E F F E C T OF THE SCALE FACTOR ON THE STRENGTH AND D U C T I L I T Y CHARACTERISTICS OF CERTAIN STEELS D. V. L e b e d e v , V. M. A f o n i n a , A. P. G u l y a e v , and B. M. O v s y a n n i k o v

UDC 539.4

It is well known that the scale effect has a considerable influence on the m e c h a n i c a l p r o p e r t i e s of m e t als and alloys under static deformation and particularly on s u b j e c t i o n t o d y n a m i c loading [1]. Many practical t e s t s have led to the establishment of an approximate proportionality ( K i e k - B a r b a law) between the work r e q u i r e d for the deformation of g e o m e t r i c a l l y s i m i l a r samples p r e p a r e d f r o m identical m a t e r i a l s and the size of the deformed sample, i . e . , to a certain degree of a c c u r a c y t h e r e is a constant specific work of deformation

W':5 PAIT=JT C PAl =

~~

where P is the tensile s t r e s s , A/ the absolute elongation, V the volume deformed, and ~ the relative elongation. Hence the specific work of rupture at the instant of failure is ec

W, = ~ ads. 0

7O

a,%

~v

20

t

1o ~.

o B, o0.~, kg/mrn 2

~0 L ~

i

~0OT

/ ?oo'c

(

o

o

\

~

/ 2OO~ / qSI

7o

6B

o B, kg/mm2

140

I

i

132

6B

~ GO0~163 30

200~C

7~

] I rd,7O 2 0 6 0d, mm o o ~ , Q7 I u z zl-~ Fig. 1 Fig. 2 Fig. 1. Mechanical p r o p e r t i e s of 40KhNM steel in the quenched (from 870~ and t e m p e r e d (at 200, 400, and 600~ states in relation to the d i a m e t e r of the test sample. I

2 # 6 8 d, mm

Fig. 2. Mechanical p r o p e r t i e s of Khl8N10 steel in relation to the sample d i a m e t e r : 1) Quenched f r o m 1050~ 2) p r e l i m i n a r y deformation (drawing) 40%. Central S c i e n t i f i c - R e s e a r c h Institute of F e r r o u s Metallurgy, Moscow. T r a n s l a t e d f r o m P r o b l e m y P r o c h n o s t i , No. 7, pp. 42-46, July, 1970. Original a r t i c l e submitted M a r c h 12, 1970. 9 1971 Consultants Bureau, a division o[ Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced [or any purpose whatsoever without permission o[ the publisher. A copy of this article is available [rom the publisher [or $15.00.

648

oB, ~g/mm2

zzo

/

200 180 160

120

/

/

/

I00

/

F

x-!

0

20

~0

60

W~ = ~8 -e (~T + 2~B) + 4. l~B (1 § Be) lg I § 8o 1 +e e

+

OB ( l

+

ge)g

l + 8~

l + 8,, '

where s is the uni.form elongation and s is the r e l a t i v e elongation.

o- 2

60

According to the Gi!lemot formula [2]

80 8pr,

Fig. 3. Tensile strength of Kh18N10 steel as a function of the d e g r e e of p r e l i m i n a r y deformation (r.pr): 1) f o r a constant d i a m e t e r of the test sample equal to 0.3 mm; 2) for a ' v a r i a b l e d i a m e t e r , f r o m 1.5 m m . a t 0K p r e l i m i n a r y deformation to 0.3 mr~ for a reduction of 9 5 ~ .

