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An analytical formula is developed to accurately represent the photoabsorption cross section of atomic Oxygen for all energies of interest in X-ray spectral modeling. In the vicinity of the K edge, a Rydberg series expression is used to fit R-matrix results, including important orbital relaxation effects, that accurately predict the absorption oscillator strengths below threshold and merge consistently and continuously to the above-threshold cross section. Further, minor adjustments are made to the threshold energies in order to reliably align the atomic Rydberg resonances after consideration of both experimental and observed line positions. At energies far below or above the K-edge region, the formulation is based on both outer- and inner-shell direct photoionization, including significant shake-up and shake-off processes that result in photoionization-excitation and double-photoionization contributions to the total cross section. The ultimate purpose for developing a definitive model for oxygen absorption is to resolve standing discrepancies between the astronomically observed and laboratory-measured line positions, and between the inferred atomic and molecular oxygen abundances in the interstellar medium from XSTAR and SPEX spectral models.

The interpretation of cosmic spectra relies on a vast sea of atomic data which are not readily obtainable from analytic expressions or simple calculations. Rather, their evaluation typically requires state-of-the-art atomic physics calculations, with the inclusion of weaker effects (spin-orbit and configuration interactions, relaxation, Auger broadening, etc.), to achieve the level of accuracy needed for use by astrophysicists. Our NASA-supported research program is focused on calculating data for three important atomic processes, 1) dielectronic recombination (DR), 2) inner-shell photoabsorption, and 3) fluorescence and Auger decay of inner-shell vacancy states. Some additional details and examples of our recent findings are given.

The Conventional Strainrange Partitioning (CSRP) method for High-Temperature, Low-Cycle Fatigue (HTLCF) life prediction has its origins in the modeling of first-order, creep-fatigue waveform effects while treating as second-order effects, the influence of metallurgical or environmental time dependencies. Procedures are proposed to include the latter explicitly in the inelastic strainrange-life relations. For brevity, only the CP life relation will be presented in detail. The exposure-time effect within the CP inelastic strainrange (tensile creep reversed by compressive plasticity) was determined by tensile stresshold-time experiments for 316 SS at 816 C. Reductions in CP cyclic life of a factor of about two were observed with an increase in exposure time or a corresponding decrease in creep rate by a factor of about 100. The CP life relation has been modified to be expressed in terms of either Steady State Creep Rate (SSCR) or Exposure Time (ET). The applicability and accuracy of the time-dependent CP life relations is demonstrated by conducting verification experiments involving complex hysteresis loops. Metallographic examination revealed time-dependent degradation attributable to oxide formation and precipitation of carbides along grain boundaries.

The Conventional Strainrange Partitioning (CSRP) method for High-Temperature, Low-Cycle Fatigue (HTLCF) life prediction has its origins in the modeling of first-order, creep-fatigue waveform effects while treating as second-order effects, the influence of metallurgical or environmental time dependencies. Procedures are proposed to include the latter explicitly in the inelastic strainrange--life relations. For brevity, only the CP life relation will be presented in detail. The exposure-time effect within the CP inelastic strainrange (tensile creep reversed by compressive plasticity) was determined by tensile stresshold-time experiments for 316 SS at 816 C. Reductions in CP cyclic life of a factor of about two were observed with an increase in exposure time or a corresponding decrease in creep rate by a factor of about 100. The CP life relation has been modified to be expressed in terms of either Steady State Creep Rate (SSCR) or Exposure Time (ET). The applicability and accuracy of the time-dependent CP life relations is demonstrated by conducting verification experiments involving complex hysteresis loops. Metallographic examination revealed time-dependent degradation attributable to oxide formation and precipitation of carbides along grain boundaries.

Procedures based on modification of the conventional Strainrange Partitioning method are proposed to characterize the time-dependent degradation of engineering alloys in high-temperature, low-cycle fatigue. Creep-fatigue experiments were conducted in air using different waveforms of loading on 316 stainless steel at 816 C (1500 F) to determine the effect of exposure time on cyclic life. Reductions in the partitioned cyclic lives were observed with an increase in the time of exposure (or with the corresponding decrease in the steady-state creep rate) for all the waveforms involving creep strain. Excellent correlations of the experimental data were obtained by modifying the Conventional Strainrange Partitioning life relationships involving creep strain using a power-law term of either: (1) time of exposure, or (2) steady-state creep rate of the creep-fatigue test. Environmental degradation due to oxidation, material degradation due to the precipitation of carbides along the grain boundaries and detrimental deformation modes associated with the prolonged periods of creep were observed to be the main mechanisms responsible for life reductions at long exposure times.

