A full factorial investigation of the erosion durability of automotive clearcoats

Tribology International 33 (2000) 559–571 www.elsevier.com/locate/triboint

A full factorial investigation of the erosion durability of automotive clearcoats R.I. Trezona, M.J. Pickles 1, I.M. Hutchings

*

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Received 8 February 2000; received in revised form 12 June 2000; accepted 21 June 2000

Abstract A full factorial experimental investigation has been carried out into factors affecting the resistance of a commercial acrylic/melamine automotive clearcoat to erosion by silica sand particles. The factor variables and their ranges were: particle size 125–425 µm; temperature 30°C–65°C; impact angle 30°–90°; particle velocity 35 m s⫺1–55 m s⫺1; and the baking process applied to the coating. An empirical linear regression model for the erosion response of the coating with R2adj=97.5% was generated from the data. The regression coefficients of this model quantify the relative strengths of the effects of each of the factors. Several interactions between the factor variables were identified. In particular, the glass transition of the coating, which occurs at 40°C, has a significant effect on its response to erosion. The study has allowed the combinations of conditions that would be of most concern for automotive paint users to be identified.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Erosion; Organic coatings; Factorial design

1. Introduction Solid particle erosive wear, the progressive removal of material caused by many small solid particles striking a surface, is relevant to both automobile and paint manufacturers, and there is a general need for an improved understanding of the factors controlling the erosive durability of paint coatings used in automotive applications. Furthermore, current moves towards “global” vehicle design and total quality engineering mean that the demand for rigorous test methods will increase since these rely on the ability to assess the performance of coatings under conditions representative of usage worldwide. It has been claimed that appropriate testing and test methods could play as important a part in future coating technology as resins and paint formulations [1]. However, the automobile industry currently lacks a quantitative test for assessing the resistance of paint coatings to erosive wear. Current standard test methods rely on subjective assessment of the onset of penetration * Corresponding author. Fax: +44-1223-334-567. E-mail address: [email protected] (I.M. Hutchings). 1 Present address: Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral L63 3JW, UK.

of the coating [2–4] or of the amount of damage sustained in comparison with a set of photographic standards [5]. They are therefore strongly operator-dependant. A quantitative erosion durability test has recently been developed for many different types of coatings [6,7]. This technique has been successfully applied to a range of multi-layer automotive paint systems [8–10] and generates reproducible values of “erosion durability” that discriminate well between the performance of different coatings. The erosion durability, Qc (units kg m⫺2), is the mass of erodent particles required to remove entirely unit area of coating under the particular conditions of the test. For any erosive wear situation, process parameters such as the particle impact velocity, the angle of particle impact relative to the surface and the particle size are expected to have a significant effect on the wear rate of the material under investigation. Furthermore, for crosslinked polymeric paint coatings, the conditions under which they have been cured (or “baked”) and the ambient temperature during exposure to the particle stream may also have important influences on erosion. Although commercial paint systems are multi-layered, it is the surface layer, a transparent “clearcoat”, that is

0301-679X/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 1 - 6 7 9 X ( 0 0 ) 0 0 1 0 6 - 7

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Nomenclature da ei E h m n p Qc Qci qct r R2 R2adj SSE SST t tcrit Tg a b gi q s2

horizontal erosion scar diameter that intersects the nozzle axis for a tilted specimen residual of measurement i erosion rate Q−1 c stand-off distance between the end of the nozzle and the measured diameter of the erosion scar velocity exponent of the erosion rate total number of different experimental conditions investigated in an experimental design p=k+1 where k is the number of regressors in the regression model erosion durability of a coating, with units kg m⫺2 Qc value obtained for measurement i specific erosion durability of a coating given by the gradient of a plot of Qc against initial coating thickness (qct=dQc/dt) radius of the circular erosion scar coefficient of multiple determination adjusted coefficient of multiple determination error or residual sum of squares total sum of squares coating thickness critical coating thickness below which erosion proceeds by delamination glass transition temperature nominal erosion impact angle dimensionless focus coefficient for the air-blast erosion rig regression coefficient for regressor variable i actual erosion impact angle overall mean square error of the regression

intended to resist multiple small particle impacts. However, no systematic, quantitative studies have been performed on the effect of process parameters on the erosion behaviour of automotive clearcoats. The investigation of a response that is influenced by several variables may be further complicated if there is interaction between the variables. For instance, it is possible that the erosive damage to the paint coating is much more sensitive to particle size at oblique impact angles than at normal impact. In order to detect and quantify these interactions and quantify the strength of the effect of each of the variables, the methods of statistical experimental design may be used [11]. A full factorial investigation, in which all possible combinations of the values of the experimental variables (the factors) are evaluated, provides a thorough method for determining all the interactions within the range of conditions of interest. This approach can also be used to generate an empirical expression for the response (here the resistance to erosive wear) in terms of the variables studied. This paper reports the use of a full factorial experimental design to study the erosion durability of a typical commercial automotive clearcoat in terms of the particle impact velocity, the angle of particle impact relative to the surface, the particle size, the coating cure conditions and the ambient temperature during the test.

