Neutron scattering in engineering applications

ELSEVIER

Physica B 234-236 (1997) 949-955

Neutron scattering in engineering applications G.A. Webster*, A.N. Ezeilo Department of Mechanical Engineering, Imperial College, London, SW7 2BX,, UK

Abstract The state of stress generated in engineering components during manufacture and use can significantly influence their load carrying capacity and resistance to fracture. Some manufacturing processes introduce damaging residual tensile stresses whereas others can produce beneficial compression. In order to make reliable estimates of component performance it is necessary to have an accurate knowledge of these stresses. In this paper a technique for measuring residual stresses non-destructively by neutron diffraction is outlined. A representative selection of stress distributions developed by a range of manufacturing processes is examined. Some comparisons are made with strain gauge, X-ray and finite element determinations. It is shown how the results can be of benefit in engineering stress analysis. Keywords: Diffraction; Metals; Residual stress

Introduction The presence of residual stresses in engineering components can significantly affect their load carrying capacity and resistance to fracture [1, 2]. These stresses can be introduced during manufacture and use. In some cases damaging residual tensile stresses are produced and in others beneficial compression. In order to quantify their effect it is necessary to have an accurate knowledge of their magnitude and distribution. Residual stresses can be measured by several methods [3]. Mostly, these involve the use of X-rays [4], neutron diffraction [5, 6] or strain gauges [-7-9]. In all cases strains are measured and stresses calculated. Neutron diffraction is the only suitable procedure available for determining these stresses non-destructively within the interior of components with sufficient accuracy. In this paper the neutron diffraction technique for measuring residual stresses is outlined briefly. *Corresponding author.

The precautions needed to obtain reliable results are discussed. A representative selection of stress distributions introduced by a range of manufacturing processes is examined. Some comparisons are made with the other methods. It is shown how the results can be of assistance in engineering stress analysis.

2. The neutron diffraction method The technique can be employed with a polychromatic or a monochromatic beam of neutrons. An illustration of the application of the method for a monochromatic beam is shown in Fig. 1. When a beam of neutrons of wavelength 2 is incident on crystalline material a diffraction pattern with sharp maxima is produced. The angular positions of the maxima for a family of crystallographic planes of separation d are given by the Bragg equation 2dsin 0 = m2

0921-4526/97/$17,00 © 1997 Elsevier Science B.V. All rights reserved PI1 S092 1-4526(96)0 122 1-5

(1)

G.A. Webster, A.N. Ezeilo / Physica B 234-236 (1997) 949-955

950

Incident bcarn

~

Mask

~

Q Scatterins vector

Fig. 1. Principles of neutron diffraction for strain measurement.

Several precautions are needed to make reliable determinations of stress. The unstrained material lattice spacing do and scattering angle 200 must be known to obtain absolute strain measurements. Also a sufficiently small sampling volume must be defined in the presence of stress gradients for adequate resolution. This can be achieved by masking the beam. In addition measurements must be made on crystallographic planes which represent bulk behaviour and which produce an intense diffraction peak at an angle 20 close to 90 ° so that an approximately square cross-section sampling volume is produced. Further detail about how to obtain accurate measurements is given in Refs [10-16]. Some examples of the use of the neutron diffraction method for determining residual stress distributions will now be considered. It will be shown how the results can be applied in practice in engineering.

3. A p p l i c a t i o n s

where 20 is the diffraction angle and m is an integer. Any change in lattice space Ad will cause a corresponding shift A0 in the angular position of the Bragg reflection so that the lattice strain e in the direction of the scattering vector Q is given by e

Ad d

-

A0 cot 0.

