Understanding the Effects of Weathering Variables on Plastics Using Factorial Experiments
Henry K. Hardcastle III
Atlas Weathering Services Group
Sophistication of experimental designs for weathering research testing continues to evolve. The majority of current weathering experiments utilize simple designs which change few variables at a time. These types of weathering experiments require more trials and result in more cost and less information than approaches using "Fractional Factorials." Conducting "Fractional Factorial" experiments before using traditional approaches focuses weathering research on the significant and important variables effecting material performance. This paper presents a methodology for applying "Screening Fractional Factorial" approaches to material performance research. This paper includes a case study and examples of weathering data.
During the summer of 1999, Atlas Weathering Services Group performed a fractional factorial weathering experiment on commercially available materials. The general purpose of this investigation was to better understand the effect of weathering variables and specific pretreatments on appearance properties using a natural accelerated weathering device. Understanding how selected variables effect weathering may indicate which variables are most important for weathering. Additionally, it was hoped this experiment would provide a check of "conventional wisdom" regarding weathering phenomena of these materials as described in the literature or by customers or in previous parametric studies.
Description of Experimental Process
The material selected for this experiment was clear polycarbonate sheet with a UV protected surface. It is commercially available at the time of this writing and was purchased from retail sources. Nine independently controllable variables were selected for this experiment from two types, pretreatment variables and exposure variables. 2 9 or 512 trials would have been required to perform this analysis using full factorial approaches. The pretreatment and exposure variables along with their high and low settings are identified in Table 1. An L16 fractional factorial array was selected for this experiment. Although the L16 can theoretically handle up to 15 independent variables, it is not appropriate to fully saturate the array with variables. The nine variables identified for this investigation fit into the L16 while leaving six columns blank. The blank columns were used in the analysis for estimating the background variance, to check for significance of results, and to check for some interactions.
Assigning each of the input variables to specific columns in the array requires some judgement and understanding of aliases in the fractional design. For instance, we believe there is a reasonable likelihood of interaction between temperature and irradiance. We want to understand the independent effects of these two variables as well as the synergy between them. The temperature variable is assigned to the first column since the first column will reveal temperature effects alone. The irradiance variable is assigned to the second column since the second column will reveal irradiance effects alone. The third column is left blank since the third column's settings will reveal any effects due to interaction between the temperature and irradiance variables. The remaining variables for this experiment were assigned using similar justification. The final array with variable assignments is shown in Table 2. This schedule details 16 trials with unique settings of nine different variables.
The 16 trials prescribed by the experimental array were performed simultaneously on 16 different EMMA (Equatorial Mount with Mirrors for Acceleration) weathering devices at DSET Laboratories from May 21, 1999 to July 29, 1999. The machines utilized were quality checked throughout the exposure. Proper variable settings were maintained for each trial. Great care was utilized to insure all variables outside the scope of the experimental design were blocked across all 16 trials. At several intervals throughout the exposure, black panel temperatures were measured in the target area.
After the exposure period, specimens were removed from exposure, measured for appearance properties, and compared to their initial values before exposure. Polycarbonate specimens were measured for transmittance Yellowness Index according to ASTM E 313-96 and Haze according to ASTM D 1003-96 Procedure A . Each specimen was measured three times across the exposed surface with the mean reported. Two specimen replicates were included in each trial. The Yellowness Index and Haze values reported are calculated deltas between the initial measurements before exposure and final measurements after exposure.
Presentation of Data and Results
The delta Yellowness Index and delta Haze for the two specimens included in each trial are shown in Table 3. The trial number for the output values corresponds to the trial numbers used in the fractional factorial array schedule in Table 2.
Analysis of the output data was performed at two levels: 1) review of experimental grouping using a graphical technique, and 2) ANOVA.
A mean was calculated for the eight sets of specimens exposed to high temperature. A mean was calculated for the 8 sets of specimens exposed to the low temperature condition. These two mean values were plotted on a graph and connected with a line. This procedure was continued for all the variables included in this design. This graphing technique allowed the effects of each variable to be compared with the effects of all other variables with a single graph. Using this analysis, it was quite simple to determine which variables had the largest effect on natural accelerated weathering of polycarbonate and the magnitude of the effect compared to that of the other variables. Figure 1 shows the graph obtained for delta Yellowness Index. Figure 2 shows the graph obtained for delta % Haze.
ANOVA analysis was performed using a software package from ASD, Inc. ANOVA performs an analysis using the F test. In an F test, an F ratio is calculated comparing variance due to treatment variables to variance due to experimental noise (experimental error, background variation, etc.). The F ratio is often described as having the between column variance in the numerator and the within column variance in the denominator.
