STRESS AND STRENGTH STUDIES TURBINE BLADE ATTACHMENTS · STRESS AND STRENGTH STUDIES dovetail joint is not uniformly distributed. This fact is important for a better under- standing

STRESS AND STRENGTH STUDIES ON TURBINE BLADE ATTACHMENTS

A. J. DURELLI, J. W. DALLY and W. F. RILEY, Armour Research Foundation of Illinois Institute of Technology, Chicago, Ill.

ABSTRACT

The objective of this paper i s to illustrate the manner in which a number of experimental techniques have been used in an integrated approach to the solution of the problems in turbine and compressor blade attachments. Experimental methods employed include brittle coatings, photoelasticity, ordinary and high-temperature electrical-resistance strain gages, and a fatigue testing assembly. Various phases of the following problems a re presented: (1) transmission of the forces from the airfoil into the dovetail joint, (2) optimization of the dovetail fillets, (3) influence of the protuberance angle, (4) influence of simultaneity of protuberance contact, (5) determination of protuberance loading, (6) high- temperature fatigue testing.

Due to the general nature of this paper em- phasis has been placed on the application of the experimental methods ,and in many in- stances the results of a particular investigation have been deleted.

I. INTRODUCTION

The joint between either a compressor or a turbine blade and the rotor is frequently the weakest part of the entire rotating assembly. A great amount of consideration has been given

Presented at the Annual Meeting of the Society for Experi- mental St ress Analysis in San Diego, Calif., October, 1957.

by designers to different means of realizing these joints, and much experimental work has been conducted to develop more efficient joint configurations.

The objective of this paper i s to review in a descriptive manner an integrated set of experiments conducted by the authors at Armour Research Foundation directed toward an im- provement of the strength of these joints. Most of the techniques employed have been described in the literature; however, their application to the blade - attachment problem presents some unusual phases and the integrated analysis ~f the results of a nuxnber of experimental methods has not been presented before.

The solution of the problem of improving the strength of the joints was approached from the point of view that i t is more important to be in a position to grade designs by order of merit than to associate a value of s t r e s s to a particular design, It was also believed that the analysis should be conducted a s far a s possible in the laboratory using model studies and simulated service testing of actual components since testing in the actual turbine or in the compressor is an extremely expensive and time consuming project.

In order to obtain a basis for an improved redesign of the blade, the general problem of blade attachment was decomposed into several parts which a re listed below:

(1) Study of the various conditions of loading to which the blade is subjected.

(2) Transmission of forces from the airfoil to the dovetail joint.

(3) Stress distribution in the dovetail joint

S . E . S . A . P R O C E E D I N G S V O L . X V I NO. 1

and influence of the following par- amete r s on this distribution: (a) fillet contours, (b) angle of the protuberance, (c) non- simultanei ty of protuberance contact.

(4) Determination of protuberance loading. (5) Simulated service testing of actual tur-

bine blades a t elevated temperatures. In the study of these pa r t s of the problem

use was made of the actual blade and of over- s i ze plastic models of the dovetail joint. Ex- perimental procedure which included brittle coatings, electrical-resistance s t ra in gages, and two-dimensional photoelasticity were f re- quently employed in combination.

I I . LOADING CONDITIONS

I t is generally agreed [I]* that the following a r e the two most important forms of loading which act on the blade: (1) a radial centrifugal force which pulls the blade away from the joint, and (2) the bending of the blade a s a cantilever. Results obtained from high- tern- pera ture e lect r ica l - res i s t ance s t ra in gages cemented to t3e blades in actual service s e e m to substantiate this conclusion.