A common method of treating the mean stress effect on fatigue life is to displace the elastic line on a Manson-Coffin-Basquin diagram while retaining the position of the plastic line. Manson and Halford pointed out that this procedure implies that mean stress significantly affects the cyclic stress-strain curve. Actually, however, they showed experimentally and by more general reasoning, that mean stress has little, if any, effect on the cyclic stress-strain curve. Thus, they concluded that it is necessary to displace the plastic line as well as the elastic line in order to keep the cyclic stress-strain curve unaltered. Another way to express the common displacement of the two lines is to keep the lines in place and change the horizontal coordinate to include a term relating to the displacement. Thus, instead of life, 2N sub f, as the horizontal coordinate, a new coordinate can become 2N sub f (1-sigma sub m/sigma sub f) superscript 1/b, thereby displacing both the elastic and plastic lines by an amount (1-sigma sub m/sigma sub f) superscript 1/b where sigma sub m is the mean stress and sigma sub f is the intercept of the elastic line at N sub f = 1/2 cycles and b is the slope of the elastic line.

A method which has evolved in our laboratories for the past 20 yr is re-examined with the intent of improving its accuracy and simplicity of application to engineering problems. Several modifications are introduced both to the analytical formulation of the Damage Curve Approach, and to the procedure for modifying this approach to achieve a Double Linear Damage Rule formulation which immensely simplifies the calculation. Improvements are also introduced in the treatment of mean stress for determining fatigue life of the individual events that enter into a complex loading history. While the procedure is completely consistent with the results of numerous two level tests that have been conducted on many materials, it is still necessary to verify applicability to complex loading histories. Caution is expressed that certain phenomena can also influence the applicability - for example, unusual deformation and fracture modes inherent in complex loading - especially if stresses are multiaxial. Residual stresses at crack tips, and metallurgical factors are also important in creating departures from the cumulative damage theories; examples of departures are provided.

A method which has evolved in the laboratories for the past 20 yr is re-examined with the intent of improving its accuracy and simplicity of application to engineering problems. Several modifications are introduced both to the analytical formulation of the Damage Curve Approach, and to the procedure for modifying this approach to achieve a Double Linear Damage Rule formulation which immensely simplifies the calculation. Improvements are also introduced in the treatment of mean stress for determining fatigue life of the individual events that enter into a complex loading history. While the procedure is completely consistent with the results of numerous two level tests that have been conducted on many materials, it is still necessary to verify applicability to complex loading histories. Caution is expressed that certain phenomenon can also influence the applicability - for example, unusual deformation and fracture modes inherent in complex loading especially if stresses are multiaxial. Residual stresses at crack tips, and metallurgical factors are also important in creating departures from the cumulative damage theories; examples of departures are provided.

Treatment of accumulated fatigue damage in materials and structures subjected to a history of nonsimple repetitive loadings has received a large amount of attention in recent years. A method used for the treatment of complex loading is known as linear damage rule. It was recognized that, this method could result in unconservative predictions of material and structural behavior. An intense flurry of activity followed in the pursuit of alternative methods of analysis that would predict behavior more accurately. So many methods were introduced that it became necessary periodically to prepare review papers placing all the new methods into perspective. The current integrated view regarding the state of the art as it applies to this effort is discussed. The more recently proposed cumulative damage life prediction methods are reviewed. The double linear damage rule (DLDR), which has evolved over the past 20 years, is reexamined with the intent of improving its accuracy and applicability to engineering problems. Modifications are introduced to the analytical formulation to achieve greater compatibility between the DLDR and the so-called damage curve approach, which is an alternative continuous representation of the DLDR.

