Hardness of coatings

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Surface and Coatings Technology 80 (1996) 117-120

Hardness of coatings A. Iost, R. Bigot ENSAM/LMP/LSPES

CNRS URA 234, 8 Boulevard Louis XIV, 59046 Lille Cedex, France

Abstract The extensiveuse of appropriate coatingsto improve wear resistance,friction coefficient,electrical properties and protection from corrosion hasstimulateda growing interestin their mechanicalproperties,and especiallyhardnessmeasurements. The objects of this study are to comparethe predictions obtained usingdifferent modelsand to understandwhy it is often reported that the Jiinssonand Hogmark model doesnot hold for indentation prints lessthan the coating thickness.Methods were reviewed for calculatingthe compositehardness,and it wasfound that the simplificationsmadeby the authors are not alwaysvalid. By taking in account all the terms of the equationsof Jiinssonand Hogmark, it wasfound that the relation betweenthe hardnessand the reciprocal length of the indentation print is not linear and dependson the ratio betweenthe t?lmthicknessand the indentation print, aswell asthe variation of the hardnessof the substrateand the film with the appliedload. Comparisonof the Burnett and Rickerby experimentaldata with the modified model led to very good agreement. Keywords: Coating; Compositehardness;Vickers hardness

1. Introduction The hardness test, because of its simplicity, is commonly used to estimate the mechanical properties of coatings. The Vickers hardness number VHN is defined as the ratio of load to the total area of the indentation produced: VHN = 2 cos 22”P/d2 = 1.8544P/d2

(1)

where P (kgf) is the applied load and d (mm) is the length of the indentation diagonal. According to the usual practice VHN is expressed in kgfmmF2 (1000 Kgf mn--2=9.81 GPa) and the units are omitted. However, two main problems arise when this technique is applied to coated materials. (a) The coating thickness varies typically between 2000 A for an ion-implanted substrate to 20 urn for hard coatings used to improve the wear resistance of tool steels. To obtain the bulk hardness value for the film it is necessary to satisfy the requirement that the film thickness should be ten times greater than the penetration depth [ 11. As the indentation depth is D = d/7, the substrate hardness generally influences the measured values and the values obtained are representative of a composite material coating + substrate . (b) In the load range commonly used in microhardness characterization (typically 5-1000 gf, or 49 mN to 9.81 N) the hardness number varies with the applied load. This load-dependence of hardness is called the 0257~5472196BlLQO Q19!% ElsevierScienceS.A,Allsights

reserved

indentation size effect (BE) and has been attributed to a wide variety of mechanisms [ 1,2]. ISE can be modeled in two ways. The first is empirical and corresponds to a power law: P=ad”

(2)

Eq. (2) is called Meyer’s relationship or the log index relationship and deviations from n=2 are a measure of ISE. The second is a linear relationship between hardness and the reciprocal length of the indentation print [3]: VHN = H,, + B/d

(3)

where H,, is the absolute hardness (i.e. the macrohardness independent of the load) and B is a constant. This relation corresponds to a variation of the indentation diagonal with the applied load [4]: P = ald + a,d2

(4)

with a2 = Ho and B= 1.8544 a,. It has been shown that Eq. (3) gives a better fit to experimental data than (2) [ 51, and some attempts have been made to give a physical significance to Eq. (3). In our opinion, the size effect in hardness is due to a formation of a pile-up at the immediate edge of the indentation [ 6,7]. This is confirmed by the investigation of Chaudhri and Winter [S] which shows that the pile-up supports a part of the indenter load. Many attempts have been made to establish a quantitative connection between the indentation hardness

118

A. lost, R Bigot/Surface and Coatings Technology 80 (1996) 117-120

number of the composite material and both the hardnesses of the coating and the substrate. The main models developed are based on the area low of mixture [g-16] or the volume low of mixture [17-211. The objectives of this study were to compare the predictions given by the different models and to attempt to understand why it is often reported that the first does not hold for indentation prints less than or similar to the coating thickness, t. 2. Interpretation microhardness

of the models of composite

Jiinsson et al. suggested that the composite hardness H, can be expressed as a weighted mean of the film hardness Hf and the substrate hardness H,. The contribution of each layer is proportional to the ratio of its flow pressure area Af or A, to the total indented area A:

H,=H,A~A+H,A,/A

(54

with

A,/A = 2CtJd- C2t2/d2,and A = A,+A,

(5b)