The bending is produced statically by the action of the gas p ressure on the airfoil and by a tazgential compoEent of the centrifugal forces due to a tilting of the airfoil. The bending load also has a dynamic component which is produced by the vibrations of the blade. This point of view assumes therefore that s t r e s s e s due to other factors such a s residual and thermal s t r e s s e s a r e secondary influences and may be neglected fo r design purposes. Following this simplifying assumption, the blade models and the actual blades were subjected to the two elementary forms of loading, namely, tensile loading and bending loading. These loads w e r e applied either separately, o r combined. In the case of combined loading the

" r a t i o between the s t r e s s produced by tensile

T E N S I L E L O A D BENDING L O A D

F I G . I . L O A D I N G O F THE TURBINE B L A D E S WHICH HAVE B E E N COATED

I N T H E S H A N K R E G I O N WITH A BRITTLE COATING (STRESSCOAT).

S T R E S S A N D S T R E N G T H S T U D I E S

loading and the s t r e s s produced by bending loading, a t a defined point, was known from high- temperature s t ra in gage deter rninations taken in the engine. This ratio of bending s t r e s s to tensile s t r e s s was maintained in the tests.

The manner in which the applied forces a r e distributed in a dovetail joint cannot be easily predicted. This i s due to the fact that the dovetail joint i s an indeterminate structure, therefore, the distribution of forces between the tangs depends upon the rigidity of the tangs and the clearance existing between pairs of

mating tangs. Another phenomenon that makes a precise determination of the force distribution difficult i s the slipping and rotating of the blade in the rotor dovetail slot. Each t ime this movement occurs the position of contact between mating tangs changes. As a resul t , in experiments conducted with oversize plastic models it was found that the s t r e s s distribution was not always a l inear function of the load. However, in general, variations in the s t r e s s concentration fac to rs for different levels of load were usually l e s s than 10 percent.

F I G . 2 . T Y P I C A L B R I T T L E COATING CRACK P A T T E R N OBTAINED

BY S U B J E C T I N G A B L A D E TO A T E N S I L E L O A D .

F I G . 3 . T Y P I C A L B R I T T L E COATING CRACK P A T T E R N O B T A I N E D

BY S U B J E C T I N G A B L A D E TO A BENDING L O A D .

S . E . S . A . P R O C E E D I N G S V O L . X V I N O . 1

Ill. ,TRANSMISSION OF FORCES FROM THE AIRFOIL INTO THE DOVETAIL JOINT

In o r d e r to determine the distribution of s t r e s s e s in the region between the airfoil and the dovetail (shank region) bri t t le coatings were applied to the shank region of the actual blades. The bri t t le coating analysis was conducted separately fo r the tensile and bending loadings. The loadings were applied in the manner i l lustrated in Fig. 1. Standard bri t t le coating procedures were utilized to obtain the typical crack pat terns which a r e shown in

Figs. 2 and 3 . The numbers etched in the coating refer to the load level necessary to crack the a r e a s of coating enclosed by the isoentatics .

The resul ts obtained for the individual loadings can be combined for any ra t io of bending to tensile forces to obtain the s t r e s s distribution associated with combined loading. One important conclusion obtained from these brittle coating analyses i s that the s t r e s s distribution in some of the shank designs was far from uniform. Consequently, the distribution of load ac ross the top neck section of the

LEVE ING E ON 1

F I G . 4. P L A S T I C M O D E L I N T H E L O A D I N G F R A M E

The jigs and f r a m e a s shown allov, the application of a t ens i l e load or. a comblned tensi le and bending load T h e magnitude of t he applied load is m e a s u r e d o p - t ical ly a t the na r row necked s e c t ~ o n of the shanks


dovetail joint i s not uniformly distributed. This fact i s important for a better under- standing of the limitations of a simplifying assumption which i s made in the following section regarding two - dimensional model analysis of the dovetail joint.

IV. STRESS DISTRIBUTION I N THE DOVETAiL JOINT

Since the dovetail geometry i s the same for any t ransverse cross-section, it is practical to think of the dovetail s t r e s s e s a s a two- dimensional problem. The loading applied to the dovetail a s shown previously i s not uniform and strict ly speaking the distribution of s t r e s s e s in the dovetail will be three-dimensional. However, if i t i s assumed that each separate sl ice of the dovetail behaves essen- tially a s a two-dimensional problem, but that

the amount of load taken by each s l ice is different, i t i s possible to use two-dimensional models to represent the cross-section of the dovetail. The load on each sl ice i s given by the previous analysis of the distribution of s t r e s s e s in the shank region.