Double Linear Damage Rule (DLDR) method for use by structural designers to determine fatigue-crack-initiation life when structure subjected to unsteady, variable-amplitude cyclic loadings. Method calculates in advance of service how many loading cycles imposed on structural component before macroscopic crack initiates. Approach eventually used in design of high performance systems and incorporated into design handbooks and codes.

The effect of exposure time (or creep rate) on the CP life relationship is established by conducting isothermal CP tests at varying exposure times on 316 Ss at 1300 and 1500 F. A reduction in the CP cycle life is observed with an increase in the exposure time of the CP test at a given inelastic strain-range. This phenomenon is characterized by modifying the Manson-Coffin type of CP relationship. Two new life relationships: (1) the Steady State Creep Rate (SSRC) Modified CP life relationship, and (2) the Failure Time (FT) Modified CP life relationship, are developed in this report. They account for the effect of creep rate and exposure time within the CP type of waveform. The reduction in CP cyclic life in the long exposure time tests is attributed to oxidation and the precipitation of carbides along the grain boundaries.

Creep rate in compression is lower by factors of 2 to 10 than in tension if the microstructure of the two specimens is the same and are tested at equal temperatures and equal but opposite stresses. Such behavior is characteristic for monotonic creep and conditions involving cyclic creep. In the latter case creep rate in both tension and compression progressively increases from cycle to cycle, rendering questionable the possibility of expressing a time stabilized constitutive relationship. The difference in creep rates in tension and compression is considerably reduced if the tension specimen is first subjected to cycles of tensile creep (reversed by compressive plasticity), while the compression specimen is first subjected to cycles of compressive creep (reversed by tensile plasticity). In both cases, the test temperature is the same and the stresses are equal and opposite. Such reduction is a reflection of differences in microstructure of the specimens resulting from different prior mechanical history.

A formula is derived for combining effects of successive hysteresis loops in the creep range of materials when one loop has excess tensile creep, while the other contains excess compressive creep. The resultant effect resembles single loops involving balanced tensile and compressive creep. The attempt to use the Interaction Damage Rule as a tool in combining loops of non-equal size and complex strainrange content has led to important new concepts useful in future studies of creep-fatigue. It turns out that the Interaction Damage Rule is basically an expression of how a set of hysteresis loops involving only single generic strains can combine to produce the same micromechanistic damage as the loop containing the combined strainranges which it analyzes. Making use of the underlying concept of Strainrange Partitioning that only the strainrange content of a hysteresis loop governs fatigue life, not order of introducing strainranges, a rational derivation of the Interaction Damage Rule is provided, showing also how it can effectively be used to synthesize independent loops and determine both damaging and healing effects.

Creep-fatigue-environment interaction is discussed using the 'strainrange partitioning' (SRP) framework as a basis. The four generic SRP strainrange types are studied with a view of revealing differences in micromechanisms of deformation and fatigue degradation. Each combines in a different manner the degradation associated with slip-plane sliding, grain-boundary sliding, migration, cavitation, void development and environmental interaction; hence the approch is useful in delineating the relative importance of these mechanisms in the different loadings. Micromechanistic results are shown for a number of materials, including 316 SS, wrought heat resistant alloys, several nickel-base superalloys, and a tantalum base alloy, T-111. Although there is a commonality of basic behavior, the differences are useful in delineation several important principles of interpretation. Some quantitative results are presented for 316 SS, involving crack initiation and early crack growth, as well as the interaction of low-cycle fatigue with high-cycle fatigue.

After pointing out many of the complexities that attend high temperature metal fatigue beyond those already studied in the sub-creep range, a description of the micromechanisms of deformation and fracture is presented for several classes of materials that were studied over the past dozen years. Strainrange Partitioning (SRP) is used as a framework for interpreting the results. Several generic types of behavior were observed with regard both to deformation and fracture and each is discussed in the context of the micromechanisms involved. Treatment of cumulative fatigue damage and the possibility of ""healing'' of damage in successive loading loops, has led to a new interpretation of the Interaction Damage Rule of SRP. Using the concept of ""equivalent micromechanistic damage'' -- that the same damage on a microscopic scale is induced if the same hysteresis loops are generated, element for element -- it turns out the Interaction Damage Rule essentially compounds a number of variants of hysteresis loops, all of which have the same damage according to SRP concepts, into a set of loops each containing only one of the generic SRP strainranges. Thus the damage associcated with complex loops comprising several types of strainrange is analyzed by considering a combination of loops each containing only one type of strainrange. This concept is expanded to show how several independent loops can combine to ""heal'' creep damage in a complex loading history.

