Document nmx0RR9rQyeV3XzJenGgqaY71

Predictive Model For Cracking of Latex Paints Applied to Exterior Wood Surfaces F. Louis Floyd Glidden Coatings and Resins, Division of SCM Corporation' While it is well-known that paints applied to exterior wood substrates will eventually develop cracks, and may, if their adhesion is deficient, subsequently peel or flake off, attempts to explain this phenome non on the basis of tensile properties have been unsuccessful to-date. The present work shows that a two-parameter model, employing fracture energy (energy required to propagate a crack through a paint film) and liquid water permeability, success fully accounts for cracking behavior over a wide range of compositional variables. From these obser vations, a mechanism for the cracking behavior of latex paint films applied to exterior wood surfaces is proposed. INTRODUCTION One of the main problems associated with, the perfor mance of exterior paints is that of cracking after a certain period of time. Cracking will frequently lead to flaking and peeling if adhesion is deficient Much effort has been directed towards understanding the cause of cracking, but the results are often confusing and** contradictory among researchers. For example, Jaffe and Fickenscher* suggested that the larger the ciongation-at-break (\b) for a free paint film, the higher the crack resistance. Later, Schur, Hay; and van Loo* proposed the opposite conclusion. They argued that the higher the tensile Presented by Mr. Floyd at the AOth Annual Meeting of (he Federation of Societies fur C'njtmj9 Technology, November 4. 1942, in Washington, D.C. * IfrbSl Sprague Kd.. Strongsville, Ohio **41,36 strength (at) of the free paint film, the better crack resistance for the paint. This would mean a relatively low Ki, in direct contrast with Jaffe and Fickenscher. More over, neither took into account the fact that random flaws and voids within the paint film will give highly irreprodudble ifesults, especially between films obtained by draw-down blade (for free films) and by brush appli cation on a porous substrate (wood). The field of fracture mechanics has arisen to reconcile such contradictory results, and would appear to be of value to the coatings industry. Fracture mechanics recog nize that the mechanical properties of free films (e.g., Xb and os) are strongly influenced by flaws in the samples, and take this into account by deliberately introducing flaws of sufficient and controllable sizes so that these are the main sources of any stress-concentration in the sample.3*** A good review of this process is given by Andrews.5 Since the primary stresses which develop in wood substrates are due to water absorption, it is naturally expected that the permeability of a paint film to water (particularly liquid water) will also play a role in the cracking process. A subsidiary hypothesis at the outset of this work was that a predictive model for cracking would probably require at least two parameters. This was based on per sonal observations over the years that one-parameter models for paint film behavior rarely work, and then only over unrealistically narrow ranges of compositional variables. Such was indeed seen to be the case in the present work. Since latex paints are recognized as having intrinsically greater crack resistances than alkyds, they were chosen for this work. This better performance is probably related to their considerably higher molecular weight.5 f.C FuOYD oo AA A AA A A AA A AA A AAA AAA Accelerated Crack Rating Figure 1--Accelerated cracking test binder variations 0.00 2.00 4.00 6.00 8.00 Accelerated Crack Rating 10.00 Figure 2--Acceleratod cracking test: pigment variations THEORETICAL The theoretically ultimate strength of filled materials can be calculated from bond Strengths. However, it is always observed that the ultimate strength is much higher than can be realized experimentally, frequently by as much as two or three orders of magnitude. In performing the theoretical calculations, it is assumed that all the bonds support an equal share of the load, and that they will all rupture simultaneously. Thus, the theoretical crack velocity is infinite. In reality, the crack velocity is finite, and the bonds break sequentially rather than simultaneously. Regions of relatively high stress occur, and from these regions, fracture is initiated,3*11 In other words, the discrepancy between the theoretical and observed values of the ultimate strength can be attributed