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

Halford, G. R.

Manson, S. S.

English

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LIFE PREDICTION OF THERMAL-MECHANICAL FATIGUE
USING STRAINRANGE PARTITIONING
by G. R. Halford
Lewis Research ^ e lter
Cleveland, Ohio 44135
and
S. S. Manson
Case Western Reserve University
Cleveland, Ohio 44106
TECHNICAL PAPER to be presented at the Symposium on Thermal
Fatigue of Materials and Components, spuasored by the
American Society for Testing and Materials,	
^^^,Lo^3^31 1 Z^ys
New Orleans, Louisiana, November 17-18, 1975
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_LIFE PREDICTION OF THERMAL-MECHANICAL FATIGUE USING
STRAINRANGE PARTITIONING
by
G. R. Halford, Lewis Research Center, Cleveland, Ohio
SO
"D
	
and
S. S. Manson, Case Western Reserva University, Cleveland, Ohio
ABSTRACT: 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 parti-
tioning, the Interaction Damage Rule, and the life relationships
determined at an isothermal temperature of 705 0 C. Implications
of the present_ study are discussed relative to the general thermal
fatigue problem.
KEY WORDS: thermal fatigue, intergranular fracture, plastic
strain, creep strain, life prediction., strainrange partitioning,
stainless steel
Several of the papers at this Symposium relate to fatigue
data obtained under thermal-mechanical strain-cycling involving
the simultaneous independent variation of both strain and temper-
ature Recently, we have been studying a method for treating high-
temperature fatigue which we feel is very well suited to such
problems. We have termed the method Strainrange Partitioning
i	 ^	 I
r	 ,
i
2
because it involves the partitioning of the inelastic strainrange
imposed daring the cycle into from one to four generic strain-
ranges. These are associated with the manner in which "creep"
and "plasticity" interact during the tensile and compressive halves
of the cycle. Several features of the method are of special
advantage In. the treatment of thermal-mechanical cycling. The
purpose of this paper is briefly to summarize these features, and
to illustrate by an example how the method is applied.
SPECIAL FEATURES OF THE STRAINRANGE PARTITIONING METHOD
The method has been described in references (1-4)*. Therefore
the full description of the principles involved and the procedures
to be followed will not be repeated here. However, to place the
method in proper perspective in relation to the analysis of thermal-
mechanical cycling of interest to this Symposium, it is relevant
to summarize several features of the method.
The basic procedure involves the partitioning of the hysteresis
loop into its creep and plasticity components in both the tensile
and compressive halves of the cycle. From these components, the
generic strainranges, Ac 
pp, 
AE PC AEcp , and A c cccan be readily cal-
culated, where,
AC 
pp= 
tensile plastic strain that is balanced by compressive
plastic strain
AE PC= tensile plastic strain that is balanced by compressive
creep strain
*Numbers in parenthesis refer to the list of references appended
to this paper.
3AE Cp tensile creep strain that is balanced by compressive
plastic strain
AC CC tensile creep strain that is balanced by compressive
creep strain.
Methods for conveniently carrying out the partitioning
process have recently been developed (4). Although the application
in the past has been for isothermal straining, the same procedures
can readily be applied when the temperature is changing during the
cycle, as will be discussed later in the paper, While the method
can be used to treat a variety of high temperature fatigue prob-
lems, it contains several features that are especially attractive
in relation to thermal-mechanical applications:
a) Accounts for Details of Cycle, Including Compressive Stress
A special aspect of Strainran;e Partitioning that is relevant
to the subject of thermal fatigue analysis is that it is possible
to distinguish between the severity of the different types of
strainranges that can commonly be generated during such cycling.
For example, if the strain is "in-phase" with the temperature
(rising tensile strain while temperature is increasing), the
strainrange will likely include a AC cp component, "Out-of-phase"
cycling (rising compressive strain with increases in temperature)
is conducive to the development of a Ae pc component of strain-
range. In no case can a cycle include both a AC cp and a Ac PC
component. Since the method associates different effects with
each of these strainrange types, it not only provides a means for
recognizing the importance of the compressive portion of the cycle
4(which some alternative methods do not, for example, that cur-
rently specified by the ASME Boiler and Pressure Vessel Code Case
1592 (5)), but it also provides a basis for distinguishing between
