Development of fatigue life criteria for experimental fusion reactor first-wall structures

Nuclear Engineering and Design 58 (1980) 283-299 © North-Holland Publishing Company

DEVELOPMENT OF FATIGUE LIFE CRITERIA FOR EXPERIMENTAL FUSION REACTOR FIRST-WALL STRUCTURES * R.E. NICKELL Poway, C.4, and Brookhaven National Laboratory, Upton, N Y 11973, USA

and E.P. ESZTEGAR La Jolla, CA. and Brookhaven National Laboratory, Upton, N Y 11973, USA

Received 15 March 1979

An approach to the rational design of fusion reactor first-wall structures against fatigue crack growth is proposed. The approach is motivated by microstructural observations of fatigue crack growth enhancement in unirradiated materials due to volumetric damage ahead of a propagating crack. Examples are cited that illustrate the effect of mean stress on void nucleation and coalescence, which represent the dominant form of volumetric damage at low temperature, and of grain boundary sliding and creep cavitation, which are the dominant volumetric damage mechanisms at high temperature. The analogy is then drawn between these forms of fatigue crack growth enhancement and those promoted by irradiation exposure in the fusion reactor environment, such as helium embrittlement and atomic displacement. An enhanced strain range is suggested as a macroscopic measure of the reduction in fatigue life due to the higher fatigue crack growth rates. The enhanced strain range permits a sepaxation of volumetric and cyclic effects, and assists in the assignment of rational design factors to each effect. A series of experiments are outlined which should provide the numerical values of the parameters for the enhanced strain range.

1. Introduction Progress toward the scientific feasibility of achieving the break-even condition on magnetic confinement fusion devices has been greatly accelerated in recent years. In the United States alone, the expenditures increased tenfold over the last decade to the current level of $360 M budgeted for 1979, with a majority of the increased funding going toward the construction of large-scale experimental facilities. As the plasma volume increased two-hunderd-fold (from 0.07 m 3 of ATC to 35 m 3 for tile Princeton Tokamak Fusion Test Reactor under construction) and with

* Work performed under the auspices of the U.S. Department of Energy, Washington, DC. 283

even larger reactors moving from the planning to the design stage, engineering problems assume greater importance in establishing the overall feasibility of a fusion power reactor. Many aspects of the engineering problems are on the boundaries of the present state of the art and some are clearly beyond. In the first category are the structural problems associated with the superconducting magnet dimensions extrapolated to the required size. As there is some experience with smaller-scale, high-field-strength magnets for bubble chambers and accelerators, the structural problems of the magnetic confinement may be classified as requiring only moderate extension of the state of the art presently available in the design of composite superconducting magnets. (The structural analysis, however, will require new analytical methodology for the adaption of finite element techniques to the

284

R.E. Nickell, E.P. Esztegar / Fatigue life design criteria

analysis of elastomagnetic stability and the interactions of conductor, steel support and coolant system components.) The mechanical design of the first wall is in the second category, for which the engineering feasibility demonstration is beyond the present state of the art for the simple reason that the ingredients necessary to establish a consistent design philosophy that combines the performance requirements, material properties, analytical rhethods and safety factors are not yet available. The most critical and longest lead-time problems seem to be in the field of material sciences, particularly in the areas of material behavior and failure limits under irradiation. Since the first wall has tO fulfill the triple function of shield (thermal and neutron), blanket and pressure vessel, the material response has to be described for a range of exposures, temperatures and stress conditions that are very different from the design parameters of conventional pressure vessels. As a neutron shield the first wall has to protect

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the components of the magnetic confinement structure (magnets, supports, dewars, etc.) against radiation damage due to high energy (14 MeV) neutrons while, as a blanket, it has to provide a heat transfer path for the fusion energy to the primary coolant. Accurate description of the material behavior of the first wall is important because the surfaces adjacent to the plasma have to resist the effects of high heat flux and the bombardment of energetic neutrons, that can cause sputtering, blistering, swelling, cracking, etc., leading to loss of mass and consequent contamination of the plasma. The description of the radiation effects on the structural strength is equally important because, in the current design configurations, the first wall serves as a vacuum vessel and also provides the primary containment for the internal pressure necessary to drive the flow in the coolant channels. For the neutron shield function of the first wall, the data base is not yet available for the candidate

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R.E. NickeU, E.P. Esztegar /Fatigue life design criteria

materials in sufficient detail to establish long-term material behavior. However, the plasma performance requirements are well enough known so that some of the limiting conditions for the first wall as a pressure vessel can be defined: fracture or excessive deformation of the coolant channels (potentially blocking coolant flow) under initial pressure and buckling or leaks under external pressure are of apparent importance. Evaluating these failure modes, the Task Group on Alloy Development [1 ] identified loss of vacuum or ingress of coolant into the plasma chamber as the most probable functional limitation for the performance of the fusion reactor. (This is in contrast to the characteristics of fission reactors, where leaks in the primary system constitute a possible safety hazard but small leakages do not terminate the fission process.) The extreme sensitivity of the plasma to contamination is illustrated in fig. 1, from [1], showing the ingress mass per unit volume of helium or molten salt coolant as a func. tion of crack area and coolant pressure. Since the allowable leak rate cannot exceed the vacuum pump capacity, the maximum tolerable crack area is shown to be on the order of 10-s-10 -4 in 2 (10-4-10 -a cm2), depending on the alpha particle production rate. This means that one small crack of 0.01 × 0.01 in 2 (0.03 × 0.03 cm 2) would be sufficient to prevent plasma ignition. Therefore, the first wall has been categorized (from the operational reliability point of view) as a leak-critical pressure vessel, with principal failure modes related to crack growth and fatigue. It is expected that a virtual freedom from even microscopic leakage paths will be one of the principal design criteria of the structure.

