Fracture mechanics and testing of steel for large rotors A. Freddi

A method is presented for integrity assessment of turbine rotors, based on theoretical and experimental evaluation o f f ront evolution for circular defects interacting with surfaces and each other.

Based on the results o f tests done on plastic models, an 'equivalent' elliptical defect is introduced to represent two interacting coplanar defects.

A fracture mechanics method is used to characterize a Ni-Cr-Mo-V steel turbine disc.

In the evaluation of highly stressed components, such as turbine wheels and rotors it is necessary for the designer to determine which defects are critical, and what size can become critical after a number of load cycles due to starting and arrest of the machine.

These requirements are today more pressing due to the consistent demand for larger forgings to pursue the economy of unit size. But there is also a trend to increase the strength of the forging and cut the size. Both require- ments can be accommodated through a development of a procedure of defect risk evaluation based on a strict quality control, a careful strength evaluation and a predic- tion analysis of crack propagation. Such an evaluation must be correct and not too conservative in order to avoid rejecting, or taking out of use, high cost forged components which are still usable and in 'safe' condition.

The experimental work described in this paper was aimed at the solution of problems involved in the develop- ment of such a method for assessing the integrity of a loaded structure containing defects.

METHOD DE VEL OPMENT

In this development of an engineering method for the assessment of the integrity of large forged rotors containing defects, it was decided that:

1) Linear elastic fracture mechanics would be a suitable tool for investigating propagation and the critical stages of defects in the plain strain condit ion. A correction for small yielding was taken into account according to the Irwin or Barenblatt-Dugdale models;

2) Only centrifugal cyclic loads due to starting and arrest would be considered;

3) Components operate at temperatures at which time- dependent creep effects are absent;

4) No stress corrosion or other environmental effects are present.

The rotor material is Ni-Cr-Mo-V steel which has been vacuum degassed and vacuum/carbon deoxidized and is produced in ingots of up to 500 tonnes in weight. In general the forgings have excellent properties and are high-quality. 1,7 However, in some cases, the results of magnetic particle and boresonic examination show that there are surface defects, and ultrasonic testing from both the outer surface and the surface of the bore, reveal the presence of internal defects.

At the acceptance stage a series of direct controls, calculations and measurements of fracture toughness must

be planned in order to determine the acceptabil i ty of the forged component or, eventually, in order to provide a way for removing defects by machining. The procedure which was developed is presented in the following sections.

UL TRASONIC ANAL YSIS FOR SIZING THE DEFECTS

Internal defects are usually recorded in terms of the size of an equivalent coin-shaped discontinuity with unknown orientation. Since natural defects do not reflect perfectly due to their geometry and posit ion and the material, it is probable that their actual area will generally be larger than their equivalent area. Often, for internal defects the actual area is taken to be at most four times the indicated area. All defects are finally treated as circular cracks (since NDT cannot discriminate between forms) oriented in the most unfavourahle manner, in axial planes and subjected to constant load at sufficient distance from cracks, Fig. 1.

CLASSIFICATION OF CRACKS

The cracks were classified as;

a) internal

b) internal but interacting with another internal defect (cluster)

c) internal but interacting with an external surface

d) surface

t "

J

Fig. 1 Assumptions for cracks location

0142--1123/81/020071--06 $02.00 © IPC Business Press Limited 1981 INT. J. FATIGUE April 1981 71

Handbooks exist in which stress analyses of cracks and the stress intensity factors for typical configurations are reported. Table 1 shows examples of approximate expressions for magnification factors of such geometries. 9 The magnifica- tion factor is defined as the ratio between K I in a certain direction and KI0 of a simple crack in a constant stress field.

A N A L YSIS OF I N T E R A C T I N G CONFIGURA- TIONS A N D SUBCRIT ICAL PROPAGA TION OF CRACKS

A detailed study of interaction effects between circular cracks was planned which used an analogical experimental method in order to define in a realistic way the form and dimensions of an 'equivalent' crack which can be substituted for two or more interacting circular cracks in a successive automatic analysis of subcritical propagation.