2. Experimental methods and materials 2.1. The erosion durability test The erosion durability test makes use of a “gas-blast” apparatus in which erodent grit particles are accelerated in an air flow along a long tubular nozzle, with a length:diameter ratio of about 60. Reproducible flow conditions are produced by maintaining a constant pressure difference between the two ends of the nozzle. As they leave the nozzle the paths of the erodent particles diverge from trajectories parallel to the nozzle axis, as shown in Fig. 1. Since the system is symmetrical with respect to rotation about the nozzle axis, the resulting erosion scar in a coating held perpendicular to the nozzle has a circular boundary separating the areas from which the coating has been completely removed from the areas where some coating is still present. The mass of erodent particles per unit area which have impacted the coating at this circular boundary corresponds to the critical mass per unit area just required for coating removal, Qc (in kg m⫺2). This value can therefore be used to characterise the durability of the coating. Values of Qc, or coating erosion durability, may be determined from measurements of the radius, r, of the circular scar in the coating

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rent automotive multi-layer paint system: clearcoat, colour basecoat, primer surfacer, electrocoat and zinc phosphate on flat 825 µm thick mild steel rectangular sheets 308 mm×100 mm in size. The clearcoat thickness was 48.7±1.2 µm (mean and standard error) and the total thickness of the multi-layer system was 270–290 µm. All the test samples were produced in the same coating run. The clearcoat was sprayed wet-on-wet on the basecoat and the two layers were baked simultaneously under “normal bake” or “over bake” conditions (see Section 2.3). The sprayed panels were cut by guillotine into 50 mm square test samples. 2.3. Factorial experimental design

Fig. 1. Schematic diagram of the air-blast erosion rig.

produced by exposure to a total mass m of erodent by using the following expression [12]: Qc⫽

冉 冊 冉 冊 b2m br exp ⫺ 2 2ph h

(1)

where h is the stand-off distance between the nozzle end and the surface of the coating and b is an empirically determined dimensionless “focus coefficient” which defines the divergence of the particle stream. The value of b depends on the geometry of the rig, the air temperature, the particle velocity, the internal roughness of the nozzle and the nature of the erodent particles. Details of the method used to determine b, and further description of the application of the erosion durability test to paint coatings are available elsewhere [8]. 2.2. Experimental material The material used in the investigation was a commercial acrylic/melamine clearcoat. The clearcoat was machine-sprayed as the outermost layer of a typical cur-

The five variables (or factors) investigated were clearcoat bake conditions, erodent particle size, air temperature, particle impact angle and particle velocity. The erodent type, angular silica sand, was the same for all the experiments although particle shape (rounded vs angular particles) and material are both factors that could be varied in future studies. All the factors except velocity were investigated at two different values (or levels); three levels of velocity were used. Hence, the study represents a 24×3 design and values of Qc were determined for all 48 different combinations of the test conditions. Three experiments were performed at each condition so that the total number of experiments was 144. The factors and levels are summarised in Table 1. The normal- and over-bake conditions correspond to levels of the bake factor of ⫺1 and +1 respectively. The baking times and temperatures are shown in Table 1. The erodent particle sizes were determined by sieving. The sizes chosen represent the typical range of airborne particles that would be expected to be encountered in automotive practice, excluding large stones that might be thrown up from another vehicle’s tyres [13]. The air fed into the erosion apparatus passed through an electric heater, and an air temperature sensor in the mixing chamber at the top of the nozzle provided feedback control; the time lag for temperature response at the mixing chamber was relatively short. In order to allow the sample and the air in the sample chamber to reach the desired temperature, the rig was run with heated air only for 10 min before each set of tests at each temperature. The lower temperature (level ⫺1) was set at 30°C to enable the heater control to maintain a steady temperature. The impact angle (defined as the angle between the nozzle axis and the plane of the specimen) was varied by tilting the specimen about a horizontal axis while keeping the nozzle vertical. For an impact angle of 30° the erosion scar in the coating is oval rather than circular. The angular distribution function for the particle flux emanating from the nozzle [12] could in principle be used to predict the particle flux striking an angled surface