(2)

In general, to define the strain tensor at a point completely, measurements in six orientations are required. However, when the principal directions are known, three will suffice. When the principal directions coincide with the coordinate directions x, y and z and the material is isotropic with an elastic modulus E and Poisson's ratio v, the principal stresses are obtained from E I-(1 - V)~x + v(ey + ~=)l (1 + v)(l - 2v)

(3)

E [(1 - v) ey + v(ex + zz)] ay - (1 + v)(1 - 2v)

(4)

E [(1 - v)~z + v (ex + e,)] az = (1 + v)(1 - 2v)

(5)

O"x

Initially the case of a thick-walled cylinder which is subjected to internal pressure loading will be examined. When this pressure is pulsating, it can cause fatigue cracks to propagate through the wall from the bore. It is common practice to subject such cylinders to an 'over-pressure' prior to use to cause tensile yielding at the bore. This process is called autofrettage and it results in a compressive residual hoop stress in the bore region. An illustration of the residual stress distribution produced is shown in Fig. 2 as a function of distance r from the bore and wall thickness W. Close agreement is achieved between the neutron diffraction method and a boring technique [6]. An indication of the increased protection gained against fatigue failure by the autofrettage process is shown in Fig. 3 [1]. The results were obtained on ring specimens which had been sliced from an 'as-received' and an autofrettaged cylinder. Each ring was provided with a radial crack at its bore and was subjected to cyclic loading at a constant applied stress intensity factor range AK. Under these conditions, fatigue crack growth/cycle da/dN is expected to be constant in the absence of residual stresses as demonstrated by the 'as-received' specimen. In contrast, in the

G.A. Webster, A.N. Ezeilo / Physica B 234-236 (1997) 949-955

~

o Neutron dlffrsction

ff ~"

v Sachsm~hininI from OD

-~0~-

o~

b~d~

Fig. 2. Influence of autofrettage on residual h o o p stress distribution in thick-walled tubing.

10"7

'

'

10_8

'

'

I

'

'

'

Z~

Z

a Autofrettaged ring O As-received ring

10. 9

I

~

~

,

I

B. 5

,

,

Fig. 3. Fatigue crack p r o p a g a t i o n at a constant AK of 20 M P a ~ / m in internally cracked rings.

autofrettaged specimen, reduced crack growth/cycle is obtained which gradually approaches that of the 'as-received' specimen with increase in crack depth. This behaviour is consistent with the crack

951

propagating out of the residual stress field adjacent to the bore and can be predicted quantitatively from the residual stress distribution shown in Fig. 2 [1, 2]. Cold hole expansion, which is achieved by use of a mandrel, is another established technique for introducing compressive residual stresses adjacent to the bore of bolt and rivet holes which are sources of failure in engineering components. Fig. 4 shows the high residual compression that can be generated at the bore by this process [17]. The figure also indicates that prolonged fatigue cycling can cause some relaxation in this high residual compression which will reduce the benefit gained from the cold hole expansion and which must be taken into account in making fatigue lifetime assessments. It is demonstrated that the stress relaxation can be predicted satisfactorily using finite element methods. The neutron diffraction technique can also be employed to map residual stress distributions throughout a component as illustrated in Fig. 5. This figure shows the results of measurements that have been made in the head of a slice of railway rail which was cut from a piece of used track [18]. It is apparent that progressive wear due to wheel contact along the running line (at approximately 6 mm) has caused an asymmetric stress pattern with steep gradients just below the surface. Such information, in conjunction with a knowledge of the applied stresses, should assist in explaining failures in track due to rolling contact fatigue and fracture. Shot-peening is a mechanical treatment process which involves firing small beads at a component to cause yielding at the surface to be treated. This results in the generation of compressive residual stresses adjacent to the surface [19]. The depth of these stresses is sensitive to the peening parameters employed as indicated in Fig. 6. This figure shows that an increase in peening intensity causes the depth of maximum compression to increase but little change in its magnitude. Results for the residual stresses measured across an electron beam weld are presented in Fig. 7 [20]. The figure shows that the region over which significant tension is observed is much smaller than is expected in a normal fusion weld and that post weld heat treatment can cause almost complete

G.A. Webster, A.N. Ezeilo / Physica B 234-236 (1997) 949-955

952

1000 800 600 400 ~

0

~-200 ..400 -600

l

-800

~ ~

r e

i

measured stresses, expanded hole

d

stresses, fatigue cycled

•

.1000 q -1200 -1400

~ , ~, 0

1

.

, 2

.

