-NiCr to a duplex microstructure. Degradation is further enhanced by the formation of voids and integranular oxidation in the thoria-free regions. These regions apparently provided sites for void formation and oxide growth since the strength and oxidation resistance of Ni-20Cr is much less than Ni-20Cr-2ThO2. This localized oxidation does not appear to reduce the static load bearing capacity of TD-NiCr since long stress rupture lives were observed even with heavily oxidized microstructures. But this oxidation does significantly reduce the ductility and impact resistance of the material. Dispersoid-free bands and voids were also observed for two other dispersion strengthened alloys, TD-NiCrAl and IN-853. Thus, it appears that diffusional creep is charactertistic of dispersion-strengthened alloys and can play a major role in the creep degradation of these materials.

Whittenberger, J. D.

Correlation of creep rate with microstructural changes during high temperature creep

Creep tests were conducted on Haynes 188 cobalt-base alloy and alpha titanium. The tests on Haynes 188 were conducted at 1600 F and 1800 F for stresses from 3 to 20 ksi, and the as-received, mill-annealed results were compared to specimens given 5%, 10%, and 15% room temperature prestrains and then annealed one hour at 1800 F. The tests on alpha titanium were performed at 7,250 and 10,000 psi at 500 C. One creep test was done at 527 C and 10,000 psi to provide information on kinetics. Results for annealed titanium were compared to specimens given 10% and 20% room temperature prestrains followed by 100 hours recovery at 550 C. Electron microscopy was used to relate dislocation and precipitate structure to the creep behavior of the two materials. The results on Haynes 188 alloy reveal that the time to reach 0.5% creep strain at 1600 F increases with increasing prestrain for exposure times less than 1,000 hours, the increase at 15% prestrain being more than a factor of ten.

Young, C. T.

Stochastic modeling of crack initiation and short-crack growth under creep and creep-fatigue conditions

A simplified stochastic model is proposed for crack initiation and short-crack growth under creep and creep-fatigue conditions. Material inhomogeneity provides the random nature of crack initiation and early growth. In the model, the influence of microstructure is introduced by the variability of: (1) damage accumulation along grain boundaries, (2) critical damage required for crack initiation or growth, and (3) the grain-boundary length. The probabilities of crack initiation and growth are derived by using convolution integrals. The model is calibrated and used to predict the crack density and crack-growth rate of short cracks of 304 stainless steel under creep and creep-fatigue conditions. The mean-crack initiation lives are predicted to be within an average deviation of about 10 percent from the experimental results. The predicted cumulative distributions of crack-growth rate follow the experimental data closely. The applicability of the simplified stochastic model is discussed and the future research direction is outlined.

Kitamura, Takayuki