Measurement of Residual Stress Distribution by the Incremental Hole-Drilling Method

A. Niku-Lari* J. Lu** and J.F. Havenot** * II'IT-International, 40 Promenade Marx Dorrnoy,

93460 Gournay sur Mame (France) ** ':TIM, 52 Av. Fdlix Louat, 60304 Senlis (France)

INDUSTRIAL SUMMARY

The h o l e - d r i l l i n g method i s w i d e l y u s e d f o r t h e measurement o f r e s i d u a l s t r e s s e s i n mechanica l components. R e c e n t deve lopments have shown t h a t s t r a i n s measured on t h e s u r f a c e d u r i n g a n i n c r e m e n t a l d r i l l i n g c a n b e r e l a t e d t o r e s i d u a l - s t r e s s d i s t r i b u t i o n . R e s e a r c h e r s , i n t ' e r n a t i o n a l y , h a v e proposed d i f f e r e n t methods o f c a l i b r a t i o n which l e a d t o r e s u l t s o f v a r y i n g d e g r e e s o f a c c u r a c y .

The p r e s e n t p a p e r d i s c u s s e s t h e d i f f e r e n t a p p r o a c h e s used. A new method o f c a l i b r a t i o n i s proposed and i t i s shown how t h e f i n i t e e lement a n a l y s i s c a n be used f o r t h e d e t e r m i n a t i o n o f t h e c o r r e l a t i o n c o e f f i c i e n t s . The v a r i a t i o n of t h e s t r a i n s measured on t h e s u r f a c e f o r e a c h i n c r e m e n t i s d u e , f i r s t l y t o t h e r e s i d u a l s t r e s s e s i n t h e l a y e r and s e c o n d l y , t o t h e change o f t h e h o l e geometry. Most a u t h o r s d o n o t c o n s i d e r t h e l a t t e r a s p e c t , b u t t h e p r e s e n t l y r e p o r t e d r e s u l t s s h t h a t t h i s c a u s e s a s i g n i f i c a n t e r r o r i n t h e e x p e r i m e n t a l d a t a . The f i n i t e - e l e m e n t method h a s been used f o r t h e c o m p u t a t i o n of t h e c o e f f i c i e n t s f o r a l l t y p e s o f s t r a i n - g a u g e r o s e t t e s when t h e h o l e d i a m e t e r i s p r e - d e t e r m i n a t e d .

Another problem o f t h e h o l e - d r i l l i n g method i s t h e s e l e c t i o n o f t h e d r i l l i n g t o o l . Two sys tems h a v e been s t u d i e d : t h e u s e o f a n u l t r a high-speed a i r - t u r b i n e and t h e u s e o f a c o n v e n t i o n a l m i l l i n g machine.

The i n c r e m e n t a l h o l e d r i l l i n g method h a s b e e n a p p l i e d t o b o t h sho t -peened and water-quenched t e s t spec imens , and r e s u l t s h a v e been s u c c e s s f u l l y compared w i t h t h o s e o f t h e bending d e f l e c t i o n and t h e X-ray method.

NOMENCLATURE

r r a d i u s : d i s t a n c e f rom t h e c e n t r e o f t h e r o s e t t e t o any p o i n t on t h e gauge c e n t r e - l i n e .

d h o l e d i a m e t e r

p r i n c i p a l s t r e s s e s

R e p r i n t f rom, The J o u r n a l o f Mechanica l Working Technology. Vol. 11, I s s u e 2 , 1985.

SHOT PEENING

principal directions

angle between the direction h of the lines of the central grid and x

mean radial direction of the central grid

current depth of the hole

increase in the depth of the hole

calibration coefficients for the geometry n and the loading i

strain measured in 3 directions ei,ei + 9 and ei + 4

displacement calculated by the finite-element method, for the geometry n and the loading i

non-dimensional displacement

Poisson's ratio

Elastic constant

total strain measured on the surface after the hoie is drilled to the depth hn (m in e 1 stands for measured)

mn surface strain changes due to the release of stress in the nth layer only

calibration coefficients using the standard elasticity laws

INTRODUCTION

It is well known that residual stresses are induced by fabrication processes into the surface layers of the processed material, and that these stresses will superimpsse on to the service scresses and alter their distribution, especially in the first layers of the surface where, in most cases, fatigue or stress corrosibn cracks initiate.

The fatigue strength of the material is either reduced or increased, depending on whether the residual stresses increase or decresae the in-service tensile stresses. It is, therefore, of importance to take this effect into account when designing the parts. To do this, it is necessary to measure precisely the level and distribution of the residual stresses induced by various fabrication processes.

To solve industrial problems, a large number of measurement methods have been devised: (i) the hole-drilling method [I-111, a traditional means of measuring residual stresses with no gradient; (ii) the bending deflection method measuring the distribution of residual stresses in plane parts C121; (iii) the Sachs . method for cylindrical parts C61; (iv) the residual-stress-source method for the prediction of the residual-stresses induced by shot-peening C21; and (v) the X-ray diffraction method C131 for the measurement of surface .stresses.

Until recent years, the experimental procedure used and the theoretical expressions involved in the hole drilling method restricted its use to the case of residual stresses distributed uniformly over the depth. New developments have brought some improvements, and now a step-by-step drilling procedure allows the determination of the distribution of stresses with depth. Several ways have been suggested for the calculation of the residual stresses from the strains measured after each step of drilling.

The present paper establishes a consensus regarding the various procedures used, and shows how a calibration by the finite-element method allows the determination of the coefficients correlating the measured strains to the corresponding residual-stresses. In order to check the validity of this calibration method, results of tests on shot-peened specimens and water-quenched

MEASUREMENT OF RESIDUAL STRESSES

specimens have been compared with those from the bending-deflection method and the X-ray diffraction method.

