ELSEVIER Surface and Coatings Technology 99 (1998) 171-183

On the hardness of coated systems

Received 9 June 1997: accepted 14 July 1997

Abstract

The hardness of a number of coated systems has been measured using a variety of experimental techniques ranging from traditional macro-Vickers indentation to ultra-low-load depth-sensin g nanoindentation. This has allowed the hardness response to be measured over scales ranging from those less than the coatin g thickness. where a coating-dominated response is expected, to much more macroscopic scales where system behaviour is dominated by the substrate. The objective has been to construct a mathematical description of the hardness performance of coated systems which well describes the behaviour over this wide range of scales. Previous attempts at such quantitative descriptions have usually involved models focusing on some particular deformation mechanism (e.g. plasticity, elastic response or fracture). In contrast, this paper presents a new approach to analysing hardness data essentially using dimensionless parameters containing descriptors equally applicable to either plasticity- or fracture-dominated behaviour with all scales measured relative to the coating thickness. The model shows an excellent fit to a wide range of experimental data. Furthermore, once the fit has been made, not only can some deductions be made regarding dominant deformation mechanisms. but the model allows predictions of the contact response of other coated systems to be made. 0 1998 Elsevier Science S.A.

Kq~~~vtds: Coatings; Mardness; Indentation: Mechanical properties

1. Introduction

Understanding the contact response of coated systems to the point whereby “reliable” quantitative models can be constructed both to explain and predict performance is a critical step in the selection and optimization of coatings for particular substrates and applications. However, since the mechanical response of coated sys- tems will vary with contact severity and scale, it is important to develop soundly based models which allow performance over a suitably wide range of scales to be successfully predicted. In this context, there is general agreement that at contact scales of dimensions less than the coating thickness (t), the coating dominates the system response, while at scales which are very large compared with t, the substrate dominates. with a mixed response occurring at intermediate scales. However, previous attempts to model this behaviour quantitatively have generally experienced two problems. The first has been the difficulty of obtaining good experimental data at contact scales less than the coating thickness -

* Corresponding author.

0X7-8972198iS19.00 G 1998 Elsevier Science B.V. All rights reserved. PII SO’57-8972(97)00522-7

something necessary to enable models to be both con- structed and tested over the necessary wide range of scales involved. The second problem has been the selec- tion of an appropriate model which can be applied at all contact scales. Previous models have been of two types: system models which separate the measured con- tact response into contributions from coating and sub- strate without detailed treatment of the deformation mechanisms in each, and mechanistic models which consider the effect of a given deformation mechanism on the measured contact response. System models become invalidated when major changes in deformation occur (e.g. cracking of coatings) that conflict with assumptions on which the model is based. Similarly, mechanistic modes have significant shortcomings when used to fit experimental data originating from systems displaying other modes of deformation. In general, most coated systems show mixtures of deformation modes and thus there is a clear need for a model which, while having soundly-based physical origins, is capable of dealing with such generalized responses. There is a further need for any such model to be sufficiently mathematically tractable as to allow straightforward fitting procedures to be used.

172 A.M. Komrnsky et al. J Smfuce and Coatings Technology 99 (1998) 171-153

Craqks

ubstrate

la)

Film

Substrate

Film

Substrate

Et > Es Fii Fi-,

Et < Es iTf iis

Fig. 1. Schematic of the deformation patterns for: (a) the area law-of- mixtures: and (b) the volume law-of-mixtures hardness models.

This paper describes the construction and application of a model designed to provide a good fit to experimental data over a wide range of contact scales and deformation modes. Essentially, the model works with a number of dimensionless parameters and. once the fit has been obtained, not only can some information regarding dominant deformation modes be obtained, but good predictions can be made as to the composite hardness displayed by a particular coated system over a wide range of conditions.

One of the earliest workers to investigate the problem was Buckle [l] who defined the measured hardness as being the sum of the hardness values within the plastic zone (or “influence zone”) at given depths beneath the indentation multiplied by an appropriate weighting factor. This simple model had some success in explaining the effect of work-hardened layers on measured hard- ness, but critically depended on the choice of weighting factor. However, the model was not applied to coated systems in the currently accepted sense of surface engi- neered systems.

A more successful model from Jonsson and Hogmark [2] used an area law-of-mixtures approach to modelling the composite hardness, H,, giving:

where Af and A, are the load-supporting area of the film and the substrate respectively, A is the total pro- jected contact area (A =A,+&) and Hf and H, are the hdrdnesses of the coating and substrate. This model implicitly assumes fracturing of the coating with much of the load support from the coating arising from the unfractured material at the rim of the contact area bending into the impression left in the substrate [Fig. 1 (a)]. From geometric considerations of the size of this rim, Johnsson and Hogmark derived an expression for the composite hardness given by:

(2)

where t is the coating thickness, n is the indentation diagonal and c is a constant dependent on indenter geometry. The model was intended to be applicable in cases where cracking and bending of the coating is well established, i.e. at large penetration depths where the surface displacement is generally > t. It was reasonably successful at determining the coating hardness of thin chromium films on a range of metallic substrates. However, the load dependence of hardness at small indentation sizes [the indentation size effect (ISE)] was not explicitly included in the first analysis, but an ISE behaviour of the form

H(d)=H,+” d’

(31

where k is a constant and Ho is the hardness at very large loads was subsequently added to increase the applicability of the model [3]. Even so, the model is not a realistic description of cases either where no fracture takes place or where the indenter penetration is a very small fraction of the coating thickness. For a data set which covers both substrate-dominated and coating- dominated indentation depths (Trig. 2a), the best fit of Eq. (2) is relatively poor (whether indentation size effects are included or not) since the hardness is overestimated at the substrate-dominated end and underestimated at the coating-dominated end. The lit can be improved by restricting the data to the substrate-dominated end only (where the model is likely to be more valid), but, in such cases, the coating hardness is greatly overestimated.