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Table 1 Factors and levels used in the experimental design Level

⫺1 0 +1

Factor Bake (°C/min)

Erodent size (µm)

Temperature (°C)

Impact angle (°)

Velocity (m s⫺1)

129/17 — 143/53

125–150 — 355–425

30 — 65

30 — 90

35 45 55

and the shape of the whole wear scar could be determined. Alternatively, by measuring the horizontal scar diameter that intersects the nozzle axis, da (Fig. 2), Eq. (1) may be used without modification. The latter approach has been used in this study. A close-fitting rod with a sharp conical end was lowered down the nozzle after each test to mark the intersection point of the nozzle axis on the erosion scar. da was defined as the scar diameter passing through this point and perpendicular to the length of the scar. The erodent velocity at a given temperature is controlled by the difference in air pressure, ⌬p, between the mixing chamber and the sample chamber (Fig. 1). In order to calibrate the rig, the speed of the erodent particles, as a function of this accelerating pressure, was determined by an opto-electronic flight timer similar to that originally described by Kosel and Anand [14, pp. 349–368] and developed by Shipway [15]. The system uses two parallel light beams, which are connected by fibre optic cables, for temperature isolation, to photodiodes. A particle passing through the first beam will produce a drop in the detected light level which triggers the start gate on a 1 MHz clock. As the particle passes

through the second light beam, its detector stops the timer and the flight time is logged by computer. This method is not a cross-correlation technique; it uses very low particle feed rates (0.02 g min⫺1 in this case) so that the mean free path between the particles is greater than the distance between the light beams. Following the procedure described by Shipway and Hutchings [12], the time of flight distribution was recorded with a resolution of 2 µs. A well-defined, narrow peak was evident. The flight time distribution was converted to a velocity distribution and the average velocity of the particle stream was taken as the midpoint of the full width at half maximum height (MFWHH) of the peak. The velocity distributions obtained for silica sand in this study were similar to those obtained previously for glass ballotini [12]. The pressure difference, ⌬p, required to give MFWHH velocities of 34.5–35.4 m s⫺1, 44.5–45.4 m s⫺1 and 54.5–55.4 m s⫺1 was determined for both particle size ranges at both air temperatures. The values of ⌬p are shown in Table 2. The sand feed rates used for the erosion tests were 2.84 g min⫺1 for the 125–150 µm sand and 2.27 g min⫺1 for the 355–425 µm sand, significantly greater than that used for the velocity calibration. Using a similar gas blast erosion apparatus Shipway and Hutchings [16] found that the velocity of various sizes of soda lime glass spheres was independent of the particle flux (and therefore the feed rate) for fluxes less than 6 kg m⫺2 s⫺1. They explained this finding by pointing out that the mass flow rate of air through the nozzle was considerably larger than the erodent mass flow rate. A simple model [17] can be used to show that the flux of air through the nozzle at the lowest pressure used in the current study (0.084 bar) is approximately 100 kg m⫺2 s⫺1. The sand feed rates in the current work correspond to values of particle flux less than 2 kg m⫺2 s⫺1. 2.4. Erosion experiments

Fig. 2. Experimental arrangement for the erosion durability test at an oblique angle a. da is the measured diameter of the erosion scar in the coating.

Values of b, the focus coefficient, were determined from measurements of erosion scar radius, r, as a function of total mass of erodent, m, and by use of Eq. (1) [12]. The focus coefficient, b, is expected to depend on the particle size, the air temperature and the particle velocity as well as other variables which were kept con-

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Table 2 Nozzle pressures associated with the three velocity levels and different particle sizes and air temperatures, as determined by calibration experiments Particle size