We see f r o m the foregoing f o r m u l a that, in o r d e r to d e t e r m i n e the specific work of deformation, we m u s t calculate t h e y i e l d s t r e s s , tensile strength, and elongation, i . e . , c h a r a c t e r i s t i c s which in the case of tough m a t e r i a l s (particularly steels) r e m a i n constant (or a l m o s t so) o n v a r y i n g the d i a m e t e r of the sample over the range usually employed in test practice. On this basis many r e s e a r c h w o r k e r s have tended to use s m a l l d i a m e t e r s a m p l e s in o r d e r to estimate the strength and ductility of metals, either with a view to economy in m a t e r i a l or else owing to the impossibility of p r e p a r i n g samples of large d i a m e ter. The ductility is often d e t e r m i n e d by r e f e r e n c e to the r e lative contraction, i . e . , a c h a r a c t e r i s t i c not entering into the calculation of the specific work of deformation and depending g r e a t l y on the original dimensions of the sample. This method of estimating the ductility of m~tal s a m p l e s may in a number of c a s e s lead to appreciable e r r o r , owing to the fact that the r e l a tive c o n t r a c t i o n s obtained for small samples a r e much g r e a t e r than those obtained for large samples.

This tends to appear p a r t i c u l a r l y sharply in dynamic tests, since under shock loading the m a s s of the test samples becomes specially important owing to the development of considerable f o r c e s of inertia. The effect of the size of the test sample should also be reflected in the conditions governing the transition f r o m elastic to e l a s t i c plastic deformation. It was shown e a r l i e r [3] by N. N. Davidenkov that, in the case of dynamic loading, it was insufficient simply to p r e s e r v e the g e o m e t r i c a l s i m i l a r i t y of the test samples in o r d e r to obtain c o m p a r a b l e results; m e c h a n i c a l s i m i l a r i t y also had to be maintained. In this communication we shall p r e s e n t the r e s u l t s of an investigation into the influence of the scale f a c t o r on the mechanical p r o p e r t i e s of steels, c a r r i e d out on samples between 0.2 and 10 m m in diameter, and involving the static application of loads a f t e r v a r i o u s f o r m s of heat t r e a t m e n t and d e g r e e s of p r e l i m i n a r y deformation, and also on s a m p l e s between 6 and 10 m m in d i a m e t e r for the case of shock (impact) elongation t e s t s . F i g u r e 1 shows changes taking place in the mechanical p r o p e r t i e s of c h r o m i u m - n i c k e l steel 40KhNM with the d i a m e t e r of the test sample. The chemical composition of the test steel was as follows: 0.4~ C, 0.62% Mn, 0.22% Si, 0.7% Cr, 1.4% Ni, 0.18% Mo, 0.005~ 02, 0.012~ N2, 0.01% S,and 0.02% P. After the heat t r e a t m e n t indicated the specimens were c h a r a c t e r i z e d by complete (through) hardenability, i . e . , the s a m p l e s w e r e s t r u c t u r a l l y homogeneous. We see f r o m Fig. 1 that, on v a r y i n g the sample d i a m e t e r f r o m 2 to 10 mm, the strength c h a r a c t e r i s t i c s (~B and %.2), and elongation (~) r e m a i n constant, in view of this, the specific work of deformation calculated f r o m the Gillemot equation is exactly the same for all the test samples of different diameter: 15.5 k g - m m . However t h e r e is a considerable change in c o n t r a c t i o n (Table 1) Qn changing the d i a m e t e r of the sample f r o m 4 to 2 m m . F o r s a m p l e s with d i a m e t e r s between 10 and 4 m m the relative contraction changes little. In view of the sharp i n c r e a s e in the contraction of s a m p l e s with d i a m e t e r s between 4 and 2 mm, it is interesting to study this c h a r a c t e r i s t i c on reducing the d i a m e t e r still further. Since for such small d i a m e t e r s (2 m m o r under) the s u r f a c e effect (the g r e a t e r ratio of surface to volume for a small sample diameter) had a considerable influence on the mechanical p r o p e r t i e s , we chose an e x t r e m e l y ductile m a t e r i a l for investigation, namely, c h r o m i u m - n i c k e l steel of the Khl8N10 type, in two states: a f t e r quenching f r o m 1050~ and a f t e r 40% d e f o r m a t i o n (Fig. 2). We see f r o m the figure that the m a n n e r in which the

