The frictional component in microhardness testing of intermetallics

Scripta METALLURGICA et MATERIALIA

Vol. 29, pp. 605-609, 1993 Printed in the U.S.A.

THE FRICTIONAL

COMPONENT IN MICROHARDNESS OF INTERMETALLICS

Pergamon Press Ltd. All rights reserved

TESTING

J. Bystrzycki and R.A. Varin* Military Technical Academy, Faculty of Materials Science, Bemowo, 00-908, Warsaw Poland *University of Waterloo, Department of Mechanical Engineering, Waterloo, Ontario, Canada N2L 3GI (Received June 2, 1993) Introduction It has been recognized for quite a long time that Vickers (and Knoop) microhardness of many metallic and non-metallic materials becomes greater at lower loads (so-called "indentation size effect" or ISE). One group of investigators attributed this peculiar phenomenon to an operator factor, or simply speaking to an experimental error, rather than to intrinsic material properties (1-3). However, an alternative analysis takes a more "physical" approach in which two factors, namely, the surface energy contribution and the volume energy contribution are suggested. The former represents the work needed to create the new surface while the latter represents the work needed to produce the volume deformation. This approach results in a general equation of the following form (4-5): p

=

ald

+ a2 d2

(i)

where P is the load, d is the diagonal length (indentation size), a I is the surface related term and a 2 is the volume (bulk) term which is believed to represent the true hardness of a material, which in turn, is related to the yield point of the material (6). However, Li et al. (7) have recently re-interpreted Eq.(1) on the basis of the proportional specimen resistance (PSR) model. In this case the physical interpretation of the two coefficients, a I and a 2 in Eq.(1) is slightly different. Now, the a 2 coefficient describes the proportional specimen resistance (the friction between the indenter facets and the test specimen) while the a 2 coefficient is related to the load -independent microhardness (7). Li et al. supported their analysis using indentation results from the test on unlubricated and lubricated iron. Also, Li et al. (7) showed that with this new interpretation hardness can be generally expressed as: H

=

const

*

(al/d

+ a2)

(2)

which clearly shows the inverse dependence of the low - indentation test load microhardness on the indentation size and a major dependence on friction represented by al, at low loads (small d). It has recently been shown (8-9) that L12 titanium and zirconium trialuminides (based on AI3Ti and AI3Zr intermetallics) exhibit a very strong ISE. In the present paper it is shown that the ISE is very characteristic for many other intermetallics and the PSR model by Li et al. (7) can be applied to explain the origin of ISE in intermetallics, as being fundamentally attributed to the frictional component of indentation testing.

605 0956-716X/93 $6.00 + .00 Copyright (c) 1993 Pergamon Press Ltd.

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Experimental The following intermetallics were selected for Vickers microhardness testing: (53.3±0.5)Ni-(46.7±0.5)AI (NiA1), (78.3±0.3)Ni-(21.8±0.3)AI (Ni3AI as-cast), (63.0±0.1)AI-(10.5±0.1)Mn-(26.6±0.1)Ti (LI 2 AI3Ti+Mn (i0)) and (62.6±0.4)AI-(8.9±O.I)Cr-(28.3±O.4)Ti (LI 2 AI3Ti+Cr (i0)). Compositions are given in at.% and were measured by a fully quantitative (high purity elemental standards) X-ray energy dispersive spectroscopy (EDS). Mean values and standard deviations from five random readings are shown. The selected intermetallics include one with a naturally occurring L12 structure (Ni3AI), two with a crystal structure transformed from a tetragonal DO22 to L12 by alloying (LI 2 AI3Ti+Mn and Cr (i0)), and one with a B2 structure (NiAI). Their Vickers microhardness values also differ in a wide range, as will be seen later. A Vickers microhardness was measured from 5 to 2000g loads (15s dwell time) for specimen surface conditions with lubrication and without (dry). Prior to hardness test the specimens were first polished through 600 grit followed by alumina powder (final 0.05~m). Lubricated measurements were carried out with a thin layer of diffusion pump oil (Apiezon) applied to the polished specimen surface. Ten indentations were made for each load. Both diagonals were measured with an optical microscope on the monitor's screen using an automated Java image analysis package by Jandel Scientific (ii). The mean values and standard deviations were calculated and are shown on the enclosed graphs. Results and Discussion Fig.l. shows Vickers indentation results for the effects of lubrication on the microhardness of intermetallics. Normalizing load in Eq.(1) by d gives a linear equation in the form: P/d

= a I + a2d

(3)

This equation yields a slope equal to the a2-value and an intercept equal to the al-value. Using an average d from ten indentations for each load, linear regresslon analyses were performed for data in Fig.l and the resulting plots are shown in Fig.2. The regression parameters are summarized in Table I. As seen, the a 2 values are very similar for the dry (unlubricated) and lubricated test conditions for each intermetallic. This is expected from the similarity of the microhardness values at the high indentation loads (Fig.l). It shows that lubrication of the specimen surface does not affect the indentation measurements at high loads. The al-values are substantially reduced by the lubrication. This confirms that the lubrication reduces the magnitude of the ISE in accordance with Eq.(2). Our data are in excellent agreement with the analysis reported by Li et al. (7) based on the proportional specimen resistance (PSR) model. As pointed out by Li et al. (7) the a2-valuesare related to the load independent indentation microhardness, H o. For Vickers test H o = 1 8 5 4 . 4 * a 2 (if d in ~m) (12). Calculated H o values are also listed in Table I. They are essentially unaffected by the lubrication, nor the friction between the indenter and the test specimens, since these values are measured at high indentation loads the above data once again substantiate that the friction between the indenter and the test specimen is a significant contribution to the ISE. Finally, it must be pointed out that if "unlubricated" and "lubricated" regression lines, calculated from Eq.(3) for a specific material, are not parallel but intersect one another, then the a2-values (slopes) will be