Bending fatigue in the low cyclic life range differs from axial fatigue due to the plastic flow which alters the linear stress-strain relation normally used to determine the nominal stresses. An approach is presented to take into account the plastic flow in calculating nominal bending stress (S sub bending) based on true surface stress. These functions are derived in closed form for rectangular and circular cross sections. The nominal bending stress and the axial fatigue stress are plotted as a function of life (N sub S) and these curves are shown for several materials of engineering interest.

It is demonstrated that creep rate of 316 SS is lower by factors of 2 to 10 in compression than in tension if the microstructure is the same and tests are conducted at identical temperatures and equal but opposite stresses. Such behavior was observed for both monotonic creep and conditions involving cyclic creep. In the latter case creep rate in both tension and compression progressively increases from cycle to cycle, rendering questionable the possibility of expressing a time-stabilized constitutive relationship. The difference in creep rates in tension and compression is considerably reduced if the tension specimen is first subjected to cycles of tensile creep (reversed by compressive plasticity), while the compression specimen is first subjected to cycles of compressive creep (reversed by tensile plasticity). In both cases, the test temperature is the same and the stresses are equal and opposite. Such reduction is a reflection of differences in microstructure of the specimens resulting from different prior mechanical history.

Starting with the basic fatigue lift formula, an inversion formula is derived. The inversion formula is valid over the entire life range of engineering interest for all materials examined. Conformity between the two equations is extremely close, suitable for all engineering problems. The approach used to invert the life relation is also suitable for the inversion of other formulas involving the sum of two power-law terms.

Simple procedures are given for treating cumulative fatigue damage under complex loading history using either the damage curve concept or the double linear damage rule. A single equation is given for use with the damage curve approach; each loading event providing a fraction of damage until failure is presumed to occur when the damage sum becomes unity. For the double linear damage rule, analytical expressions are given for determining the two phases of life. The procedure comprises two steps, each similar to the conventional application of the commonly used linear damage rule. Once the sum of cycle ratios based on Phase I lives reaches unity, Phase I is presumed complete, and further loadings are summed as cycle ratios based on Phase II lives. When the Phase II sum attains unity, failure is presumed to occur. It is noted that no physical properties or material constants other than those normally used in a conventional linear damage rule analysis are required for application of either of the two cumulative damage methods described. Illustrations and comparisons are discussed for both methods.

This paper describes the applicability of the method of Strainrange Partitioning to the life prediction of thermal-mechanical strain-cycling fatigue. An in-phase test on 316 stainless steel is analyzed as an illustrative example. The observed life is in excellent agreement with the life predicted by the method using the recently proposed Step-Stress Method of experimental partitioning, the Interaction Damage Rule, and the life relationships determined at an isothermal temperature of 705 C. Implications of the present study are discussed relative to the general thermal fatigue problem.

Two methods are presented for separating the inelastic strain components of a complex hysteresis loop so that Strainrange Partitioning formulas can be applied to accurately determine cyclic life at elevated temperatures. These methods are required only if lower bounds established by Strainrange Partitioning concepts have been deemed inadequate in the establishment of expected lifetime. In one method rapid loading and unloading is applied in the tensile and compressive half to isolate the plastic strain. In the second method the 'creep' is measured at a discrete number of points along the hysteresis loop by combining load-control tests into the general pattern of strain cycling under arbitrary temperature. Both methods are shown to give good results.

A summary of the angular momentum transfer formulation of the differential photoionization cross section is presented and photoionization amplitudes in LS coupling are considered. The application of the theoretical concepts and relations developed is illustrated with the aid of an example involving the calculation of the angular distribution of photoelectrons ionized from atomic sulfur according to a certain reaction. The investigation shows that anisotropic electron-ion interactions in atomic sulfur lead to measurable differences between photoelectron angular distribution asymmetry parameters corresponding to alternative ionic term levels.