A more generally applicable model, particularly in cases where the indenter penetral.ion is very low. is the volume law-of-mixtures hardness model originally sug- gested by Sargent [4] and subsequently extended vari- ously by Bull, Burnett, Page and Rickerby [5-81. In this model, the zone of plastic deformation beneath the indenter is assumed to be hemispherical [Fig. 1 (b)]. Thus, by calculating the proportions of the total deform- ing volume that lie in the coating and substrate, L$ and V,, respectively, the composite hardness (for the case of

173

Area law-of-mixtures Hardness Model

25

0.1 I IO

Normalised indentation depth (6/t)

Full Volume law-of-mixtures Hardness Model 40

35-

30-

25-

20:

IS-

IO-

5-

0 001 001 01 01 I I IO IO

Normalised indentation depth (Sit) Normalised indentation depth (Sit)

Thomas model Thomas model

o,., o,., ,1 ,1 ,,,,,,,,,,, ,,,,,,,,,,, I,, I,, , , ,,, ,,, ,,, ,,, 0 0 2 2 4 6 4 6 8 8 IO IO 12 12 14 14

l/h’ormalised indentation depth (t/S) l/h’ormalised indentation depth (t/S)

H,> H,) was expressed as:

where I/ is the total deforming volume (V= V,+x3Vs) and Hi and H, both include indentation size effect behaviour of the form

H(d)=H,d”-‘, (5)

where H, and 12 are constants, H, is a hardness value at a standardized indentation size, while II is the ISE index (which has a value of 2 if no ISE occurs) [9]. 1 is a dimensionless factor which represents the modification to the deforming volume of the soft substrate due to the constraint caused by the presence of the coating. This is expected to be a strong function of the difference between the plastic zone radii in the coating and sub- strate and. based on an expression due to Lawn et al. [lo], Burnett and Rickerby expected x to take the form of a power law:

where Ef and E, are the Young’s moduli of coating and substrate, H, and H, are the hardnesses of coating and substrate at the scale of the contact (i.e. incorporating any indentation size effects) and ~1 is a constant which can be determined by fitting to experimental data. The volume law-of-mixtures approach has been very success- ful at separating out the hardness of the coating from composite hardness data measured where plasticity dominates - i.e. there is no fracture (e.g. metal on metal substrate) or in cases where the indenter penetra- tion is very low and cracking is not well established. Thus, the model had success in fitting to data for soft layers on harder substrate (e.g. surfaces softened by an implantation [5]) or harder metallic layers on softer substrates. The fit achieved on the same test data set as that used in Fig. 2a is much better than the area law- of-mixtures model (Fig. 2b), but the fit begins to degrade as the indenter penetration increases. The successful use of the model not only requires several complex fitting operations to enumerate all the various constants but also needs good estimates to be made of the deforming volumes (which are difficult to validate experimentally). Furthermore, the fitted coating hardness is very sensitive to the quality of input data since apparently high-quality fits can be achieved to most experimental data sets due

Fig. 2. Model fits to experimental hardness data obtained for a 2.8 pm NbN coating on M304 stainless steel. (a) Area law-of-mixtures; (b) volume law-of-mixtures; and (c) the Thomas model. The best fit across the entire normalized indentation depth range is produced by the volume law of mixtures hardness model which requires the most com- plicated fitting approach.

174 A. M Korsw~sk~ el al. / Swface and Coaiiqs Technology 99 (1998) 171-183

to the number of fitting parameters and operations required. As such, it is not really suitable for routine use and certainly should not be used in instances where fracture plays any significant role in system response.

An alternative approach suggested by Thomas [I l] relied on the fact that the empirical data for H, could often fit an expression of the form:

H,=A+Z, (7)

where A and B are constants. This is very similar to the form of the indentation size effect equation used by Vingsboo et al. (Eq. (3)) and is effectively a fitting approach that treats the effect of the coating as a contribution to the ISE behaviour. The physical basis for this approach is dubious, but it does give a conve- nient and simple method for assessing coating-substrate hardness since it can be shown that:

(8)

where B, and B, are the constants measured for compos- ite and substrate respectively and A is the large-scale hardness (i.e. the substrate hardness). Central to this approach is an assumption that the indentation diagonal should be numerically greater than the square of the coating thickness so the approach is only really valid for large indenter penetrations. The fitting approach is reasonably easy to implement, but, generally, the fit quality is poor (Fig. 2c) as the assumptions inherent in Eq. (7) are not based on sound mechanistic models. This equation only provides a value for Hf (rather than describing the system response over a range of scales) and even this value relies critically on determining the empirical constant B,.

Most recently, McGurk and co-workers [12,13] have proposed a new model applicable when the coating has cracked. As with the Jonsson and Hogmark model, this primarily considers the effect of the unfractured coating around the rim of the indentation, but is now couched in terms of the coating constraining the upwelling of the displaced substrate as it tries to “pile up” and upwardly bend the coating around the indentation site. Using plate bending theory, this model has produced quantitative estimates of the hardness enhancements produced in such cases, but was never intended to describe the hardness behaviour at small displacements before the coating cracks.

