On the relations between ball indentation hardness measurements and the tensile flow behaviour of some ferrous and non-ferrous metals

On the relations between ball indentation hardness measurements and the tensile flow behaviour of some ferrous and non-ferrous metals

Materials Science and Engineering, 59 (1983) 197-205 197 On the Relations between Ball Indentation Hardness Measurements and the Tensile Flow Behavi...

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Materials Science and Engineering, 59 (1983) 197-205

197

On the Relations between Ball Indentation Hardness Measurements and the Tensile Flow Behaviour of Some Ferrous and Non-ferrous Metals M. DEMIRKOL* and ~. E. KISAKUREK

Department of Mechanical Engineering, Bo~azifi University, Bebek, Istanbul (Turkey)

(Received July 14, 1982; in revised form November 2, 1982)

SUMMARY

A n experimental investigation was undertaken to seek a possible correlation between the ball indentation hardness characteristics and tensile flow behaviour o f A I S I 1015, 1035 and 8620 steels, electrolytic tough pitch copper and commercial brass, which had been processed using various thermomechanical treatments. The overall tensile flow curves for any material tested, as well as the plots o f mean pressure against diametral deformation, were observed to obey a p o w e r law relation. Quantitative relations were also sought between the two sets o f curves for each group o f materials; these relationships were then employed to develop general expressions for the tensile flow curves in terms o f the ball indentation hardness readings. Good agreement was obtained between the flow curves resulting from the tensile tests and those from the hardness measurements.

1. INTRODUCTION

The idea of estimating the mechanical properties of metallic materials using a simple method, such as hardness measurements, rather than the application of tension or compression tests has been the subject of considerable attention over the past decade. Tabor [1] was the first to present an empirical relationship defining the ultimate tensile strength of steels in terms of the diamond pyramid hardness and strain-hardening exponent. Numerous other studies using this approach include the attempts to derive the relevant portion of the compressive stressstrain curve for several steels and copper [2], *Present address: Materials Research Division, Marmara Research Institute, Gebze, Kocaeli, Turkey. 0025-5416/83/0000-0000/t~03.00

to obtain the proportionality limits for steels [3] to establish a correlation b e t w e e n the hardness and the 0.2% offset yield strength for many steels in the quenched-and-tempered condition [4], as well as the yield strength of severely cold-worked materials [5], annealed Fe-Cr alloys [6] and age-hardenable aluminium alloys and steel [7]. On the basis of the similarities between the shape of the compressive llow curves and the plots of Meyer's hardness Pm versus diametral deformation (defined in this paper as the ratio of the diameter d of indentation to the indenter ball diameter D), Tabor [1] has also proposed an interesting method of estimating the region of homogeneous deformation of the flow curves from ball indentation hardness measurements. Briefly, for indentations obtained using spherical balls of various diameters D, the flow stress was found b y dividing the mean pressure Pm by 3 and the corresponding true strain was taken as 0.2(d/D). Good agreement was obtained when the m e t h o d was applied to mild steel and electrolytic copper. The method has also been verified by other work on Duralumin and OFHC copper [8]. In this paper the efforts made basically in search of an empirical relationship between the ball indentation hardness values and the tensile flow properties of metals are described. Attempts were also made to establish a quantitative relationship between the hardness and flow curve parameters. 2. EXPERIMENTAL DETAILS

Tests were conducted on plain carbon steels AISI 1015 and 1035, low carbon low alloy steel AISI 8620, electrolytic tough pitch copper and commercial brass. The chemical data obtained from the test pieces utilized in © Elsevier Sequoia/Printed in The Netherlands

198 TABLE 1 The chemical compositions of the steels in this study Steel

C (%)

Mn (%)

Si (%)

S (%)

P (%)

Cr (%)

Ni (%)

Mo (%)

AISI 1015 AISI 1035 AISI 8620

0.15 0.32 0.22

0.46 0.74 0.78

0.03 0.20 0.23

0.049 0.047 0.032

0.008 0.028 0.014

--0.52

--0.43

--0.24

TABLE 2 The chemical compositions of the metals in this study Metal

Cu (%)

Zn (%)

Pb (%)

Sn (%)

Fe (%)

Ag (%)

0 (%)

Copper Brass

99.99 57.8

-39.9

Trace 2.0

-Trace

-0.01

Trace Trace

Trace --

2°°°I

,

i

i

i

12oo

oooI

200

20

100

I 5

,

I 10

I 20

TRUE STRAIN ~"T

I 50

100

('/.)