Assuming perfect elasticity allowed the use of different elastic materials to simulate steel. 10 Two different models, in polyester and epoxy resin, were manufactured in which coin-shaped cracks were created in pre-established positions either by inserting artificial discontinuities (circular discs of thin teflon foil), or by generating cracks at the bottom of holes by impact loading.

The cracks were then stressed by static loading. Load- ing the cracks themselves is equivalent to infinite load regarding the values of stress intensity factor (SIF).

The experimental programme proceeded along the steps of; (a) visualizing the evolution of the crack fronts during fatigue crack propagation to isolate the main parameters controlling the phenomenon; and (b) determining the numerical values of these parameters in some critical con- figurations by using photoelastic 3-D analysis, holographic interferometric analysis, and numerical (3-D finite elements) calculations. Three basic configurations were investigated:

1) A single crack, representing an internal defect in a thick body under constant stress. A calibration performed for this case demonstrated that the fatigue propagation test is well interpreted in terms of classical laws of fatigue crack propagation.

2) Two coplanar cracks. The evolution front was recorded by using a projection polariscope as a profile projector, Fig. 2. The photoelastic technique of freezing and slicing

Fig. 2 Evolution of crack fronts during sub-critical propagation

Tab le 1. Magnif icat ion factors f o r d i f f e r e n t c rack con f i gu ra - t i ons

M = I

/ / / / ~ / / / / / ~ M = 1. )2

I

h y / z / / / / / / / / / / / / / / / /

M = 0 .48 (a /d ) 3 - O.15(a /d) 2 ~ 1

Q Q ~, ~ j ,,q

M = 0 . 4 8 ( 2 a / d ) 3 - 0 .15 (2a /d ) 2 ÷ ]

I

,,..q

X 1 = ( d + a 1 - a2 j / 2 ,X 2 =d 2(1

M 1 =0 .48 (a1 /X1 ) 3 - 0 . 1 5 ( a l / X 1 ) 2 + 1

M 2 = 0 .48 (a2 /X2 ) 3 - O ,15(a2 /X2) 2 + 1

I

X 1 ( d ' + a I a2) /2 , X 2 d ' X1

M~I =0 .48 (a1 /X l } 3 - 015 (a1 /Z l l 2 ~ 1

M~ l ' -O .48 (a1 /d ' ) 3 O . | 5 (a l / d " l 2 + 1

M ~ - 0 . 4 8 ( 8 2 / X 2 ) 3 0 . 1 5 ( a 2 / X 2 ) 2 4 1 ; M 2 ' 1 1 2

M, - ~*(M;, M','}; M~ - m~×(M~, M~'i

M i = m a x j ( M i j ) ;

72 I N T . J. F A T I G U E A p r i l 1981

was utilized. Slices cut perpendicular to the crack front were analysed according to the methods proposed in the hterature 11 for the determinat ion of SIF from isochromatic patterns.

A special holographic technique 12 was employed for measuring displacement fields and then KI, along the crack tips. Fig. 3 shows the arrangement of the holo- graphic bench. The surface on which measurements were made was obtained by placing an opaque plate at a certain distance from the symmetry plane where the cracks are localized.

Experimental results are presented in Fig. 4

3) Two parallel cracks in planes at a pre-estabhshed distance. Photoelastic analyses were performed for the con-

figuration of maximum interaction. The case of two coplanar circular cracks validates a theoretical assumption of an 'equivalent ' elliptical defect tangential to the circular initial cracks, 8 Fig. 5.

FRA C T U R E TOUGHNESS D A T A

Use of this procedure is demonstrated by considering a steel disc for the low pressure stage of a steam turbine. A disc weighing 12 tonnes (Fig. 6) which had been tested non-destructively and rejected due to the presence o f defects, was subjected to a fracture toughness analysis to obtain a complete description of its properties along the radius. From a first sector and twelve sub-sectors, specLmens for tensile, impact, fracture toughness and fracture appearance transit ion temperature (FATT) tests were obtam_ed. Chemical composit ion, mechanical properties and thermal treatments of this material are shown in Table 2.