125–150 µm

Temperature

30°C

65°C

30°C

65°C

0.084 0.131 0.188

0.061 0.100 0.150

0.143 0.221 0.344

0.131 0.215 0.339

Pressure ⌬p required 35 m s⫺1 for each velocity (bar) 45 m s⫺1 55 m s⫺1

stant such as the internal diameter and roughness of the nozzle tube. Surprisingly, the variation of b with velocity was found to be almost insignificant for the range of velocities under investigation, and thus only the four different b values shown in Table 3 were used in the data analysis. The erosion resistance of the paint samples was evaluated as described in Section 2.1. The nozzle was a 308 mm long stainless steel tube with an internal diameter of 4.75 mm which had been conditioned to achieve its steady state internal roughness before being used in the tests [12]. The stand-off distance, h, was 20 mm. Various erodent doses (from 30 g to 200 g) were used to ensure that the erosion scar diameter was greater than 6 mm since it was found that the erosion behaviour for scars smaller than this deviated from Eq. (1). For each of the 48 test conditions, three separate experiments were made, using the same amount of sand. The diameters of the wear scars were determined with a calibrated optical microscope under oblique illumination. Although it has been shown that the value of Qc obtained by the erosion durability test depends on the thickness of the coating [10], it was not necessary to normalise the Qc values with respect to thickness for this study since all the samples tested had nominally the same thickness of 48.7±1.2 µm. 3. Statistical analysis The goal of the statistical analysis of the data was to produce an empirical equation to describe the erosion durability of the paint system as a function of the five factors bake (b), particle size (s), air temperature (t), impact angle (a) and velocity (v). A multiple linear regression model of the following type was applied: Table 3 Values of the focus coefficient, b, determined experimentally and used in the data analysis. b was found to vary by less than ±0.4 over the velocity range from 35–55 m s⫺1 β values

125–150 µm silica

355–425 µm silica

30°C 65°C

24.5 22.2

31.6 29.3

355–425 µm

Qc⫽g0⫹g1B⫹g2S⫹…⫹g5V⫹g55V2⫹g12BS⫹g13BT ⫹…⫹g123455BSTAV

(2)

2

where the g values are constant “partial regression coefficients”. The factors b, s, t, a, v were normalised to produce the “regressor” variables B, S, T, A and V where the low, intermediate (for velocity only) and high levels of each factor correspond to regressor values of ⫺1, 0 and +1. For the factors investigated at only two levels (i.e. all except v) it is implicitly assumed that the response in Qc is linear. Since only three levels of velocity were investigated, and thus only one turning point could be detected, a simple quadratic approximation should be sufficient to describe the results of this study and thus V2 and interaction terms containing V2 were included in Eq. (2). The linear regression equation may be used to determine which of the factors has the greatest effect on erosion durability and to detect any significant interaction between the factors. The values of the factor and quadratic factor regression coefficients g1 to g5 and g55 are referred to as the main effects and quantify the strength of each factor’s independent influence on Qc. The other regression coefficients quantify the interaction between two or more variables. For this study, including all interactions with the quadratic velocity factor (V2), there are a maximum of 6 main effects and 41 interactions that could be included in the model. However most of these are expected to make no significant contribution to the ability of the model to describe the data. The purpose of the analysis is to calculate the effects and interactions and to determine which are significant. It is possible to use least squares fitting to obtain the regression coefficients of a given model and evaluate their significance. However, for a 2 or 3- level full factorial design, all the possible regression coefficients may be evaluated more elegantly from a two-dimensional “contrast matrix” as described by Grove and Davis [11]. The significance of each coefficient may then be evaluated in comparison to the variability in the data and the non-significant terms removed from the model. This is possible because, for a full-factorial experiment, the regression coefficients are not affected by the other regressors in the model. However, this treatment does make some assumptions about the data and it is neces-

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sary to check that these are satisfied once the model has been established. If Qc⫽f(B,S,T,A,V)

(3)

is the linear regression model, then each of the original experimental results, Qci, may be expressed in the following way: Qci⫽f(Bi,Si,Ti,Ai,Vi)⫹ei

(4)

where ei is the error, or residual, of observation i. It is assumed that the residuals are uncorrelated random variables with zero mean and constant variance. Initial analysis of the experimental data from this study by the contrast matrix method and a half-normal probability plot (see below) produced the following regression equation which excludes all the insignificant terms: Qc/(kg m−2)⫽360⫺51.2S⫹94.5T⫹87.5A⫺211V

(5)

Fig. 4. Half-normal probability plot of all the possible effects and interactions that could be included in a linear regression model for ln(Qc).

Fig. 3 shows the residuals of Eq. (5) plotted against the fitted values of Qc predicted from Eq. (5). There is clearly a tendency for the variance in the residuals to increase with Qc and thus one of the assumptions used to generate Eq. (5) is invalid. However, it is often possible to transform the response (Qc) data so that the trend in the variance of the residuals becomes insignificant. It was found that this could be achieved for the data in this study by taking the natural log of the Qc values before applying regression analysis. The 47 possible regression coefficients were therefore re-evaluated by the contrast matrix method to generate a further model in terms of ln(Qc). In order to determine which coefficients are significant and thus, which factors and interactions have a real influence on the response, a

half-normal probability plot [18] was used. Fig. 4 shows the moduli of the regression coefficients against a halfnormal score obtained by ranking the moduli. Since this is a three-level design, the coefficients were also standardised with respect to their standard errors [11] to account for their different inherent variances. All the smaller coefficients that are due to random error fall on a straight line through the origin. The points to the right of this trend-line represent the statistically significant coefficients for the ln(Qc) model. The significant effects on ln(Qc) are the main effects of all five factors and the size–temperature, size–angle and temperature–angle interactions, but not the quadratic velocity effect. The most efficient regression equation for ln(Qc) is thus:

⫹29.7V2⫹38.7TA⫺45.9TV⫺53.7AV

ln(Qc)⫽g0⫹g1B⫹g2S⫹g3T⫹g4A⫹g5V⫹g23ST

(6)

⫹g24SA⫹g34TA where the values of the regression coefficients, gi, and their standard errors are shown in Table 4. Table 4 Regression coefficients for the dependence of ln(Qc) on the factors investigated

Fig. 3. Plot of the residuals of the linear regression model for Qc against fitted values from the model.

Factor

Coefficient

Value

Standard error

Constant B S T A V ST SA TA

g0 g1 g2 g3 g4 g5 g23 g24 g34

+5.66505 −0.06535 −0.19376 +0.28338 +0.24207 −0.61760 +0.08331 +0.06156 +0.04748

0.01571 0.01571 0.01571 0.01571 0.01571 0.01925 0.01571 0.01571 0.01571

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The constant value, g0, is the grand average of all 144 observations and the standard error terms se(gi) and se(gij) are given by: se(gi)=√{Ci(SSE/n−p)}

Ci=1/48 i⫽5 Ci=1/32 i=5

(7)

se(gij )=√{Cij (SSE/n−p)} Cij =1/48 i,j⫽5 where SSE is the sum of the squares of the residuals, n is the number of different treatment combinations (in this case 48), p is the number of regression coefficients in the equation (in this case 9) and s2=(SSE/n–p) is the overall mean square error for the regression model. Fig. 5 is a plot of the residuals for the ln(Qc) regression model against the fitted values of ln(Qc) predicted from Eq. (6). The variance in the residuals shows no significant dependence on ln(Qc); similar plots have also been constructed to confirm that the variance in the residuals is also approximately constant with respect to the factors and the order in which the experimental observations were made (i.e. with time of observation). Another assumption implicit in this analysis is that the residuals are normally distributed. This can be checked with a normality plot of the residuals, Fig. 6, which is close to a straight line and confirms that the residuals are approximately normally distributed. The overall adequacy of the model in describing the experimental data may be evaluated by the coefficient of multiple determination, R2, which is a measure of the proportion of the overall variability in the response, in this case ln(Qc), that is accounted for by the regressor variables that have been selected. However, R2 will always increase when a variable is added to the model whether or not the variable is significant and thus models with large values of R2 may yield poor predictions of future observations. A more meaningful measure is R2adj, the adjusted value of R2, which will only increase

Fig. 6. Normal probability plot of the residuals of the linear regression model for ln(Qc).

when a new variable is added if there is enough reduction in the residual sum of squares (SSE) to compensate for the loss of a degree of freedom. SSE/(n−p) R2adj⫽1⫺ SST/(n−1)

(8)

SST is the total sum of squares, a measure of the overall variability in the data, given by SST⫽⌺i(lnQci⫺具lnQc典)2

(9)

where 具lnQc典 is the overall mean of the values of ln(Qc) (equal to g0 in Eq. (6)). For the linear regression model of ln(Qc) the adjusted R2 value is 0.975. 4. Discussion 4.1. The main effects

Fig. 5. Plot of the residuals of the linear regression model for ln(Qc) against fitted values from the model.

4.1.1. Velocity All five of the experimental variables, or factors, were found to have a significant influence on the resistance of the clearcoat to erosive wear. The relative magnitudes and directions of these influences are given by the regression coefficients g1 to g5 in Table 4 but are also summarised graphically in the main effects plot, Fig. 7. Each point in the plot represents the mean value of ln(Qc) at that level of the factor. The factor which has the strongest influence on erosion durability is erodent particle velocity. The slope of the velocity line is negative indicating that, on average, ln(Qc) decreases as the velocity increases. Thus, over the range 35–55 m s⫺1 at least, coating durability decreases as the erodent velocity increases, as would be expected. Since the V2 regressor variable was found to have an insignificant coefficient,

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Fig. 7.