Fig. 1. The true stress vs. true strain plots for AISI 1035 steel (A, o, ~) and electrolytic copper (4, e, m) on a logarithmic scale: A, A, annealed; 0, o, hot rolled; D,., cold swaged.

the e x p e r i m e n t s are p r e s e n t e d in Tables 1 a n d 2. E a c h g r o u p o f materials was e x a m i n e d in t h r e e d i f f e r e n t c o n d i t i o n s : (1) h o t rolled, (2) fully annealed and (3) fully annealed and t h e n 40% cold w o r k e d b y swaging. The t e r m full annealing refers t o heating f o r 90 min at 1 1 7 3 K, at 6 7 3 K and at 7 2 3 K for steels, electrolytic c o p p e r a n d c o m m e r c i a l brass respectively, f o l l o w e d b y f u r n a c e cooling.

T e n s i o n tests, in w h i c h r o u n d specimens o f 10 m m original d i a m e t e r and 50 m m gauge length were e m p l o y e d , were p e r f o r m e d at an average strain rate o f 1 X 10 -4 s-1, using a 100 k N I n s t r o n test m a c h i n e . The tensile f l o w curves were o b t a i n e d b y measuring the gauge d i a m e t e r b y m e a n s o f a pin-edged m i c r o m e t e r having an a c c u r a c y o f • 0.01 m m at regularly i n t e r r u p t e d loadings t o failure.

199 TABLE 3 K and n for each class o f materials e x a m i n e d

Material

A I S I 1015 AISI 1035 AISI 8620 Copper Brass

I

I

Cold swaged

Hot rolled

Annealed n

K (MN m -2)

n

K (MN m -2)

n

K (MN m -2)

0.26 0.33 0.22 0.19 0.27

784 1127 980 490 784

0.23 0.28 0.20 0.17 0.23

833 1225 1078 499 833

0.17 0.20 0.16 0.13 0.12

931 1372 1274 529 931

I

.+-.

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1400

0.3O

13O0

c

1 oo z

8 ~

~ 110a _

,

53o

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tlJ

0.10

500

-- 470

o.o

I

I

I

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35

40

45

50

,_~,_. ~

HARDNESS

I

I

I

~0

90

100

(NRB)

Fig. 2. The e f f e c t of cold working o n the strain-hardening e x p o n e n t n (A, 4) and the strength coefficient K (D, m) for AISI 1035 steel (&, n) and electrolytic c o p p e r (A, ,,).

The hardness data were collected from axial measurements on cylindrical specimens 8 mm in diameter and 10 mm high [9], using a universal Karl-Frank hardness tester with a loading capacity which could be varied in the range 9.8-245 N.

3. R E S U L T S A N D D I S C U S S I O N

Irrespective of the previous treatments that the materials had received, for every material tested the logarithm of the true stress o w was noted to be linearly related to tim logarithm

of the true strain {~T throughout the plastic region of the tensile deformation process. Accordingly, the overall flow curve could be approximated by a well-known power law 0 T -- Kew n

(1)

where K is the strength coefficient and n is the strain-hardening exponent as usual. Two examples of the plots of lnow v e r s u s lnew obtained from testing AISI 1035 steel and electrolytic copper of various thermomechanical histories are presented in Fig. 1. The average values of n and K for each group

200

seems possible, where K = P + QRB and n = P ' + Q 'R B. In contrast, the data gained from the ball indentation hardness measurements were collected in the form of the plots of mean pressure Pm versus diametral deformation diD. Two examples are presented, on a normal scale in Fig. 3 and on a logarithmic scale in Fig. 4. When Fig. 1 and Fig. 4 are compared, it can be seen that in general the overall relationship between Pm and diD for a given material of arbitrary history, within the limits employed, is quite similar to the tensile flow curve of that particular material. Moreover, the plots of lnPm against ln(d/D), as shown in Fig. 4, suggest an approximately linear variation, thereby enabling the mean pressure to be described b y

of materials, which were mathematically computed from the slopes of these curves and from the stress value at true strains of unity respectively, are listed in Table 3. Apparently, K and n attained different values depending on the treatment that the material had previously received; the general behaviour was that n decreased and K increased as the ductility of the material decreased. When the hardness of the material was measured in terms of the Rockwell B scale and plotted against the strength coefficient as well as the strain-hardening exponent, the relationships were found to be almost linear on a normal scale, as demonstrated in Fig. 2. Accordingly, the redefinition of the tensile flow curves using OT = ( P +