649

TABLE

TABLE 2

1 r

Increase in contraction, %, for change in diameter. mm

for d. mm

Ttemp, *C 10 200 400 600

4

39 43 60

2

from I0 f r o m 4

to 2

to 4

from 10 to 2

Increase in contraction, %, for diameter change from 2 to 0.2 mm

State of material Quenched from 1050~ Quenched from 1050~ + deformation 40%

4 20

43 44 13

43 48 60

r

kg/mm z

150

,-

I'1

/

too 120

5~

80

/

. J

~0

o 0 O2

63

6# Fig. 4

65

QO d. mm

loxlo

2ox2o

3ox3o

~ mm z

Fig. 5

F i g . 4. Effect of the d i a m e t e r of the t e s t s a m p l e of Khl8N10 s t e e l p r e v i o u s l y 90% d e f o r m e d on the t o r s i o n n u m b e r n. F i g . 5. V a r i a t i o n in the s t r e s s c o r r e s p o n d i n g to the t r a n s i t i o n f r o m e l a s t i c to e l a s t i c - p l a s t i c d e f o r m a t i o n d u r i n g the i m p a c t bending of St. 3 s a m p l e s with d i f f e r e n t c r o s s s e c t i o n s . p r o p e r t i e s v a r y i s a n a l o g o u s to that in which the s t r e n g t h and d u c t i l i t y c h a r a c t e r i s t i c s v a r y f o r d i a m e t e r s of 2 to 10 m m (Fig. 1). The a b s o l u t e i n c r e a s e in the c o n t r a c t i o n is i n d i c a t e d in T a b l e 2. It should be noted that the c o n t r a c t i o n i n c r e a s e s m o n o t o n i c a l l y , a s it w e r e continuing the p a r t of the c u r v e between d i a m e t e r s 4 and 2 m m (Fig. 1). The s l o w e r i n c r e a s e in the c o n t r a c t i o n with f a l l i n g s a m p l e d i a m e t e r f o r s a m p l e s of quenched (as c o m p a r e d with c o l d - w o r k e d ) m a t e r i a l is due to the high d u c t i l i t y of the m a t e r i a l (~b ~- 70%) and the a l m o s t c o m p l e t e r e a l i z a t i o n of t h i s d u c t i l i t y in s a m p l e s with l a r g e d i a m e t e r s (for t h i s s e r i e s of e x p e r i m e n t s ) . F r o m the point of view of the influence of s c a l e on the d u c t i l i t y , t e s t s on c o l d - w o r k e d m e t a l of high s t r e n g t h and low d u c t i l i t y a r e p a r t i c u l a r l y i n t e r e s t i n g . On r e d u c i n g d f r o m 2 to 0.2 m m the c o n t r a c t i o n c h a n g e s by 20%; t h i s fully s u p p o r t s the p o s s i b i l i t y that an o v e r e s t i m a t e d v a l u e of ~ m a y be o b t a i n e d when testing high-strength steels. The e x p e r i m e n t a l data s e c u r e d ( F i g s . 1 and 2) show that the s t r e n g t h (aB) r e m a i n s c o n s t a n t on v a r y ing the d i a m e t e r of the t e s t s a m p l e . However, in the s m a l l - d i a m e t e r r a n g e (0.2 to 2 m m ) , t h i s only h o l d s f o r two s t a t e s of the m e t a l : quenched, and 40% c o l d - w o r k e d . In o r d e r to s e c u r e a m o r e c o m p l e t e p i c t u r e of the effect of t e s t s a m p l e d i a m e t e r on the s t r e n g t h c h a r a c t e r i s t i c s of the s t e e l , we s t u d i e d the t e n s i l e s t r e n g t h a s a function of the d e g r e e of p r e l i m i n a r y d e f o r m a t i o n (0 to 95%). To t h i s end we m a d e two s e r i e s of e x p e r i m e n t s : in the f i r s t s e r i e s we t e s t e d s a m p l e s with equal d i a m e t e r s (0.3 ram) and d i f f e r e n t d e g r e e s of p r e l i m i n a r y d e f o r m a t i o n , and in the second we t e s t e d s a m p l e s with d i f f e r e n t d i a m e t e r s (1.5 to 0.3 mm) f o r the s a m e d e g r e e s of r e d u c t i o n a s in the f i r s t c a s e , i . e . , the o r i g i n a l s p e c i m e n was s u b j e c t e d to 10, 20, . . . % d e f o r m a t i o n . With i n c r e a s i n g d e g r e e of d e f o r m a t i o n , the d i a m e t e r of the w o r k e d s a m p l e was c o r r e s p o n d i n g l y r e d u c e d (Fig. 3). We s e e f r o m the f i g u r e that, f o r s a m p l e s with c o n s t a n t and v a r y ing d i a m e t e r s , the v a l u e s of t e n s i l e s t r e n g t h r e m a i n i d e n t i c a l . Some slight d e v i a t i o n s m a y be due to the n a t u r e s c a t t e r in the e x p e r i m e n t a l data. Thus the s t r e n g t h of t h e m e t a l i s in no way d e p e n d e n t on the d i a m e t e r of the t e s t s a m p l e w i t h i n the r a n g e of s a m p l e d i a m e t e r s c o n s i d e r e d f o r d e f o r m a t i o n s b e t w e e n 0 and