"TRADITIONAL" HOLE DRILLING METHOD

In the traditional method, the hole is drilled to a depth of up to 1.5 times its diameter. From the surface strains - measured by means of the three gauges in a rosette, in the centre of which the hole is drilled - the mean values of the two principal stresses 01 and 02 down the hole can be calculated [l-111. to obtain the profile of the residual stresses, the hole is drilled in steps [14]: for each hole-depth, z, the surface strains Ei(z) are measured. Once the drilling is completed, the residual principal-stresses Ui(z) and a2(z) can be calculated from equations involving measured values of Ei(z) and the calculated correlation coefficients. The essential problem in the measurement of the distribution of residual stresses by the hole-drilling method lies in the determination of these theoretical coefficients. In addition, this new procedure requires the drilling of a flat-bottomed hole, which is suitable for each material and which will not introduce additional residual stresses in the part at the edges of the strain gauges, and which will result in a hole geometry which is as precise and repeatable as possible.

CALIBRATION OF THE HOLE-DRILLING METHOD

There are various calibration methods for the measurement of residual stresses. In articular may be quoted the methods suggested by Bathgate 1151, Owens [16], the Vishay Measurements Group [171 and Bi j ak-Zochowski [181.

The method suggested by Bathgate C151 and Owens El61 is based on the calibration of the coefficients by a uniaxial (or biaxial) loading method, using the method of finite elements for the computation. The method consists of loading the test specimen uniaxially (owens) or biaxially (~ath~ate), where, since the applied force. is known, the applied stress can be deduced. The hole is drilled step-by-step and for each increment the known stress and the measurement strains are introduced into the equation, hence the coefficients Ain and Bin for each step can be determined.

In the method suggested by the Vishay Measurements Group, the two coefficients A and B are first calculated using the standard elasticity laws, then on a tensile test specimen the relaxation curve for a uniform stress with respect to the relative hole depth z/d is determined. The relaxation of the true stress for each increment (AE) during hole drilling is calculated, using the relaxation curve defined previously. For example, when the hole depth is changed from hi to h2 can be found from the curve referred to above. Hence, the equivalent strain, Ei(z) is determined: Ei(z) = ( A E ~ / E ~ ) x loo%, where Aci is the variation of the surface strain.

By i~troducing Ei(z) into the general equation (see C171) for the calculation of the residual stresses, the true stress for each depth is obtained. The two methods referred to above are based on the following assumption: the values of

as measured for each increment, correspond only to the stress removed, which existed in the layer concerned,

For each.layer of material removed, however, there is a re-distribution of the stresses. In any layer, the same stress produces different surface strains for different hole geometries since, as the drilling of the hole progresses, the geometry of the hole changes. Variations in strain are thus measured at the surface of the part, even If drilling is done in unstressed layers of the material. The strain change measured by strain gauges is in this case only due to the change in geometry. Bijak-Zochowski [la] and Schajer C191 have noted the same point, and the present calculation methuod is based on the theoretical work of these authors.

EFFECT OF THE HOLE GEOMETRY

SHOT PEENING

C a l c u l a t i o n o f S t r e s s e s from t h e Measured S t r a i n s

I n o r d e r t o d e t e r m i n e t h e d i s t r i b u t i o n o f t h e s t r e s s e s i n a g i v e n m a t e r i a l by t h e h o l e - d r i l l i n g method, t h e f o l l o w i n g a s s u m p t i o n s a r e made: t h e m a t e r i a l i s e l a s t i c and i s o t r o i p i c ; t h e measured s t r e s s e s a r e below t h e e l a s t i c l i m i t o f t h e m a t e r i a l * ; t h e component o f t h e s t r e s s normal t o t h e s u r f a c e is n e g l i g i b l e ; i n e a c h l a y e r removed, t h e s t r e s s e s were c o n s t a n t ( a mean v a l u e i s u s e d ) ; between s u c c e s s i v e l a y e r s , t h e s h e a r f o r c e s a r e n e g l i g i b l e ; t h e bo t tom o f t h e h o l e i s f l a t ; t h e d imens ions o f t h e w r o s e t t e a s d e f i n e d by t h e m a n u f a c t u r e r s , a r e a c c u r a t e .

Cons ider a specimen w i t h a n a r b i t r a r y d i s t r i b u t i o n o f r e s i d u a l s t r e s s e s . Denote t h e p r i n c i p a l d i r e c t i o n s by a l h and a 2 h ( i t i s assumed t h a t t h e s e c o i n c i d e w i t h t h e a x e s x and 9 o f F i g . 1 ) . A h o l e i s d r i l l e d , o f d i a m e t e r D and d e p t h H. I f a s t r e s s e q u i v a l e n t t o t h e s t r e s s e s removed i s a p p l i e d , t h e s t a t e o f e q u i a l i b r i u m remains unchanged. The e q u i l i b r i u m s t r e s s e s t h a t e x i s t e d between t h e l a y e r s removed and t h e r e m a i n d e r of t h e p a r t a r e t h e r a d i a l s t r e s s or and t h e s h e a r s t r e s s Tre (it is assumed t h a t rr, = 0).

The r e a c t i o n of t h e p a r t t o t h e s t r e s s e s which a r e removed by d r i l l i n g o f t h e h o l e i s e q u i v a l e n t t o t h e a p p l i c a t i o n t o t h e p a r t of a s t r e s s o f o p p o s i t e s i g n . I n t h i s model, t h e a c t u a l s t r e s s d i s t r i b u t i o n i s t o be r e p l a c e d by a s t e p - w i s e - c o n s t a n t d i s t r i b u t i o n ( ~ i g . 21..

F i g . 1 True d i s t r i b u t i o n o f r e s i d u a l s t r e s s e s w i t h d e p t h .

I n t h e l a y e r i , t h e e q u i l i b r i u m s t r e s s e s U r i i n t h e d i r e c t i o n of ei , b e f o r e t h e h o l e i s d r i l l e d , c a n be e x p r e s s e d by two e q u a t i o n s :

Q + a a - 0

Q = l h i 2 h i + l h i 2 h i cos 28. r i 2 2 L

u - a T - - l h i 2 h i sin Zei r e i - 2

*According t o t h e s t r a i n - g a u g e and t h e h o l e geometry t h e measured s t r e s s e s must be b e l o w . 3 3 t o 80% of t h e y i e l d stress .of t h e m a t e r i a l C61.