By considering the volumes displaced during indenta- tion, an expression was obtained for the upthrust pres- sure, q, which is analogous to the increase in hardness resulting from the presence of the coating. From this

1o-3 lo-’ 10’ IO3 lo5 lo7 Coating Stiffness Parameter

Fig. 3. Using the plate bending approach, a dimensionless plot of coat- ing effect parameter (AH/H,) versus coating stiffness parameter (G?/d3H,) in log-log space for MO53 (NbN, total-thickness, h=- 2.8 pm on M304 stainless steel) and MO57 (CrN. total thickness, /I= 7.75 pm on M304 stainless steel). The data show an approximately linear relationship in the cracked plate bending region (left han$Ie) and a deviation from this behaviour associated with the inhibition 01 crack initiation at low loads (right hand side). Each data point is the average of a miniumum of 10 indentation tests and extends over a large range of indentation loads 1300 kN (30 kgf) - 5 mN).

approach, the dimensionless proportionality,

AH EC fi3

u,” #Ho ? (95

was identified as being a powerful controlling parameter for describing the hardness enhancement expected from this type of mutual deformation, where AH is the increase in hardness resulting from the presence of the coating, Ho is the substrate hardness, E, is Young’s modulus of the coating, h, is the coating thickness, and L[ is the characteristic diagonal length (.proportional to the depth) of the indentation. The left hand side of Eq. (9) is referred to as the conring efft>ct pamnrneter as it is a direct measure of the effect of adding a coating to the system, whilst the right hand side of the equation can be regarded as the coating st~~~ze.~~.spnrnrlzeter. Fig. 3 shows the data sets for samples MO53 and MO57 (see Section 3 for details as an example of this approach). When plotted in this way, the right hand side of the log-log plot is linear up to ( 105, lo’), a point in coating effect space which indicates the transition from fractured to unfractured coating. At lower loads (higher contact stiffness parameter) where there is no fracture, the model breaks down. Thus, there are considerable disparities not only between the range of applicability of existing models. but also their ease of use. The most widely applicable model with the best fit to experimental data, the volume law of mixtures, is very difficult to apply and requires a large number of fitted parameters, whilst the simplest model, which is easy to apply, is not physically based and has only limited applicability. There is thus a need for a model that is applicable at a

A.M. liors~msk~~ ei ul. I Surface and Coatings Technology 99 (1998) 171-183 175

wide range of contact scales, is easy to fit, relies on few empirical fitting parameters, has some basis in physical reality and has the potential to be developed into a predictive design tool. We now describe the construction of such a model and how it can be applied to a range of coating-substrate systems.

2. The model

In an indentation experiment with a sharp pyramidal or conical indenter, the highest applied load. P, is almost invariably found to relate to the maximum penetration depth, S (measured after the removal of the load and thus after elastic recovery of any surface flexure, but ignoring any small elastic recovery of the depth of the indentation itself) by:

2

p-HJ

where H is the measured hardness and K is a parameter describing the indenter geometry. For Vickers indenters, 6=d/7 where d is the indentation diagonal. Similar expressions can be derived for other indenter geometries. The total energy required to produce an indentation of depth 6 is then given by:

i

8 HJ3 w,ot = Pdx = - (11)

0 31; .

This is termed the “work of indentation” and, if mea- sured [as can now readily be achieved with continuous recording indentation techniques (CRIT)] can be used to deI?ne an effective value of H which usefully describes the resistance to deformation over the penetration 6. The following derivation of the model will be based on the application of an “inversion” of this formula, whereby the hardness is expressed in terms of this energy, i.e. :

s3 (12)

Note that no assumptions need to be made about the way the energy was expended. The above expression may therefore be justifiably applied both to the coated system and its substrate separately. It is the compurison between these two situations that will be important.

It is clear that the total energy dissipated in deforming the composite will contain contributions from both the substrate and the coating. However, the partitioning of the energy expended between deformation of the coating and the substrate will vary depending on the scale of indentation. It is convenient to start by considering the case when the indenter penetration depth is very large compared with the coating thickness. Under these condi-

tions, the energy term relating to the plastic deformation of the substrate dominates. The energy contribution from the coating is very small in comparison and one can expect to recover the substrate hardness from Eq. (12). Examining the case for progressively smaller indentation depths, it is clear that while a substrate term will remain (but become increasingly smaller), a further term due to the coating will start to become increasingly significant and the energy balance will favour the coating more and more, i.e. the share of its contribution to the total energy will increase.

The total energy expenditure will now be composed of two parts: the plastic work of deformation in the substrate (W,), and the deformation and fracture energy in the coating ( Wf)> i.e.:

w,,, = w, + Wf (13)

Extensive experimental evidence exists on the indenta- tion of hard-coated systems. In developing the present approach, we have reviewed the similarities between deformation and fracture modes observed in a variety of materials used for substrate and coating and over a range of coating thicknesses and deposition techniques, etc. (Fig. 3). These observations suggest that while plastic deformation usually occurs in both coating and substrate (Fig. 4b) - and is primarily responsible for the permanent impression left by the indenter - fracture also occurs at larger loads and indenter displacements (typically, exceeding one tenth of the coating thickness where substrate deformation starts to assume signifi- cance [ 141). Certain similarities also exist for all hard- coated systems, namely, that coating deformation is most often dominated by cracking, which occurs at the indentation apex, along the edges of the indenter pyra- mid, and in the form of circumferential cracks around the indentation perimeter (Fig. 4a). At low loads, frac- ture is localized along the indenter edges, with possibly one or more peripheral cracks being present. With increasing load, multiple cracking starts to dominate, producing a web pattern concentric around the indenter tip. Plasticity and fracture must be considered separately, although the resulting models show some convergence and may be combined into a single master formula.