The applicability is described of the method of Strainrange Partitioning to the life prediction of thermal-mechanical strain-cycling fatigue. An in-phase test on 316 stainless steel is analyzed as an illustrative example. The observed life is in excellent agreement with the life predicted by the method using the recently proposed Step-Stress Method of experimental partitioning, the Interation Damage Rule, and the life relationships determined at an isothermal temperature of 705 C. Implications of the study are discussed relative to the general thermal fatigue problem.

Two methods are presented for separating the inelastic strain components of a complex hysteresis loop so that strainrange partitioning formulas can be applied to accurately determine cyclic life at elevated temperatures. These methods are required only if lower bounds established by strainrange partitioning concepts have been deemed inadequate in the establishment of expected lifetime. In one method, rapid loading and unloading is applied in the tensile and compressive half to isolate the plastic strain. In the second method, the creep is measured at a discrete number of points along the hysteresis loop by combining load-control tests into the general pattern of strain cycling under arbitrary temperature. Both methods are shown to give good results.

The angular distributions of photoelectrons from atomic oxygen, nitrogen, and carbon are calculated. Both Hartree-Fock and Hartree-Slater (Herman-Skillman) wave functions are used for oxygen, and the agreement is excellent; thus only Hartree-Slater functions are used for carbon and nitrogen. The pitch-angle distribution of photoelectrons is discussed, and it is shown that previous approximations of energy-independent isotropic or sin squared theta distributions are at odds with the authors' results, which vary with energy. This variation with energy is discussed, as is the reliability of these calculations.

A summary of papers is presented which covers the following broad aspects of high temperature metal fatigue: (1) materials development and characterization; (2) environmental factors, including air, vacuum, helium, iodine, sodium, and radiation environments; (3) general fatigue life relationships; (4) crack growth laws; (5) design code activities; and (6) design and service experience. Illustrative tables accompany the summary.

Expressions are given for atomic photoelectron angular distributions in LS coupling in which the role of anisotropic final state electron-ion interactions emerges explicitly. Calculations of photoelectron angular distributions for atomic sulfur are presented in which these anisotropic interactions produce clear deviations from the predictions of the Cooper-Zare model. Such effects are expected to be a general feature of photoelectron angular distributions for most open-shell atoms.

The angular distribution of photoelectrons from atomic oxygen is investigated using Hartree-Fock (HF) wave functions. The correct formulation is used to compare HS and HF results. Agreement between these results is good and the HS calculations have been extended to atomic nitrogen and carbon as well.

The photoelectron asymmetry parameter beta in LS-coupling is obtained as an expansion into contributions from alternative angular momentum transfers j sub t. The physical significance of this expansion of beta is shown to be that: (1) the electric dipole interaction transfers to the atom a charcteristic single angular momentum j sub t = sub o, where sub o is the photoelectron's initial orbital momentum; and (2) angular momentum transfers indicate the presence of anisotropic interaction of the outgoing photoelectron with the residual ion. For open shell atoms the photoelectron-ion interaction is generally anisotropic; photoelectron phase shifts and electric dipole matrix elements depend on both the multiplet term of the residual ion and the total orbital momentum of the ion-photoelectron final state channel. Consequently beta depends on the term levels of the residual ion and contains contributions from all allowed values of j sub t. Numerical calculations of the asymmetry parameters and partial cross sections for photoionization of atomic sulfur are presented.

Expressions are given for atomic photoelectron angular distributions in LS coupling in which the role of anisotropic final state electron-ion interactions emerges explicitly. Calculations of photoelectron angular distributions for atomic sulfur are presented in which these anisotropic interactions produce pronounced deviations from the predictions of the Cooper-Zare model. Such effects are expected to be a general feature of photoelectron angular distributions for most open shell atoms.

Strainrange Partitioning provides unifying framework for characterizing high-temperature, low-cycle, creep-fatigue properties of metals and alloys. Method offers distinct advantage to designers of immediately providing reliable upper and lower bounds on cyclic life for any type of inelastic strain cycle that may be encountered in service.