to flaws which act as stress-concentrators. The wide scatter in data usually found in the results ofdetermining ultimate strengths can be explained by assuming a statis tical distribution of flaws in the samples studied. Such a statistical theory also explains the observed inverse dependence of strength on sample size (the larger the sample, the more likely that a critical flaw will be encountered). : The first serious study of the conditions needed for propagation of a crack in a material was by Griffith,1 who in 1920 'studied crack propagations in glass. He argued that the increase in surface free energy provided by tear ing must be less than the loss of elastically stored energy from the deformed sample. For an infinite plate of elastic materia) containing a sharp central cut of length 2a lying in a plane perpendicular to the stress, Griffith showed that where E = Young'S modulus, y -- Specific surface energy (fracture energy), at, = Tensile strength. Brown and Strawley8 noted that specimens of finite width with a flaw in one edge, possess a stress field at the crack-tip which is influenced by the proximity of the free edges, so that a modification of equation (I) is required: where y is a shape correction factor calculated as follows: y = 1.99 - 0.41 (a/w) + 18.7 (a/w)' - 38.48 (a/w)3 S3.8S (a/w)` (3) and w = specimen width a - one half the initial crack length. Since the strain energy W (work-at-break) is given by W=| (4) Table 1--Reliability of Laboratory Crack Resistance Test Study Dependent Variable Binder variations ..................... Exterior crack resistance Pigment variations ...... ...........Exterior crack resistance Independent Variable Accelerated crack resistance Accelerated crack resistance Correlation Coefficient 0.863 0.840 Confidence Level 99+% 99+% 74 I of Coatings Technology MODEL FOR CRACKING OF LATEX PAINTS Elongatiorwt-Break Figure 3--Correlation to elongation substituting the value of W from equation (4) into equation (2) yields W y/ay'. (5) Thus, tests ofspecimens containing various flawsizes can be employed to determine y as the slope of a plot of W vs 1/ay2. The parameter y is the energy required to create a unit area of new surface in a body, and is therefore, a property of the material alone. Indeed, experiments by Rivl'm and Thomas9 showed that y is independent of the sample shape. More recently, Reid10 utilized fracture mechanics to explain the cold-checking behavior of lacquer films. Unfortunately, statistical analysis was not employed to quantify the correlation found. The present work employed the procedures suggested by Reid, and multi ple regression techniques" were employed to quantify the results. EXPERIMENTAL Fracture Energy Studies Using a sharp razor blade and a low-powered micro scope with a calibrated eyepiece, cuts of definite lengths were introduced across one edge of the tensile test piece. The cuts were placed as accurately as possible half-way between the upper and lower ends of the test piece being stressed. Cut lengths varying between 0.5 mm and 7.6 mm were obtained on different specimens. Stress-strain measurements on these specimens were then obtained (kg/cm2) Stress-at-Break Figure 4--Correlation to tensile strength Figure 5--Correlation to fracture energy F.L FLOYD Table 2--Correlations for Plastic Pigment Variations Independent Variable Dependent Variable Correlation Confidence Coefficient* Level Crack resistance . ,, .Fracture energy Tensile stress Tensile strain 0.907 0.155 0.212 99+% Low Low Fracture energy.. Tensile stress Tensile strain 0.907 0.245 0.220 99+% Low Low (a) 1(7 Data points. on an lnstron Tensile Tester. Sample dimensions were I" X 0.75". The value of W from equation (5) can be determined from a calibration plot of W against various elongations for an uncut specimen. From measurement of elongation- at-break for the cut specimen, the value of W for the specimen can then be obtained. From a plot of W vs l/(ay2), the fracture energy can be obtained from the slope of the plot. Laboratory Freeze/Thaw/Wet/Dry Cycling On a 8" X 18" board of Douglas fir plywood, the sur face area was equally divided to accommodate four paints being tested, plus a control paint for each panel Table 4--Effect of Binder Variations on Correlation Dependent Variable Independent Variable Correlation Confidence Coefficient" Level Accelerated crack resistance................ Fracture energy 0.814 99+% (a) 20 Data Points. (Spred House Paint Y-3600). The paints were self- primed and allowed to dry for 24 hours before the second coat was applied. The underside and edges were sealed with an alkyd primer (Glidden's Y-195I). Panels were allowed to dry for one week before testing. Testing included the following steps for a complete cycle: (1) soaking the painted panels in water for one hour, (2) freezing the wet panels at about --20 F over night; (3) thawing at room temperature; and (4) letting the panels dry at room temperature, completing a 24-hour cycle. ASTM numerical ratings were assigned to each sample, Pancl-to-panel variations were minimized by normalizing the data to the control paint: /Test s Normalised _( paint Value \ rating, 'Control ' Mean ' paint Control rating on same panel. + paint .rating 1 (6) Sprtd Is registered trademark of the SCM Corp. \ Table 3--Effect of Binder Variations I.D. Type R-88 R*88 R-88 R-88 R-88 Acrylic Acrylic Acrylic Acrylic Acrylic P-J0 P-10 P-10 P-10 P-10 Yj-08 U-08 U-OS U-08 U-08 Acrylic Acrylic Acrylic Acrylic Acrylic Vinyl Acrylic Vinyl Acrylic Vinyl Acrylic Vinyl Acrylic Vinyl Acrylic K-45 K-45 K-45 K-45 K-45 Styrene-Acrylic Styrene-Acrylic Styrene-Acrylic Stvrene-Aerylic Styrene-Acrylic PVC 24 32 40 48 56 24 32 40 48 50 24 32 40 48 56 24 32 40 48 56 Fracture4 Energy 16.90 10.00 4.96 2.S7 1.91 30.30 11.00 6220 3.20 1.90 32.30 21.80 11.20 3.50 1.01 31.04 10.92 530 2.52 1.57 (a) fcg'cm. (bl 2S Fr7;Tto-; Wei / Diy Cyc\a - ASTM Vaacv Accelerated6 Crack Rating 9 8 6 4 3 7 7 3 2 2 9 9 5 3 2 10 9 4 3 2 76 Figure S--Effect of binder variations al of Coatings Technoloav MOOEL FOR CRACKING OF LATEX PAINTS Extender Pigment Varied Talc J-2p Pain! Formulation Low Cost Premium Talc IO-30/i Low Cost Premium Clay S/x Low Cost Premium Mica <0/i Low Cost Premium * Table 5---Effect of Variations In Pigmentation Pigment Volume Concentration <10 48 56 64 40 48 56 64 40 48 56 64 40 48 56 64 40 48 56 64 40 48 56 64 40 48 S6 64 40 48 56 '64 Fracture* Energy 31.50 13.20 6.30 2.30 9.96 4.08 3.54 1.05 14.70 8.80 3.60 2.20 13.70 S.40 2.20 UO 20.51 10.03 3.00 1315 5.74 3.38 1.89 1.3S 6.82 4.59 2.20 1.62 6.01 2.46 1.77 1.02 Ext." Creole Rating 7 5 3 3 8 4 2 2 .5 5 3 3 8 6 .5 4 2 2 2 2 6 2 2 2 8 7 7-. 4' 7 7 6 3 (a) kg/cm. (b) A5TMA values. 6 mooibs exposure <g) $-4$ m Cleveland. Ohio. (c) ASTM valuer 70 cycles of accelerated lot (tf) Higher values represent lower permeability; hence, correlation is positive. ND Not deiermfacrf. Aec. Crack Rating 6 5 4 3 9 7 4 3 7 fi 2 2 9 8 4 3 4 3 3 2 2 2 2 2 9 9 7 6 10 9 7 5 Permeability15 Time (Minutes) 14 0 17.0 14.0 9.0 7,0 7.0 4.0 ND 1Z5 7.1 4.0 zo 9.0 7.5 . 5.0 ND 11.0 7.0 ZO 1.3 6.0 9.0 1.2 ND 23.0 23.0 15.0 4.0 21.0 22.0 7.0 2.0 Exterior Exposure Panels submitted for exterior exposure were prepared as above. Exposure was in Cleveland at 45 facing south. After six months the panels were removed and examined for cracking. Ratings were assigned as .above. Permeability Filter paper was soaked in a 3% solution of CoC^ in water. The filter paper was then dried in an oven so that it became blue in color. The blue filter paper was sand wiched between a free film of the coating being evaluated and a pieee of glass and secured to the glass with electro plating tape in which five 1 cm diameter holes had been cut. The glass plate was then submerged in water, tape side down, and the amount of time for the CoCl2 paper behind three out of five of the tape holes to turn from Vol. - - - btue to red was measured in minutes. Higher numbers therefore correspond to lower permeability. Regression Analysis11 The BMPD statistics package of the University of California (particularly P-1R and P-9R) was used to correlate data. A multiple correlation option was em ployed to look for linear and nonlinear correlations of various combinations of independent variables with cracking. The best fits were reported. The magnitude of experimental error in the measurement of the dependent variable (cracking) was considerable, preventing high correlations except in the simplest case. For example, the mean crack rating of the control paints in Figure 5 was 7.4 with a standard deviation of 2.7. This means that 7.4 + 5.4 is the 95% confidence interval for this mean.' 77 F.L. FLOYD Table E--Effect of Extender Pigment Variations on Correlations Dependent Variable Independent Variable (a) Correlation Confidence Coefficient* Level Exterior crack resistance............ log [fractUTe energy] Permeability Fracture energy 0.726 0.621 0.301 99+% 95% 90% Accelerated crack resistance log [fracture energy] Permeability Fracture energy 0.748 0.655 0244 99+% 99+% 70% (a) Sample size of 32. Fortunately, normalization techniques filtered out enough of this variability so that meaningful correlations could be observed. For this study, the author chose to recognize only; those correlations which exceeded the 99% confidence level due to inherent data scatter. This means that there is less than one chance in 100 that the correlations occurred by chance. RESULTS AND DISCUSSION Accelerated Test In order to study the phenomenon of cracking ofpaint films on wood substrates, it was first necessary to develop an accelerated test for such behavior. The lest described in the preceding section (freeze/thaw/wet/dry cycling) was employed (30 cycles) in comparison to six months of exterior exposure at 45 south in Cleveland, Ohio. The comparisons were made for two separate systems em ployed in this study: binder variations and pigmentation variations. The results can be seen graphically in Figures 1 and 2. By employing a simple linear regression analysis tech nique, the correlations shown in Table I were obtained. From these data, it can be seen that the laboratory test can indeed predict exterior results in approximately 1/ 6th the time. While the correlation is less than perfect, it is within the limits normally encountered for this type : of" testing; i.e., experimental errors involved in cracking behavior prevent the correlation coefficient from rising above the 0.7-0.9 range. Preliminary Experiments The initial experiments involved an examination of selected exterior prototype products from the author's work on plastic pigment.12 Since these were already under study in a separate program, they were chosen for the initial test of the fracture energy concept. The prototype systems were based on Glidden's Spred House Paint, and involved substitutions of various plas 78 tic pigments for various extenders, and of various com mercially available acrylic latex binders for the latex originally employed. All systems were prepared as PVC ladders, holding volume solids and TiOj level constant, as is typical of commercial development studies. PVC ladders were used throughout this work in order to obtain a range of cracking behavior for each system studied. The PVC ranges chosen all centered roughly on CPVC. Since previous workers have strongly adhered to ten sile properties as the controlling properties for crack resistance, stress- and strain-at-break versus accelerated cracking were determined and are shown in .Figures 3 and 4, respectively. The fracture energy of these systems vs accelerated cracking is shown in Figure 5. While the tensile strength (os) and elongation (Xs) display classical responses to PVC changes,the correla tion to cracking is poor. Figure 5 illustrates the high correlation between cracking and fracture energy. Table 2 summarizes the results of linear regression analysis of the data in Figures 3-5. As can be seen, tensile properties do not account for cracking behavior, while fracture energy provides a highly significant correlation. Indeed, the tensile properties do not even adequately predict fracture energy, which readily agrees with theory. Effect of Binder Variations In order to determine the effect of binder type on crack ing resistance, four latex binders were formulated into PVC ladders using a low cost prototype exterior house paint formula, again keeping volume solids and TiOj level constant. The binders were acrylic in nature, some pure and some copolymers. The first three are commer cial products; the fourth was synthesized for this study. Table 3 displays the results, from which one can sec the expected PVC effect (inverse) and apparent correla tion between fracture energy and cracking. Figure 6 illus trates this latter correlation graphically, and Table 4 summarizes the regression analysis results. From these results it is apparent that the two properties are highly correlated, although experimental error is still significant. Effect of Pigmentation Variations Pigmentation effects were studied by varying the ex tender pigments in both low cost and premium exterior house paint formulations. Each change was'constructed into PVC ladders as before. Table 5 lists the extenders studied, together with the test results. Table 6 lists the results of the regression analysis of the data in Table 5. Contrary to the findings of the first two studies, the exterior exposure and accelerated exposure crack ratings