QRB)eTP'+Q'RB

I

I

I

I

B

Pm=

(2)

(3)

I

3000

300

250C

200 ~EE

A 200(3 uE

~_E

~e w 1500

==

uJ

~: 1000

100

500

/

l/ o

0

/

I 10

1 20 DIAMETRAL

I 30

1 4O DEFORMATION

I 5O

-o 60

d/D (°/o)

Fig. 3. Mean pressure Pm vs. diametral deformation d / D plots for AISI 1035 steel (A, o, D) and electrolytic copper (A, o, m) (D = 2.5 ram): A, A, annealed; o, e, hot rolled; D, m, cold swaged.

201 l

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30O0

300

2OOO

20o c~

~E E

%

E

0_

==

1000

100

o_

500-

-

10

I

I

20

50

50

100

DIAMETRAL DEFORMATION dl D ('/,)

Fig. 4. Mean pressure Pm vs. diametral deformation diD curves for AISI 1035 steel (A, ©, ~) and electrolytic copper (A, o, m) on a logarithmic scale (D = 2.5 mm): A, A, annealed; o, o, hot rolled; o, m, cold swaged.

TABLE 4 B and t for each class of materials examined Material

AISI 1015 AISI 1035 AISI8620 Copper Brass

Annealed

H o t rolled

Cold swaged

t

B (MN m -2)

t

B (MN m -2)

t

B (MN m-2)

0.19 0.15 0.12 0.08 0.16

1225 1960 1715 1020 1430

0.22 0.20 0.17 0.11 0.21

1470 2352 1960 1078 1617

0.28 0.27 0.28 0.15 0.28

2744 3185 3626 1156 2548

where B is the value of the mean pressure at d i D = 1.0 and t is the slope of the straight line in the logarithmic plots. The values of B and t for each group of materials are given in Table 4. It is w o r t h noting t ha t the parameters B and t in eqn. (3) are strongly depend e n t on t h e history o f t h e materials under e x a min atio n and t h a t b o t h terms increase

almost linearly with the hardness for any class of materials, if the hardness is expressed in terms of the Rockwell B scale, as demonstrated in Fig. 5. Consequently, linear variations in K and n with respect to B and t respectively were sought and proved, as shown in Fig. 6. On this basis, K and n may be expressed as K = aB + b and n = a't + b ', and

202 i

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I

0.3( 3000

250O

0.2(

'E

lID -- 1200

0.10

~ W U

U -- 1100

1000

00

40'

' 45

' 50

4-

I

I

I

60

90

100

HARDNESS (NRB)

Fig. 5. The effect of cold working on the coefficient B (0, t) and the constant t (o, e) for AISI 1035 steel (0, o) and electrolytic copper (0, e). the tensile flow curve of the materials could be redefined by OT =

(aB + b)eT a't+b'

(4)

The specific expressions describing K and n in terms of B and t respectively are listed in Table 5. It should be pointed out that these expressions were derived from hardness data obtained using an indenter ball 2.5 m m in diameter. Equation (3) which is the most general empirical relationship involving Pm, d and D suggests t h a t the mean pressure markedly depends on the indenter ball diameter. The present investigations revealed that the change in Pm with respect to D is also accompanied by a change in the coefficient B, while the effect exerted by t was found to be negligibly small, an observation in good agreement with the findings of Meyer [10]. The data obtained from the hardness measurements with indenter balls 1.25, 2.5 and 10 m m in diameter are given in Table 6. Unfortunately, the work using the ball 10 mm in diameter was confined to AISI 1035 steel and electrolytic copper only, simply because the size of the other materials (especially those o f the cold-worked materials) could not

meet the standard dimensional requirements. As a result, the strength coefficient K requires to be redefined by an equation of the form

K = a(D)B + b(D)

(5)

in order to develop a more general expression for the tensile flow curve involving an indenter ball diameter term such as 0 T :

{a(D)B + b(D)}eT ''t+ b'