the details of the cycle that can have effects on fatigue life.
b) Avoids Ambiguity Regarding Effect of `.;mperature on Life
Relations
Once the hysteresis loop has been partitioned, and the
pertinent components of strainranges Acpp , oecc and Accp or Acpc
determined, the method makes use of an Interaction Damage Rule (2)
to combine the effects of two or three strainranges present. In
applying the rule, the life relations for each component strain-
range become the important material characterization parameters.
It has been found thaT for 316 stainless steel (and 2 1/4 Cr-1 Mo
steel) the life relationships are essentially independent of
temperature (3). This feature bestows a distinct advantage to the
method because it removes the ambiguity "f determining which
temperature within the spectrum covered by temperature variation
throughout the cycle is the important one for the choice of
pertinent life relation. Of course, temperature is in itself
important, because the temperature not only governs the strain-
range imposed, but it influences how much of the imposed strain-
range is absorbed as Ac 
pp, 
Acpc , Oc cp and Ac cc . The higher the
temperature, the more likely an input inelastic strain is absorbed
as creep rather than as plasticity. But for a given magnitude and
type of strainrange, the life is essentially independent of the
temperature.
i
5c) Provides Upper and Lower Bounds on Life
The method lends itself especially well to the determination
of bounding values on life. Thus, once the strainrange is known,
a lower bound on cyclic life can be obtained by assuming that all
of the strainrange present is of the most damaging type (for most
materials, Accp , but for some, ocpc ). An upper bound on life can
likewise be determined by assuming that the entire strainrange is
of the most benign type (Ac pp ). If the bounding values are
acceptable, a detailed analysis to determine the actual hysteresis
loops and to partition them in detail becomes unnecessary; if not,
the need for a more detailed study is indicated. This feature
had special merit to designers who may wish to apportic design
effort according to the needs of a particular situation, rather
than making detailed analyses. It is also of special value to
Code bodies in specifying under what conditions minimal analyses
will be required (i.e., when the most pessimistic estimate of
life associated with the lower bound can be tolerated), and when
detailed analyses are needed (i.e., when the designer is motivated
to take full advantage of the potential life of the part).
AN EXAMPLE ANALYSIS
As a demonstration of the applicability of the method of
Strainrange Partitioning to the thermal-mechanical strain-cycling
problem, an axially loaded tubular test specimen as described in
Ref. (6) was subjected to the test listed in Table I.
The cyclic test was interrupted occasionally throughout its
life of 307 cycles to failure in order to apply the Step-Stress
6Method (4) to partition the creep and plastic strain. A hyster-
esis loop, typical of the stabilized thermal-mechanical condition,
is reproduced in Fig. 1 showing the selected step-stress levels
(points C through K of loop A through K). The temperature is at
a peak of 7600 C at point G and is at a minimum of 230 0 C at
point A.
S ,:ep-Stress Partitioning
The partitioning procedure followed is to halt temporarily
the temperature and strain programmers at a Celected point such
as C, switch the servo-controller from strain to load control
and hold the stress and temperature constant at the stabilized
values associated with point C while the creep strain is measured
as a function of time. This condition is held until a steady-
state creep rate can be established. At point C', the controller
is switched back to strain control and the strain and temperature
programs are resumed. Before stopping at the next :step-stress
level, the hysteresis loop is restabilized by tra-versing another
one or two cycles,
From the creep rate information measured at the various
stress and temperature levels, a plot is made of the steady-state
creep rate versus time for one complete cycle. Figure 2 was
constructed for the cycle of interest. The integrated area under
the steady-state creep rate versus time curve is equal to the
steady-state creep strain accumulated within the cycle. Fol-
lowing the suggestion of Ref. (4), the steady-state creep strain
is taken as the significant "creep" strain and all of the other
7i
I
inelastic strain is considered to be "plastic". For the case at
hand, the compressive steady state creep strain is 0.00006. Since
the compressive inelastic strain is 0.00616 and the creep strain
is 0,00006, the plastic strain in compression is 0.00610. Sim-
ilarly, the tensile creep strain from Fig. 2 is 0.00145 and the
compressive plastic strain is 0.00471, Hence, the partitioned
strainranges (1) are:
AC 
pp V"
	