In the case of fracture-dominated coating response, at indentation depths smaller than and up to the coating thickness, the relationship between the fractured surface area and the indentation diagonal (which for a given indenter geometry scales with the indentation depth) is often found to be approximately linear. Under these conditions, the total energy contribution due to coating cracking may be approximately expressed in the form:

W,=;,G,t6 (14)

where G, denotes the through-thickness fracture tough- ness of the coating and 2, is a parameter which describes the dependence of the crack length on the material pair,

176 A.M. Korsmdy et al. / Swface atd Coutings Teduwiog.~ 99 (1998) 171-183

Sink-In Pile-Up

i P '1

Sink-In Pile-Up

Fig. 4. Schematic of the processes occurring in the indentation testing of hard and soft coatings. Depending on the substrate deformation mechanism. material may pile-up or sink in around the indentation. In the case of pile-up, fracture of hard coatings is Far more common.

as well as other factors such as the indentation depth and diagonal, crack geometry, work-hardening proper- ties of the substrate, interfacial adhesion, etc.

In the case of plasticity-dominated coating response, the expenditure of energy may be assumed to be propor- tional to the plastically deforming volume. Since plastic flow appears to be localized around the indenter edges? in bands of thickness comparable or linearly dependent on the coating thickness, the energy may be written as:

These results may now be recast in terms of the compos- ite hardness. by using Eq. (12) to express H, via the total indentation energy W,,,. Substituting the coating energy contributions either from Eqs. (14) and (151, H, is obtained in Ihe form:

where P=d/t denotes the indentation depth normalized with respect to the coating thickness and has been termed the relative indentation depth, RID [ 151 and AH

is the hardness enhancement provided by the coating. For the case of a cracked coating:

rAH=3~?b~ G,,

while for plastically-deforming coarings,

xAH=&Hft. (18)

AH has the dimension of stress (hardness) and the parameter a has the dimension of length.

The above formula may be expected to hold for relatively large penetration depths, e.g. j? > 0.1. However, in its present form, the model obviously fails at low indentation depths, where the deformation is confined to the coating, fracture may not yet have occurred, and the substrate is hardly involved. In order to develop a universal formula applicable at limits of both very large and very small 0, the asymptotic behaviour of hardness at these two extremes must be merged. The problem may be formulated as follows:

Find a function H,=f(H,, H,, t, fi, etc.) such that:

(1Ya)

and

H,=H, as b-0. (1%)

There is a considerable practical utility in posing such a problem in that provided the transition between the two regimes above occurs over a rest_ricted range of p (e.g. approximately one order of magnitude), any expres- sion found in this way will remain largely valid through- out the range of all indentation depths!

All the above requirements are satisfied by the single expression:

4-K Hc=Hs+7 (20-t

This formula shows that the composite hardnrhh, H,, depends not only on the hardness difference between the coating and the substrate, but is modified by X, ,0 and t. The parameter CL. having the dimension of length, may be expected to depend primarily on the ratio GJH, for fracture-dominated cases (see Eq. (17)) and be largely proportional to the coating thickness, t, for plastically deforming coatings (see Eq. (18)).

The predictions of Eq. (20) are shown in Fig. 5, which plots the hardness enhancement to a system as a function of ,l?. The change in behaviour from coating-dominated to substrate-dominated is clearly shown as is the way the transition region shifts with the parameter CC. Thus, as a increases. the curves are shifted to the right anal vice versa. For fracture-dominated cases. CL primarily depends on the combination G,/H, (and thus high values

A.lll. Ii~).~~m~ky et al. 1 Surface and Coatings Technology 99 (1998) 171-183 177

MO57 - 7.8pm CrN on M304

0.01 0.1 1 10 Normalised indentation depth (s/t)

MO59 - 3.2pm ZrN on ASP23 50 lllllN1

1 :I

I I

1

(b) Nofialised indenkion depth (4:)

Fig. 5. Hardness-P plots of: (a) MO57 (CrN on M304 stainless steel); and (b) MO59 (TiN on ASP23 tool steel) showing identical transitional behaviour to M053. Limits of the transition behaviour are: near-sub- strate only for j> 1 down to coating-only behaviour for /?<O.l. The matching curves are fits of Eq. (20) to the data (see text). Comparing MO57 and MO53 [Fig. 7 (b)] highlights the effects of changing the thick- ness on the robustness of the model whilst comparing MO59 and MO53 [Fig. 7(b)] performs a similar function for changing substrates.

of E are associated either with coatings of high fracture energy or substrates of low hardness), while for plastic- ity-dominated cases, x primarily depends on the ratio H,IpI, and the coating thickness t.

For ease of fitting we have used the equation:

Hi-H, H,=H,+p

1 +/?p* ’

where the fitting parameters H,, Hr- H, and 1~ (= t/a) are determined by fitting to the experimentally deter- mined variation of H, with fi. In the case of the cracked coating, the constant I< should be proportional to t, whereas in the case of the plastically-deforming coating,

the constant k should only be weakly dependent of thickness (since accr).