Two-dimensional models of the blade and wheel dovetails were machined f rom Columbia Resin (CR-39) five to ten t imes the s i z e of the prototype. The models were subjected to ten- s i le loads and combined tensile and bending loads in the loading fi,xture i l lustrated in Fig. 4. The loaded models were examined in a polariscope to obtain the isochromatic fringe patterns associated with both forms of loading. Typical examples of the isochromatic fringe patterns obtained a r e shown in Figs. 5 and 6.

The directions of the principal s t r e s s e s oc- curring in the models were determined for both fo rms of loading through the use of brittle

F I G . 5 . T Y P I C A L I S O C H R O M A T I C F R I N G E P A T T E R N FOR A

D O V E T A I L J O I N T S U B J E C T E D TO T E N S I L E L O A D .

F I G . 6 . T Y P I C A L I S O C H R O M A T I C F R I N G E P A T T E R N FOR A

D O V E T A I L J O I N T S U B J E C T E D TO C O M B I N E D LOADING.


F I G . 7 . I S O S T A T I C ( C R A C K ) P A T T E R N A S S O C I A T E D WITH

T E N S I O N LOAD ON THE D O V E T A I L J O I N T .

coatings. The isostatic (brittle coating cracks) associated with tensile and combined loading a r e shown in Figs. 7 and 8 respectively.

Stress concentration factors obtained at the fillets of both the blade and rotor were obtained from the isochromatic fringe patterns. By comparing the s t r e s s concentration factors for various dovetail designs i t was possible to grade them in their order of merit .

V. OPTIMIZATION OF THE FILLETS

An ideal fillet, stresswise, i s a fillet along which the s t r e s se s a r e uniformly distributed. The contour of an ideal fillet can be determined photoelastically by notin the fringe 5 positivn relative to the boundary[ 931. A poorly designed fillet will have at least one point a t which the fringes concentrate; on the other hand a well designed fillet (see Fig. 9) has about the same fringe order along the major

F I G . 8 . ISOSTAT IC ( C R A C K ) P A T T E R N ASSOCIATED WlTH

COMBINED L O A D I N G ON T H E D O V E T A I L J O I N T . <

portion of the fillet length. The process for redesigning fillet contours

which a r e in general circular i s primarily a t r i a l and e r r or process. Elliptical fillets, combinations of circular fillets and straight lines, and compounded circular fillets were investigated. Since the shape of the ideal fillet depends on loading conditions, and a turbine blade i s subjected to varying ratios of combined tensile and bending loadings, the fillet shape had to be the result of a compromise between the best shapes obtained for tensile loading and those obtained for bending loading. The fillet shape recommended was not general but depended on the design of the blade (i.e. two- or three-protuberance design, split- or solid-type-blade design) and the particular fillet under consideration (i.e. fillet at the top neck section on the wheel and the fillet a t the bottom neck section on the blade would have different shapes).


POOR F I L L E T I D E A L F I L L E T

F I G . 9 . P H O T O E L A S T I C FRINGE PATTERNS O B T A I N E D FROM A N E A R L Y

I D E A L F I L L E T AND FROM A POORLY D E S I G N E D F I L L E T .

Note how the highest o r d e r fr inge i s nearly para l le l over a l a r g e portion of the fillet boundary for the ideal fillet while for the poorly designed fillet the f r inges concentrate a t a point on the boundary.