2. Loading and environmental conditions The cyclic heating and pressure pulsing operational mode of tokamaks indicates that major effort in the structural evaluation should concentrate on the fatigue performance of the first wall materials. The temperature pulses in tokamaks induce severe cyclic stresses that promote crack propagation and fatigue damage, while the high temperatures and intense neutron radiation under relatively constant pressure stresses induce intergranular voids. Since irradiation embrittlement, swelling and creep accel-

285

crate the cyclic fatigue damage, the primary failure mechanism for the first wall is a time-dependent fatigue precess, similar in principle to the creepfatigue process encountered in high-temperature fission reactors. The initiation and propagation of cracks due to cyclic loading combined with time-dependent creep damage is a potential failure mode in many types of structures operating at elevated temperatures, ranging from fossil fuel boilers to jet engines and gas turbines. Thus, there is a body of material information and analogous pressure vessel fatigue design practice that may be used as the starting point in the development of a design method for fusion reactor first wall structures. Since there are also similarities between fission and fusion reactor neutron environments, the first-wall design studies for the test reactors may be assisted by the systematic evaluation of the available fission neutron damage information, using the methodology for time-dependent fatigue to guide us in the development of preliminairy design criteria for the first wall. This is our purpose in th e present paper, but we have to proceed with caution because, while there are similarities in creep-fatigue and fast neutron damage processes, there are major differences as well. Furthermore, there is virtually no data that is directly applicable to the first-wall loading and environmental conditions to check the validity of the proposed life prediction method. When the Materials Study Group at the Blanket and Shield Workshop [2] examined the materials qualifications for the primary pressure boundary, the increased rate of material degradation due to the effects of irradiation by the energetic neutrons was identified as the major difference between the fission and fusion reator environments. The current approach to simulate fusion radiation effects is by approximating dpa, helium level and ratio in low fluence tests. Then, an existing theory for damage production is used to extrapolate the rate of embrittlement, swelling, irradiation creep, cold work recovery, etc. scaled by the dpa and helium ratio. The experimental difficulties are in reploducing the radiation characteristics of fusion reactors by non-fusion sources, simulating the dpa density, helium production rate and ratios simultaneously. While the dominant fission neutron energies are below 1 MeV, about

286

R.E. Nickell, E.P. Esztegar /Fatigue life design criteria

80% of the d - T fusion energy is released as 14.1 MeV neutrons (the balance being 3.5 MeV alpha particles which are confirmed in the plasma) and the fluence levels are in excess of 3 × 1023 n/cm 2 for the projected design life an order of magnitude higher than in a fission reactor. Such high fluence levels are or will be soon available in EBR, FFTF and other fast reactor irradiation test facilities, but the E > 0.1 MeV fission neutrons delivered by these reactors yield only a fraction of the damage energy of 14"MeV neutrons, judging from the dpa and helium ratios in specimens irradiated by 14 MeV neutrons deposited by low fluence (1018 n/cm 2) tests in the rotating target source. Notwithstanding the uncertainties in the damage correlation, the extrapolation is not a completely hopeless task, (at least for the test reactors), as pointed out by Steiner and Clarke [3] in discussing the ORNL tokamak model-T fusion reactor design. (For this machine the blanket is constructed from stainless steel, approximately 80 cm thick, wRh liquid lithium transferring the energy from the blanket to an intermediate molten salt loop.) They state: "It is well known from fission reactor experience that deleterious changes in physical and mechanical properties occur in structural materials as a result of neutroninduced atomic displacements and transmutatiofi gas products - particularly helium, which has a very low solubility in the metal lattice. Calculations indicate that, in general, atomic displacement rates will be comparable 1 in the first wall region of a fusion reactor blanket and in the highflux region of advanced fission reactors; however, the helium production rates will be much higher in the fusion reactor environment because of the differences in neutron energy spectrum between fusion and fission reactors." The fast neutron damage can therefore be separated into two components, one governed by the dpa density, the other governed by the helium production rate. The latter is progressively reduced as the maximum temperature approaches the critical fraction of Tm (for stainless steel this value is approximately 500°C, for titanium 550°C, for vanadium 600°C). The deposited helium strongly affects the crack propagation process by diffusion to the grain boundaries where it forms bubbles and, due to its low solubility,

1 Within an order of magnitude (our note).

embrittles the metal, While there is little information available to define quantitatively the increase in crack growth rate for materials and temperature levels projected for the power reactors, the current first-wall designs for the experimental facilities are based on the use of 316 stainless steel, with a cooling system capacity that limits the maximum temperature to values below 500°C. Since the helium embrittlement is not expected to interact significantly with the other fast neutron damage mechanisms under these operating conditions, this complex interaction problem can be avoided in the present discussion of the neutron damage in experimental reactors. However, for power reactors (EPR, DPR and CTR) the first-wall material selection and cooling system design will have to account for the increase importance of helium embrittlement at higher operating temperatures. Even if damage due to helium production can be neglected, reductions in short-time tensile strength and ductility, creep rupture life and creep ductility have been observed for materials irradiated by 14 MeV neutron exposure. A limited amount of fatigue data on similar exposed materials suggests a significant reduction in fatigue endurance, as well. The degradation of fatigue strength due to void formation under neutron bombardment test is similar in principle to creep-fatigue processes where strain-rangedependent grain boundary sliding mechanisms are interacting with a time-dependent creep cavitation. The design method for creep-fatigue live evaluation described in the current ASME Code Case N 47 [4] separates the cyclic (strain range) dependent and time-dependent (creep or relaxation) effects on the basis of life fractions: for the cyclic part the life fraction is n / N f and for the time-dependent part it is t/tr, where Nr is the fatigue endurance under "pure" fatigue (high frequency, reversed cycling) conditions and tr is the creep rupture time under "pure" (monotonic) creep conditions. The failure limit is expressed by the sum of these life fractions reaching 100%, that is n / N f + t/tr = 1 .