(6)

where a(D) and b(D) are functions in terms of the ball diameter D which compensate for the a m o u n t of change in B with respect to the ball diameter in order to maintain the constancy of K. Equation (6) has been specified for AISI 1035 steel and electrolytic copper on the assumption of a linear variation in B with ball diameter D (which is either 2.5 or 1.25 mm); the results are listed in Table 7. Provided t h a t tests are conducted using other ball sizes, then a and b in eqn. (4) can be clearly defined in terms of D, and thus eqn. (6) can be rewritten in a more general form. The expressions in Table 7 could well be employed in constructing the approximate flow curves of the corresponding materials

203 I

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0.3C c

w 0.20 z

z ~: 0,1C

I

|

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010

020

030

(a)

CONSTANT COEFFICIENT

l B

(kgf

mr'E 2 )

100

110

120

200

250

30O

i

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I

I

1400

140

1300

130

r~ IE 1200

120

?E E

110

1100

_w u u. w ° o

uJ 540

--

z° 520

54

--52

500

480

~fl 1000

(b)

z _w £9 E.

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1100

1200

,'~

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2000

COEFFICIENT

2500 B

--

50

-

48

S z w (x

I 3000

(MN r~ 2 )

Fig. 6. (a) Variation in the strain-hardening exponent n with the constant t; (b) variation in the strength coefficient K with the coefficient B: A, annealed AISI 1035 steel; 4, annealed electrolytic copper; o, hot-rolled AISI 1035 steel; o, hot-rolled electrolytic copper; D, cold-swaged AISI 1035 steel; m, cold-swaged electrolytic copper. and are valid for t h e values o f d/D in the range 10%-70%, t h e u p p e r limit being imp o s e d by t h e l a b o r a t o r y c o n d i t i o n s available w h e n t h e e x p e r i m e n t s are carried o u t , and t h e l o w e r limit being d e t e r m i n e d by t h e

c o n d i t i o n s for w h i c h full plasticity is r e a c h e d . R e s u l t s o b t a i n e d using t h e i n d e n t e r ball 2.5 m m in d i a m e t e r are c o m p a r e d in Fig. 7 w i t h t h e f l o w curves d e v e l o p e d f r o m tensile measurements. Obviously, good agreement

204 was a t t a i n e d b e t w e e n t h e h a r d n e s s results o b t a i n e d as suggested a b o v e a n d t h e d i r e c t measurements. However, deviations exist and d o n o t a p p e a r t o e x c e e d + 5%, d e p e n d i n g o n t h e s t a t e o f tensile strain. T h e w e l l - k n o w n l o g a r i t h m i c t r a n s f o r m a t i o n was t h e n e m p l o y e d t o c o n s t r u c t engineering s t r e s s - s t r a i n curves w h i c h c o u l d b e 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 u l t i m a t e tensile s t r e n g t h values a n d the e x t e n s i o n o f u n i f o r m strains, in a d d i t i o n t o t h e g e o m e t r i c m e t h o d s available w h i c h allow the determination of these properties directly f r o m t h e tensile f l o w curves [11]. T h e c o n v e n t i o n a l s t r e s s - s t r a i n curves c o n s t r u c t e d in

this m a n n e r are c o m p a r e d w i t h t h e d i r e c t l y m e a s u r e d curves in Fig. 8. I t a p p e a r s t h a t t h e h a r d n e s s m e t h o d gives u l t i m a t e tensile s t r e n g t h values w i t h 90% a c c u r a c y whilst t h e e s t i m a t e s o f u n i f o r m strain m i g h t d e v i a t e c o n s i d e r a b l y f r o m t h e actual values.

4. CONCLUSIONS As a result o f a c o m p a r a t i v e s u r v e y o f t h e ball i n d e n t a t i o n h a r d n e s s c h a r a c t e r i s t i c s a n d tensile f l o w b e h a v i o u r o f A I S I 1 0 1 5 , 1 0 3 5 a n d 8 6 2 0 steels, e l e c t r o l y t i c t o u g h p i t c h c o p p e r a n d c o m m e r c i a l brass, t h e f o l l o w i n g conclusions w e r e arrived at. (i) B o t h t h e tensile f l o w curves o f t h e s e m a t e r i a l s (0" w v e r s u s e T ) a n d t h e p l o t s o f m e a n pressure Pm against d i a m e t r a l d e f o r m a t i o n d i D c a n b e e x p r e s s e d b y simple p o w e r law r e l a t i o n s s u c h as

TABLE 5 The values of n and K developed as linear functions of t and B respectively for each class of materials in the study Material

n = n(t)

