DEPARTMENT DES ETUDES MECAMQUE5 ET THERMIQUES

- Racheting - Experimental tests and pr'tical method of analysis

- P. COUSSERAN - J. LEBEY - D. MOULIN - R. 30CHE - G. CLEMENT

International conference on engineering aspects . of creep. Sheffield, GB, September 15 - 19, 1980. CEA - CONF 5480

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I - INTRODUCTION

In absence of creep, and when the behaviour of material is solely elastic-plastic, it is easy to define the ratcheting, or progressive distortion. There is ratcheting when, under the effect of cyclic solicitations, an increment of deformation appears at each cycle. This state is the opposite of shake-down where, after application of a few cycles, the structure keeps the same geometry.

When creep can not be neglected, that is to say when phenomena are time-depending, such a simple definition is no longer suitable. In this paper, one will call ratcheting the acceleration of deformation, under controlled load, due to imposed cyclic defor­mations. In other words, we give our attention to the increase of creep elongation in presence of cyclic deformations, such as ther­mal straining.

With the development of modern techniques, and in par­ticular Liquid Metal Fast Breeder Reactors, the survey of conse­quences of this phenomenon has become very important, in order to get a safe design. Thus, there is a strong need for convenient, effective, and safe design rules.

Concerning the design of nuclear reactors, construction Codes give some indications C 1 } ' C 23- When creep is not to be con­sidered, rules are rather of nature to get a pure elastic behaviour, required for the validity of fatigue analysis. At high temperature, various very conservative rules are proposed of which the field of application is very limited. The aim of this paper is to bring a contribution for the establishment of a conservative design rule, with a wide field of application and an easy mode of utilization.

II - PREVIOUS WORKS AND PRACTICAL USE

The rules proposed in the construction Codes result only from theoretical works. The first ones were carried out by Miller ^3] and Hill £4] ; important developments were made by Edmunds and Beer C5], and by Bree t 63' C 73 w n o n a s established well known dia­grams. Additional studies are due to Burgreen £8, 9, IO] as well as Townley £lll and Zarka C 1 2J« More suited to creep problems are the

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O'Donnel-Porowski contributions £l3]. The state of the matter v/as reviewed by Leckie ̂ 14] r Roche £l5], Finley and Spence £l6], and Krempl £l7].

Nevertheless, noticeable efforts were made in the field experimental investigations by various authors. Experiments on structures were performed by Kano £l8], Corum £l9], Moreton and Moffat £20].

More basic tests on structural elements and various spe­cimens were carried out by Ainsworth £21], Conway [[22], Ronay £23], Inoue £24], Anderson £25, 26], Udoguchi £27], Nozue £28], Boulais £29, 30], Uga £31, 32], Lebey £33, 34], Cousseran £35],

Under examination, it seems to be surprising to the au­thors of this paper that these various experimental data were not put; under consideration for the establishment of design rules. This situation seems very strange for all the theoretical works are ba­sed on very simplified behaviour models of materials, such as no hardening or kinematic hardening, whereas it appears from experi­ment that no one of these models fits correctly the actual beha­viour of materials £.36].

It must be pointed out that cyclic hardening effects are never taken into account in these computations, and that strain har­dening models are very far from the real behaviour of material^ 2,4 3]

Results of tests performed in Saclay have led the authors to develop an evaluation of the experimental data usable to set up a design rule. Thus, it is useful to give some indications about the way used for this purpose.

Ill - DESCRIPTION OF TESTS PERFORMED IN SACLAY

These tests are extensively reported in references £29, 30,33, 34, 35], Only the main features are given here. The ratchet tests were performed on thin tubular specimens (O.D. 11 mm, thiefc2"* ness 0.5 mm, length 300 mm) subjected to a constant tensile load and, simultaneously to a cyclic twist motion (fig. 1).

The materials of interest are 304 L and 316 L stainless steel ; the tests have been performed at room temperature and at 300°C.

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The fir. t stage of the tests was the measurement of me­chanical characteristics of these steels at the test temperatures ; relating to 316 L steel, a moticeable cold creep v/as observed.

The results obtained are the values of incremental and cumu­lative elongations, function of number of twist cycles, see exam­ple on Fig. 2.

IV - METHOD FOR EVALUATION OF EXPERIMENTAL DATA

In such tests, it is easy to distinguish the tensile primary stress (load controlled stress in this case), and the torsional secondary stress (deformation controlled stress).

The primary stress intensity is equal to :

p _ Tensile load Cross section area

and, according to the TRESCA criterion, the range AQ of the secon­dary stress intensity is given by :

AQ = 2 G-lAy

These two quantities define the loading conditions. The main result obtained from each test is the non elastic elongation e , depending on the test duration, and on the number of cycles (for a given material and test temperature).

A first presentation of results consists in the cons­truction of sets of isodeformation (e ) curves in the field of the two loadings (Bree diagrams type). Such a diagram is shown, for illustration,on fig. 3, on which the values of P and AQ are rela­ted to the yield strength a 0.2 of the material.

It was found judicious to translate this elongation in*-to terms of stress by introduction of an effective rrimary stress P ~~. This effective primary stress is defined as follow :

(i) It is a primary stress (ii) It is applied without secondary stress (iii) It gives the same deformation as the one due to both the

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actual primary stress P and the secondary stress ÛQ applied toge­ther during a ratchet test, the time of application of P e f£ being equal to the duration of the ratchet test.