VI. INFLUENCE OF PROTUBERANCE ANGLE

Following the two - dimensional approach outlined previously, investigations were conducted to determine the s t r e s s distribution in turbine blade and wheel dovetails designed with 30, 40, and 50 degree flank angles. Some of the isochromatic fringe patterns obtained for blades designed with different flank angles a r e shown in Fig. 10. The designs were com- pared on the basis of s t r e s s concentration factors at the three fi l lets associated with both tensile and combined fo rms of loading.

It was found for the tensile loading that the s t r e s s concentration factors for a l l fillets decreased with increasing protuberance angle. However, the conclusions for the combined form of loading a r e not s o clear-cut, for while the s t r e s s concentration factors at the top neck section decreased with an increase in flank angles, the s t r e s s concentration factor at the middle and bottom neck sections increased with increasing flank angles.

VII. INFLUENCE OF SIMULTANEITY OF PROTUBERANCE CONTACT

For most of the t es t s conducted on plastic models simultaneous contact between tangs was accomplished by individually fitting each pair of tangs by filing the mating surface whenever necessary. Since machining toler - ances on the actual prototype permit a protuberance mismatching, a preliminary study was conducted to show the influence of the lack of simultaneous contact between the protuberances on the s t r e s s distribution in the joint .

The method followed to determine this influence consisted, briefly, of machining a photoelastic model of the dovetail joint and fitting the blade into the wheel slot so that the contact between the s i x pa i r s of protuberances was simultaneous. Shims of known thickness were then inserted between various pairs of protuberances to dest roy the simultaneity of contact. This shimming process produced

S . E . S . A . P R O C E E D I N G S V O L , X V I N O . 1

4 0

T E N S I L E L O A D

40

COMBINED L O A D

F I G . 10, I S O C H R O M A T I C FR INGE PATTERNS OBTAINED FOR

5 0

M O D E L S WITH VARIOUS

PROTUBERANCE A N G L E S SUBJECTED TO TENSION AND COMBINED LOADING.

The flank angle is defined a s the angle between the mating surface and a horizontal line.

clearances between the pairs of protuberances isochronlatic fringe pattern obtained in this which were not shimmed. Next, a load was manner i s shown in Fig. 11. In this case shims applied to the model until the clearance be- of equal thickness were located between the tween the pairs of tangs which were not upper right, middle left and lower right pairs shimmed was overcome and contact was made of protuberances. on all s ix pairs of protuberances. A typical A preliminary evaluation of the elastic


FIG. I I . PHOTOELASTIC FRINGE PATTERN OBTAINED UNDER T E N S I L E LOADING

AFTER S IMULTANEITY OF CONTACT W A S DESTROYED BY I N S E R T I N G

S H I M S I N T H E UPPER RIGHT H A N D , MIDDLE LEFT H A N D AND LOWER

RIGHT HAND PAIRS OF PROTUBERANCES.

After i n s e r t i n g the s h i m s load was applied until contact was obtained on the other th ree tangs.

s t r e s s e s which occur a t the top fillet, indi- Approach 1 - Combining the photoelastic cated that an interference produced by allow- (isochromatic fringe patterns) and the brittle able machining tolerances at the upper two coating (isostatics) data, the radial and trans- pa i r s of protuberances on the prototype may verse components of s t r e s s ac ross the neck resul t in s t r e s s e s of about 50.000 psi before sections were determined f rom the s t r e s s the other two pairs of protuberances make equations of equilibrium. The law of equi- contact and begin to c a r ry their part of the librium was then applied a t each neck section load. and a relation was established between the

protuberance load and the s t r e s s distribution VIII. DETERMINATION OF PROTUBERANCE across the neck sections. It was found that

LOADING e r r o r s introduced through the graphical integration using the isostatic data were too large

Determination of protuberance loads is im- for this approach to be satisfactory. It is pos- portant in dovetail design. Toward this end, sible that i f isoclinic data had been used in three basic approaches have been employed. place of the isostatic data the results would


have been more satisfactory. This was not attempted because other approaches not em- ploying graphical integration were used.