M E A S W M E N T OF RESIDUAL STRESSES

'Fig. 2 D i s t r i b u t i o n o f r e s i d u a l s t r e s s assumed f o r t h e t h e o r e t i c a l model.

where B i i s t h e a n g l e between gauge No. 1 and p r i n c i p a l d i r e c t i o n ' l . These s t r e s s e s may be r e l a t e d t o t h e r a d i a l s t r a i n a t t h e s u r f a c e o f t h e spec imen, E ( B i ) ,

i n

The c o e f f i c i e n t s A i n and Bin a r e f u n c t i o n s o f t h e h o l e d i a m e t e r , t h e geometry of t h e s t r a i n g a u g e s , t h e p o s i t i o n o f t h e l a y e r i and t h e d e p t h of t h e h o l e ,

The r a d i a l s t r a i n s c a n b e measured i n t h r e e d i r e c t i o n s Bi, Bi + q , Bi + $ b y a th ree-gauge r o s e t t e . Hence, t h e t h r e e unknowns, Bi, Ulhi and 62hi , ca.n be de te rmined . When a h o l e of d e p t h h l i s d r i l l e d , and t h e s t r a i n s i n t h e t h r e e d i r e c t i o n s

1, E? and E'" t h e n by ( 3 ) a r e : E ' 1 '

here : alhl = a l , aZhl = O2

By s o l v i n g eqns . ( 4 ) t h e v a l u e s of t h e s t r e s s e s U l h l , 0 2 h l and t h e i r r e s p e c t i v e d i r e c t i o n s f o r t h e f i r s t . l a y e r c a n be d e t e r m i n e d .

I f t h e h o l e i s d r i l l e d i n n i n c r e m e n t s t o a t o t a l d e p t h o f h n , and t h e n t h e s t r a i n a t t h e s u r f a c e i s measured ; t h e r e l a t i o n s h i p w i l l be s i m i l a r t o t h o s e o f e q u a t i o n ( 4 ) : however , t h e r e i s need t o c o n s i d e r t h e change of s u r f a c e ' s t r a i n s due t o t h e removal o f t h e p r e v i o u s l a y e r s .

The s t r a i n s due t o t h e removed n t h . l a y e r a r e :

SHOT PEENING

€in cor responds t o t h a t p a r t of t h e t o t a l s t r a i n which i s r e l a t e d t o t h e i t h l a y e r w h i l s t removing t h e n t h i n c r e m e n t , and i s c a l c u l a t e d a s f o l l o w s :

I f a G 5 " r o s e t t e i s u s e d , t h e 3 unknowns en , Uphn and 02hn c a n be c a l c l u l a t e d from t h e r e l a t i o n s h i p s :

€'(A,, t Bnn s i n 28 ) - E ( - n n X Ann Bnn cos Zen) a*. =

1 hn Z~, ,B,~(sin 28 + c o s 2en)Ahn n

E;(A,~ + Bnn cos 20 ) - & ' ( A - Bnn s i n 20,) u - n n nn

2hn - ~A,,B,~( s i n Zen + c o s 20 )Ah *n n

h e r e : 9 = 225", (l~ = 90"

To o b t a i n t h e f i n a l s o l u t i o n s i t i s s t i l l n e c e s s a r y t o c a l c u l a t e t h e c o e f f i c i e n t s A i n and B i n .

THEORETICAL CALCULATIONS FOR THE COEFFICIENTS A i n

To c a l c u l a t e t h e c o e f f i c i e n t s A i n , c o n s i d e r , a n a x i s y m m e t r i c a l p a r t , t o which i s a p p l i e d a n a x i s y m m e t r i c a l load . I n t h i s c a s e , t h e s t r e s s Ulh i and 02hi w i l l b e i d e n t i c a l , and i t i s n e c e s s a r y t o c a l c u l a t e t h e s t r a i n i n one d i r e c t i o n o n l y . Equat ion ( 3 ) i s s i m p l i f i e d t o :

MEASUREMENT OF RESIDUAL STRESSES

Using t h e f i n i t e - e l e m e n t method, t h e r a d i a l d i s p l a c e m e n t U ( r ) a t t h e s u r f a c e when a s t r e s s i s a p p l i e d a t t h e c i r c u m f e r e n c e of t h e h o l e can be c a l c u l a t e d . S i n c e t h e d i s p l a c e m e n t and t h e s t r a i n a r e r e l a t e d , t h e c a l c u l a t e d d i s p l a c e m e n t s a r e r e l a t e d t o t h e c o e f f i c i e n t s A . -

1 n

To s i m p l i f y t h e c a l c u l a t i o n s , f o r t h e s m a l l a r e a o f i n t e r e s t , i t c a n b e assumed t h e v a r i a t i o n o f Uin(r) i s l i n e a r , and t h u s :

where ; i s t h e non-dimensional r a d i u s ; = r / d .

I t can be s e e n t h a t t h e v a l u e s o f A a r e d e p e n d e n t on t h e p o s i t i o n r l and r 2 , i n o t h e r words, on t h e e x a c t p o s i t i o n s o f t h e s t r a i n gauges w i t h r e s p e c t t o t h e c e n t r e - l i n e o f t h e h o l e .

F i g . 3 Geometry of t h e s t r a i n - g a u g e r o s e t t e .

For a r o s e t t e o f r a d i i rl and r2 , ( s e e F i g .

;2 ;1 ' in - 'in R G ~ ) - F ( ; ~ )

TO s i m p l i f y t h e c a l c u l a t i o n o f t h e c o e f f i c i e ' n t s Atn u s i n g a f i n i t e - e l e m e n t program, a u n i t s t r e s s a h i ( i n Mpa) f o r e a c h l a y e r of m a t e r i a l c o n s i d e r e d i s i n t r o d u c e d .