, 3

FE calculations, fatigue , , , i , ~ 4

5

6

,

d

,

7

distance from bore (ram) Fig. 4. Comparison of hoop residual stresses adjacent to an expanded hole before and after fatigue cycling.

Fig. 5. Transverse residual stress distribution in a used rail head.

elimination of the detrimental tension. Fig. 8 shows that soaking of a low alloy steel at n o r m a l operating t e m p e r a t u r e can also cause relaxation of an initially introduced residual stress field. These examples d e m o n s t r a t e that neutron diffraction can

be e m p l o y e d to investigate the influence of heating on modifying residual stress distributions. Localised h e a t - t r e a t m e n t by laser surface melting is able to produce a hard surface layer and generate beneficial residual stresses which can i m p r o v e

953

G.A. Webster, A.N. Ezeilo / Physica B 234-236 (1997) 949-955 200

L

I .:oo

¢

-4oo

/

,

I

(>..-

/

m.

-800

A w

light peen

D---

low peen

--

medium peen

A -1000 0.0

w.

no peening

0.2

.

heavy peen I

i 0.1

I

0.3

I

I

0.5

0.4

0.6

depth from shot peened face (mm)

Fig. 6. Influence of peening intensity on the near surface residual stresses generated by shot-peening the nickel base alloy Waspaloy.

6O0

5oo I

I

[

I

400 ]~ .......................................... ! ........ ~:. . . . . . . . . . .

0hrs

5OO

4OO • •

3001

before afmrPW

2o0 [ ................................................ f

......i............................... 4.....................

. . . . . . . . .)/;iiiiiiiii . . . . . i i!i

T

t

..r

-100

. ° ; . . . ~ . . . ~ .,o ". . . . . . . . . . . . . .

,

i°°• ::;'~

100 -300

0

25 I

-100 0

10

I

I

I

I

20

30

40

50

i

i

30

35

; ."

40

45

50

Radius (ram) 60

distance from weld centre-line (mm)

Fig 8. Influence of soaking for 250 h at 550°C on the residual stress distribution in a low alloy steel half ring.

Fig. 7. Longitudinal residual stress distributions across an electron beam weld in steel before and after post weld heat treatment.

resistance to c o r r o s i o n a n d w e a r in m a r t e n s i t i c steels. T h e results of residual stress m e a s u r e m e n t s m a d e on this steel are s h o w n in Fig. 9 a s s u m i n g a c o n s t a n t do a n d a linearly v a r y i n g do t h r o u g h the m e l t e d region a n d heat affect zone ( H A Z ) for the n e u t r o n diffraction d e t e r m i n a t i o n s [21]. It is a p -

p a r e n t t h a t close a g r e e m e n t is achieved with X - r a y d a t a when a l l o w a n c e is m a d e for c h a n g e in do. These results d e m o n s t r a t e t h a t n e u t r o n diffraction can be a p p l i e d satisfactorily for m e a s u r i n g residual stresses t h r o u g h v a r y i n g m i c r o s t r u c t u r e s p r o v i d e d p r o p e r a l l o w a n c e is m a d e for c h a n g e s in the reference unstressed lattice spacing.

954

G.A. Webster, A.N. Ezeilo / Physica B 234-236 (1997) 949-955 800

.

.

.

.

.

.

.

.

.

700 600 500 400

~ 3oo

} 2®

-200 -300 ~ -400[

o---" ~a---

"~ ~ ~

do=constant linear variation in do X-ray stresses

-500 -600

,

i

,

,

•

,

•

,

•

,

•

,

•

,

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 [<--- meltedzone'-->~ HAZ .d~ base material

.

,

.

,

•

0.8 0.9 1.0 depth (mm)

Fig. 9. Residual stress generated along the laser traverse direction for a laser treated sample of a martensitic steel.