95%. 650

TABLE

3

TABLE

Lpeci e wor

Material

Steel 45

Sample Iof deforms-]Relative diameter .... ]elongation Ition ~/v, Kg-i % d ' m m [m/mS i~'~'~ 212 9 I06

6

283 9 l0s

6

354 9 t0s

6

700 9 105

0,33 0,032 0,~

6

462. 106

6,0 6,0

10 I0 1O 10 Steel 18Kh2N4MA

0 0 0,~

6

I0

6 8

I0 6

425. 108

0,~2

4

Samples Continuous With internal drilling

Sample diameter d, mm 8 10 8 i0

Cross-sectional area F, mm 2 50.5 78.5 28.7 28.3

Absolute deformarion A, mm 0.12 0.04 0.17 0.16

Note: For all the samples A/V= 354. l0 s kg-m/m s.

0,61

3,0 2,46 2,0 5,8 5,8 5,9

T h e c h a n g e in d u c t i l i t y with t e s t s a m p l e d i a m e t e r a p p e a r s v e r y s h a r p l y in c o n n e c t i o n with t o r s i o n t e s t s ( F i g . 4).

A s a l r e a d y noted, in d y n a m i c l o a d i n g t h e effect of the scale factor may greatly alter the resultant mechanical characteristics. Impact elongation tests were carried out on t h e m e c h a n i c a l p r o p e r t i e s of 6 t o 1 0 - m m d i a m e t e r s a m p l e s of s t e e l 45 a f t e r n o r m a l i z a t i o n a n d 18Kh2N4MA s t e e l a f t e r q u e n c h i n g a n d t e m p e r i n g a t 170~ 8