Approach 2 - The distribution of the radial and t ransverse components was determined a t interior points using electrical - resistance s t ra in gages (see Fig. 12) and at the boundaries using photoelastic data. This method was suf- ficiently accurate, but the amount of work involved in the s t ra in gage installation was considered excessive.

Approach 3 - This approach differs from the f i r s t in that the graphical integration is avoided and that a greater degree of freedom is exercised in selecting the section. If one separates the protuberance from the dovetail with a vertical cut and applies the law of equilibrium, the vertical component of the load acting onthe protuberance is given by the sum

of the shearing s t r e s se s acting on the surface exposed by the vertical cut [see Fig. 13(a)]. The distribution of the shearing s t r e s se s acting on the vertical cut i s obtained without graphical integration from photoelastic isochromatic and isoclinic patterns. This approach was a s accurate a s the second approach and was less time consuming.

In the case of combined loading, the t ransverse components of the protuberance load become significant. In applying this method to determine the t ransverse component of load, i t i s necessary to make an inclined cut in addition to the vertical cut. Integrating the shears over the twoi cuts one obtains the two equations shown below:

Vertical Cut / rxy CIA = p y = P C O S a ,

Inclined Cut j rx Iy t d ~ = P C O ~ l o - p , .

F I G . 12 . E L E C T R I C A L R E S I S T A N C E S T R A I N G A G E I N S T A L L A T I O N O N A

P L A S T I C M O D E L OF A T U R B I N E B L A D E D O V E T A I L U S E D T O

D E T E R M I N E R A D I A L A N D T R A N S V E R S E C O M P O N E N T S O F S T R E S S

A C R O S S T H E T H R E E N E C K S E C T I O N S .


i F R E E SLiRFACE IN T H I S REGION

( a ) VERTICAL AND INCLINED CUTS. ( b ) T R A N S V E R S E CUTS.

FIG. 13, ILLUSTRATION OF CUTS USED TO DETERMINE

PROTUBERANCE LOADING.

FIG. 14. FATIGUE TEST ASSEMBLY USED IN APPLYING A COMBINED

TENSILE AND BENDING LOAD TO THE TURBINE B L A D E .


All symbols used in these relations a r e defined in Fig. 13(a). These two equations permit solution of the two unknowns P and a .

Another cutting o r sectioning method is illustrated in Fig. 13(b). This method of cutting provides a very direct way of determining the t ransverse protuberance loading P, for the split-type dovetail design. The interface between the two blade halves opens up under the action of centrifugal fo rces and a s a result the interface is a f ree surface. This permits the determination of the t ransverse components directly from the shearing s t r e s s e s acting upon the t ransverse sections shown in Fig. 13(b).

IX . HIGH-TEMPERATURE FATIGUE TESTING

Using the methods just described one can obtain enough information regarding s t r e s s distribution at the shank and at the dovetail joint to intelligently redesign both of them. However, the question a r i s e s of the significance of the design modifications on the behavior of the blade in the engine. Since engine testing is extremely expensive, i t was found desi rable to compare in the laboratory the behavior of blades of different designs and mater ia ls subjected to simulated service conditions. The test assembly used to apply the simulated loads was a special adaptation of a Sonntag Fatigue Testing Machine (SF - 1 - U) used in conjunction with a high-temperature e lect r ical furnace. The overall tes t assembly is illustrated in Fig. 14. A steady radia l centrifugal load was applied to the blade by a calibrated spring and cable assembly. In addition a n alternating bending load of control- lable magnitude was applied to the blade by the fatigue testing machine. The temperature of the blade was maintained a t 1200°F by a chromel-alumel thermocouple and temperature- controlling equipment. The magnitude of the alternating load applied to the blade was verified by high - temperature s t ra in gage readings taken on the airfoil*.

s -N curves for a number of different blade designs and for a number of different blade mater ia ls were established using this method. It was found that the origin of failure of the

* The high-temperature gages used were the Karma wire type developed by General Elec t r ic Company and manufactured a t Arnlour Research Foundation following G.E. specifications.