(1)

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This "linear damage summation" method suffers from numerous shortcomings, including the inherent assumption of load-path independence of the fatigue and creep damage processes, as discussed in [5], but has the advantage of basic simplicity. The inaccuracies of this approach are compensated for by large safety factors applied to the allowable damage D and to the pure fatigue, Nf, and pure creep endurance, tr, limits of the material (e.g., N d = Nf/S.F.). In general, this approach gives conservative design limits, as shown m fig. 2, primarily because the interactions between the volumetric creep damage accumulation and cyclic crack growth rate are mild, and the explicit and hidden safety factors are large. In fusion reactor environment the interactions between the volumetric neutron damage and cyclic extension rate are more strongly history and load-

path dependent. Thus, the values of safety factors that are generally adequate to compensate for the inaccuracy of the path-independent linear damage summation method under creep conditions, may not suffice for the cusion environment. As a result, an extension of the path-independent method for fusion reactiors might lead to impractical design criteria, if safety factors are to cover the stronger neutron damage and interaction phenomena. Instead of relying on such undefinable "conservative" assumptions, our approach is aimed at the functional isolation of the micro-structural damage mechanisms so that the safety factors can be assigned to the damage components on the basis of judgement of the relative importance of the different damage mechanisms under the particular fusion reactor operating conditions. Rather than applying excessive ignorance factors to cover all applications and all possible combinations of the complex damage processes, we suggest simplified but specifically adaptable damage models for firstwall design criteria. The additional benefit of this

288

R.E. Nickell, E.P. Esztegar / Fatigue life design criteria

approach is in the guidance obtained for the development of programs, since the test variables can be rationally selected and the extrapolation methods can be based on mechanistic models of the damge accumulation.

3. The fatigue crack growth enhancement model We are motivated by the foregoing to extend current fatigue crack growth concepts developed for unirradiated materials to include the effects of irradiation damage. In order to accomplish this, the relationship between crack growth rate and cyclic life must be established, and those microstructural mechanism that promote crack growth must be amenable to macroscopic measurement. The conceptual framework used is the fatigue crack driven by deviatoric stress through a volume of material that exhibits varying degrees of microstructural d a m a g e hereafter referred to as volumetric damage - due to a number of loading and environmental conditions. This volumetric damage influences the rate of fatigue crack growth, and thus the fatigue life, by providing weakened and partially-intergranularlycracked volume ahead of the principal crack. In the following we examine this framework in terms of fatigue crack growth enhancement for unirradiated materials. A later section deals with an analogous treatment for irradiated materials. We begin with the observation that the connection between low-cycle fatigue life and fatigue crack growth is based upon the macroscopic correlation with effective plastic strain range [6]. This correlation is justified by microstructural studies showing that stage I and stage II fatigue cracks grow along planes of maximum resolved shear, as well as by the successful correlations of cyclic life macroscopic strain range for uniaxially loaded fatigue specimens. Attemps to extend this concept to incorporate damage ahead of the propagating fatigue crack have been notably less successful. Cyclic life is reduced when sustained load periods at creep temperatures are interspersed with load reversals. Neutron irradiation can be expected to provide similar life reductions, as will later be shown. In order to successfully incorporate damage ahead of the propagating fatigue crack into the effective

strain range criterion for stage I and stage II growth, the similarities and differences in the damage mechanisms should be noted. It has been pointed out [7] that the maximum deviatoric stress is at the tip of a crack, while the maximum mean stress is some distance ahead of the crack tip. This distance depends principally upon the crack geometry. Plastic deformation tends to increase this distance, as does time-dependent deformation, since both influence the redistribution of stress, eventually leading to the condition of virtually uniform mean stress over a substantial volume ahead of the crack tip. Under some conditions the combination of this mean stress and a defective microstructure will enhance the fatigue crack growth rate by creating a damaged volume through which the principal crack can propagate more readily by ligament rupture and linking of intergranular voids. At temperatures below the creep range or at sufficiently high cyclic frequency, unirradiated metals exhibit a mean stress (or mean strain) effect Table 1 Data for curves pertaining to fig. 3 Room temperature Aez (A2/Oz)

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289

R.E. Nickell, E.P. Esztegar /Fatigue life design criteria

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on low-cycle fatigue life. A telling example o f this effect is the discrepancy between uniaxial and torsional fatigue life at the identical shear strain range. To account for this, Brown and Miller [8] have suggested that low-cycle fatigue data m y be macroscopically correlated by a damage function including two parameters - the maximum deviatoric strain range and the normal strain range in the maximum shear surface. Lobitz and Nickell [9] adopted the Brown-Miller hypothesis in order to develop an "enhanced" shear strain range for use with proposed modifications o f the ASME Boiler and Pressure Vessel Code rules for c r e e p - f a t i g u e damage evaluation. The evaluation o f the 304 stainless steel t e n s i o n torsion fatigue data obtained b y Blass and Zamrik [10] illustrates this process. The data show a vertical shift, where the magnitude o f the shift is a function

o f the ratio o f axial strain range to shear strain range, R. The motivation for the interpretation o f the shift is the Brown-Miller hypothesis, which requires that uniaxial fatigue data exhibit a normal strain range effect on the maximum shear plane while torsional data would not. Shown in tables 1 and 2, and plotted in fig. 3, are two cruves extracted from the B l a s s Zamrik data. The raw data (axial strain range, Aez; torsional strain range, A6oz; in-phase strain range ratio, R; and number o f cycles to failure, N ) are shown in the first three columns o f tables 1 and 2. The conver. sion to the "enhanced" strain range is developed through the relations Aems