SHOT PEENING

To d e t e r m i n e t h a t p a r t of t h e measured s t r a i n which i s due o n l y t o t h e removal o f t h e s t r e s s e s i n t h e l a y e r Ohi, i t i s n e c e s s a r y o n l y t o c a l c u l a t e t h e d i f f e r e n c e between t h e t o t a l s t r a i n s measured by t h e g a u g e s and t h e sum o f t h e s t r a i n s r e l a t e d t o t h e removal of t h e upper l a y e r s .

where f in is t h e s t r a i n i n d i c a t e d by t h e s t r a i n gauges and En, i s t h e s t r a i n due t o t h e removal o f one l a y e r . f o r a u n i t s t r e s s Uhi , t h e r e l a t i o n s h i p between E, and t h e c o r r e s p o n d i n g s t r e s s (0,) i n t h e l a y e r is:

hence

The c a l c u l a t i o n o f t h e c o e f f i c i e n t s A:,, h a s been c a r r i e d o u t w i t h r e s p e c t t o a m a t e r i a l of e l a s t i c c o n s t a n t s Em and vm.

F o r a m a t e r i a l w i t h t h e e l a s t i c c o n s t a n t s E, and v,, t h e c o e f f i c i e n t s Ain a r e :

CALCULATION OF COEFFICIENTS Bin

C o e f f i c i e n t s Bin can b e c a l c u a l t e d by u s i n g a s i m i l a r p r o c e d u r e a s was u s e d f o r t h e d e t e r m i n a t i o n of c o e f f i c i e n t s A i n . I n t h i s c a s e , t h e l o a d i n g around a l a y e r i s no l o n g e r a x i s y m e t r i c a l . I n s t e a d o f a u n i t p r e s s u r e a h i = 1 MPa, a normal s t r e s s e q u a l t o l ; c o s ( 2 8 > and a s h e a r s t r e s s e q u a l t o - l : s i n 2 8 , a r e u s e d f o r each s t e p ( F i g . 4 ) .

Fig. 4 B i a x i a l s t r e s s d i s t r i b u t i o n .

MEASURlEMENT OF RESIDUAL STRESSES

In this way the applied stresses al and a2 change with respect to 9:

9 = 0 a = 1 MPa 1

a2 = o 8 = 45" Ul = 0 a2 = -1 MPa

8 = 90" dl = -1 MPa o2 = 0

hence, from equation (3)

From equations (13a) and (13b)

For the more general case, coefficient B is: in

where c . = Ui/d, the non-dimensional displacement.

THE USE OF FINITE ELEMENTS FOR THE CALCULATION OF COEFFICIENTS Ain

Coefficients Ai, and Bin are calculated for 17 increments of a given depth. The method can thus be applicable for the determination of residual stress distribution induced by various surface treatments. For the shot-peening treatment, for example, about ten measurements are required (down to a depth of 0.5 or 0.6 mrn). For an induction-hardening treatment, where the pre-stressed layer is thicker, the number of measurements must be greater (17 for example). The value of the increments varies as the hole depth increases, from 0.01 d to 0.25 d. the total number of coefficients Ai, to be calculated is:

In this approach, interest is in the strains, and not in the displac.ements obtained by finite elements. For this reason, the values in the table of displacement (non-dimensional) with respect to the radius ; (non-dimensional) have been smoothed.

The deformation caused by a unit pressure applied to the layer i, is:

SHOT PEENING

The non-dimensional f u n c t i o n s F(;) c a n be a p p l i e d t o any h o l e d i a m e t e r and any t y p e o f gauge.

To f a c i l i t a t e t h e u s e o f eqn. 1 7 , p r a c t i c a l nomograghs have been drawn up ( F i g . 5). To f i n d t h e s t r a i n between two r a d i i r l and ~2 i t i s o n l y n e c e s s a r y t o f i n d t h e v a l u e s of t h e two f u n c t i o n s F ( ; ~ ) and ~ ( r ~ ) , c a l c u l a t e t h e d i f f e r e n c e , and d i v i d e t h e r e s u l t by t h e non-dimensional l e n g t h of t h e s t r a i n gauge.

The t e s t s which have been c a r r i e d o u t have shown t h a t t h e a c t u a l h o l e d i a m e t e r ' o b t a i n e d i s always s l i g h t l y g r e a t e r t h a n t h e d i a m e t e r o f t h e t o o l : i t i s n e c e s s a r j t h e r e f o r e t o c a l c u l a t e c o e f f i c i e n t s Ain f o r a l l h o l e d i a m e t e r s which a r e l i k e l y t o be o b t a i n e d . A s t h e v a l u e s o f A t n must b e c a l c u l a t e d f o r some g i v e n t y p e s o f r o s e t t e s , t h e y have i n f a c t been c a l c u l a t e d f o r t h e two t y p e s o f s t r a i n gauge r o s e t t e s (HBM RY 2 1 and HBM RY 61) c u r r e n t l y used i n t h e s e t e s t s .

v z p 2 . 4 2 . S St ls qP W 4 e

F i g . 5 V a r i a t i o n o f F(;) w i t h r e s p e c t t o ;: l o a d i n g o f t h e 1 2 t h increment .

Fig. 6 Example o f a mesh f o r t h e c a s e o f N = 1 2 ( l o a d i n g c a s e f o r t h e 1 2 t h i n c r e m e n t ) .

hIfEASlJREMIENT OF RESIDUAL STRESSES

For the calculation of coefficients Ain, finite-element software developed by CETIM was used (CASTOR 2D). This program consists of a set of modules for the mechanical and thermal analyses of two-dimensional mechanical components and of an automatic meshing modulus and a drawing modulus (see Fig. 6).

For rosette RY 21, coefficients Ain have been calculated for the hole diameters between 5 and 5.7 mm at 0.01 mm increments (5.01; 5.02; etc ... ) while for the rosette of type RY 61, the calculation has been made for diameters of from 1.4 to 2.1 mm varied by the same increments. For the other gauge dimensions, software has been developed with which the coefficients Ain can be computed. AS an example, Fig. 7 illustrates the case of the 4th drilling step for which the four coefficients A14 - A44 can be computed.