Fig. 3 Arrangement of the holographic bench

Fig. 4 Contour lines of the displacement f ield on a plane at a certain distance f rom the crack plane

/

' d

b= (d+ 2a) /2 [o/(d+ a)] I /z

a= [(d+2o) slZ/(d+ o) l/z]/2 Fig. 5 Equivalent elliptical defect for two circular coplanar cracks

0 928

1-- ~2410

Fig. 6 Disc for low pressure stage of a steam turbine

Table 2. Material properties composit ion and thermal treat- ment

Composition (%) C = 0.22 - 0.26 Mn = 0.25 - 0.35 Mo = 0 . 4 5 - 0.55 S i = 0 . 1 0 m a x Cr = 1 . 4 0 - 1.60 V = 0 . 0 8 - 0 . 1 3 S =O.015max Ni = 2 . 6 0 - 2 . 8 0 Sn = 0 . 0 2 m a x P = 0 . 0 1 5 m a x

Yield stress

Impact test

0.2% YS = 600 N/mm 2 min R A = 19% min Elong = 57% min

charpy - V at 25°C KV = 90J min

Transition temperature FATTso = - 3 7 ° C max

Thermal treatments Austenizing 845°C 1 h/25 mm Tempering 580°C 1 h /25mm Relieving 580°C 1 h/25 mm

By using common methods and relationships 15 fracture toughness values were calculated. Fig. 9 shows the distribu- tion of these values along the radius. Fractographic (Fig. 10) and structural analysis, confirms the presence of an area in the inner part of the disc which is more brittle than other parts of the forging.

These results were compared with others from litera- ture 4 where Kic is given as function of test temperature minus FATT (excess temperature).

INT. J. FATIGUE Apri l 1981 73

1601_

~>J3

,o

' J l '

(.)

Fig. 7 KV-impact energy values in the disc

kV (d)

-6 U o t_~ -10

-14

f

I_ ,

I

m 1

- - m C.

I I I m L

f Fig. 8 Transition temperature FATT distribution

PROPAGATION ANAL YSIS Assuming a classical propagation law of the Paris type, for a crack with a genera] form gives;

dr --=CK~ n (1) dN

where, from Fig. 11

g~(~) K I ( ~ ) = Ko(a) (2)

Ko(a) and Ko(a ) is a known value of SIF.

20(

L~ 180

~ 160

IOC

[ - - . . . . I . . . . . _J _ _ _

I .L

-I

I t I - - I I L . .

0 928

0 2410

Fig. 9 Fracture toughness distribution

Fig. 10 Structures distribution (x600)

74 INT. J. FATIGUE Apri l 1981

Zc

K, (9)

Fig. 11 El l ip t ica l crack

The ratio K I / K 0 is a function of a series of non- dimensional ratios which describe the crack form.

/ ~ - - - - f(oq,Ol2,..., ¢) Ko(a)

For every load d i s t r i bu t i on M is a shape-parameter. Fo r an e l l ip t ica l crack a is the length o f a semiaxis and a 1 the ra t io a / c . Given a crack w i t h in i t ia l shape

a0, (Xl0, OL20, • . • , O~n0

increments in radial directions dr can be calculated by substituting Equation (2) in Equation (1), for each value of ~, as the crack reacts to applied load.

Any subsequent shape generally differs from the preceeding one and so in order to continue the theoretical t reatment of the crack front, the new M ( ~ ) parameter must be estimated.

Since crack instabili ty occurs when the maximum value of I(i at the crack tip reaches the critical value KIc , it must be concluded that, only if the function M is known at each stage of propagation can the critical dimensions of the crack be determined. The condit ion:

K~ nax = Kic

is inadequate for determinat ion of the critical dimensions of a defect in the presence of the set of unknown variables a, a l , a 2 . . . , a n and only by making particular assump- tions is it possible to overcome the problems associated with the theoretical treatment. Experimentally the evolution of the front of two interacting cracks was visualized through transparent models.