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R.E. Niekell, E.P. Esztegar / Fatigue life design criteria

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normal strain range is in the neighborhood of four to five times more damaging than the shear strain range, with this multiplier increasing slightly with tempera~ure. A valid interpretation of this mean strain range effect is that the plastic deformation (and dislocation density) developing in the form of plastic "wings" on maximum shear surfaces ahead of the crack interacts with the mean stress to amplify grain boundary incompatibilities into voids. The creation, amplification, and coalescence of these voids provide the weakened, or damaged, structure into which the dominant fatigue crack propagates. As an indication that this macroscopic approach to fatigue life reduction by volumetric damage is reasonable, the failure model proposed by Norris et al. [7] can be cited. This model is patterned after the McClintock [11 ] and Hancock and McKenzie [12] void formation and growth theories, and is applied by Norris et al. to dynamic crack extension under a single application of load. A time-volume integral of macroscopic variables is proposed to account for

R.E. Nickell, E.P. Esztegar / Fatigue life design criteria

the effect of hydrostatic tension on void nucleation and growth, including the effective plastic strain rate and mean stress as a crack-driving energy, defining the damage D in the form D

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where t is the time, Om is the mean stress, and-b-p is the effective plastic strain rate. The integral is evaluated over a volume Vc enclosed by a sphere of radius re in front of the existing crack tip. When the integral exceeds the critical damage threshold, Dc, the crack extends. The model is calibrated against uniaxial smooth and notched-bar experiments (the radius, rc, the damage threshold, Dc, and the functional form of .f(Om) are derived by independently fitting the uniaxial test data; then Charpy impact experiments are used to provide an independent test of the theory. We find this form of the damage equation convenient, not just as a means of curve fitting of existing failure data, but because of the form chosen for the integrand. By choosing a linear polynomial for the distribution of the mean stress, f(Om) = a + born we observe that the integral of damage becomes an additive combination of plastic strain and a mean-stressmodified plastic strain. This type of additive enhancement for single application of load and for low-temperature, high-frequency fatigue has a great deal of appeal, but the method would be more powerful if demonstrated on combined fatigue-creep crack growth at elevated temperature. This problem has been discussed by Lloyd and Wareing [13] who have proposed a simple model that accounts for the effect of time-dependent material behavior on the cyclic crack growth rates in austenitic stainless steels. The model is based upon a surface-nucleated or pre-existing fatigue crack propagating into a volume of material that has been progressively damaged by grain boundary creep cavitation, and depends upon the knowledge of the cracktip-opening displacement (CTOD) and two length parameters carbide precipitate particle size and spacing between carbide particles. The difference between these two length parameters provides a measure not only of crack growth rate and transgranular-intergranular crack growth dominance, but also

291

offers some insight into the effect of prior heat treatment. In particular, the carbide precipitation into the grain boundaries acts as a dislocation barrier, leading to a reduction in grain boundary slip and to an increase in grain boundary cavitation, for appropriate stress and temperature states. There is ample evidence to indicate that tensile hold periods during uniaxial fatigue tests promote cavitation while compressive hold periods promote the healing, or "sintering" of cavitation damge. However, this evidence should be tempered by the knowledge that a combination of shear and mean tension is needed to drive the cavitation process, as wedge cracking adjacent to the carbide precipitates can be attributed principally to the shear stress. Because of the close associated between the geometry of carbide precipitation and intergranular discontinuities - either wedge cracks or cavitation - it is possible to discuss the interaction of fatigue cracks with damaged volume by noting the transition from transgranular crack extension to intergranular crack extension in the presence of volumetric damage. Along these lines, Micheal, Smith and Watson [14] compared the fatigue crack growth rates for 20% coldworked 316 stainless steel in both the unirradiated (2.2 × 1022 n/cm 2, E > 0.1 MeV, 427°C) condition. The crack growth rates for the irradiated specimens were somewhat more than one order of magnitude greater than those for the unirradiated specimens when continuous cycling was used. This change in crack growth rate was virtually identical with that obtained by adding a 1-min tension hold period to the unirradiated specimen fatigue cycles. A qualitative similarity of the hold-time and irradiation effect on the crack growth rate extends to the terminal failure conditions as shown in fig. 4. The fatigue endurance of the irradiated material is comparable to the 3 - 6 rain hold-time less results of the unirradiated thermally aged stainless steels. Although no metallurgical investigations were conducted on the irradiated samples, scanning electron microscopy studies of the unirradiated samples revealed transgranular crack growth for the continuous.cycle tests and a transition to intergranular extension for the hold-time tests. By analogy with the results of hold-time and low-energy irradiation tests, the effect of energetic neutrondamage is postulated to pro-

292

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mote intergranular crack extension by creating grain boundary damage ahead of the principal crack. All of these considerations are in general agreement with both the Lloyd-Wareing model and the McClintock et al. model, and provide some insight into a modification of the effective strain range procedure that might account not only for hold periods at high temperature, but also for neutron irradiation effects.