3. Experimental

A range of coatings produced by different PVD process on different substrates were investigated to vali- date the model and these are listed and identified by system codes in Table 1. Coatings were produced under controlled conditions by sputter ion plating [ 161, plasma-assisted PVD [ 171 and arc evaporation [ 181. A series of thin (i.e. 12 < 10 urn) PVD arc-evaporated TIN, NbN, CrN and monolithic coatings on both soft M304 stainless steels and hard ASP23 tool steel substrates were used. Details of these samples and their preparation can be found in Ref [ 191.

Nanoindentation experiments were performed using a NanoIndenter II@ (Nano Instruments Inc., Knoxville, TN, USA). In order to make indentations whose dis- placements spanned a range which exceeded the coating thickness at higher loads, indentations were made to peak loads between 5 and 500 mN. The raw data was then processed using proprietary software to produce load-displacement curves and values for load-off hardness using the approach of Oliver and Pharr [20]. A standard approach-load-partial unload-complete unload cycle was used with a 60 s hold (at 70% of peak load during unloading) to calculate thermal drift. [21].

Conventional macro and microhardness tests were performed using a standard Vickers hardness machine and a Shimadzu (Type M) microhardness tester. The data presented in later sections is for hardness values calculated at 5, 10, 50, 100, 250 and 500 mN (nano- indentation); 50, lOO> 200, 300. 500 and 1000 gf (micro-Vickers); and 1, 2.5, 5, 10, 20 and 30 kgf (macro-Vickers).

Scanning electron microscopy of the indentations was performed using secondary electron imaging with a CamScan S4-80DV with a high brightness LaB, fila- ment. In order to optimize signal strength, image reso- lution and minimize penetration of the beam into the coated sample, the typical accelerating voltage used was 15kV with a probe current of - 1 x lo-“A. Coating thicknesses were determined by ball-cratering and profi- lometry [ 191.

Table 1 Experimental systems used in the validation of the model

Sample ID Coating/thickness (urn) Substrate

Sputter ion plating series (SIP) 2-9.8 TiN M304 PAPVD series 0.5-25 TiN ASP 23 MO53 2.8 NbN M304 MO57 7.8um CrN M304 MO59 3.2um ZrN ASP23

175 A. M. Kotxmsl~~ ri al. / Sul:face and Coatings Tecl~nolog~ 99 ( 1998) 171-183

All the data quoted below is original to our experi- ments except where specific reference is made to the work of others. With the exception of the SIP series (which were averaged over five indentations) all data points represent the average of 10 indentations.

4. Results

Fig. 6a contains hardness data plotted in the tradi- tional sense, i.e. a plot of hardness against depth for MO53, It is clearly unsuitable for displaying the wide range of data necessary to fully validate the model. Fig. 6b replots the same hardness data for MO53 in partially non-dimensionalized form. Now, the relative indentation depth (,0 = d/t) parameter scales the indenta- tion depth with respect to the individual coating thick- ness. Semilog axes have also been used.

cb)

Fig. 6. High-resolution SEM micrographs showing examples of: (a) Fig. 7. Schematic plot of coated system hardness, H,, versus relative fracture-dominated: and (b) plasticity-dominated responses for nomi- indentation depth /I (/I=S/l) showGng the scaling etfect of the parame- nally identicai 500 mN Berkorich nanoindentations in (a) NbN on ter CI. Coated systems hardness varies between, H,, the near coating- M304 stainless steel and I b) TIN on ASP23 tool steel, respectively. only hardness and, H,, the near substrate-only hardness.

It is now immediately apparent from this figure that there is a transition in behaviour between the points fi- 10 and p-0.1. i.e. for indentation depths between 10 times the full coating thickness and l/l0 of the coating thickness. Thus, as expecl.ed at depths approxi- mately equal to the coating thickness, the data appears to reduce asymptotically to a near-substrate value of hardness, whereas for depths shallower than the l/l0 coating thickness, the coating hardness “levels off” at a fairly high hardness value. This behaviour is also appar- ent for samples MO57 and MO59 (Fig. 7) but the near- substrate behaviour now occurs at somewhat larger values of fi (> 1) than for sample M053.

The fit provided by Eq. (21) to these results is also plotted as a solid line in Figs. 6b and 7a and b. Modelling parameters and their estimated errors are presented in Table 2 alongside the statistical parameters derived from the x2 and correlation coefficient tests. Included in the table are data for the other systems tested. Each of the systems tested shows a remarkably good agreement with the derived expression which is reflected in the consis- tently high values of R returned by the modelling process. The three coatings M0.53, MO57 and MO59 have been deliberately chosen to highlight both hard and soft substrates (compare MO59 and M053) as well as coatings of significantly differing thickness (compare MO53 and M057).