10

462. 106

By way of a c r i t e r i o n of s i m i l a r i t y , we u s e d t h e r e l a t i o n b e t w e e n the. v o l u m e d e n s i t y and the i m p a c t e n e r g y a b s o r b e d by t h e s a m p l e ( A / V ) a n d the r e l a t i v e r e s i d u a l d e f o r m a t i o n ( s t r a i n ) (a). T h e d i a m e t e r s o f t h e t e s t s a m p l e s w e r e c h o s e n in s u c h a way t h a t the s c a l e e f f e c t w a s l e s s m a r k e d u n d e r c o n d i t i o n s of s t a t i c d e f o r m a t i o n , i . e . , t h e t e s t c o n d i t i o n s w e r e not p a r t i c u l a r l y f a v o r a b l e f r o m the p o i n t of v i e w of the s i g n i f i c a n c e of the r e s u l t s o b t a i n e d . T h e i m p a c t t e s t s w e r e c a r r i e d out with a p e n d u l u m - t y p e L o s e n h a u s e n i m p a c t t e s t e r f u r n i s h e d with a n a t t a c h m e n t f o r p r o d u c i n g i m p a c t e l o n g a t i o n with a s p e c i f i e d i m p a c t e n e r g y . T h e r e s i d u a l s t r a i n w a s d e t e r m i n e d by m e a s u r i n g t h e d i s t a n c e s b e t w e e n punch h o l e s ( m a d e with a h a r d e n e d n e e d l e on the w o r k i n g l e n g t h of t h e t e s t s a m p l e s ) to a n a c c u r a c y of 0.002 m m with a r e a d i n g m i c r o s c o p e . T a b l e 3 s h o w s t h e r e s u l t s of i m p a c t e l o n g a t i o n t e s t s on p r o p o r t i o n a l ( g e o m e t r i c a l l y s i m i l a r ) s a m p l e s ( d f l =const) of v a r i o u s s t e e l s s t r u c k by l o a d s of e q u a l m a s s . W e s e e f r o m t h e r e s u l t s of T a b l e 3 t h a t in the r e g i o n o f s m a l l e l a s t i c - p l a s t i c d e f o r m a t i o n s t h e r e l a t i v e e l o n g a t i o n s a r e by no m e a n s i d e n t i c a l u n d e r c o n d i t i o n s o f c o n s t a n t s p e c i f i c w o r k of d e f o r m a t i o n (A/V = c o n s t ) , i . e . , t h e l a w of s i m i l a r i t y is i n f r i n g e d . H o w e v e r f o r a w e l l - d e v e l o p e d p r o c e s s of p l a s t i c d e f o r m a t i o n ( A / V = 462.106) t h e g e n e r a l l a w of s i m i l a r i t y r e m a i n s valid. T h e r e s u l t s of t h e d y n a m i c e l o n g a t i o n s t e s t s ( T a b l e 3) a g r e e c l o s e l y with t h e d a t a o b t a i n e d f r o m s t a t i c t e s t s ( F i g . 2) in t h a t on v a r y i n g t h e s a m p l e d i a m e t e r in a m a t e r i a l with a s m a l l e r s t o r e of d u c t i l i t y ( c o l d - w o r k e d s t a t e ) , t h e r e i s a g r e a t e r c h a n g e in r e l a t i v e c o n t r a c t i o n ( c a s e in which t h e p r o c e s s of p l a s t i c d e f o r m a t i o n i s l e s s d e v e l o p e d ) , it f o l l o w s f r o m t h i s t h a t , f o r m a t e r i a l s with a l a r g e r e s e r v e of d u c t i l i t y t h e s c a l e e f f e c t i s l e s s m a r k e d , a n d h e n c e t h e m e c h a n i c a l p r o p e r t i e s of s u c h m a t e r i a l s m a y v a l i d l y be e s t i m a t e d by u s i n g t h e g e n e r a l law of s i m i l a r i t y . T h e p r o p e r t i e s o f m a t e r i a l s with a s m a l l r e s e r v e of d u c t i l i t y c a n n o t be e s t i m a t e d on t h e b a s i s of t h i s law, s i n c e in t e s t s on s a m p l e s w i t h a s m a l l d i a m e t e r ( u n d e r 4 m m ) t h e d u c t i l i t y c h a r a c t e r i s t i c s a p p e a r 2 0 to 40% too high. A n a l y s i s o f t h e d i s t r i b u t i o n of r e s i d u a l s t r a i n s a l o n g t h e t e s t s a m p l e s (by r e f e r e n c e to t h e m e a s u r e d d i s t a n c e s b e t w e e n t h e punch h o l e s ) s h o w e d that, f o r s a m p l e s with d = 10 n u n , t h e r e w a s a g r e a t e r l o c a l i z a t i o n of t h e s t r a i n s , with a g r e a t e r d e g r e e of d e f o r m a t i o n in i n d i v i d u a l p l a s t i c a l l y - d e f o r m e d r e g i o n s , t h a n f o r s a m p l e s with d = 6 m m . T h i s s u g g e s t s t h a t t h e o b s e r v e d d e v i a t i o n f r o m the law of s i m i l a r i t y f o r s m a l l e l a s t i c - p l a s t i c d e f o r m a t i o n s i s a s s o c i a t e d with t h e i n c r e a s e in t h e l o c a l i z a t i o n of t h e l a t t e r on i n c r e a s i n g t h e d e f o r m e d v o l u m e . In o r d e r to c o n f i r m t h i s p o i n t o f v i e w , we t e s t e d s o m e s t e e l 45 s a m p l e s d r i l l e d i n t e r n a l l y s o a s t o o b t a i n s a m p l e s with d i f f e r e n t d i a m e t e r s but t h e s a m e c r o s s - s e c t i o n a l a r e a ( T a b l e 4).