Simple procedures are presented for treating cumulative fatigue damage under complex loading history using either the damage curve concept or the double linear damage rule. A single equation is provided for use with the damage curve approach; each loading event providing a fraction of damage until failure is presumed to occur when the damage sum becomes unity. For the double linear damage rule, analytical expressions are provided for determining the two phases of life. The procedure involves two steps, each similar to the conventional application of the commonly used linear damage rule. When the sum of cycle ratios based on phase 1 lives reaches unity, phase 1 is presumed complete, and further loadings are summed as cycle ratios on phase 2 lives. When the phase 2 sum reaches unity, failure is presumed to occur. No other physical properties or material constants than those normally used in a conventional linear damage rule analysis are required for application of either of the two cumulative damage methods described. Illustrations and comparisons of both methods are discussed.

Systems studies and critical technology issues for the development and evaluation of Satellite Power Systems (SPS) for the photovoltaic generation of electrical energy and its transmission to earth are reviewed. Initial concept studies completed in 1976 and system definition studies initiated in the same year have indicated the technical feasibility of SPS and identified challenging issues to be addressed as part of the SPS Concept Development and Evaluation Program. Systems considered in the study include photovoltaic and solar thermal power conversion configurations employing klystron or solid state microwave generators or lasers for power transmission, and power transmission options, system constructability and in-orbit and ground operations. Technology investigations are being performed in the areas of microwave power transmission, structure/controls interactions and the behavior of key materials in the space/SPS environment. Favorable results have been obtained in the areas of microwave phase distribution and phase control, dc-RF conversion, antenna radiating element, and no insurmountable problems have been discovered in any of the investigations to date.

The paper concentrates on three subjects: (1) further development of the double-linear damage rule for cumulative fatigue damage summation in the sub-creep temperature range; (2) a new consideration of the effect of strain reversals in the creep range of materials, whereby reversals that occur later in the histogram can influence the degree of damage caused by earlier loading events; and (3) the application of the minimum-commitment time-temperature parameter to the treatment of creep rupture of multiheats wherein considerable differences in properties of individual heats may occur. Numerical examples and plots are given.

Developments in the analysis of creep-rupture data are reviewed with particular reference to time temperature relations for the correlation and extrapolation of creep and stress rupture data, the minimum commitment method, and successive regression methods. Some contributions to the development of time-temperature parameters are noted.

The paper presents closed-form solutions (collocation method and spline-function method) for the constants of the cyclic fatigue life equation so that they can be easily incorporated into cumulative damage analysis. The collocation method involves conformity with the experimental curve at specific life values. The spline-function method is such that the basic life relation is expressed as a two-part function, one applicable at strains above the transition strain (strain at intersection of elastic and plastic lines), the other below. An illustrative example is treated by both methods. It is shown that while the collocation representation has the advantage of simplicity of form, the spline-function representation can be made more accurate over a wider life range, and is simpler to use.

This report summarizes various aspects of predictive approaches in high cycle fatigue, hcf. The distinction between hcf and low cycle fatigue, lcf, is discussed in relation to the transition life and strainrange, and curves are presented to establish regions wherein each range predominates depending on the properties of any material of interest. The role of loading order on hcf in cumulative damage analysis is also discussed, together with mean stress effects and their relaxation. Also briefly discussed are high temperature fatigue and ultra-high cycle fatigue.

The effects of frequency, stress and strain hold periods, stress and strain ramping, creep-fatigue interspersion, and thermomechanical cycling were studied. Of special interest was the establishment of a set of universalized life relations which were normalized by the ductility of the material. These relations together with a set of rules that were devised for treating multiaxiality by the method, were, for example, useful in predicting torsion behavior, and in particular in establishing a new relationship between torsion and tension that had previously not been considered. They also were useful in the development of a framework for treatment of environmental effects.

An outline is presented of approaches for treating multiheats on the basis of the focal point convergence method. The method has been employed in the case of two highly characterized multiheats, including a 304 stainless steel studied in Japan and a low alloy carbon steel studied in England. The method makes use of the same functional form for all materials. Only the constants are varied for each multiheat. Completely computerized procedures are employed for the determination of the constants. Once the basic analysis has been performed, the representation of various members in the same system is achieved by adding linear expressions of log stress, changing only two constants in the equations to represent a selected heat.