The data in Table 2 allow us to read off the near- substrate hardness. H,, and “coating-only” hardnesses, H,. For the two samples with nominally identical sub- strates, the results of H, are very similar and all three values correspond well with independently measured H V30 Kg of 7.9 and 1.5 GPa for ASP23 and M304L respectively, e.g. Refs [22,24]. The coating-only hard- ness, H,? is calculated as 40.5, 31.4 and 39.3 GPa for NbN, CrN and ZrN. respectively, and these values agree reasonably with literature values for these materials [22?23]. It should be noted that, at present. most of the published hardness data for coated systems is produced

179

Table 2

Curve-fit data produced from the model validation process (model used: H,=&iA&‘( I +k*/i * 2): input starting values for the curve fit f&=5; AH=30: h-=7)

Sample H, NC-H, ii Confidence

4 Err AH Err Ii Err z2 R

SIP series 9.8 3.96 0.47 45 4.93 48.8 14.863 0.528 0.999 7 2.14 0.178 ‘3 1.78 29.7 0.462 0.304 0.999 4.8 2.02 0.148 21 1.15 11.8 0.588 0.435 0.999 2.7 1.96 0.146 17 1.34 6.4 1.372 0.145 0.999 2 1.54 0,0436 I I 1.67 6.7 029.5 0.0366 0.999

PAPVD series 23.9 9.76 0.886 19.8 1.055 15.4 3.9 3.506 0.971 6.25 9.32 0.461 14.8 1.22 6.65 0.701 1.71 0.988 0.94 - _ - - 1.2 0.29 -

0.861” 0.48 - - - - 5.0 18.6 - 0.58”

Arc evaporation series MO53 1.73 0.476 38.8 I.3 25.9 MO57 1.9 0.403 29.5 0.709 25.5 MO59 7.7s 0.497 31.5 0.918 13.8

“Insufficient data for high quality fit.

2.67 7.4 0.991 3.06 18.4 0.996 1.81 13.1 0.997

using microhardness testers and thus the hardnesses quoted here are generally slightly higher than most literature values. In general, interpretation of literature data is hamstrung by poor specification of how the hardness number was obtained. i.e. no mention of load used, coating thickness and/or relative penetration depth into the coating, making accurate like-for-like compari- son difficult (an issue currently being addressed by the NIST/NPL comparative study VAMAS TWA-22 [25]).

SEM micrographs of 500 mN Berkovich nanoindent- ations in NbN-coated M304 stainless steel and TiN- coated ASP23 tool steel are reproduced in Fig. 8. Fig. 8a displays a typical fracture-dominated response for this type of coating, which shows very little evidence of plasticity other than along the indentation diagonals. The fracture itself has occurred aIong the indentation diagonals as well as in ring cracks around the indentation outline. In marked contrast, coating plasticity is far more prevalent in Fig. 8b. At higher loads, large peri- pheral cracks appear around indents on this sample leading to the formation of the famiIiar picture-frame crack regime.

Figs. 9a and b reinforces the data atready presented for two series of nominally identical TIN coatings (within the series) of different thicknesses. The coatings in Fig. 9(b) span the range 0.5-25 pm TiN on the tool steel ASP23. The use of the fi parameter has alIowed the data to collapse on to the same curve which is fitted by Eq. (21). Fig. 9a shows the same behaviour for TIN in the range 2-10 pm on M304 stainless steel,

MO53 - Conventional Hardness Plot

0 20000 40000 60000 80~00 Displacement (nm)

MO53 - 2.8pm NbN on M304

IO 40 *..+j --..-... ..I...... j_ ,..,........... .._.. _.._. i ..,.,..,._,....,........,......., t

L ,;.

-. -i-h--,---- ‘/ ’

100 ib) Nkkalised i&eutation d!$h (&I)

Fig. 8. (a) Conventional plot of hardness versus depth for Vickers and Berkovich indentations in a coated system for 2.8 pm NbN on M304 stainless steel (M053) showing a hardness increase from just under 2 GPa at 300 kN (30 kgf) up to 40 GPa at 50 mN. (b) Partially de-dinlensional~z~d plot of the data in Fig. I for the NbN coating MO53 using log axes and the relative displacement parameter, /3= Ls/f. Plotting data in this form allow the full range of hardness data to be adequately analysed. A change in behaviour is immediately apparent from near-substrate only behaviour for p> IO down to coating-only behaviour for /i<O.I. The matching curve is a fit of Ey. (21) to the data (see text ).

5. Analysis and discussion.

The model described here shows very good quality of fits to a range of experimental data obtained from different coating-substrate systems. Correlation coeffi- cients close to unity are maintained throughout and reasonable fits to the hardness of the substrate are obtained for both the M304 and ASP23 steel substrates. These fits are much better than can usually be achieved by any other hardness model and are much easier to perform as the number of unknown fitting parameters

180

2-1Opm SIP TiN on M304

4 ! . . . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- e- -h=5.+m

0.01 0.1 1 10 ia) Normalised indentation depth (8/t)

0.5-25pm PVD TiN on ASP23

W

0.1 1 10 100 Normalised indentation depth (s/t)

Fig. 9. Hardness-b plots of: (a) sputter-ion-plated TiN on M304 stain- less steei. thickness range 2-10 pm: and (b) TiN on ASP23 tool steel, thickness range 0.5-X urn. Both series show identical transitional behaviour to MO53. Limits of the transition behaviour are: near-sub- strate only for p > 1 down to coating-only behaviour for /I? < 0.1, The spread of data is almost certainly due to batch to batch variation in properties. The matching curves are fits of Eq. (21) to the data (see

text 1.

is relatively small (two if the substrate hardness is known, otherwise three).

Examination of the data in Table 2 shows that the fit is remarkably good for SCVPZ~ samples within a series, but not all. The reason for this can be derived by inspection of the curves. Not all of the data for each sample covers a large enough range to adequately describe the change in behaviour from near-substrate to coating only. Hence, the H, data in Table 2 is not accurate or obtainable in all cases, i.e. it is accurate for the thinner coatings in the range where sufficient data above ,B= 1 is available. For similar reasons, there are insufficient data points below fl= 0.1 to be sure that the Hr data presented is accurate. In practical terms, this

means that the data for SIP TiN on 304 stainless steel is most accurate at the mid-thickness range (5-7 urn), where sufficient data is obtained at the low end of the /3 range. The values of (Hr-H,) obtained in this case are around 25G Pa, which correspond to the values measured on similar samples by very-low-load indenta- tion tests. At low coating thickness, the film hardness is underestimated, whereas for very thick coatings the result is overestimated. In both cases, this is due to a lack of data below fl =O. 1 and, as such, the values obtained are untrustworthy.