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damage-fatigue

analogy

The Michel et al. data provide a crack growth rate analogy between creep-enhanced fatigue life reduction and irradiation-enhanced fatigue life reduction. The background of the present elevated temperature creep-fatigue design rules is briefly discussed in section 2. We have shown that the current approach to creep-fatigue interaction assumes the macroscopic damage mechanisms to be independent and linearly superposable. Experimental data on materials for elevated temperature nuclear application have shown that such an assumption is of marginal

validity. Fig. 2 illustrates some of the data for 304 and 316 stainless steels, and the comparison with creep-fatigue design allowables. A number of other approaches using linear damage summation for creep-fatigue interaction have been suggested, including the use of t - N diagrams [ 15,16], strain-range partitioning [ 17], frequency separation [18], hysteresis energy [19], and average crack growth per cycle [20]. A recent paper by Jaske and Begley [21] offers a method based upon fracture mechanics principles to account for stage III crack growth and its interaction with creep damage, through a linear summation of fatigue and creep crack growth rates. Irradiation-fatigue damage evaluation for fast breeder fission reactor service was also proposed on the basis of linear damage summation by Brinkman et al. [22], who developed an empirical "fraction modification" of the elastic and plastic components of the continuous cycle strain range Aet = Aee + Aep = AN~ + B N # , where the constants A, B, a and b are found from fitting fatigue data for unirradiated materials. The number of cycles to failure is Nf, while the total,

(7)

R.E. Mckell, E.P. Esztegar / Fatigue life design criteria

To account for the radiation damage, a modification of the strain range partitioning used was explored by Blackburn [23]. His results are shown on fig. 6, indicating that even though the damage fractions (t/tr, n/Nf) show a large scatter for both the irradiation material, the irradiation data is significantly below the average limiting values used in the ASME Code. A possible explanation for the significant reduction in fatigue life can be deduced from the comparison of t - N diagrams assembled for unirradiated and irradiated materials, as shown in fig. 7. The unirradiated material exhibits a saturation limit of the hold time effect, while such a limit disappears for irradiated material. The saturation of the time-dependent effect, which can be attributed to the limitations on thermally-activated creep strain accumulation under strain-controlled (relaxation) conditions, is a conservative feature of the material behavior. The elimination of this saturation effect is due to the interaction of the similar volumetric (cavitation) damage intro-

elastic and plastic strain ranges are given by Act, Ace and Aep, respectively. The reduction in fatigue endurance is assumed to be proportional to the irradiation.caused changes in the tensile strength, Ou, and the fracture ductility, d. The corresponding fractional corrections to the "elastic" and "plastic" terms in eq. 7 were suggested by Brinkman et al. in the form A c t , irrad =

~uAN~f + $dBN~,

(8)

where (9)

t~u = Ou, irrad/Gu ,

and

~Pd dirrad/d .

(lO)

=

The properties are all referenced to the same temperature. The evaluation of 304 SS fatigue data using eq. 8 is shown on fig. 5, indicating a life reduction by a factor of approximately 8 to 10.

IOO.O

~

'

' ......

ANNEALED

I

293

........ AGED

I

'

'

''""1

'

'

''"'

0~,~ ACTUAL FAILURE VALUES ( Nf ,t r ) ~'~

I0.O

ooOg°'m o

_O~[~ DESIGNFAILURE VALUES ( Nd , t d )

0

0

o

o

o

o

o

o z=

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•

•.

w"

.o:.

°i. '~ "~o :°~~=

O.

uJ ILl

0.1

o

II I'-Ieo

3 0 4 STAINLESS

_

• O o o 316 STAINLESS • • umo IRRADIATED

¢J

/4 SPECeMENDIDNOTFAIL o¢@~O0~ UNIRRADIATED O.01 O.OI

,

,

,,,,,,I

,

0,I

FATIGUE

......

,I

i

i

i

i

1.0

iiiiI

J

I0

i

i

i

I i ii

IOO

n D A M A G E , ~ f OR N'~

Fig. 5. t - N diagram for tension-hold fatigue test of annealed 316 SS at 593°C (1100°F) (adopted from ref. [22]).

294

R.E. Niekell, E.P. Esztegar / Fatigue life design criteria 1.2

I

i

I

I

0 H O L D - T I M E FATIGUE TESTS USING 516 SS MATERIAL

1.0

O UNIRRADIATED • IRRADIATED ~ = .3 x I0 zz (E > OIMeV)

0.8

Z~t/t r + n/Nf ) = D CREEP-FATIGUE DAMAGE FOR UNIRRADIATED MATERIAL

hi

(.9

< 0.6,,~ o

0

13..

w ~,J rr

•

~0.4-

0

o

0.2

LINEAR CREEP-FATIGUE INTERACTION= D= I 0

O0 0

0

• •

I

I

I 0.2

I FATIGUE

I 0.4

I DAMAGE

1 0.6

I

I 0.8

I 1.0

T. n/Nf

Fig. 6. Comparison of ASME creep-fatigue allowable with tension-hold fatigue tests of annealed, aged and irradiated 304- and 316 SS (adapted from [22]).

duced by fast neutrons ('>0.1 MeV) and the creep process. The combined effect is a drastic reduction in the design margin available for irradiated material, when using the ASME Code allowables Nd, td, D in the damage summation by eq. 2. The originally large safety factors shown in fig. 2 are reduced for irradiated material to the point where no margin remains when compared to the ASME Code allowables in fig. 6. These data and comparisons are shown only to illustrate that there are similarities in the long-holdtime fatigue behaviour of irradiated and unirradiated 316 SS material; however, the linear damage summation method, which is based on terminal failure parameters (Nf, tr, q~u,@d), cannot account for this behaviour. The enhanced strain range damage model advocated here builds upon the microstructural simil-

larities between the incremental cyclic crack growth processes at elevated temperature under creep conditions and under intense neutron irradiation. Recent papers on creep crack growth by Wareing and Vaughan [24] and Sadananda [25], and on fusion neutron irradiation by Vook [26] and Brager et al. [27] are instructive in this regard. Wareing and Vaughan [24] observe that the ductile striation spacing on the fracture surface for elevated temperature crack growth and for conventional low-cycle fatigue crack growth are strikingly similar in shape, but not with respect to crack growth rate. The time-independent plasticity crack growth model tends to underpredicts the actual crack growth rates for 316 stainless steel at 625°C by a factor of five and the ductile striation spacing by a factor of two. They attribute this crack growth rate

295

R.E. Nickell, E.P. Esztegar / Fatigue life design criteria SATURATION

LIMIT AGED 316 SS

\

10 3

I !