K = K ( B ) (MN m -2)

AISI 1015 AISI 1035 AISI 8620 Copper Brass

n=--l.00t+0.450 n=--1.09t+0.495 n=--0.37t+0.264 n = - - 0.87t+ 0.262 n=-l.27t+0.482

K=0.090B+686 K~0.135B+883 K=0.141B+768 K = 0.340B+ 136 K=0.123B+620

OT = KeT n

and

TABLE 6 The various B values for different indentation ball diameters Material

AISI1015 AISI1035 AISI8620 Copper Brass

B (MN m-2), annealed material, for the

B (MN m-2), hot-rolled material, for the

f o l l o w i n g indentation ball diameters

following indentation ball diameters

1.25 m m

2.5 m m

10 m m

1.25 m m

2.5 m m

10 m m

1294 2107 1813 1078 1509

1225 1960 1715 1020 1430

-1862 -941 --

1509 2421 2009 1117

1470 2352 1960 1078

-2313 -1058

1646

1617

--

TABLE 7 General expressions describing the flow stress in terms of the indenter ball diameter,

Meyer's hardness test data B and t and true strain (where B is in meganewtons per square metre and D is in millimetres) Material

AISI 1035 Copper

True tensile f l o w stress o T (MN m -2)

1 09t+O 495 O T = { ( O . 5 3 5 - - O . 1 6 D ) B + 3 6 7 D - - 3 5 } e T- " "

(7T ={(0.160 + 0 . 0 7 2 D ) B - 68D + 306}eT"0"s7t+0"262

205

-I

I

l

1

I

Like K and n, the parameters B and t are also strongly dependent on the thermomechanical history of the materials considered. (ii) For any group of materials the parameters K and n vary almost linearly with B and t respectively; the slopes of the K versus B straight lines vary with the indenter ball diameter. Thus, the relation for the flow curve can be written in a general form involving the terms OW, eW, B , t and the indenter ball diameter D. This general expression can then be employed to construct the approximate flow curve of the corresponding material by simple ball indentation hardness measurements.

lOO

9O

800

8O

700

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3o

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ACKNOWLEDGMENTS I

I

I

I

10

20

3O

4C

TRUE

STRAIN

ET

(°to)

Fig. 7. Experimental (I) and calculated (A) true stresstrue strain curves for AISI 1035 steel and electrolytic copper.

7.1

I

I

I

I

I

I

The authors would like to thank the authorities at Marmara Research Institute for the provision of laboratory facilities required by the work, A. ~. Rabak and A. ~. Kroman for materials support and Mr. H. Altin for drawing the line diagrams.

70

6OO

REFERENCES

6O

A ISI 1035 STEEL ~_ 500

5o

lo m ku

~oo

40

3OO

3o ~

UJ u~

+

o

I..-

20

~o 200

§

ELECTROLYTIC COPPER 100

10

I

I

I

I

I

I

10

20

30

40

50

60

CONVENTIONAL STRAIN E ('/o) Fig. 8. Experimental (m) and calculated (A) engineering stress-engineering strain curves for AISI 1035 steel and electrolytic copper.

1 D. Tabor, J. Inst. Met., 79 (1951) 1. 2 A. G. Atkins and D. Tabor, J. Mech. Phys. Solids, 13 (1965) 149. 3 M. C. Davenport and A. S. Weistein, J. Mech. Phys. Solids, 18 (1970) 213. 4 ' E. C. Bain and H. W. Paxton, Alloying Elements in Steel, American Society for Me~als, Metals Park, OH, 1966, p. 223. 5 D. Tabor, The Hardness o f Metals, Clarendon, Oxford, 1951, p. 102. 6 M. J. Marcinkowski, R. M. Fisher and A. Szirmae, Trans. MetalL Soc. AIME, 230 (1964) 676. 7 J. R. Cahoon, W. H. Broughton and A. R. Kutzak, Metall. Trans., 2 (1971) 1979. 8 R. E. Lenhart, WADC Tech. Rep. 55-114, June 1955, p. 55. 9 A N S I - A S T M Stand. A 370-E 10, in Annual Book o l A S T M Standards, Part 10, ASTM, Philadelphia, 1974. 10 E. Meyer, Z. Ver. Dtsch. Ing., 52 (1908) 645. 11 G.E. Dieter, Mechanical Metallurgy, McGrawHill, New York, 2nd edn., 1976, p. 337.