AE cc = 0.00006, AE cp 	0.00139
where:
AC in = AE 
pp+ 
AC cc + AE cp = 0.00616
The strainrange fractions for use in the Interaction Damage Rule
(2) are:
0.00471Fpp = AEpp/Aein = 77= - 0.765
0.00006Fcc = AE cc /AE in = U-^-5 = 0 010
Fcp = AEcp/Aein = U— 
0,00139  
= 0.225
Prediction of Thermal-Mechanical Strain-Cycling Life
The partitioned strainrange life relationships for 316
stainless steel have been reported previously (1) for use with
the Linear Damage Rule and have also been shown (3) to be essen-
tially independent of test temperature. Hence, these relation-
4
ships are ideally suited for application to the life prediciton
of the thermal-mechanical strain cycle under consideration. Iiow-
ever, these earlier relationships do not account for the newest
interpretation of creep strain (i.e., using only the steady-state
F
component) nor for the use of the new Interaction Damage Rule.
8Saltsman and Halford (7) have recently reported the partitioned
strainrange versus life relationships for 316 stainless steel
for use with the Interaction Damage Rule. To be consistent within
this paper these relationships have been modified to include the
new interpretation (4) of creep strain as being only the steady-
state component. Hence, for an inelastic strainrange cf 0.00616,
the Npp , Ncc , and Ncp lives are 1330, 405, and 94 cycles respectively.
The predicted life Npr is computed from the Interaction Damage
Rule (2) as follows:
F 
PP +R— +FM
 