Using the equivalent defect concept (see Fig. 5), an expression for the component life can be derived.

21r m/2 /Yc = (a0(l-rn/2) _ ac(l-m/2))

2 m CM rn o rn (m - 2)

In order to derive the coefficients of the Paris law, fatigue tests were performed on specimens of compact type with different thicknesses. The mean values obtained from these tests for C and m were 8.03 × 10 - 5 m m / c y c l e / ( k N m m - 3 / 2 ) m and 2.09 respectively.

This work was summarized in an automatic computer programme 18 that for each defect (or group of defects), calculates, the new defect configuration corresponding to that number of cycles. The program, which is shown schematically in Fig. 12 also calculates the number of cycles beyond which the defect will exceede the critical size.

CONSIDERATION OF FRA CTURE TOUGHNESS TESTS

Both the E-integral and crack opening displacement (COD) have been proposed as single-parameter crack initiation criteria applicable under condit ions of either contained or large plastic deformation. Since J and COD for small scale yielding are simply related to the plane strain SIF KIc , both are used to provide a simple inexpensive method of measuring KIc with small, often fully plastic, laboratory specimens. Comparisons of the different procedures for measuring fracture parameters have been made. t4,15 The principal formulas are:

(1 - v 2) Ei = Gi - - - K z2c

E

(COD)i - E(YS) (YS)

Different relationships have been established between KV impact test values and Kic:

Kic = 19(KV) 1/2 Kic(MPam 1/2)

Kic = 14.6(KV) 1/2 KV = (J)

YS -- (N/ram 2)

~-~-~-)! = 0.62 L \ ( Y S ) / J

= 0.225 ( K V ) 3/2 E

I t

(s)

(4)

is generally accepted that:

Correlation between Kic and KV can be used provided the different meaning of transition temperature for the two type of tests is accounted for.

It is important to make comparisons of JIe and KIc for consistent measurement points. The difference in measure- ment point for the two values is shown in Reference 14. Kic is measured from the R-curve at 2% crack extension and JIc at the point of first crack growth. Hence, the simi- larity of the two values depends on the shape of the R-curve and comparison may not be necessary as JIc

Initial mop of crocks Material constants C, rn, o-y

I I i - - I N - - 0 ]

I Calculation of crocks mutual ]

distances and from the free surfaces I I

FOr iterocting aucks ] I

<~ For each type of crack ~ . . . . . I

Calculation of magnifications factors (and correction for plasticity at ~ tip) ] N Wi~.l + W

I

The Crock is critical 2 >

Sub-critical propagation dimensions ] [ calculation after N cycles

Transition test to ~n equivalent crack and substitution with an equivalent crock ]

+- Fig. 12 Flow-chart of computer program for the crack propagation pred ic t i on

INT. J. F A T I G U E Apr i l 1981 75

could be regarded as a fracture toughness value on its own merits. A similar discrepancy is seen in Fig. 315 where two different points, 0 and PQ on the load v e r s u s

deflection curve are used as the critical points at which COD and Kic respectively are measured.

New concepts (strain energy density or absorbed specific energy)16,17 will probably aid future clarification of these important experirnental aspects. Once done, this will allow the definition of a fracture toughness parameter which will represent the material behaviour and which should be measurable with small simple specimens.

A CKNO W L ED G EM EN TS

The author wishes to thank R. Riccioni, and C. F. Camponuovo for permission to publish and their collabora- tion in research partially performed as ISMES Laboratories (Bergamo). Thanks are also due to F. Persiani of Bologna University, and A. Barozzi and Frisoni of ANSALDO (Genova) for permission to present some of the results obtained by the author with the appreciated collaboration of G. Maccid and Mi Sflei of the same company. The author is also indebted to Professor S. Curioni and Professor G. P. Cammarota of Bologna University for their valuable help with the experimental programme for material charac- terization.