were not predicted by fracture energies. The regression analyses provided very low correlations of 0.30 and 0.24 with nonsignificant T values on 32 data points. However, it was observed that exterior crack ratings were correlated to permeability as demonstrated in Table 6, with a correlation coefficient of 0.62 with a T value of 4.12 on 29 data points (confidence level: 99%). This suggested that a multiple-parameter model may wcli be more appropriate than the single-parameter model. tsiruiilsi! rtrvai!nn<* Additional calculations bore out this speculation. In Table 6, it can be seen that the best correlation to crack ing (either exterior or accelerated) was with the combi nation of permeability and log (fracture energy). This yielded correlations of 0.726-0.748, with a confidence level in excess of 99%, based on 29 data points. Permeability measurements were subsequently made for the first two studies, but this parameter was not significant. It therefore appears that permeability is largely controlled by pigmentation, while fracture energy is jointly determined by binder and pigment type and level. It is such behavior which leads to multiple param eter models, and which prevents single parameter models from working well. It also suggests why earlier workers drew erroneous conclusions: their range of variables was inadequate. Effect of Artificial Weathering On Fracture Energy In this work, the free film samples evaluated for frac ture energy were aged six days at ambient conditions and one day at 70 F and 50% relative humidity prior to testing. In order to evaluate the effect of aging on the relative values of these fracture energies, a series of paints were evaluated for fracture energy after 0,500, and 1,000 hours of Weather-Ometer exposure. The paints em ployed were the R.-88 variations of the Low Cost House Paint Formula described in Table 3. Figure 7 provides a graph of fracture energy vs Weathcr-Ometer exposure (carbon arc with Corex D filters) and demonstrates that although some fracture energies decreased slightly after extended exposure, the values obtained with virgin samples maintained their relative rank orders during exposure. This lack ofvariation was probably due to the choice of a highly .durable acrylic binder, and is not expected to hold true for less durable systems such as alkyds. SOURCES OF ERROR This project did not attempt to develop improved theories of fracture energy, but rather, concentrated on determining the value of an existing approach. A post evaluation of this project, however, illuminated three areas of possible oversimplification, with possible cor rections. First, although elastic behavior was assumed in the mathematical derivations, the samples evaluated in this work were viscoelastic in behavior. It is possible that the more brittle lacquers employed in Reid's evaluations broke prior to extensive yielding, therefore, approach ing elastic behavior more closely than the thermoplastic materials evaluated in this work. A possible solution to this problem would be to not apply the elastic behavior assumptions of equations (1) to (5), but instead to obtain the fracture energy by obtaining the slope of a graph of "az" vs as flaw size is varied [see equation (I)]. The second area of concern was the use ofa calibration Weuther-Omerer u rcpMCTCd trademark f Aria's Flcetfic Dnisc Co. Voi. 55, No. 696, January 1 MODEL (-"OR CRACKING OF LATEX PAINTS curve to determine the Work-at-Break of the flawed samples. This assumed identical shape for the Instron curves of the flawed and unflawed samples when in real ity the Instrori'shapes often differed considerably. Evalu ation of the actual Work-at-Break of the flawed samples would avoid this concern. The third area of concern was that, contrary to the theory, the graphs of "Wnn vs from equation (5) were slightly convex rather than linear and did not pass through the origin. While all ofthese elements can affect the absolute value of fracture energies obtained, available literature sug gests chat such errors should occur equallyin allsamples. Thus, rank orders, which were our real interest, would be unaffected. Such was seen to be the case within the limits of the work reported here. MR. F. LOUIS FLOYD is Technical Man ager of the Coatings Research Dept of Glidden Coatings & Resins Div. of SCM Gotp. in Strongsville. OH. A previous recipient of the Roon Award, he is a mem ber of the Cleveland Society and also serves as a member of the Federation's Editorial Review Board. His current re search interests include corrosion control via organic coatings, multiple parameter modeling of coatings behavior, and het erogeneous polymer systems. 