Main effects plot showing the mean effect on ln(Qc) of changing each of the factor variables.

it is concluded that there is essentially no curvature in the effect of velocity on ln(Qc); the slight deviation from linearity in the velocity plot is due to random error. The main effect plot for the influence of velocity on Qc is Fig. 8 and shows that the relationship does exhibit some curvature when plotted in terms of linear erosion durability Qc, although this effect cannot be quantified by a regression model because of the inhomogeneity in the residuals. For bulk metals and polymers, a power law dependence of erosion rate, E, on erodent velocity is expected [19]. E⬀Vm

(10)

Here E is expressed as the mass or volume removed by

Fig. 8. Main effect plot of the mean value of Qc at each of the three levels of velocity. A curve of the form y⬀x−m has been fitted to the data.

unit mass of erodent particles and m typically has a value between 2 and 3. Taking Qc to be proportional to 1/E, the value of m for the data in this study may be evaluated from the main effects plot if it is assumed that there is no significant interaction between velocity and the other factors. Since there are no velocity interaction terms in the regression model, Eq. (6), this assumption appears to be valid. Fitting a curve of the form Qc=constant×vn to the data gives a value of m=2.69. Models for erosion by plastic mechanisms typically generate values of m in the range 2.0–2.5 [20, pp. 69–126], whereas for brittle fracture models, the velocity exponent is typically higher, in the range 2.4–3.2 [21,22]. In some experiments, polymers that erode by brittle fracture mechanisms have shown exponents greater than 3 [23–25]. However, values of m as high as 2.95 have also been found for ductile polymers [26]. Thus, the value of m exhibited by the clearcoat in the present work cannot be used to discriminate clearly between ductile and brittle erosion behaviour. 4.1.2. Impact angle After velocity, the test temperature and the angle of impact were found to have the next greatest main effects. The erosion durability increased with impact angle so that higher erosion rates were seen, on average, for the lower impact angle (30°). This behaviour is typical of the erosion of ductile materials, which experience more erosion for shallow impact angles at which plastic mechanisms such as cutting and ploughing are favoured [27–29,19]. Because of the divergence in the trajectories of the particles as they leave the nozzle there is, in fact, a distribution of particle impact angles for each nominal angle,

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a, determined by the orientation of the specimen to the nozzle axis. However, the value of Qc relates only to the impacts that have occurred at the circular boundary of the wear scar. Although the particle flux on the specimen surface has been determined empirically for this test method [12], the impact angle distribution is not so well known. It is not sufficient to treat the end of the nozzle as a point emitter of particles since it has been shown that the particles emerge from points over the whole area of the end of such a nozzle [30]. However, upper and lower bounds for the impact angles at the wear scar boundary, q, can be readily calculated by assuming that the particles travel in straight lines once they leave the nozzle, giving:

tan−1

冢

冑h

h sin a 2

ⱕtan−1

冣

cos2a+(r+a)2

冢

冑h

ⱕq

h sin a 2

cos2a+(r−a)2

(11)

冣

where a is the internal radius of the nozzle. Thus for the nominal impact angles of 30° and 90° used in this study at a stand-off distance of 20 mm and the average erosion scar radius of 3.24 mm, the ranges of the actual impact angles were 28.8°–29.97° and 74.3°–87.5° respectively. For the lower nominal angle the range is thus negligible. Although, for nominally normal impact, there were a wider range of actual impact angles, most studies of the erosion of ductile polymers suggest that their wear behaviour is relatively insensitive to impact angle at angles close to 90°. 4.1.3. Temperature The erosion durability, Qc, of the clearcoat was significantly higher at 65°C than at 30°C. This is perhaps a surprising result since the coating was significantly softer at the higher temperature. However, it has been shown that the erosion durability of acrylic/melamine and urethane clearcoats is best correlated with their failure strain and tensile failure energy (i.e. the area under the tensile stress–strain curve) [8,31]. No correlation was found between tensile yield or failure strength and Qc. Recent work [32] on weathered coatings indicates that there may well be a negative correlation between erosion durability and hardness for automotive clearcoats. Furthermore, the glass transition temperature, Tg, for