Two modes by means of which the film adjusts itself to the shape of the indentation have been proposed: (i) plastic strain, C = C1 = 2 sin2 11” = 1; (ii) crack formation, C = C2=2 sin2 22” z 0.5. The hardness variation with applied load was introduced by Vingsbo et al. [15] through Eq. (3):

equation does not hold for indentation depths of less than the thickness of the film; (3) Chicot et al. [22,23] argued that the Jiinsson et al. model is irrelevant for hard thick coatings. The model was critized on the grounds of Fig. 1 obtained for thick (155-440 urn) Cr&‘NiCr thermally sprayed coatings on low carbon steel. Three conclusions were drown by these authors: (a) application of Eq. [7] leads to H, values lower than H, in zone I, which corresponds to CcO.5; (b) for an infinite applied load, B, = B, and C = 0; (c) in zone III, H, tends to Hf, then Af tends to A, the product (0) tends to d, and so C= 1. All of these correlations should be viewed with some degree of reservation, and what is more they are inconsistent with the observations. The main reason is not the inaccuracy of the model, but the authors’ simplifications, which neglect the second order l/n terms. In fact, the variation of the composite hardness with the reciprocal length of the diagonal is not linear, and this variation, satisfactory for a bulk material, has no physical meaning for the composite material. Let us now consider the relation (5) without the authors’ simplification. Taking into account the secondand third-order l/a terms, we can express H,(d) using the following expansions:

H,=H,,tAl/dtA,/d2tA3/d3 (9) with A,=20 AHo t B,; A,=20 AB - C2 t2AH,; A3= -C2 t2AB; and AHo=Hof-Has; AB=Bf-B,; A=

When the second-order l/d terms are also ignored, this equation reduces to:

AH,/AB. This third-order equation has some particularities, depending on the coefficients Bi and Hoi: (i) one bending point: l/d = l/d1 = 2/(2Ct) - A/3; (ii) intersection between H, and H,: l/d= l/d= l/Ct; (iii) intersection between Hf and the tangent at the zero point: l/d = l/d, = AH,,/(2Ct AHo t B,); (iv) slope of the tangent at the curve representation of H,( l/d) is equal to Bf

H,=H,,,+B,/d

l/d= l/P=

Hf=Hof+Bf/d, and H,=H,,+B,/d

(6)

Introducing this variation in Eq. (5) and neglecting the second-order l/n terms, the composite hardness becomes:

H,=H,,+B,/d+(H,,+B,/d-Ho,-B,/d)2Ct/d

(7)

(8)

with

By postulating a variation of the composite hardness by as W. (3), Eq. (8) was obtained simultaneously Thomas [lo]. This latter equation is widely used to calculate the film hardness and reasonable fits with experimental data are generally achieved. In contrast, it is sometimes reported that this equation has limitations and was not confirmed experimentally: (1) Vingsbo et al. [15] pointed out that the interval of linearity was limited for d values higher than a critical one, which is probably characteristic of the material combination ; (2) Burnett and Rickerby [17,18] have shown that the

l/Ct=

l/d,;

l/d= l/d** =(l-2CtA)/(3Ct)

These particularities are resumed and shown in Table 1 and Fig. 2 versus the product Act.

F H OS

Fig. 1. Hardness versus l/d for a hard coating on a soft substrate from Refs. [ 221 and [ 231,

A. lost,

R BigotJSwface

and Coatbzgs

Techtzology

80 (1996)

119

117-120

Table 1 Particularities of the course of hardness in terms of l/d

Inflexion point 1 d, Existence of -& Fig. 2

0
0.5
yes
yes

Ct<

l
yes

1 >d” no

ll0

(4

(‘4

(4

4@00

2
Ct<2

>O and <--

yes

1

1 >O and
d

(d)

4000

t a)

3500

3500

&

3000

.

3oOG

I

2500

2500

2000

2ooa

1500

1500

1000

loo0 500

500

m-e-m---

I/d ->

0 0

0.0s

0.1

/

r\

0 0.2

0.15

. ’

. ’

I

1400 I1200 --

1800

1600 1400 1200 1000 800 600 400 200 \

0

0.01

0.02

0.03

0.04

0.05

0.06

0

0.01

0.02

0.03

.-.-e-./

0.04

I/d -> 0.05

0.06

Fig. 2. A schematic representation of the composite hardness (kgf mm-“) versus l/d (urn-‘) with respect to the product Act. (a), (b), (c) and (d) are referred to Table 1. Tangent at H,; modified model; --Hf; ---H,.

To test whether this modified model is a reasonable approximation, we applied it to Burnett and Rickerby’s [ 171 results for hard TiN coatings (5.5 and 2 pm thick) deposited on stainless steels. It must be emphasized that the Jijnsson model does not hold [ 17,181. However, two difficulties arose. First, in this work, the variation of hardness with the applied load was described by the use of the Meyer relationship in spite of Eq. (3). The second troublesome point is that the determination of the film hardness is rather tricky. Our solutions to these difficulties are as follows. (a) To express the substrate hardness as H,= 113 + 838/d. The values of H,, and B, fitted well with the experimental results. (b) To take H,,$ = 1200, as reported in Ref. [ 171, for the macrohardness of the film.

