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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

Creep rupture data analysis model based on minimum commitment station function approach, generalizing hypothesized time temperature stress relation

Collection of theoretical and experimental studies covering basic mechanisms of fatigue in the subcreep and creep ranges, fatigue damage detection, field practices for fatigue damage repair in jet engine components, and fatigue damage avoidance and control. Individual items are abstracted in this issue.

The framework of a new method is outlined for treating creep-fatigue behavior of metals. Inelastic strain-ranges are partitioned into the components of (1) completely reversed plasticity, (2) tensile plasticity reversed by compressive creep, or tensile creep reversed by compressive plasticity, and (3) completely reversed creep. Each of these components is shown to be related to cyclic life by a Manson-Coffin type power-law equation. A linear life fraction rule is used to combine the damaging effects of the individual components enabling the prediction of life. Test results are presented for a 2.25 Cr-1 Mo steel as well as limited information for a Type 316 stainless steel.

A summary is presented of various methods available to the engineer for dealing with fatigue problems. Design, metallurgical, and service factors are considered. An attempt is made to provide a rational basis for each approach, resorting in each case to an understanding of the fundamental mechanism of the fatigue process.

Strain range components and creep fatigue behavior of metals related independently to cyclic life by equations in both tension and compression

Specialized model for analysis of creep-rupture data by minimum commitment, station function approach with general time-temperature-stress relation to include all commonly used parameters

Thermal stress and thermal fatigue data for utilization in design problems

High temperature low cycle fatigue estimation from known static tensile and creep-rupture properties at temperature involved

Metal alloys high temperature low cycle strain fatigue resistance in creep range estimated from tensile and stress rupture data

Fatigue life for high temperature reversed strain cycling estimated in first approximation from static tensile and creep rupture properties

High temperature low cycle creep range strain fatigue behavior estimation from tensile and stress rupture properties

Low cycle fatigue of notched steel and aluminum alloy specimens by consideration of crack initiation and propagation

Mechanical properties used to estimate low cycle fatigue behavior in creep range of components in high-temperature systems

Cumulative metal fatigue damage predicted by double linear damage rule with formulas for crack formation and propagation

Method for estimating high temperature low cycle fatigue behavior of materials

Double linear damage rule used in conjunction with crack initiation and propagation equations, applied to cumulative fatigue damage

Crack initiation and propagation formula through fatigue process applied to interface problems, noting creep

Cycles required to start crack, and cycles for crack propagation to failure estimated for notched specimen

Fatigue in quasi-brittle materials, fatigue in creep range at elevated temperatures and cumulative fatigue damage

Text on thermal stress and low-cycle fatigue covering elastic stresses, plastic flow and creep, stress cycling, etc