\

ANNEALED "

-" ..J

so, IRRADIATED

i

o

fl_

~"(o.s)/\ \ ~ "

IO2 -

/ , ~ STRAIN

0

'~.,,C-.._. \

RANGE : I %

(2.9) ~

TEST TEMP. : 5 9 3 ° C ( , l O 0 ° F )

,GEDSO, SS

io>~ / \

\ \,~\(~,~

I,I

~ I--

_ • 3 0 4 STAINLESS I01" •

516 STAINLESS

IRRADIATED

. )

%

17 3 0 4 UNIRRADIATED, AGED 0 316

j

UNIRRAOIATED, AGED

( ) FLUENCE x i~ 2~ n/cm z

I0 o I0 °

,

IRRADIATED

(6.o);

E>O.IMeV

I01

10 2

10 3

#

104

CYCLES TO FAILURE, Nf Fig. 7. Construction of iso-strain t--N diagrams for irradiated effects under hold time fatigue tests.

enhancement to the effects of crack surface oxidation and to creep deformation, both of which lead to intergranular crack extension. These observations are in agreement with the theoretical creep crack growth model of Sadananda [25], which contrasts two competing thermally-activated processes - the diffusion of defects in the grain boundaries and the nucleation• coalescence of voids ahead of the principal crack. At moderately high temperatures the mobility of defects may not be increased significantly above that at low temperature, while the sustained application of load may contribute significantly to redistribution of stress near the principal crack tip, to grain boundary readjustment and local deformation incompati. bility, and to time-dependent growth of microcracks and voids. At even higher temperatures and at lower values of sustained load, the effects may be reversed, with the annihilation of defect microstructure dominating the damage mechanisms.

The microstructural effects of fusion neutrons irradiation have been described by Vook [26] as a process of void production and swelling, similar to those produced by inelastic deformation. The vacant lattice sites and self-interstitials that are generated by irradiation tend to recombine , or annihilate, at elevated temperatures to some extent, but the mobility of the defect structure at reactor temperatures may be insufficient to permit compete annihilation. This is particularly true for intense neutron bombardment in a fusion environment at relatively low first-wall tem. peratures. In addition, neutron-alpha reactions produce helium that is not soluble in the metal, which therefore tends to accumulate in the grain boundaries, pinning the grain boundary against sliding. The macroscopicaUy observed result is helium embrittlement of the material. This problem can be circumvented by limiting the wall temperature to 0.4 of the melting temperature, as discussed earlier, but this implies a

296

R.E. Niekell, E.P. Esztegar / Fatigue life design criteria

trade-off between helium embrittlement and void generation by incomplete defect annihilation. Based on our analogy with creep-fatigue interaction, the enhanced strain range concept may be able to accomodate the irradiation damage due to void generation ahead of the fatigue crack by suitable modification of the mean strain multiplier. In this case, the duration of neutron exposure is important in determining the magnitude of the multiplier, and there is evidence to indicate that the effect of irradiation is dependent not only on total exposure, but on applied stress during irradiation also. Brager et al. [27] provide an instructive example of combined stress and irradiation on both solutionannealed and 20% cold worked 316 stainless steel at 500°C in the Experimental Breeder Reactor (EBR-II). The specimens were 92.54 cm long tubes, with a thickness of 0.38 mm and an outside diameter of 5.84 ram, pressurized internally hy helium and subjected to an external stagnant sodium environment. The fluence levels varied between 2 and 3 × 1018 n/m 2 (E > 0.1 MeV), with nominal circumferential pressure stresses varying between 0 and 327 MPa. Transmission electron microscopy was used for posttest examination. The major conclusion was that the number of dislocation loops (and, eventually, the voids) is sensitive to the resolved normal stress. A secondary effect was the hydrostatic-tension-enhanced growth of these defects. Therefore, by analogy to the model of fatiguecreep fracture, the reduction in fatigue life due to intense 14 MeV neutron irradiation is modeled by a two-comopent damage model. The atomic displacement from neutron bombardment increases the volumetric damage through nucleation and growth of voids, which in turn enhances the intergranular crack growth. A simple enhanced strain range model is suggested here in the form of eq. (4) z2xe= AA6ms + aPAems ,

(1 1)

where the coefficients, A, a and P are temperature and fluence dependent. (The strain range quantities are defined in eqs. (3)-(5).) Functional forms of these coefficients may be developed on the basis of relatively short-term fatigue tests and crack growth rate measurements on the material in annealed, aged, post-irradiated and irradiated-under-stress con-