The minimum commitment method has been applied to the analysis of creep-rupture data. The method is based on a parameter representing the focal point of convergence of all isothermals when extended to the long or short times necessary for such convergence to occur. The technique may be applied by manual-graphic analysis on computer code. It is illustrated for the nickel-base alloy Astroloy.

An outline is presented of a new procedure, termed the oblique translation method, which emerged in the development of the focal point convergence method. Approaches for implementing the oblique translation method are discussed. It is shown that the new method is essentially a minimum commitment method when manually-graphically implemented, in the sense that the form of the functions involved are not forced into particular analytical forms. The individual constants and functions are independently determined. The minimum commitment concept is extended to the analysis of creep rupture data wherein each isothermal is to be generated by an oblique translation of the 'master curve' when plotted. Attention is given to a manual-graphical analysis, the preassessment of data, and an analysis by computer code.

The Minimum Commitment Method was applied to two sets of data for which multiple heat information was available. For one alloy, a 304 stainless steel studied in Japan, data on nine well characterized heats were used, while for a proprietary low alloy carbon steel studied in the United Kingdom data were available on seven heats - in many cases to very long rupture times. For this preliminary study no instability factors were used. It was discovered that heat-to-heat variations would be accounted for by introducing heat identifiers in the form A + B log sigma where sigma is the stress and the constants A and B depend only on the heat. With these identifiers all the data could be collapsed onto a single master curve, even though there was considerable scatter among heats. Using these identifiers together with the average behavior of all heats made possible the determination of an accurate constitutive equation for each individual heat. Two basic approaches are discussed for applying the results of the analysis.

The framework in which minimum-commitment analyses of creep-rupture data can be implemented is outlined. The approach is termed the focal point convergence method (FPCM) because the basic parameter A, also known as stability factor, is geometrically the (imaginary) focal point of convergence of all isothermals when extended to the very long or very short times necessary for such convergence to occur. The method can be implemented either by manual-graphical analysis or by computer code. The method is illustrated in detail for the nickel-base alloy Astroloy, as well as for steels, other nickel-base alloys, and aluminum alloys. The minimum-commitment concept is extended to the analysis of creep-rupture data where each isothermal is generated by an oblique translation of the 'master curve' when plotted on log rupture time and log stress axes. The oblique translation method uses the same types of functions in the FPCM. Approaches for treating multiheats on the basis of the FPCM are discussed in detail.

A procedure for treating creep-fatigue for low strainranges and long hold times is outlined. A semi-experimental approach, wherein several cycles of the imposed loading is actually applied to a specimen in order to determine the stable hysteresis loop, can be very useful in the analysis. Because such tests require only a small fraction of the total failure time, they are not inherently prohibitive if experimental equipment is available. The need for accurate constitutive equations is bypassed because the material itself acts to translate the imposed loading into the responsive hysteresis loops. When strainrange partitioning has been applied in such cases very good results have been obtained.

The strainrange partitioning concept divides the imposed strain into four basic ranges involving time-dependent and time-independent components. It is shown that some of the results presented at the symposium can be better correlated on the basis of this concept than by alternative methods. It is also suggested that methods of data generation and analysis can be helpfully guided by this approach. Potential applicability of the concept to the treatment of frequency and hold-time effects, environmental influence, crack initiation and growth, thermal fatigue, and code specifications are briefly considered. A required experimental program is outlined.

Examination is made of the influence of temperature on the strainrange partitioning approach to creep-fatigue. Results for Cr-Mo steel and Type 316 stainless steel show the four partitioned strainrange-life relationships to be temperature insensitive to within a factor of two on cyclic life. Monotonic creep and tensile ductilities were also found to be temperature insensitive to within a factor of two. The approach provides bounds on cyclic life that can be readily established for any type of inelastic strain cycle. Continuous strain cycling results obtained over a broad range of high temperatures and frequencies are in excellent agreement with bounds provided by the approach. The observed transition from one bound to the other is also in good agreement with the approach.

Metal and polymer matrix materials research based on stringent requirements for thermal reactors, jet engines and space vehicles, discussing tests and analysis methods

Creep-fatigue analysis by strain range partitioning, considering metals inelastic deformation at high temperature due to plastic flow