Once the fit has been performed and the hardness describing the coating-dominated response identified, there remains the question of how this hardness value should be interpreted. In the vast majority of cases r and certainly those involving sharp indenters - we would expect this hardness value to represent the penet- ration hardness of the coating material itself, measured at the relevant contact scale; that is, we expect the loaded indenter to be creating a plastically-deformed indentation in the coating itself with only the deforma- tion of the substrate being elastic. An implicit assump- tion in this is that the contact-induced shear stress in the coating is sufficient to create coating yield and recently Hainsworth et al. [14921] have described pro- cedures not only for determining this condition during nanoindentation experiments (essentially using plots of load versus displacement squared), but also how the necessary indentation depth may be calculated as a fraction of the coating thickness. However, if the yield of the coating immediately under the indenter has not occurred, then the interpretation of Hf requires more care. If the coating has been bent to displacements of the order of its own thickness, we would expect there to be local plastic deformation at the points of maximum bending strain. In this case, the hardness value may reflect some other function of the yield stress of the coating rather than simply its conventional hardness. However, there remains the possibility that all that is happening at the small contact scales is purely elastic fIexure of the coating into the substrate as the substrate either yields plastically or deforms elastically. In this case, the hardness value is best interpreted in terms of some form of elastic flexure parameter based on plate bending theory as described by McGurk et al. [ 121. There remains the further possibility that in the absence of localized plastic flow, microfracture events accommo- date the indentation. In this case, the interpretation of Hris impossible without a detailed fracture energy model and knowledge of the crack distribution. We suggest that either experience or direct high-resolution micro- structural observation of the indentations (using either high-resolution SEM or SPM methods) are necessary to enable these cases to be unambiguously distinguished and thus the hardness number to be associated with some deformation mechanism.

A.M. Ko~~nsl;~ et al. 1 Surface arxi Coatings Technology 99 (1998) 171-183 181

Since the sputter ion plating series were produced using identical coating parameters, including positioning of the sample in the coating chamber, and are thus less likely to show variations due to the method of prepara- tion apart from coating thickness, they can be examined in more detail to determine the details of the deformation mechanisms occurring in the coating. Plotting /C versus coating thickness shows an approximately linear increase (Fig. 10) which indicates that the hardness response is dominated by fracture in the coating. Well-established “picture-frame” cracking is visible in all of these samples confirming this hypothesis. The variation of l/r with thickness is close to being constant though there is a slight change which could indicate that some plasticity is occurring. 3: varies from 0.3 for thin coatings to 0.2 for thick coatings. Since r depends on Cc/H,, which is expected to remain approximately constant for these films, this would imply a reduced propensity for fracture in the coating as its thickness is increased. This is not an unexpected result since the bending of the coating produced by substrate pile-up, which leads to enhanced coating fracture (Fig. 4), is reduced as the coating thickness increases. However, more work is needed to develop a better physical understanding the meaning of CI which appears to be a potentially powerful diagnostic of deformation mechanisms.

The sequence of events envisioned (for the case of fracture-dominated response) to contribute to the overall indentation behaviour of the coated system is described in Fig. 11. The five major stages comprise: (1) (2)

(3)

an elastic-only response (region 0); an elasto-plastic coating dominated response (region I); post-through thickness fracture coating-substrate mixed transition (region Ha):

0 2 4 6 8 IO

Thickness (pm)

Fig. 10. Variation of k and z with coating thickness for sputtcr-ion- plated TiN on M304. The units of 1;~ are inverse microns in this plot in order to enable a comparison with the dimensionless k on the s&me scale.

Ia

III

Oil i io Relative Indentation Depth p

Fig. 11, Schematic representation of the principal deformation mecha- nisms which make up the overall indentation response of a coating-- substrate system dominated by coating fracture. Region 0 (not shown): elastic-only system response. Region I: initial highly localized coating elasto-plasticity and fully elastic substrate before the generation of an eiasto-plastic enclave in the substrate. leading to coating conformal stretching/deformation, radial fracture possible along the indentation diagonals. Region Ha: substrate deformation and concomitant confor- ma1 coating deformation sufficient to begin circumferential through- thickness fracture which grows to completion creating an island of “dead coating”. Region IIb: repeated circumferential or “picture- frame” fracture occurs in the coating, as it is bent to conform to the plastically deforming substrate. Region III: true substrate-only behavi- our where the energy absorbed by coating, stretching, flexure and frac- ture is insignificant compared to the amount dissipated by substrate plastic deformation.

(4) substrate-dominated mixed transition (region IIb); (5) totally substrate-dominated response (region III).

Region 0, the coating and substrate elastic-only response region, whilst important in most applications, has no meaning in terms of hardness measurement and is not shown. Region I is characterized by highly local- ized coating plastic deformation on an elastic substrate. The “coating-only plateau” is where the system proper- ties are dominated by intrinsic coating properties and any membrane stresses generated prior to coating frac- ture. By the use of P-6 curve analysis, this region has been further split into regions Ia and Ib [26].