Fig. 7 Illustrating the case of the 4th increment.

POSSIBILITIES OF CALCULATING THE COEFFICIENTS Bin

From the calculations using only the coefficients can be determined Ain, the profiles of the residual stress with respect to depth, for the case of isotropic residual stresses only (i.e. 01 = 0 2 ) . This condition is true only for certain surface treatments and for simple geometries (for example, shot-peening of flat surfaces). For the determination of non-uniform stresses, it is necessary to calculate the coefficients Bin. As was the case for the coefficients Ain, the calculations for Bin are carried out for an axisymrnetrical component with a non-axisymetrical loading. In this case, the mathematical model upon which is based modulus EFZD of CA.ST.OR 2D is used. Modulus EF2D performs elastic analyses of small strains and small displacements of axisymmetric bodies, but under non-axisymmetric loadings. A fast Fourier transformation is performed on the loadings.

EXPERIMENTAL RESULTS

Experimental Procedure

During drilling, the process of relaxation of the stresses around the hole is subject to laws which derive from the theory of elasticity. For experimental purposes, they require that the operative conditions (machining of the hole) do not cause work-hardening or overheating. It is also necessary that the bottom of the hole be flat: only under this condition the mathematical model is valid, and for this reason, special attention must be paid to the choice of the drilling method. In practice, four drilling methods have been used so far, and are referred to by the authors listed in the references: standard drilling [9, 10, 17, 20, 211 ; spark-erosion drilling [lo, 201; drilling by air-abrasive C22-241; ultra high-speed drilling, using an air turbine [251.

SHOT PEENI[NG

\

A more detailed analysis of these different methods is outside the scope of this paper. However, tests carried out with drilling by air-abrasive have shown that it is difficult to obtain an accurately-dimensional hole. Spark- erosion drillings, on the other hand, either cause overheating, or result in drilling times which are too lengthy. For the present tests, a milling method and a high-speed drilling system with air turbine were used. The two methods are very simple and produce a flat-bottomed cylindrical hole.

Description of the Experimental Cutting Conditions

A breliminary series of tests was carried out to analyse the cutting conditions, and their effect on hole geometry. Firstly, a drilling device using a compressed- air dental turbine (Kavo-Ewl) was developed. The drilling machine is hand held, and a holder was designed to ensure accurate drilling.

In analysing the influence of drilling conditions on.the shape of the holes and on the, micro-structure of the material, three drilling devices were used: universal milling machine with pre-set stepping-feed device (type 1); fixed bench milling machine with continuous-feed device (type 2); air-turbine drilling machine. (type 3).

Table 1 is a summary of the materials and drilling conditions used in tehse tests. Figure 8-12 show the results obtained with the different materials and drilling conditions.

Metallurgical examination of the holes revealed that the drilling methods used had practically no effect on the micro-structure of the materials investigated, and that there was no work-hardening. As to the geometry of the hole and the shape of its bottom, i~ was found that holes drilled with type 2 machine, with an in-feed of 10 mm/min, were satisfactory (see the aluminium-alloy case in Fig. 8) . On the other hand, when the in-feed was increased to 25-50 mm/min, the hole geometry was no longer uniform for that alloy.

The holes drilled by air turbine (Figs. 9-11) have a uniform geometrical shape and a£ lat bottom entirely satisfying the assumptions of the hole-drilling method:.this was no the case for the results obtained with the universal milling machine of type 1 (Fig. 12).

TABLE 1 Summary of Materials and Drilling Conditions used in Tests

steel carburized st'ainless steel aluminium Material : , AISI-1038 steel steel (~533, type B, alloy

AISI-3115 class 1) AISI-2024

Type of drilling machine 1 3 3 3 3

Feed (mmlmin) 0.02 - - - 10

Kind of feed step by step manual manual manual continuous

Hole diq. (mrn) 5 1.8 1.8 1.8 5

Hardness of material (HV) 180 450 206 230 6 0

MEASUFWVENT OF RESIDUAL STRESSES

B o t t o m of t h e hole x 200 ~ e i e r a l view of t h e hole x 9

F i g . 8 showing t h e h o l e made i n AUG4G aluminium a l l o y w i t h a t y p e 2 machine a t a con t inuous ' i n - f e e d of 1 0 mm/min; on l e f t i s t h e bot tom o f t h e h o l e ;

on r i g h t i s a g e n e r a l v i e w o f t h e h o l e (5.00 d i a m e t e r ) .

F i g . 9 Showing t h e f l a t - b o t t o m e d h o l e d r i l l e d w i t h o u t v i s i b l e work-hardening i n t o AISI 316 s t a i n l e s s s t e e l by a n a i r t u r b i n e sys tem w i t h manual i n - f e e d ; on l e f t i s t h e bo t tom o f t h e h o l e ; on r i g h t i s a g e n e r a l

v iew o f t h e h o l e (1.8 mrn d i a m e t e r ) .

F i n a l l y , t h e main a d v a n t a g e s o f t h e c o m p r e s s e d - a i r t u r b i n e s y s t e m may be l i s t e d a s f o l l o w s : t h e s y s t e m is p o r t a b l e , a l l o w i n g t e s t s t o b e c a r r i e d o u t on s i t e ; t h e h o l e s a r e o f small d i a m e t e r (0.8-2.00 mm); v e r y l o c a l i s e d t e s t s may be c a r r i e d o u t .

E f f e c t of t h e D r i l l i n g O p e r a t i o n on R e s i d u a l S t r e s s e s

I n o r d e r t o d e t e r m i n e any i n f l u e n c e o f t h e d r i l l i n g o p e r a t i o n o n r e s i d u a l s t r e s s e s , some t e s t s . w e r e c a r r i e d o u t o n s t r e s s - r e l i e v e d specimens.