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the clearcoat was approximately 49°C. The material was thus in the rubbery regime at the higher test temperature. Rubbery polymers can show extremely high erosion and abrasion resistances. Hutchings and co-workers [33,34] have found the erosion resistance of bulk rubbers to decrease with increasing hardness (i.e. elastic modulus), and Marei and Izvozchikov [35] found a positive correlation between the difference between the test temperature and Tg and erosion resistance. The implication for the design and selection of automotive coatings is that vehicles that are used in a warm environment will be less susceptible to paint erosion damage than those that are used in cold conditions. At temperatures of 20°C and below, the particular coating studied will be well below its glass transition temperature and thus more susceptible to erosion by highly damaging brittle fracture mechanisms. Evidence for this type of mechanism in clearcoats eroded at 18°C has been reported by Rutherford et al. [8]. 4.1.4. Particle size The coatings were in general less resistant to erosion by 355–425 µm silica particles than by 125–150 µm silica particles. For most bulk polymers, the erosion resistance also decreases with increasing size of erodent, but tends to level off for particles larger then about 100 µm so that the erosion resistance (expressed in terms of the mass of the particles required to remove unit volume or mass of material) becomes independent of particle size. Thermosetting polymers, in contrast, have been observed not to display such a plateau, even for erodent particles as large as 1000 µm [19]. Automotive topcoats are crosslinked thermosets, and it appears that they also show a similar response to erodent particle size. The erosion response of any coating is likely to be affected by the substrate to which it is applied and by any intermediate layers. The effect of coating thickness on erosion durability has been investigated previously [10]. In that work Qc was found to be almost proportional to the paint film thickness, t. However, a change in erosion mechanism was identified as the coatings became very thin: once the coating had been worn to a critical thickness, tcrit, it delaminated from the substrate or underlying layer and became entirely removed by individual impacts. For thick coatings, this effect is small and for most of the lifetime of the coating it is being eroded at a constant rate. This rate can be described as a specific erosion resistance, qct, the gradient of a plot of Qc against coating thickness. Thus, for a thick coating, Qc⬇tqct where t is the coating thickness. However, if tcrit is a significant proportion of t, then the erosion durability of the coating will be significantly less than tqct. The value of tcrit may be determined by stylus profilometry of the edge of the erosion scar since a sharp “cliff” is seen at the eroded edge once the critical thick-

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ness has been reached [10]. For the clearcoat investigated in this study, the critical thickness values were found to be 9.4±0.9 µm and 15.8±1.0 µm for erosion by the 125–150 µm and 355–425 µm particles respectively (under standard conditions of 30°C, 90° impact angle and 55 m s⫺1). On average over all the conditions tested, the effect of changing the erodent size from 125–150 µm to 355–425 µm caused only a 7% decrease in Qc. Thus, the observed effect of particle size on erosion rate could be entirely attributed to the fact that significantly less of the 50 µm thick clearcoat required to be eroded by 355–425 µm silica than by the 125–150 µm silica before it started to delaminate. 4.1.5. Coating bake conditions The baking treatment of the coating represented by far the smallest of all the main effects, but it is nevertheless statistically significant. The over-baked coatings were, on average, less durable than coatings exposed to the normal baking treatment. It is suggested that the overbaked coatings became more highly cross-linked and thus harder and more brittle that the normal-baked coatings. This is similar to the effect of temperature on Qc. It is interesting that the temperature effect is much stronger than the bake effect (Fig. 7). It can be concluded that the physical state of the coatings, i.e. the amount of crosslinking, is less important for their durability than the temperature at which they are tested. 4.2. Interactions between variables The statistically significant interactions between the factor variables are summarised in an interaction plot, Fig. 9. The three interactions, size–temperature (ST), size–angle (SA) and temperature–angle (TA) generate a total of six interaction plots although only three of them are independent. Interaction between two two-level factors occurs when the difference in the mean response (lnQc) between the levels of one factor is significantly different at each level of the other factor. In Fig. 9 each point represents the mean of the quarter of the lnQc values recorded at that combination of the levels of the two factors. Thus, if there is any interaction, the lines connecting the points at the same level will not be parallel. The size–temperature (ST) interaction has a value of 0.08331 making it the largest of the three. The two plots in Fig. 9 that pertain to the ST interaction show that the effect of temperature is stronger for larger particles and that the effect of particle size is greater for lower temperatures. The difference in the responses at the two levels of temperature may be attributed to the glass transition. At 65°C the coating is in its rubbery state and it has been shown that the erosion of crosslinked bulk rubbers exhibits much less sensitivity to particle size than that of glassy thermosets [36]. Another way of rep-