4. Conclusions T h e n e u t r o n diffraction m e t h o d of m e a s u r i n g residual stress d i s t r i b u t i o n s has been described. S o m e e x a m p l e s of its use have been considered. It has been s h o w n t h a t it can be a p p l i e d to q u a n t i f y the effects of residual stress on the fatigue perform a n c e of c o m p o n e n t s , to m a p residual stress fields a n d to assist in optimizing, for e x a m p l e , s h o t - p e e n ing, h e a t - t r e a t m e n t a n d laser surface t r e a t m e n t p r o cesses. It has also been d e m o n s t r a t e d t h a t it can be e m p l o y e d in regions of v a r y i n g m i c r o s t r u c t u r e when the c h a n g e in unstressed lattice s p a c i n g with m i c r o s t r u c t u r e is k n o w n .

References [1] A. Stacey and G.A. Webster, in: Analytical and Experimental Methods of Residual Stress Effects in Fatigue, eds. R.L. Champoux, J.H. Underwood and J.A. Kapp, ASTM STP 1004 (American Society for Testing and Materials, Philadelphia, 1988) pp. 107-121. I-2] G.A. Webster, in: Fatigue and Stress, ed. H.P. Lieurade (IITT International, Gournay-sur-Marne, France, 1989) pp. 9-20.

[3] J. Lu. (Ed). Handbook of Measurement of Residual Stress, (Soc. Expt. Mech., Fairmont Press, USA, 1996). [4] H. Hughes, Strain 3 (1967) 26. I-5] A. Allen, C. Andreani, M.T. Hutchings and C.G. Windsor, NDT International 14 (1981) 249. [6] A. Stacey, H.J. Macgillivray, G.A Webster, P.J. Webster, and K.R.A. Ziebeck, J. Strain Analysis 20 (1985) 93. [7] E.M. Beaney and E. Proctor, Strain 10 (1974) 7. [8] J.G. Williams, J.M. Hodgkinson and A. Gray, Polymer Eng. Sci. 21 (1981) 816. [9] G. Sachs, Zeits. Metall. 19 (1927) 352. 1,10] A.J. Allen, M.T. Hutchings and C.G. Windsor, Adv. Phys. 34 (1985) 445. [11] D.J. Smith, R.H. Leggatt, G.A. Webster, H.J. Macgillivray, P.J. Webster and G. Mills, J. Strain Analysis 23(4) (1988) 201. 1-12] A.N. Ezeilo, G.A. Webster, P.J. Webster and X. Wang, Physica B 180 and 181 (1992) 1044. [13] P.J. Webster, X. Wang and G. Mills, in: Measurement of Residual and Applied Stress Using Neutron Diffraction, eds. M.T. Hutchings and A.D. Krawitz, (Kluwer, Dordrecht, 1992) p. 517. [14] P.J. Webster, ibid, 235. 1-15] A.N. Ezeilo, P.S. Webster, G.A. Webster and P.J. Webster, ibid, 535. [16] G.A. Webster, and A.N. Ezeilo, Principles of the measurement of residual stress by neutron diffraction, in: Proc. 4th Summer School on Neutron Scatter, Zuoz, August 1996 (ETH, Zurich).

G.A. Webster, A.N. Ezeilo / Physica B 234-236 (1997) 949-955 [17] A.N. Ezeilo, G.A. Webster, P.S. Webster and P.J. Webster, in: Proc. 4th Int. Conf. on Residual Stress, Baltimore, USA, June 1994, (Soc. Exp. Mechanics, 1994) p. 1275. [18] P.J. Webster, K.S. Low, G. Mills, and G.A. Webster, in: Proc. Mat. Res. Soc. Symp. 166 (1990) 311. [19] A.N. Ezeilo, G.A. Webster, P.J. Webster and P.S. Webster, Proc. 5th Int. Conf. on Shot Peening, Oxford University, September 1993, p. 274.

955

[20] G.A. Webster, in: Measurement of Residual and Applied Stress Using Neutron Diffraction, Eds. M.T. Hutchings and A.D. Krawitz (Kluwer, Dordrecht, 1992) p. 21. 1-21] A.N. Ezeilo, G.A. Webster, P.J. Webster, M. Roth and W.J. Muster, In: Proc. 2nd European Conf. on Adv. Materials and Processes, Cambridge, 1991, p. 389.