ditions. Thus, the model at this point is regarded as a first approximation to guide the testing of more complex interacting phenomena. A logical first step would be to conduct pure torsion fatigue tests, at two or three temperatures, on post-irradiated specimens, in order to isolate the effect of volumetric damage strictly due to irradiation. Ideally, tinder purely deviatoric straining in a torsion test, prior volumetric damage would not affect the crack propagation rate and fatigue endurance. However. the microvoids encountered by the dominant crack could alter the shear crack propagation rate in heavily irradiated material. The shear strain parameter A call account for this passive effect. The value of A can also be adjusted for the temperature dependence of the transgranular crack growth rate. The normal strain parameter, P, is to account for the increase in the crack growth rate and decrease in cyclic life under tension-torsion or axial straining over that observed for unirradiated torsional fatigue specimens. A second step would be to examine the synergism between normal stress and irradiation damage by active volumetric damage on irradiate material under multiaxial strain conditions (as observed in the tension-torsion tests of Blass and Zamarik [13]) conducting tension fatigue tests and combined tension-torsion fatigue tests on post-irradiated material. The parameter P would now be expected to rise dramatically , analogous to the increase in crack growth rates observed for 316 stainless steel by Lloyd and Wareing. The change in P is a function of the neutron fluence levels, and the neutron energy, the relative damage intensity of high energy fast neutrons is accounted for by the parameter a. (The value for a at the present has to be extrapolated from data on low energy neutron damage under high fluence and fast neutron damage generated under non-fusion low fluence conditions.) Then, the more difficult step of factoring the effects of hold periods at peak strain (or peak stress, for load-controlled tests) could be taken. The t--N diagram could be a useful tool for differentiation of the interacting phenomena if constructed carefully. The iso-strain t - N plots of figs. 4 and 5 are interpretive aids, depicting the several phenomena that are intertwined in a strain-controUed tension hold test. Hold periods at temperatures in a torsion test isolate the relaxation phenomenon, where creep strain is

R.E. Nickell, E.P. Esztegar / Fatigue life design criteria

being exchanged for plastic strain and dislocation damage is being annealed by grain boundary sliding. The degree of crack growth enhancement and cyclic life reduction will be relatively modest, since grain boundary cavitation will be conf'med to the region very near the crack tip and no normal stress is present to promote coalescence. Long hold periods should be marginally more damaging than periods of the order of relaxation time. However, for a sufficient larger shear strain range, it would be possible for the stress relaxation and grain boundary sliding to produce an intergranular failure (creep rupture), even in onequarter cycle. In tension hold test introduces an additional phenomenon: significant volumetric damage ahead of the deviatoric-stress-driven crack and the possibility of time-dependent intergranular crack extension near cavitated regions. While the parameter P can accomodate some of this effect, the t - N plot is able to capture the full spectrum of behavior. The normal strain enhancement shifts the data leftward along the cyclesto-failure axis and downward along the time-tofailure axis, but hold-time saturation for low strain range does not coincide predominantly with material relaxation time. extending beyond to include timedependent cavitation (a compressive hold period at low shear strain range would have a "sintering" effect). Irradiation, either prior to fatigue testing or during a hold period, adds another layer of complexity. While the parameter P may be able to account for prior irradiation in a relatively straightforward manner, the t - N diagram can illustrate the effect of irradiation damage during hold periods through a "reduced" total time to failure, where the hold time is modified by the neutron flux energetics increasing the total effective fluence. The actual hold period would be shorter than the "apparent" hold period, with the duration calculated from and calibrated by the volumetric damage produced by creep cavitation. At temperatures below the creep range, relaxation and dislocation annealing would not be of concern; however, a torsion fatigue test with a period should exhibit a normal strain effect and little or no difference in cyclic life should be seen between a prior-irradiated torsional fatigue test with no hold period and a torsional fatigue test with identical irradiation exposure during hold periods. Again, a sufficiently large

297

shear strain range combined with sufficiently high irradiation damage should produce quarter-cycle failure ("volumetric irradiation creep rupture"). No such simplistic explanation suffices when normal stress and irradiation interact. The t - N diagram can only be extended by a double "reduced" time to failure, one reduction for prior irradiation and another to account for radiation exposure during hold periods under various load levels. At low shear strain ranges and low normal stress levels, the effect of neutron fluence should exhibit a saturation limit analogous to the saturation effect found in relaxation type hold-time tests. Fig. 8 provides an example for the construction of a hypothetical t - N plot that illustrates some of the phenomonelogy that might be observed during a series of torsion and tension fatigue tests, both will prior irradiation damage and neutron fluence during hold periods. Such t - N diagrams can be used to give very approximate estimates of the fatigue life fractions for different operating conditions evaluated by linear damage summation criterion in the form of i

(n/Nf)i <~Dirr ,

(12)

where n is the number of service cycles and N is the number of cycles to failure from the t - N diagram for the maximum neutron flux and hold time values. Notwithstanding the recognized inaccuracies, this method has the advantage that it permits the construction of an approximate damage map based on only a very few strategically located data points if the best conditions are carefully selected to anchor the isostrain lines at predictably extreme operating conditions. 5. Conclusion The review of the various microstructural phenomena activated in fusion reactor environments leads to the conclusion that rationalevaluation procedures for treating low-cycle fatigue, creep-fatigue and irradiation damage are required to establish engineering feasibility of commercial fusion reactors. We are suggesting a fatigue damage analysis method that, with a modest extension of the current volumetric creep evaluation procedures can include fusion neutron irradiation and hold-time effects.

§

F-

o

=,

(~

*~

I

I/4

~t ~

-

LOG Nf

-

CYCLES TO FAILURE

0~,~ ~

....--7. \olo

-~%.?~.:.;,~

N ? e a ~

~wo..

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UNIRRADIATED

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~,,',..

UNDER 0 LOAD

IRRADIATION UNDER CYCLIC LOAD

.~

(a)

(d)

ISO-STRAIN t - N DIAGRAM FOR ~ , ° ,% AT ~93°c

" ~ ,~,% ~ ^ \ ,,~', ~ /

I

/

I

(CYCLES)

EXISTING DATA FOR 516SS MATERIAL IRRADIATED IN FISSION REACTOR

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~/

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(E>O.I MeV)

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!