resenting the interaction shows that the coating is least durable for impacts with larger particles at 30°C. In fact, this combination of levels produces the overall lowest value of lnQc of 5.105; this corresponds to a Qc value of 165 kg m⫺2 that is only just over half the average. Since, in practical terms, it is only the lower temperature that poses a problem for paint users, then the fact that large particle impacts are so much more damaging at this temperature suggests that impacts from large airborne particles should be a primary concern. However, the size distribution of erodent particles encountered in practice must also be taken into account. The size–angle (SA) interaction is the second largest. Fig. 9 shows that the size effect is greater for oblique impact and that the effect of angle is more pronounced for the larger particle size. The durability of the coating for impacts at 90° is well above average for either particle size; since most impacts to a vehicle exterior will occur at oblique incidence anyway it is thus reasonable to conclude that normal impacts are of little concern in practice. The most damage will be caused by relatively large particles at low impact angles. The temperature–angle (TA) interaction is less significant than the other two (it has about half the magnitude of the ST interaction). The influence of angle is slightly greater at the higher temperature and the effect of temperature is more pronounced for normal impact than oblique. The glass transition of the coating may also explain this behaviour. It has been found that for bulk elastomers the erosion rate falls much more rapidly with increasing angle than for bulk glassy polymers [37]. If it is assumed that this coating behaves in a similar way to a bulk elastomer at 65°C, this may explain why the increase in Qc (the inverse of erosion rate) with angle is greater at the higher temperature. This is, however, the only interaction for which the stronger effect occurs in both cases at the level likely to be of least concern to paint users: at the 90° level of angle and at a temperature of 65°C. 5. Conclusions 1. A full factorial experimental design has been used successfully to generate an empirical linear regression model for the following factors that affect the erosion durability of a polymer paint coating: the baking process applied to the coating, the erodent particle size, the temperature, the impact angle and the mean impact velocity. The residuals of the model with respect to the data, when expressed as the natural logarithm of erosion resistance, are normally distributed and have constant variance with respect to the variables, the response and the observation order. The model has an adjusted coefficient of multiple determination (R2adj) of 0.975 and thus represents a very close fit to the experimental data.

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Fig. 9. Interaction plot for the size–temperature, size–angle and temperature–angle interactions. The data points are the mean ln(Qc) values for the appropriate quarter of the measurements.

2. The factor that had the greatest influence on erosion durability (Qc) was erodent velocity. An increase from 35 to 55 m s⫺1 produced a reduction in the average value of Qc from 535 kg m⫺2 to 156 kg m⫺2. The average erosion rate E, which can be considered to be the inverse of Qc, was well described by a powerlaw dependence on velocity with an exponent of 2.69.

This is at the upper end of the range of velocity exponents that have been reported for ductile erosion mechanisms in bulk polymers. The coating shows a response to impact angle that is typical of a ductile material. The erosion rate is greater for oblique impacts, at 30° to the surface, than for normal incidence.

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3. The coating is significantly (by 76%) more durable at 65°C than at 30°C. This is attributed to its glass transition at approximately 49°C. Although the coating is softer and weaker at the higher temperature, it is nevertheless more erosion resistant because it is in a rubbery state. The implication for paint users is that the coating is likely to be more susceptible to particle impact damage in colder environments where the coating is in a glassy and more brittle condition. The mechanical properties of the coating also depend on the extent of cross-linkage. Coatings that have been baked under higher temperatures or for longer times will have a greater concentration of cross-links and will tend to behave in a less rubbery way. It was found that the lightly crosslinked, “normal bake”, coating was more erosion resistant than the “overbaked” paint, but that this effect was much less than that produced by changing the exposure temperature by 35°C. 4. Erodent particle size had a significant effect on the erosion of the paint coating. It was found that 355– 425 µm silica caused more damage to the coating per unit mass (by 47% on average) than 125–150 µm silica. Most materials display an increase in erosion rate with particle size for small erodent, but for particles larger than about 100 µm in diameter, the erosion behaviour becomes independent of size. It is suggested that the change in erosion mechanism from steady-state removal of coating material to delamination of the remaining thickness of the coating occurs at an earlier stage (i.e. when the remaining coating is thicker) for larger particles. This could explain the dependence on size since erosion by delamination occurs at a much greater rate. 5. The glass transition of the coating also produces interactions between the factors. The effects of both particle size and impact angle are different at the two test temperatures. The particle size effect is significantly smaller at 65°C than at 30°C, whereas the effect of impact angle is larger at the higher temperature. This change is consistent with rubbery behaviour at 65°C and glassy properties at 30°C. 6. There is also an interaction between the impact angle and the particle size: the size effect is more pronounced for oblique than normal impact. The coating thus displayed very low durability for erosion by large particles at shallow angles. Since most of the impacts on the painted surfaces of a vehicle will be at shallow angles, it is suggested that the design and testing of erosion resistant coatings should concentrate on resistance to oblique impact. Although larger particles are more damaging, it has yet to be established whether they represent a significant proportion of the airborne particles encountered in practice.

Acknowledgements This work was supported by the UK Engineering and Physical Sciences Research Council and Ford Motor Co., UK via the CASE studentship scheme, and also by Visteon, USA. The assistance of L.W. Partridge with the experimental work is acknowledged. We thank A.C. Ramamurthy of Visteon and A.P. Weakley of Ford Motor Co. for providing the paint samples, and K. Page for the design and development of the particle flight timer.

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