As an example the values concerning one of our tests (n° 39) are the following :

P = 246 MPa AC = 3i0 MPa Duration of test : 335 h. E

p = i- 3 0 *

From the isochronous curve of the material (for t=335 h) this elongation could be obtained by the application of a stress

( equal to 291 MPa ; this i\» the value of the effective primary stress P e f f

Using P _f is justified when the number of cycles rea­ches a few tens ; nevertheless, it appears from experiment that there is only a little influence of lower numbers of cycles on the validity of this method. The deformation obtained for various frequencies going from 3 to 68 cycles per hour (tests n° 41-42-43) is given, as a function of time, on fig. 4.

One can see that the effect of the frequency vanishes ( after a relatively short while. For the tests plotted on this dia­

gram, the elongation at t = 100 hours is equal to 3 % ; from cold creep curves these values are met for a stress equal to 330 MPa ; consequently the va?ue of P e ff is 330 MPa. Th« cold creep curve for a 330 MPa tensile stress, drawn on fig. 4, fits well the rat­chet test curves, the higher the frequency, the faster the concor­dance.

The complete evaluation of a test is as follow :

(i) Determination of P e fr as said previously (ii) Calculation of the secondary stress ratio SR

S R = AQ S R P + LQ

« • M M M B

(iii) Calculation of the efficiency index V

V = P

Peff

(iiii) Plotting of experimental points on an efficiency diagram in the field SR - V (fig. 5)

V - PROPOSITION FOR A ROLE

When examining the points of Fig. 5, it appears that they are groupei into a rather narrow band ; so it seems possible to propose a curve giving an upper bound of the progressive dis­tortion. The choice of such a curve requires a large amount cf ex­perimental data.

A first attempt can be made by using the well known Bree diagram. In this diagram, the material is assumed elastic per­fectly plastic. When a primary stress is applied to the material, only two events can happen. If the stress is below the yield strength, there is no plastic deformation ; on the contrary, if the stress is equal to yield strength, the plastic deformation can reach any value. There is the same distinction in the Bree diagram : in one part of this diagram, there is no ratcheting ; in the other part, the plastic deformation can reach any value de­pending on the number of applied cycles. Hence, the curve sharing these two parts must be considered as equivalent to an effective stress equal to the yield strength of the material. The equation is

for V < 0.5 SR =

for V > 0.5 SR =

1 + V 2

1 - V 1 - 0.75 V

This curve,which is drawn on fig. 6, can be used for the design in order to avoid large distortions when ratcheting can occur in the creep temperature range (it can be used too when creep ef­fects are not significant), When a primary stress P is applied in combination with a cyclic straining corresponding to a secondary stress of intensity AQ, the following process must be applied :

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(i) Computation of SR = p ^ (ii) Determination of V with the help of the design curve (see

fig. 6) p (iii) Computation of P e f f - «

All design limits concerning the primary stress must be applied to P f f in lieu of P itself. For instance, if the gene­ral primary membrane stress P is concerned, it is necessary to determine P e* f _ according to the precedent process. P e « _ should not exceed S_. (level A and B s r -vice limits) mt

{ i i i i > Peff m « Smt

f where S . is determined for the duration of application of the loa­ding.

Code requirements [2] related to primary stress must be applied to the effective primary stress instead of the primary stress itself. S. limits the deformation to 1 % during the time of application of the load ; accordingly, this method limits also the membrane deformation to 1 %.

VI - VALIDATION

. Various published experimental data have been used for the validation of the proposed design curve.

Analyses of these data, according to the proposed method are made in ref £37, 38, 39, 403 • All the results are gathered on fig. 7, where one can see that the curve is conservative.

A particular mention can be made concerning the test TT-1 from réf £37^. After the third cycle of this test, the Qum»r lative strain is equal to 0.207 %, for a 504 hours accumulated hold time. By application of the proposed method, the P f i f f value for this case is equal to 12,764 psi. When considering the thir­teenth cycle, the cumulative strain is 0.338 %, for a time equal to 2184 hours, arid P , f is now equal to 12,667 psi. The two values of P f f are almost identical, but very different from the primary

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stress which is equal to 7/527 psi-

It is also interesting to compare the design rule propo­sed here with the 0*Donnel-Porowski approach. In using the same way that the one used for the Bree diagram, it can be seen that a lot of curves are obtained at the vicinity of the design curve, this latter one being the most conservative.

VII - CONCLUSIONS

From available experimental results known up to now, one can propose a simplified method to prevent ratcheting ; it is based on the notion of an effective primary stress P-f*.--

Nowadays, a very conservative design curve has been chonen, of which the efficiency can be improved by further works, involving new tests data and more careful analysis.

This process is included in a RAMSES rule £4l]. From use, it appears that the main difficulty consists in the good choice of the primary stress, if one considers the risk of elastic follow-up, but this is a problem different form the ratchet one.

This method could also bean improved by taking in ac­count some characteristics of the material, such as the yield strength (see fig. 5). The authors think that cyclic characteris­tics could be used.

ACKNOWLEDGMENTS :

The authors wish to acknowledge the members of RAMSES Committee for stimulating discussions about this subject, and the C.E.A. for its support and interest in this study.

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