79 ' ''f I. FLOYD PROPOSED MECHANISM FOR CRACKING As a result of the accumulated data and observations, the following speculations for grain cracking are offered': (1). Differences in coefficients- of expansion along grains of the wood substrate generate cracks in the wood itself, during exposure to weather cydes. (2) As cracks in the wood propagate or widen, paint films bridging the cracks become highly stressed. (3) Inclusions in the paint film generate different stress ' distributions in different parts of the film. These inclu sions may consist of voids, pigments, microcracks, etc. They become stress-concentrators when the film is stretched across the wood crack. Cracks are initiated at these sites. (4) As further stress is applied to the film, these cracks will propagate until the strain energy is consumed in generating new surfaces. (5) The rate of initiation of cracks is related to the permeability of the paint film to water. A film with low permeability to water will protect the wood substrate from swelling, hence minimizing the initiation step in cracking. (6) The rate of new surface generation (crack propa gation) is related to the surface energy of the composite; i.e., the fracture energy. A composite with low fracture energy thus requires low strain energy and, therefore, propagates cracks more easily. (7) Actual cracking behavior of a given paint film will be a composite result of its intrinsic permeability and fracture energy. Such behavior will tend to be highly variable due to the nonuniformities inherent in brushapplication of paints. Statistical analysis is thus required to obtain quantitative results. SUMMARY (1) An accelerated laboratory test has been designed which reasonably predicts the cracking behavior of paints applied to exterior wood surfaces. (2) Single parameter models are inadequate for de scribing coatings behavior. In the present case, a twoparameter model involving fracture energy and permea bility was required to account for cracking behavior. (3) Statistical analysis is required of such data since experimental error tends to be great, and the correlations of multiple parameter models arc not obvious by inspection. (4) Normalization procedures were introduced to minimize the impact of experimental error in cracking tests. (5) Earlier claims that tensile properties per se accounted for cracking behavior were clearly shown to be in error. ACKNOWLEDGMENTS The author gratefully acknowledges the contributions of Dr, C. L. Leung for the initial fracture mechanics work, and Messrs. J. J. Beauregard, F. A. Wickert, S. S- Shepler, and R. L. Groseclosc for much of the experimental work. The author also acknowledges the Glidden Division of SCM Coip. for its support of the work and. permission to publish these results, and Mrs. L. Hogg for her patience and expertise in preparing the manuscript. References (1) Jaffe, H. 1_ and Fickenschor, J. H., "Stress Strain Measurements of P.V.A. Films as Correlated with Natural Exterior Exposures," Official Dig e s t . 33, No. 434,331 (1961). (2) Schurr, 0. 0., Hay, T. K., and van Loo, M., "Possibility of Pre dicting Exterior Durability by Stress/Strain Measurements," Jo u r n a l o f Fa in t Te c h n o l o g y , 33, No. 501, 591 (1966). (3) Timoshenko, S. and Ooodier, J. N,, "Theory of Elasticity," 3rd Edition, McGraw-Hill. NY, 1970, p 92. (d) Pugh, 5. 'F.'fBril. J. AppL Phys., 13, 129 (1967). (5) Andrews, E. H.,"Macromoleeular Science," IRS Physical Chem istry Ser. Two, Volume 8, Butterwonh, 1975, Chapter 6. (6) Moon, P. C. and Barker. R. E., Jr.. I. Polymer Set,: 'Polymer Physics Ed,, 11, 909 (1973). (7) Griffith, A. A. Phil, Trans., A 221, 163 (1920). (8) Brown. W, F. and Strawley, J. E., ASTM STP 410, 1966. (9) Rivlin, R. S. and Thomas, A. G., J. Polymer Sci,, 10.291 (1953). (10) Reid, J. D., J. Oil & Colour Chem. Assoc.. S9. 278 (1976). (11) BMDP Biomedical Computer Programs, P-Series: Health Sci ences Computing Facility, Dept, of Biomathematics, School of Medicine, UCLA (12) Floyd, F. L. and Ramis. A, Jr,, "Plastic Pigment: A Novel Approach to Microvoid Hiding. Part II: Controlling Parameters for Performance," Jo u r n a l o f Co a t in g s Te c h n o l o g y , SI. No. 658,71 (1979). (13) ToussainL A.. Prog. Org, Coatings, 2,237-267 (1973/74). 80 it of Coatings Technology