REFERENCES

1. Greenberg, H. D., Wessel, E. T., Clark, W. G, and Pryle, W. 'Appendix D: Application of F M technology to turbine/ generator rotors' Scientific Paper 69-1Dg-MEMTL-P1 October 15, 1969 (Westinghouse Research Lab Pittsburgh, P A. October 15, 1969)

2. Greenberg, H. D., Wessel, E. T. and Pryle, W. 'Fracture toughness of turbine -- generator rotor forgings' Mater Syrup on Fracture Mech (Leigh University, 1968)

3. Brothers, A. J., Newhouse, D. L. and Wundt, B. M. Results of bursting tests of al loy steel disks and their application to design against britt le fracture

4. Newhouse, D. L. and De Forest, D. R. 'Meeting require- ments for larger generator rotors' In t Foregemasters" Meeting (Terni, 1970)

5. Japan Steel Works REF No MS-73-5-39 Research Center Muroran Plant the Japan Steel Works Ltd (May 31,1973)

6. Sawada, S., Tokuda, A., Homma, R. and Jin, T. 'Manufacture of the low pressure turbine rotor forgings with high strength

and good toughness' JS W Tech Review Number 12 (Tokyo, Japan 1976)

7. Coulon, A. 'Essais metallgiques et, de la mechanique de la ropture sur aciers pour disques de turbines de grandes dimen- sions' Revenue de Metallurgie (October 1977)

8. Freddi, A. and Persiani, F. 'Contr ibuto alia stesura di un manuale oer la valutazione dei difett i nei rotori dei turboalter- natori ' V 0 Convegno Naz AlAS (Bari, 29 September--1 October 1977)

9. Persiani, F. and Freddi, A. 'La meccanica della frattura per la valutazione della aff idabil i ta strutturale degli elementi delle macchine' Difett i nei forgiati per rotor i (edited by Pitagora, Bologna, 1978)

10. Camponuovo, G. F., Freddi, A. and Borsetto, M. 'Hydraulic fracturing of HDR: Three<limensional studies of cracks propagation and interaction' 2nd /nt Semin on Advances in European Geothermal Research (Strasbourg, March 1980)

11. Kobayashi, A. S. Experimental Techniques in Fracture Mechanics (SESA Monograph Number 1 1973 and Number 2 1975)

12. Freddi, A. and Persiani, F. 'Holographic interferometric analysis of displacement fields of cracks embedded in trans- parent models'. 6th In t Conf on Experimental Stress Analysis (Munchen, September 1978) pp 203 -208

13. Landes, J. E. and Begley, J. A. 'Test results from J-integral studies: an attempt to establish a JIc testing procedure' ASTM STP 560 (1974) pp 170--186

14. Landes, J. D. and Begley, J. A. 'Recent developments in JC testing' ASTM STP 632 (1977) pp 57-81

15. Griff is, C. A. 'Elastic-plastic fracture toughness: a comparison of J and COD displacement characterizations'. Trans o f ASME JPres Vess Tech (November 1975) p 279

16. Ivanova, V. S. 'The concept of fatigue fracture toughness and its use in determination of the fracture toughness of materials' Rep Res Inst Strength and Fracture o f Mater 14 (Tohoku University, 1978) pp 1--27

17. I vanova, V. S., Maslov, L. I. and Zotov, A. D. 'A new approach to determination of the fracture toughness under conditions of elastic and elastic-plastic behaviour of materials' In t J Fatigue 3 (April 1981 ) pp 77--84

18. Freddi, A., Persiani, F., Maccid, G. and Silei, M. 'Un pro- gramma di calcolo per las valutazione della vita dei rotori per turbomacchine basato sui criteri della meccanica della frattura' To be published

AUTHORS

Professor Freddi is a member of the Engineering Faculty at the University of Boloqne in Italy.

76 INT. J. F A T I G U E A p r i l 1981