Npp	 cc	 cp	 pr
765	 010225 _ 1
X3'6 + "U + 
-W  Npr
000575 + .000025 + .002395 - .002995
	 1
Npr
Npr = 334
Agreement between the predicted (334) and observed (307) lives
is excellent in this case.
Bounding the Life Values
An alternative approach here, instead of quantitatively
determining life by detailed partitioning, is to estimate bounding
values on life from a knowledge of the total inelastic strainrange
and an estimate of the types of strainrange likely to be present.
Here, because of the nature of the cycling, the most damaging
type of strainrange is of the Ac cp type. If the entire cycle
produced a Aecp type strainrange, the life would be 94 cycles to
9failure. Thus, this value is a lower bound on life. Its value
is determined without detailed partitioning. Had the test been
of the "out-of-phase" type, the lower bound on life would have
been 410 cycles (i.e., the life if the strainrange were entirely
of the Ac PC type). In both cases, the upper bound on life would
have been the Npp value of 1330 cycles to failure.
Some Metallurgical Aspects
As was shown in Ref (1), application of a Accp type strain-
range is conducive to intergranular creep cracking in 316 stain-
less steel. The photomicrographs of the failed specimen shown in
Fig. 3 also reveal intergranular cracking (particularly evident
in Fig. 3a), thus substantiating qualitatively the measured
presence of a significant amount of this type strainrange in the
present test. Figure 3c shows the wall thickness of the tubular
specimen on the side of the tube from which the major crack
originated and propagated. This cracking was along grain bour.daries.
Intergranular secondary cracks are also noted, although there is
an indication that these were initiated in a transgranular mode,
possibly by the action of the pp type component of strainrange
Figure 3b is a photomicrograph of the wall thickness on the
opposite side of the tube. The 45 degree shear angle across the
thickness illustrates the final tearing-off of the specimen into
two pieces on the 307th cycle This tearing action opened up a
number of internal intergranular cracks that had formed during the
thermal-mechanical strain-cycling It should be noted that the
failed specimen is free of cycle-dependent buckling cr other
10
geometric instabilities (Fig 3d) such as discussed by Coffin (8)
at this Symposium:
C014CLUDING REMARKS
We have presented in this paper details of how the method of
Strainrange Partitioning would be applied to a thermal-mechanical
strain-cycling problem, Extension of the method to an actual
thermal fatigue problem would not be a difficult task provided
an analysis were available to indicate the temperature and strain
versus time histories of the cycle of interest An axially loaded
laboratory specimen could then be programmed to follow thes;
temperature and strain histories The specimen would respond to
give the magnitude of the inelastic strainrange and the stress
(and thus the steady-state creep rate) as a function of time-
From that point on_, the determination of the creep and plastic
strains, the partitioned strainrange components, etc would follow
the procedures described in this paper. As an alternative to
experimental partitioning, constitutive equations representative
of cyclic behavior could be determined for the material over the
temperature range covered, and an analytical partitioning could
be applied However, this is a subject for a future paper. Of
course, bounds on cyclic life can be established without having
to resort to either experimental or analytical partitioning.
REFERENCES
1 Manson, S. S , Halford, G. R., and Hirschberg, M H., "Creep-
Fatigue Analysis by Strain-Range Partitioning". Symposium on
Design for Elevated Temperature Analysis, American Society of
Mechanical Engineers, 1971, pp. 12-28
11
2. Manson, S. S., "The Challenge to Unify Treatment of High
Temperature Fatigue - A Partisan Proposal Based on Strain-
range Partitioning", Fatigue at Elevated Tem eratures, ASTM
STP 520, American Society for Testing a:ice ter a s, 1973,
pp. 744-782.
3. Halford, G., R., Hirschberg, H. M., and Manson, S. S., "Tem-
perature Effects on the Strainrange Part' tior.ing Approach
for Creep Fatigue Analysis," Fatigue aL Elevated T eratures,
ASTM STP 520, American Society tor Testrng anmaterials,
1973, pp. 658-669,
4. Manson, S. S., Halford, G, R., and Nachtigall, A, J.,
"Separation of the Strain Components for use in Strainrange
Partitioning," Advances in Design for Elevated Temperature
Environment, Amer can Society 
of 
ec ar.Aca ng^neers, 1975,
pp.
	 -
5. Code Case 1592, ASME Boiler and Pressure Vessel Code, April 1974.
6. Hirschberg, M. H:, "A Low-Cycle Fatigue Testing Facility,"
Manual on Low Cycle Fatigue Testing,, ASTM STP 465, American
Society for Testing and materials, 1969, pp. 67 - 86.
7. Saltsman, J. F, and Halford, G_ R.., "Prediction of Creep-
Fatigue Lives of Type 304 and 316 Stainless Steel uai.ng the
Method of Strainrange Partitioning," NASA TM-Y (In Press).
8. Coffin, L. F:, Jr., "Instability Effects in Thermal-Mechanical
Fatigue," presented at ASTM Symposium on Thermal Fatigue of
Materials and Components, New Orleans, November 1975
12
TABLE I Specimen and Test Procedures used for Example Problem
Material: AISI Type 316 stainless steel, fully annealed
Specimen: Tubular, hour-glass test section (6)
Strain:	 Diametral extensometer, diametral strain cyclically
ramped linearly with time between limits resulting
in an axial total (mechanical) strainrange of 0.00923.
The resultant inelastic strainrange was 0.00616. The
cycle period was 30 minutes.
Temperature: Silicon carbide internal heating element, temperature
ramped linearly with time between temperature limits
of 230 and 7600 with a period of 30 minutes. The
temperature was phased with the strain such that the
maximum temperature occurred at the peak tensile strain.
This is referred to as an "in-phase" thermal-mechanical
strain cycle.
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Life prediction of thermal-mechanical fatigue using strain-range partitioning

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