Region IIa begins immediately after an initial large circumferential through-thickness failure occurs and continues until the fracture grows into a complete ring or picture frame. Region IIa is characteristically domi- nated by the substrate, but for a significant depth there remains a contribution from the coating as it bends, flexes and fractures around the indentation site in response to the elasto-plastic upthrust of the substrate. Region IIb runs from the point where a complete ring, or picture-frame, through-thickness fracture occurs until

182 A.M. Kommsk~~ et al. /Surface and Couiings Twhology 99 (1998) 171-153

repeated cycles of this type of fracture reduce the coating’s hardness until it is almost level with that of the substrate.

Region III is the true substrate-only response and begins when the coating has suffered multiple fractures, and the energy absorbing contribution of any coating flexure, fracture or bending around the indentation is small compared with the energy being absorbed by plastic flow of the substrate. In the present analysis, the influence of ISE (the indentation size effect) on the measurements has been consciously neglected since the hardness, H,, was expected to approach a plateau deter- mined by the value of Hf at infinitely small depths. This approximation is very well suited to depth-sensing meas- urements of coated systems with hardness values recorded as exemplified in Fig. 6b since the scale of the effect due to the presence of the coating is much greater than any likely indentation size effect. However, in micro- and macrohardness measurements, apparent hardness increases at low loads due to ISE are unavoid- able and must be taken into account. An approach which may be particularly suitable to the present formu- lation is that of Bull et al. [9], which predicts the apparent hardness as:

I 2 Kpp=Ho l+r ,

i 1 (22)

where n is the indentation diagonal and ! is a material parameter having the dimension of length related to the spacing of discrete bands of deformation below the indenter. The incorporating on ISE in the analysis will require a more complicated fitting approach and will be the subject of a future paper.

Although this model has been developed for hard coatings on soft substrates, there is no reason to believe that it should not be equally applicable to softer coatings on hard substrates. If H,<H,, the second term in Eq. (21) will be negative and H, < H,, as is usually observed. Further work is underway to investigate the quality of the fits in this situation. The advantage of the present fitting approach over previous hardness model- ling attempts is that it is possible to make predictions about the hardness of a coating-substrate system under different contact conditions without always having to produce appropriate test samples. For instance, if a sufficient amount of coating data is generated for a given system (such as TiN/304 stainless steel) so that good values for Hf and a can be determined, it is then possible to make calculations of the composite hardness for other coating-test-load combinations using a combi- nation of Eqs. (10) and (20). Suppose we need to know how thick a TIN coating must be on 304 stainless steel (H,=2 GPa) in order to give a composite Vickers hard- ness of 8.5 GPa at a test load of 200 g, In such a case, the indentation depth can be calculated from Eq. (10)

using an appropriate value for k (in this case, k =0.3763 if P is in grams and d is in microns to give H, in GPa) and is 3 w. If we now choose reasonable values of !X (0.3 x 10m6 m, the average value from Fig. 7) and HI (32 GPa), we can solve Eq. (20) for the thickness, t. This gives the required thickness as 8.3 pm. From the data determined here. the thickness at which the compos- ite hardness reaches 8.5 GPa at a 200 g test load is between 7 and 10 pm so this value is not unreasonable. Clearly, some further work is necessary to determine the quality of the predictions, but the fitting approach developed here would seem to show considerable prom- ise as the basis for a design tool to select the appropriate coating thickness and substrate hardness to give a required composite hardness.

6. Conclusions and further work

A novel approach to understanding the hardness of coated systems has been developed. The composite hardness is known to vary depending on the applied load and/or indentation depth. In the proposed model, the composite hardness is considered to be a simple function of the relative indentation depth fi (the indenta- tion depth normalized with respect to the coating thick- ness), and the substrate and coating hardnesses. The function contains a single fitting parameter X-, which describes a wide range of composite and indenter proper- ties such as coating brittleness, interfacial strength, indenter geometry, etc.

The model has been tested on a range of coating-sub- strate systems. The remarkable result of these tests is that the two parameter model put forward here appears to be applicable to a wide variety of situations. These include various coating thicknesses, deposition tech- niques, hardness mismatch between coating and sub- strate, and even whether the coating behaviour is dominated by plasticity or cracking. The quality of fit obtained in all examples where sufficient data were available is excellent. However, we must emphasize that the quality of the fit relies in obtaining experimental hardness data over a wide range of p values and almost always this will have to include nanoindentation data.

These findings suggest the possibility of using the proposed formulation to predict the likely effect of coating properties. such as the fracture toughness and thickness, and the substrate properties. primarily its hardness, on the overall substrate-coating composite hardness. This may form a basis for a design guide aimed at determining the appropriate coating spectica- tions for a given application, although further refinement and verification of the model will be required in order to ensure the reliability of such predictions.

The indentation size effect has been consciously neglected in this initial work. This was prompted by the

high quality of the fits and the fact that the fitting process returns reasonable values for both coating and substrate hardnesses. These observations support the view that in the cases considered, this effect was relatively minor. However, further versions of the present model can be expected to take size effects into account.

Acknowledgements

The authors would like to thank colleagues at AEA Technology, Multi-Arc and Tecvac for providing samples. MRM acknowledges the support of EPSRC in carrying out this work. A version of the fitting software can be found on the World Wide Web at http://www.ncl.ac.uk,/- nmatldiv/materials/CHEAP/ and we invite readers to try it out for themselves.

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