SHOT PEENING

Fig. 1 0 A s f o r F i g . 9 , f o r A508 s t e e l o f h a r d n e s s 230 HV

F i g . 11 A s f o r F ig . 9 , f o r c a r b u r i s e d s t e e l o f h a r d n e s s 45 HRC.

The d r i l l i n g c o n d i t i o n s and t h e m a t e r i a l s t e s t e d a r e summarized i n T a b l e 2 . T a b l e s 3 t o 5 g i v e t h e change i n t h e mean s t r a i n measured by t h e t h r e e g a c g e s on t h e s u r f a c e o f t h e specimen, w i t h r e s p e c t t o t h e d e p t h o f t h e h o l e . Ar c a n be s e e n , t h e s t r a i n s a r e v e r y s m a l l , and i t c a n be assumed t h a t no s t r e s s e s have been i n t r o d u c e d , c o n f i r m i n g t h e r e s u l t s o f t h e m e t a l l u r g i c a l e x a m i n a z i o n s r e f e r r e d t o e a r l i e r .

During t h e t e s t s , i t was found t h a t t h e r e was a d i f f e r e n c e i n d i a m e t e r b e c - ~ e e n t h e t o o l and i t s h o l e : it was n e c e s s a r y t h e r e f o r e , t o measure t h e t r u e d ' i c e t e r of t h e h o l e i n o r d e r t o be a b l e t o c a l c u l a t e t h e r e s i d u a l s t r e s s e s w i t h g c ~ d accuracy .

OF RESIDUAL STRESSES

Fig- 12 Showing the hole drilled without visible work-hardening into XC38 steel by a universal milling machine (type 1) at an in-feed of 0.02 mm

per increment: on left is the bottom of the hole; on right is a general view of the hole (5.00 mm diameter). Note that the hole is not perfectly

cylindrical,

TABLE.^ Hole-Drilling Conditions for the Different Materials

XC38 Steel 35NCDI.6 Steel XC38 Steel Type of Material AISI-1038 (~-S-835M30) AISI-1038

Heat treatment Annealing

Type of gauge

Diameter of cutter (rnm)

Diameter of hole (mm)

Hardness

Drilling conditions

Total depth of hole (mm)

Type of machine

Type of gauge bridge

Type of amplifier

RY 21

4

4.06

180 HV

900 rpm

6.8

1

half-bridge

KWS 3073 HBM

Quenched and tempering

RY 21

5

5.12

37 HRC

900 rprn

8.5

2

half-bridge

KWS 3073 HBM

Annealing

RY 61

1.6

1.65

$80 HV

Manual in-feed

3

3

half -bridge

KWS 3073 HEM

APPLYING THE METHOD TO THE EVALUATION OF RESIDUAL STRESSES INDUCED BY SHOT-PEENING: COMPARISON WITH THE BENDING-DEFLECTION METHOD

In shot-peening, the layer affected by plastic deformation is relatively thin, of the order of 0.1 to 1 mrn: for this reason, it seemed useful to apply the' method to this treatment (however, the methuod is valid for any other surface

SHOT PEENING

TABLE 3 S t r a i n s Measured i n XC38 S t e e l , R e l a t e d t o t h e Depth o f t h e Hole D r i l l e d by a U n i v e r s a l M i l l i n g Machine ( t y p e 1 )

Depth (mm) 0.04 0.08 0.16 0.24 0.32 0.4

T o t a l s t r a i n (w) 0 0.3 0.3 0.3 0.3 0.3

Depth (mm) 0.6 0.8 1.0 1.2 1.6 2 - 4

T o t a l s t r a i n ( w ) -0.3 -0:3 0 0.3 0 - 3 -1.3

Depth (mm) 3.2 4.0 5 .O 6.0 6.8

TABLE 4 S t r a i n s Measured i n 35 NCD 16 S t e e l R e l a t e d t o t h e Depth of t h e Hole D r i l l e d on a F i x e d Bench M i l l i n g Machine ( t y p e 2 )

Depth (nun) 0.4 0.1 0.2 0.3 0.4 0.5

T o t a l s t r a i n (PC) -0.3 -0.8 -1.2 -1.3 -1.5 -1.6

Depth (mm) 0.74 1.0 1.24 1.5 2.0 3.0

T o t a l s t r a i n ( W E ) -1.6 -1.5 -1.5 -1 -8 -1.7 -2.7

Depth (mm) 4.0 5.0 7.5 8.5

T o t a l s t r a i n ( ~ € 1 -2.8 -3 -4.1 -5.1

TABLE 5 S t r a i n s Pleasured i n XC38 S t e e l R e l a t e d t o t h e Depth of t h e Hole D r i l l e d w i t h a n A i r - T u r b i n e System ( t y p e 3 )

Depth (mm) 0.018 0.036 0.054 0.01 0.02 0.04

T o t a l s t r a i n (ME) -0.1 -0.2 -0.4 -0.8 -1.2 -1.8

Depth (mm) 0.06 0.1 0.15 0.2 0 a 3 0.5

T o t a l s t r a i n (PC) -1.9 -1.2 -2.4 -2.7 -3 -3.1

Depth (m) 0.7 0.9 1.1 1.5 2.3 3.0

T o t a l s ' t r a i n ( ~ € 1 -3.3 -3.5 -3.6 -3.8 -3.9 -4

t r e a t m e n t g i v i n g a n a f f e c t e d l a y e r o f up t o 10 mm t h i c k n e s s ) . Tab le 6 summarizes t h e t e s t - s p e c i m e n m a t e r i a l s and t h e s h o t - p e e n i n g c o n d i t i o n s used i n t h e s e t e s t s . To i n c r e a s e t h e a c c u r a c y o f t h e measurements a t t h e s u r f a c e , t h e f i r s t inc rements were 0.01 d , b u t a s t h e h o l e s became d e e p e r t h e i n c r e m e n t s were i n c r e a s e d t o 0.2 d o r 0.25 d - The s t r a i n s measured once t h e h o l e was d r i l l e d a r e g i v e n i n F i g . 13. Each c u r v e r e p r e s e n t s t h e mean v a l u e s measured on t h e t h r e e g a u g e s of t h e r o s e t t e . F i g u r e s 14-16 show t h e r e s i d u a l - s t r e s s

MEASUREmNT OF RESIDUAL STRESSES

0 1 2 Hole depth (mm)

F i g . 13 V a r i a t i o n i n t h e s t r a i n measured a t t h e s u r f a c e w i t h r e s p e c t t o t h e d e p t h o f t h e h o l e , f o r t h e 3 shot-peened specimens.