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MICROHARDNESS

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slightly different. According to the PSR model they should be exactly the same. If the difference between the a2-values becomes relatively large then the difference between the al-values (intercept) for lubricated and dry conditions will also be large. Such an intersection of regression lines may result from the inhomogeneity of hardening or chemical composition, or both. This effect is clearly seen in the present results for Ni3AI (Fig.2), which exhibits the greatest difference of a 2 and H o for lubricated and dry conditions (Table I). Ni3AI was investigated in the as-cast microstructural condition (to achieve high hardness), i.e. its composition could be quite inhomogeneous. In turn, this could be responsible for the observed scatter of VHN data points in Fig.la, which does not indicate a strong lubrication (friction) effect as suggested by a relatively large difference between dry and lubricated al-values for Ni3AI in Table I. A caution should then be exercised in the frictional analysis of microhardness data from hard and inhomogeneous intermetallics. Conclusions The proportional specimen resistance (PSR) model of Li et al. (7) is applied to the analysis of Vickers microhardness data for four intermetallics: Ni~AI, NiAI, L12 AI3Ti+Cr and L12 AI3Ti+Mn. It confirms that the indenter/speclmen interracial friction has a major effect on the microhardness results of intermetallics tested at low loads. Acknowledqements Research performed during Dr. J. Bystrzycki scientific internship at the University of Waterloo, Department of Mechanical Engineering. Financial support by grants from the Polish Committee for Scientific Research and the Natural Science and Engineering Research Council of Canada is gratefully acknowledged. References F.G. Yost, Metall. Trans. A. 14A, 947 (1983). G.F. Vander Voort, in Accreditation Practices for Inspections, Tests and Laboratories, ASTM STP 1057 (H.E.Schock, Jr., ed.), pp.47-77, ASTM, Philadelphia, PA (1989). 3. G.F. Vander Voort, in Factors That Affect the Precision of Mechanical Tests, ASTM STP 1025, (R.Papirno and M.C.Weiss, eds.), pp.3-39, ASTM, Philadelphia, PA (1989). 4. E.O. Bernhardt, Z. Metallkde. 33, 135 (1941). 5. F. Fr~hlich, P. Grau and W. Grellmann, Phys. Status Sol. 42, 79 (1977). 6. K.L. Johnson, J. Mech. Phys. Solids, 18, 115 (1970). 7. H.Li, A. Ghosh, Y.H. Han and R.C. Bradt, J. Mater. Res. 8, 1028 (1993). 8. I.S. Virk, M.B. Winnicka and R.A. Varin, Scripta Metall. Mater. 24, 2181 (1990). 9. I.S. Virk and R.A. Varin, Metall. Trans. A. 23A, 617 (1992). i0. M.B. Winnicka and R.A. Varin, Metall. Trans. A. 23A, 2963 (1992). ii. Glenn Albinger, Java Jandel Video Analysis Software, Jandel Scientific, p.4.8, Corte Madera, CA (1988). 12. H. Li and R.C. Bradt, Mater. Sci. Eng. A142, 51 (1991).

i. 2.

607

608

MICROHARDNESS

TESTING

Vol.

6~

29, No.

68o

o o o o o U n lubr IootedZ

OOO00Unlubr looted eeoeeLubr Icoted

oooooLubrlceted

see

I

I

01 v

v

Z >

=

I

Z I >

I 38o

(b)

a) ,,,u 18

E E \

\

,

,

r-o

' '''"I I~

Load

00o00 eeeee

I

''''I 18

(g)

'

Un i ubr t o o t e d Lubr t o o t e d

'

I

Loed

' ,',,'l 1 ~

(g)

o o o o o Un I ubr t o o t e d ooooo Lubr L e a t e d

:

tt

E E % 2E~

(o)

(d) ........

,,,,u

16

FIG.I.

t~

, I~ loed

........

i

I~ (g)

~I~

. . . . . . . . . . . . .

I~

I~ Loed

......

I"~

(g)

Vickers indentation results for the effects of lubrication on the microhardness of (a) Ni3AI, b) NiAI, c) Ll 2 AI3Ti+cr and d) Ll 2 AI3Ti+Mn.

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5

MICROHARDNESS

TABLE I. Parameters analysis.

for the m i c r o h a r d n e s s

results

609

from the r e g r e s s i o n

a 2 (gl~m 2)

a I (g/~m)

Intermetallic

Dry

Lubric.

Dry

Ni3AI

0.456

0.176

NiAI

0.739

L12 AI3Ti+Cr L12 AI3Ti+Mn Note:

TESTING

H o (kg/mm 2)

Lubric.

Dry

Lubric.

0.247

0.261

458

484

0.288

0.146

0.152

271

282

0.176

0.165

0.118

0.119

219

221

1.504

0.895

0.068

0.066

126

122

For all m e a s u r e m e n t s

correlation

coefficient

25-

/

2e4

/ / N L3AI

r~0.99

F:

TI.AI3 +Cr

"I \10'

I ~

-

0_

s

T t A I 3+Mn

.s

oooooUn lubP Leered oooooLubr Leered 0

0

50

Inden

FIG.2.

1oo tot

Ion

150

SLze

200

(~m)

The V i c k e r s indentation results from Fig.1 by linear r e g r e s s i o n as P/d vs. d (r=0.99).

presented