F I G . 15. F R A C T U R E S U R F A C E OF A T Y P I C A L

F A T I G U E F A I L U R E .

fatigue f ractures was located at points of high s t r e s s concentration indicated by the experimental analyses. A typical example of this is illustrated in Fig. 15 where the surface of a dovetail f racture is shown. In this case the brittle coating analysis had indicated a concentration of s t r e s s a t points adjacent to the two r ibs of the shank. The f racture originated a t these points.

X. ACKNOWLEDGEMENTS

This program was sponsored by the Aircraft Gas Turbine Division of the General Electric Company. The authors gratefully acknowledge the technical ass is tance and support provided by Mr. G. N. Gauthier, Mr. K. W. Mason, Mr. M. Bobo, and Mr. G. Wile of the General Elec- t r i c Company. Method 3 to determine the load on the protuberances was suggested to the authors by Dr. P, D. Flynn of the General Electric Company.

REFERENCES

[I] Smith, C. W., "Aircraf t Gas Turbines", John Wiley & Sons, New York, 1956.

[2] Heywood, R . B., "Designing by Photoelasticity", Chap- man & Hall, London, 1952.

[ 3 ] Baud, R. V., "F i l le t Profi les for Constant S t ress" , Ma- chinist, June 23, 1934: and Product Engineering, April 1934.

DISCUSSION

P. D. FLYNN, General Electric Company, Schenectady, N. Y..

of the Preceding Paper Entitled: STRESS AND STRENGTH STUDIES ON

TURBINE BLADE ATTACHMENTS

The authors a r e to be cbngratulated for their presentation of an interesting paper on the application of bri t t le coatings, photoelasticity, s t ra in gages and fatigue testing to a study of turbine and compressor blade attachments.

The authors acknowledged that Method 3 for the determination of protuberance loading was suggested to them by the discusser . The discusser wouldalso like to acknowledge that this idea was developed jointly with R. Guernsey and B. S. Angel1 of the General Electric Com- pany. The discusser and his associates haye tested a number of dovetails photoelastically using somewhat different techniques than those of the authors. The purpose of this discussion is to describe the techniques used at the Gen- e r a l Engineering Laboratory, especially in regard to the determination of protuberance loading, and to briefly discuss the significance of the precision methods employed.

Fig. 1 shows a model of a two-hook, steam- turbine dovetail in which the upper member is the bucket dovetail and the lower member i s the wheel. Of in teres t to the designer a r e the maximum fillet s t r e s s e s , the hook-load distribution and the horizontal component of the tang load. The maximum fillet s t r e s s e s a r e determined from s t r e s s patterns (isochro- matics) such as Fig. 2. In o rder to determine the hook-load distribution and tang load, the hooks and tang a r e imagined to be isolated by vertical and horizontal cuts, respectively. The shearing s t r e s s acting a t any point on the surface of the cut can be calculated from the iso-

' chromatic fringe order , n, and the direction

FIG. I . P H O T O E L A S T I C M O D E L OF A TWO-HOOK,

S T E A M - T U R B I N E D O V E T A I L . E X P E R I M E N T A L

SETUP FOR T E N S I L E L O A D I N G .


. FIG. 2 . T Y P I C A L STRESS P A T T E R N ( I S O C H R O M A T I C S ) O F

D O V E T A I L S U B J E C T E D T O T E N S I L E L O A D .

of the principal s t r e s s e s , 8, a t the point [l I*. From conditions of equilibrium, the resultant of the shearing s t r e s s e s gives the required load.