F i g . 14 R e s i d u a l s t r e s s d i s t r i b u t i o n s o b t a i n e d i n XC38 s t e e l by s h o t peen ing . C o n d i t i o n s : c a s t - s t e e l s h o t o f 1 mrn d i a m e t e r ;

Almen i n t e n s i t y 8-10 C (SAE s t a n d a r d )

0

-100

-200

-300

F i g . 1 5 a l l o y

Hole drilling method

8end1ng deflexion method

R e s i d u a l - s t r e s s d i s t r i b u t i o n o b t a i n e d i n 7075 aluminium by s h o t p e e n i n g . C o n d i t i o n s : g l a s s beads of 0.4 mm

d i a m e t e r ; Almen i n t e n s i t y 0.15-0.20 A (NF s t a n d a r d ) .

SHOT PEENING

i S Hole drilling method

Fig . 1 6 R e s i d u a l - s t r e s s d i s t r i b u t i o n o b t a i n e d i n 7075 aluminium a l l o y by s h o t peening. C o n d i t i o n s : C a s t - s t e e l s h o t of 0.6 mm d i a m e t e r ;

Almen i n t e n s i t y 0.26-0.31 A (NF s t a n d a r d ) .

TABLE 6 M a t e r i a l s T e s t e d and Shot -Peening C o n d i t i o n s Employed ( r e s u l t s : s e e F i e s . 13-16)

Specimen Thickness S h o t Almen Coverage No. M a t e r i a l of t e s t Type o f s h o t d i a . i n t e n s i t y (%I

specimen (mm) (mm) ( ~ / m i n )

1 XC38 s t e e l 1.5 8550 c a s t 1 .0 8-1OC 100 s t e e l

2 7075 1.2 G l a s s beads 0.4 0.15f0.20A 200 Aluminium

3 70 75 1.2 S230 0.6 0.26/0.31A 100 Aluminium

d i s t r i b u t i o n s o b t a i n e d w i t h t h e h o l e - d r i l l i n g method and w i t h t h e bending- d e f l e c t i o n method [12,26] . The c u r v e s i n F i g . 1 4 g i v e t h e r e s i d u a l - s t r e s s d i s t r i b u t i o n s induced by s h o t - p e e n i n g i n s t e e l XC38.

The r e s u l t s o b t a i n e d on aluminium a l l o y AISI 7075 used i n t h e a i r c r a f t i n d u s t r y , a r e shown i n F i g s . 1 5 and 16.

D e s p i t e t h e d i f f e r e n c e s i n b o t h t h e o r y and e x p e r i m e n t , v e r y c l o s e agreement was found between t h e r e s u l t s o b t a i n e d w i t h t h e two methods. I n a l l c a s e s , t h e v a l u e s f o r t h e maximum s t r e s s , t h e s t r e s s a t t h e s u r f a c e and t h e d e p t h o f p r e - s t r e s s e d n e t a l a r e s i m i l a r .

APPLYING THE METHOD TO THE EVALUATION OF RESIDUAL STRESSES INDUCED BY WATER QUENCHING: COMPARISON WITH THE X-RAY DIFFRACTION METHOD

Assuming t h e r e s i d u a l s t r e s s e s induced by q u e n c h i n g t o be i s o t r o p i c t h r o u g h o u t e a c h l a y e r removed by d r i l l i n g of t h e h o l e ( a l ( z ) = a2 (z ) ) , t h e method c a n be a p p l i e d c o n s i d e r i n g o n l y t h e c o e f f i c i e n t s Ain. The v a l i d i t y o f t h i s a s s u m p t i o n i s conf i rmed by t h e X-ray d i f f r a c t i o n method. I n t h e c a s e o f a quenched XC48

MEASUREMENT OF RESIDUAL STWSSES

Strain ( p d ) 450

0 2 4 6 8 85 Hole depth (mmj

F i g . 1 7 V a r i a t i o n i n t h e s t r a i n measured a t t h e s u r f a c e w i t h r e s p e c t t o t h e d e p t h o f t h e h o l e f o r water-quenched XC48 s t e e l .

. --

A -200 { A X ray method

Hole drilling method

F i g . ' l 8 R e s i d u a l - s t r e s s d i s t r i b u t i o n o b t a i n e d i n a water-quenched XC38 s t e e l specimen.

s t e e l , t h e r e s i d u a l s t r e s s e s were measured u s i n g t h e same d r i l l i n g methods a s f o r t h e p r e v i o u s t e s t s . Due t o t h e h a r d e n a b i l i t y o f t h i s s t e e l , quenching r e s u l t e d i n a c a s e - h a r d e n i n g c l o s e t o t h a t which would have been o b t a i n e d w i t h i n d u c t i o n h a r d e n i n g . F i g u r e 1 7 shows t h e v a r i a t i o n i n s t r a i n measured a t the. s u r f a c e o f t h e t e s t spec imen, a s t h e d e p t h o f t h e h o l e i n c r e a s e s .

F i g u r e 1 8 shows t h e r e s i d u a l - s t r e s s d i s t r i b u t i o n o b t a i n e d ' w i t h t h e h o l e - d r i l l i n g methuod and w i t h t h e X-ray d i f f r a c t i o n method: t h e r e i s s e e n t o be f a i r l y good agreement between t h e r e s u l t s o b t a i n e d w i t h t h e two methods.