(c) To estimate B, as 3000 Kgf urn mmM2, according to Fig. 3 [7], and to take C =0.5, thus crack formation occurs [ 171.

0

500

1000

1500

2000

2500

Fig. 3. Relation between the slope, B (kgf urn mm-‘) and the intrinsic hardness, H, (kgfmmm2) for different materials from Ref. [7].

A. lost, R Bigot/Surface and Coatings Technology 80 (1996) 117-120

& a)

3ooo t

_ I

. -

_

_

_

- _P

d (P)

-’

l/d

0

-5

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

rouo

2500 --

loa,

0 4 0

I SO

100

I50

2oc

0

Fig. 4. Comparison of the prediction of the modified (solid line) with experimental results from Ref. [ 181 TiN on stainless steel substrate: (a) 2 pm thick; (b) 5.5 l.trn thick. The lines have the same signification than in Fig. 2, the units are kgf mm-’ for HV and ltm for d.

The final problem is that there may be measurement errors that seriously bias the estimated correlations, especially for indentation prints less than 10 pm. The errors in the composite hardness were estimated by considering an error of +0.25 pm over the diagonal length. With these estimated parameters, it is shown in Fig. 4 that the modified model is verified to a good degree of accuracy using results given in Ref. [ 171. 3. Conclusions From the above discussion it follows that the discrepancies between hardness measurements of coated materials and the use of the Jiinsson et al. model [9] may be attributed to the authors’ simplifications. This work demonstrates that the area law of mixture for microhardness is convenient for thick hard coatings or indentation depths similar to the film thickness when the modified model is used. References [l]

H. Buckle, in Westbrook and Conrad (eds.), Science of Hardness Testing and its Research Applications, ASM, Metals Park, Ohio, 1971, pp. 453-491.

[2] D. Tabor, in Blau and Lawn (eds.), Microivdentatiou Techniques in Materials Science and Engineering, ASTM STP 589, Chap. 7, Am. Sot. for Testing Metals, Philadelphia, 1986, pp. 129-159. [ 31 F. Frohlich, P. Grau and W. Grellmann, Phys. Stat. Solidi A, 42 (1977) 79. [4] H. Li and R.C. Bradt, J. 1Mnfer. Sci., 25 (1993) 917. [S] A. Iost, J. Aryani-Bouffette and J. Fact, M&I. Sci. Reu. Mkt., 11 (1992) 681. [6] A. Iost and R. Bigot R. J. Mat. Sci., in press. [7] A. Iost, R. Bigot and L. Bourdeau, J. Mat. Sci., in press. [S] M. Chaudhri and M. Winter, J. P11ys.D: Appl. Phys., 21 (1988) 370. [P] B. Jonsson and S. Hogmark, Thin Solid Fibns, 114 (1984) 257. [lo] A. Thomas, Szr$ Eng., 3 (1987) 117. [ 111 L.J. Bredell and J.B. Malherbe, Thin Solid Film, 125 (1985) L25. [ 121 P.A. Engel, E.Y. Hsue and R.G. Bayer, Iveear;162-l 64 (1993) 538. [13] P.A. Engel, A.R. Chitsaz and E.Y. Hsue, T/ml Solid Films, 207 (1992) 144. [ 141 S. Betsofen, Russ. Metall., 2 (1993) 156. [15] 0. Vingsbo, S. Hogmark, B. Jdnsson and A. Ingemarsson, in Blau and Lawn (eds.), Microindentation Techrlipes irt Materials Science and Engineering, ASTM STP 889, Chap. 15, Am. Sot. for Testing Metals, Philadelphia, 1986, pp, 257-271. [ 161 P. Nemec and V. Navratil, J. Mater. Sci. Lett., 13 (1994) 1179. [ 171 P.J., Burnett and D.S. Rickerby, Thin Solid Film, 148 (1987) 51. [ 181 P.J. Burnett and D.S. Rickerby, Th Solid Film., 148 (1987) 41. [ 191 S.J. Bull and D.S. Rickerby, Sw$ Coat. Techno2., 42 (1990) 149. [20] P.J. Burnett and T.F. Page, J. &ter. Sci., 19 (1984) 845. [21] B.D. Fabes, WC. Olivier, R.A. McKee and F.J. Walker J. Mate) Res., 7,11 (1992) 3056. [22] D. Chicot and J. Lesage, Thirl Solid Films, 254 (1995) 123. 1231 D. Chicot and J. Lesage, M&c. Ind. Mat., 47 (1994) 374.