651

F r o m an equal c r o s s - s e c t i o n a l a r e a F the absolute elongations of samples with different d i a m e t e r s were in fact equal. Some interesting r e s u l t s were obtained for samples of St. 3 subjected to impact bending tests. The aim of the experiment was to determine the work of deformation A at which there was a residual sag of 0 -< f -< 0.005 mm, in s a m p l e s with different c r o s s sections: 30 x 30, 14 x 14, 7.5 • 7.5 mm. The d i s t a n c e s between the supports were proportional to the sample c r o s s section. F r o m the resultant value of A we determined the s t r e s s [4] corresponding to the appearance of the f i r s t residual plastic deformations: (yl

A = I-]-~-V. We see f r o m the resultant experimental data (Fig. 5) that, with i n c r e a s i n g sample dimensions, there may be a very g r e a t i n c r e a s e in the r e s i s t a n c e of metals to the transition f r o m elastic to e l a s t i c - p l a s t i c deformation. CONCLUSIONS 1. In the uniaxial static elongation of g e o m e t r i c a l l y s i m i l a r samples, the strength c h a r a c t e r i s t i c s (a B and %.2) and the relative elongation (~) a r e p r a c t i c a l l y independent of sample d i a m e t e r . The relative contraction (r i n c r e a s i n g with falling diameter, this effect being p a r t i c u l a r l y sharp below 4 m m . 2. in estimating the mechanical p r o p e r t i e s of m a t e r i a l s tested in two states (annealed and c o l d worked), the diameter has the g r e a t e r effect on the relative contraction for the cold-worked metal, i . e . , the scale effect a p p e a r s m o r e strongly for a less well-developed p r o c e s s of plastic deformation, such as o c c u r s in high-strength samples. 3. In the shock (impact) extension of g e o m e t r i c a l l y s i m i l a r s a m p l e s by loads of equal m a s s , over the range of small e l a s t i c - p l a s t i c deformations the relative elongations a r e no longer constant when the specific absorbed impact energy r e m a i n s so (A/V = const); however, in the c a s e of a well-developed p r o c e s s of plastic deformation the general law of similarity r e m a i n s intact. 4. An estimate of the ductility of h i g h - s t r e n g t h m a t e r i a l s based on the relative contraction of s a m p l e s of small d i a m e t e r (under 4 mm) tends to be too high (by 20 to 40%) and cannot s e r v e as a c r i t e r i o n for justifying any p a r t i c u l a r technical operation c a r r i e d out with a view to improving the mechanical p r o p e r ties of metals. LITERATURE 1.

2. 3. 4.

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CITED

B. B. Chechulin, The Scale F a c t o r and the Static Nature of the Strength of Metals [in Russian], Metallurgizdat, Moscow (1963). L. Gillemot and G. Sinay, Acta Technica, 22 {1958). N. N. Davidenkov, Some P r o b l e m s in the Mechanics of Materials [in Russian], Lenizdat, Leningard (1943). G. I. Pogodin-Alekseev, P r o p e r t i e s of Metals under Impact Loading [in Russian], Metallurgizdat, Moscow (1954).