CONCLUSIONS

The o b j e c t o f t h i s i n v e s t i g a t i o n h a s been t o improve t h e h o l e - d r i l l i n g method f o r d e t e r m i n i n g t h e d i s t r i b u t i o n s f r e s i d u a l s t r e s s e s t h a t v a r y w i t h d e p t h .

SHOT PEENING

Using theoretical approaches already existing in the technical literature, and the finite-element software developed at CETIM, simple equations have been derived for calculating the calibration factors for the hole-drilling method. The coefficients Ain and Bin have been calculated assuming isotropy of stresses in each layer (i.e. 01 = 0 2 ) .

At the present time, the method may be used in cases where isotropic stresses are introduced by surface treatment ( ~ h o t - ~ e e n i n ~ , inductyon hardening, etc ...).

The calculations carried out have shown that the variation of surface. strain of each layer is not only due to the removal of material but is also dependent on the geometry of the hole. The influence of drilling conditions on the metallurgical structure of the material and introduction of residual stresses has been examined, from which it has been determined that the drilling method used does not induce any significant residual stresses. The method has been tested on several types of steels and an aluminium alloy subjected to different shot-peening treatments, and on a quenched steel. Comparison of the results with those obtained by the bending-deflection method and the X-ray diffraction method, has shuown a very good agreement. Further tests will be required to allow the method to be applied to the more general case (ol f a2) and to make it valid for a large number of surface treatments or manufacturing processes ,which induce residual stresses.

REFERENCES

Mathar, J. (1932) Ermittlungen von Eigenspannungen durch Messung von Bohrlochverfomungen. Archiv fur das is en hut ten we sen, 6 (6) pp. 277-281,

Soete, W and R. Van Crombrugge (1947) Een quasi nietdestructive werkwijze voor het bepalen van eigen spanningen. Laschtijdschrifti~evue de la Soudure, Belgique, 4, pp. 161-174.

Soete, h'. and R. Van Crombrugge (1948) Het meten van eigen spanningen en diepte. LaschtijdschriftJRevue de la Soudure, Belgique, 1, pp. 17-28.

Soete, W., R. Van Crombrugge and Ch. De Wulf (1948) ~etermination des tensions residuelles dans quelques constructions soudees. Ossature &tallique, 12 ( 5 1 , pp. 256-255.

Soete, L ,and R. Van Crombrugge (1950) An industrial methuod for the deternination of residual stresses. Proc. S.E.S.A. VIII (11 , pp. 17-28.

Chabenat, A. and R. Hartin (1975) M&noires Techniques du CETIM no. 24, I

Decenber . Boiten, R. G. and W. Ten Cate (1952) A routine method for the measurement of residual stresses in plates. Applied Scientific Research, ~ ( 2 1 , pp. 317-343.

Victor, Y. (19 ) Technique d'extensometrie, Sedem, 88, rue Bobillot, Paris 13em , Etude extraite des no. 88, 89, 91 et 93 de la Revue * Electronique Industrielle, pp. 1-3.

Rendler, N. J. and J. Vigness (1966) Hole-drilling strain-gage method of measuring residual stresses. Experimental Mechanics, 5 (121, pp. 577-586. Decenber.

Beaney, E. M. and E. Procter (1974) A critical evaluation of the centre hole-drilling technique for the measurement of residual stresses. Strain, 1, pp. 6-14. - -

Riparbelli, C. (1950) A method for the deterrnhation of initial strtsses. Proc. S.E.S.A. VIII (11, pp. 172-196.

Flavenot, J . F. and A. Niku-Lari (19 ) La Mesure des Contraintes ~esiduelles. &moire technique no. 15 du CETI-M. '

Saint-Etlenne, A . , F. Lecroisey and B. ~ i e ~ e (19 La Mesure des Contraintes ~esiduelles. Memoire technique no. 33 du CETIM.

Kesley, R. A. (1956) Measuring non-uniform residual stresses bv the hole drilling method. Proc. S.E.S.A., XIV (11, pp. 181-194-

Bathgate, R. G. (1968) Measurement of non-uniform bi-axial residual stresses by the hole drilling method. Strain, 4 (2), pp. 20-29. . I

MEASUREMENT OF RESIDUAL STRESSES

[l6] Owens, A. (1981) Calibration of the Centre-Hole Technique of Residual Stress Measurement- Stress Engineering Service Ltd., Report, Sheffield, UK.

[17] Vishay Measurements Group, Measurement of Residual Stresses by the Blind Hole-Drilling Method, Tech Note TN-503.

[18] ~ijak-Zochowski, M- (1978) A semi destructive method of measuring residual stresses. Proc. 6th Int. Conf. Experimental Stress Analysis, VDI-Verlag GmbH, Dusseldorf, pp. 469-476.

[I91 Schajer, G. S. (1981) Application of finite element calculations to residual stress measurements, J. Eng. Mats. and Tech., 103, pp. 157-163.

[20] Rumelhart, C. and J. Bahuaud (1970) Contribution a l'analyse des contraintes residuelles par la m6thode du trou et de la rosette. R.F.M., 2, pp. 47-68.

[21] Delameter, W. R. and T. C. Mamaros (1977) Measurement of Residual Stresses by the Hole-Drilling Method. Sandia-Laboratories Report SANS-77-8006, April.

(223 Bush, A. J. and F. J. Kromer (1973) Simplification of the hole-drilling method of residual stress measurement. ISA Trans. Vol. 12 (3), pp. 249- - 259.

[23] Bynum, Julian E. (1981) Modification to the hole-drilling'technique of measuring residual stresses for improved accuracy and reproducibility. Exp. Mech., 2 (11, pp. 21-33.

[24] Beaney, E. M. (1978) Accurate measuring of residual stresses on any steel using the center-hole method. Strain, 12 (31, pp. 99-106, July.

[25] Flaman, M. T. (kg821 Brief investigation of induced drilling stresses in the centerhole method of residual-stress measurement. Exp. Mech., 22 (1), pp. 26-30.

[261 Niku-Lari, A. (1982) Proc. First Int. Conf. Shot-Peening, Paris, Pergamon Press, Oxford, pp. 237-247.