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IRRADIATION SOURCE SPECTRAL INTENSITY NORMALIZED BY FISSION SOURCE

(1)E2

(:~E i

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iN= N f / N f , IRRAD. OR I(:I:) =

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~

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UNDER LOAD"

0

.

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.

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2.75

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l-co ~z l.,d l.l.l ZI.Z

~

d

z (..9 0

t~

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Fig. 8(a). Existing post-~radiated fatigue test data for material irradiated in fission reactor; (b) fatigue life constructed from irradiation creep-rupture and postirradiated fatigue test for expected fusion spectrum; (c) relative neutron damage intensity for fission and fusion sources in terms of effective total fluence and fatigue life reduction; (d) construction of iso-strain t - N diagram for fusion first wall service conditions from unirradiated ~e = 1% tension hold time fatigue data and irradiated (under 0.5% maximum load) creep rupture data.

I/4

I

I

I,.

~~l I

-~_, ~.." ~ .,,.~:t1(/2 .___--05"/*~

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I

LOG Nf

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0.5

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,SO-STRA,N ~'-N D,AGRAM FOR ~ e : , ~ AT ROOM TEM~

R.E. Nickell, E.P. Esztegar / Fatigue life design criteria We suggest that the parameter P will be able to account for duration o f the irradiation exposure, the duration of the hold period at stress, damage annealing due to compressive mean strain and temperature and initial heat treatment. The neutron damage identity parameter, a, can be used to adjust P for different neutron exposures. The advantage of such a method, in terms of design rules and evaluation criteria, is that safety and ignorance factors are easily introduced separately, in terms of the damage mechanism, through these parameters. For situations involving very high shear strain levels and high irradiation-damage levels, where time to failure becomes a more meaningful measure of life than cycles to failure, the enhanced strain range concept will not be useful. Instead the t - N diagram may best interpret the damage characteristics and provide estimates for the fractional fatigue life for different operating cycles. At this stage we are suggesting that the techniques and conceptual models discussed can be used to plan and critically evaluate the results o f the new type of test programs needed to generate the data base necessary for assembling even purely empirical fatigue criteria. Extrapolation into untested or untestable service conditions can be put on a firmer basis by tests that isolate the damage mechanisms and damage rates. We suggest this approach rather than continuing the reliance on "conservatively small" fractions of the life measured in the terminal failure state type of fatigue test, that represent, o n l y particular damage combinations and give no information on the incremental damage process.

References [ 1 ] Alloys for the fusion environment - Technical assessment DOE/ET0007 (1978). [2] J.R. Powell et al., Eds., Proc. Magnetic Fusion Energy Blanket and Shield Workshop, ERDA- 76 / 117/1, Brookhaven National Laboratory (1976). [3] D. Steiner and J.F. Clarke, Science 199 (1976) 13951403.

299

[4] ASME Boiler and Pressure Vessel Code, Code Case N-47 (1977). [5] B. Tomkins and J. Wareing, Met. Sci. 11 (1977) 414424. [6] C.E. Jaske, H. Mindlin and J.S. Perrin, Proc. Int. Conf. on Creep and Fatigue in Elevated Temperature Applications, Sheffield, 1974. [7] D.M. Norris, Jr. et al., UCRL-80478, Lawrence Livermore Laboratory, CA (Dec. 1977). [8] M.W. Brown and K.J. Miller, Proc. Inst. Mech. Engrg. 187 (1973) 745. [9] D.W. Lobitz and R.E. Nickell, Nucl. Engrg. Des. 51 (1978) 61. [10] J.J. Blass and S.Y. Zamrik, in: ASME-MPC Symposium on Creep-Fatigue Interaction, Ed.: R.M. Curran, MPC3 (1976) 129-159. [11] F.A. McClintock, Trans. ASME, J. Appl. Mech. 35 (1968) 363. [12] J.W. Hancock and A.C. McKenzie, J. Mech. Phys. Solids 24 (1976) 147. [13] G.J. Lloyd and J. Wareing, Trans. ASME, J. Engrg. Mater. Tech., to appear. [14] D.J. Michel, H.H. Smith and H.E. Watson, in: Symposium on Structural Materials for Service at Elevated Temperatures in Nuclear Power Generation, MPC-1 (ASME, New York, 1975) 10. [15] E.P. Esztergar, ORNL-4757 (1972). [16] J.R. Ellis and E.P. Esztergar, Trans. ASME Symposium on Design for Elevated Temperature Environment (1971) 29-43. [17] S.S. Manson, G.R. Halford and G.R. Hirschberg, Trans. ASME Symposium on Design for Elevated Temperature Environment (1971) 12-28. [18] L.F. Coffin, MPC-3-ASME (1971) 349-363. [19] W.J. Ostergen, Ph.D. Thesis, Rensalear Polytechnic. Inst. (1976). [20] S. Majumdar and P.S. Maiya, in: ASME-MPC Symposium on Creep-Fatigue Interaction, Ed.: R.M. Curran, MPC-3 (1976) 323-335. [21] C.E. Jaske and J.A. Begley, in: Ductility and Toughness Considerations in Elevated Temperature Service, Ed.: G.V. Smith, MPC-8 (ASME, New York, 1978) 391409. [22] C.R. Brinkman, G.E. Kirth and R.R. Hobbins, Nucl. Technol. 16 (1972) 297. [23] L.D. Blackburn, HEDL TME 75-15 (1972). [24] J. Wareing and H.G. Vaughan, Met. Sci. (1977) 439. [25] F.L. Vook, Phys. Today (Sept. 1975) 34. [26] H.R. Brager, F.A. Garner, and G.L. Guthrie, HEDLSA-1064 (April 1976).