The authors have determined the direction of the principal s t r e s s e s , 8, in the model by two methods - f r om photoelastic isoclinic pat terns and f rom an additional test using br i t t le coatings (isostatics) . The discusser p re fe rs to work only with the isoclinics, and Fig. 3 i s a typical isoclinic pattern. In the actual determination of protuberance loading, the discusser does not use photographs such a s Figs. 2 and 3 . Instead, B and n a r e meas-

ured by precision methods, point by point on the model, along the l ines of interest[2]. At each point, the isoclinic parameter, 8 , i s determined by using a photometer to indicate minimum light intensity, and then the fringe order , n, is measured by means of a com- pensator with the aid of the photometer. Since i t may take several hours to obtain the neces- s a ry data, Castolite [3 ] is used a s the model material in o rder to avoid creep and time- edge effects. A s an overall check on the accuracy of the work, the sum of the vertical components of the hook-loads must equal the applied load, and a static check of within two to three percent i s usually obtained. These

* S u p e r i o r s in b r a c k e t s per ta in to re ferences listed at the techniques have been to end of the discussion. dovetails containing a s many as four pairs

1 D I S C U S S I O N i

F I G . 3. T Y P I C A L I S O C L I N I C P A T T E R N ( 0 = 0 " ) O F

D O V E T A I L 5 U B J E C T E D T O T E N S I L E L O A D .

of hooks. ment in accuracy may be especially significant The direct measurement of B and n on the when one uses two cuts to determine both the

model by precision methods a s outlined above magnitude and direction of the resultant load is probably faster and more accurate than the on the protuberance [as described by the techniques used by the authors. The improve- authors and shown in Fig. 13(a)].

REFERENCES

[ I ] F roch t , M. M., "Photoe las t i c i ty , Vol. I", John Wiley & Sons, Inc. , New York , 1941, p. 252.

[ 2 ] F roch t , M. M.! P ih , H. and Landsberg , D., "The Use of P h o t o m e t r i c Devices in the Solution of the Genera l T h r e e - Dimensional Pho toe las t i c P r o b l e m " , S.E.S.A. Proceed ings , Val. XI1 No. 1, 1954, pp. 181-190.

[ 3 ] Froch t , M. M. and P ih , H . , "A New Cementable Mate r ia l f o r Two- and Three-Dimens iona l Pho toe las t i c Research" , S.E.S.A. Proceed ings , Vol. XI1 No. 1, 1954, pp. 55-64.

AUTHORS' CLOSURE

The authors appreciate Dr. P. D. Flynnls interest in their paper. It is the authors1 be- lief that good results can be obtained in photoelasticity a s in other experimental s t r e s s analysis methods by using several alternative methods and that the decision on the best method to be used in each particular instance depends not only on the technical features of the method itself but also on the operators' personal preferences, previous backgrounds, skills, and on the instruments available.

The question of whether photometric devices should be recommended in photoelasticity to obtain higher accuracy does not seem to have been settled. It might be proper to mention M. M. Leven1s opinion on the subject*. Leven s tates that he does not feel that the increase in accuracy of the photometric devices war- rants the extra equipment and the increased

* Leven, M. M., "Quantitative Three-Dimensional Photo- elasticityt' , S.E.S.A. Proceedings, Vol. XI1 No. 2 , 1955, pp. 157- 172.

number of measurements that must be made. The authors have increased the accuracy of isoclinic and isochromatic measurements by placing in front of the model to be studied, a piece of thin metal with small holes drilled at the desired positions. Using this technique, isoclinic angles can be reproduced to - 1 4 degrees. The addition of the vertical components of the protuberance loads determined in this way checks within 1i percent the total load applied to the dovetail. This figure seems to be of about the same order of magnitude a s the one mentioned by the discusser and it seems to prove that in this type of test the use of photometric devices is not necessary.

The authors believe that with their equipment, an increase in accuracy can be obtained by more precise angle measurements, the use of more uniform quarter-wave plates, and the use of more uniform photoelastic materials. For most engineering purposes the accuracy obtained with this present equipment is suf- ficient.

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STRESS AND STRENGTH STUDIES TURBINE BLADE ATTACHMENTS · STRESS AND STRENGTH STUDIES dovetail joint is not uniformly distributed. This fact is important for a better under- standing