For this analysis, we simply compare the effects caused by input variables to the background variation of the experiment. As this ratio approaches one, we say that the effects due to the input variables are not significantly different than the background variation of the experiment or that the effect of input variables is not significant. However, as the F ratio becomes larger and larger, the effects due to the input variables become more different than background experimental noise. A large F ratio indicates the effect of the input variables is significant.
An estimate of the variation due to experimental noise (experimental error, background variation) comes from a combination of two sources for this analysis. First, since replicate samples were used in the experiment (n=2), the sample to sample variation in the results represents a good estimate of within treatment variation. Second, the columns that were left blank in the orthogonal design represent a rich source for estimating experimental error once interaction effects are ruled out. It is with this experimental error term that the effects of treatments are compared to determine significance.
Once the F ratio is calculated from the experimental data, it may be compared to values found in the standard F distributions given the degrees of freedom for the numerator and denominator and the desired confidence level. If the data generated F ratio value exceeds the critical F ratio value (from the table of standard F distribution values), the effect of the input variable can be said to be significant (the output due to that variable exceeds what would normally be expected due to random experimental noise).
For this analysis, the ANOVA table, treatment variables, pooled sources of experimental variance, and calculated F ratios are shown in Tables 4 and 5. Using the F column and r column in the ANOVA table, we can begin to assign a rank order to the significant input variables and understand the magnitude of effects compared to each other.
Interpretation of Data
Once the significance of the individual treatments is understood, it is appropriate to decide which input variables are important. The customer identified differences exceeding approximately two Delta Yellowness Index units and 10% Haze at this level of exposure to be important. Based on this information, the significant and important information can be completed as shown in Tables 6 and 7.
Confirmation trials should always be conducted in conjunction with fractional factorial screening experiments. Confirmation trials should also be considered as a critical part of the screening experiment. This is especially important if high levels of input variable saturation are designed into the orthogonal array and where significant interactions are identified between several input variables. Only confirmation trials can decode alias characteristic of the fractional array. Two confirmation trials are currently being conducted with input variables set as shown in Table 8.
There has been an evolution in the sophistication of experimental designs for weathering tests. The vast majority of current weathering exposures utilize more fundamental designs effecting few variables. This type of experimental design requires far more trials and, thus, more cost, less information, and poorer quality than more sophisticated approaches using screening fractional factorial experiments. Preceding fundamental level, few variable weathering trials with fractional factorial screening and confirmation experiments represent an efficient, stochastic, powerful approach for improving knowledge regarding weathering's n-dimensional hyper- volume of environmental effects on materials degradation.
|Variable||Low setting||High Setting|
|Temperature of Exposure (TEM)||Nominal -7° C||Nominal +7° C|
|Irradiance of Exposure (IRR)||8 Mirrors (-10 %)||10 Mirrors (+ 10 %)|
|Day Time Spray on Exposure (DTS)||No Day Time Spray||With Day Time Spray|
|Night Time Soak on Exposure (NTS)||No Night Time Soak||With Night Time Soak|
|Abrasion Pretreatment (ABR)||Not Abraded||Abraded|
|Soak-Freeze-Thaw Pretreatment (SFT)||No Soak-Freeze-Thaw||Soak-Freeze-thaw|
|Chemical Pretreatment (CHM||No Chemical Pretreatment||Chemical Pretreatment|
|High UV Pretreatment (ARC)||No High UV Pretreatment||High UV Pretreatment|
|Oven Pretreatment (OVN)||No Oven Pretreatment||Oven Pretreatment|
Table 1. High and Low Variable Settings
|1=Variable at Low Setting |
2=Variable at High Setting
|Temperature||Irradiance||Day Time Spray||Pretreat |
|Night Time Soak||Pretreat |
Table 2. L16 Fractional Factorial Array
|Trial Number||Delta Yellowness |
Index of Replicate "A"
|Delta Yellowness |
Index of replicate "B"
Haze of "A"
Haze of "B"
Table 3 Delta Yellowness Index and delta % Haze for Exposed Polycarbonate Replicates
Table 4 ANOVA Table for delta Yellowness Index
Table 5 ANOVA Table for delta % Haze
|Variables Tested That Are |
Insignificant for Yellowness Index
|Variables Tested That Are |
Significant But Unimportant for Yellowness Index
|Variables Tested That Are |
Significant And Important for Yellowness Index
|1. Temperature||1. Abrasion Pretreatment||1. High UV Pretreatment|
|2. Day Time Spray||2. Night Time Soak|
|3. Soak -Freeze- Thaw Pretreat||3. Irradiance|
|4. Oven Pretreatment|
|5. Chemical Pretreatment|
Table 6. Interpretation for Yellowness Index
|Variables Tested That Are Insignificant for % Haze||Variables Tested That Are Significant But Unimportant for % Haze||Variables Tested That Are Significant And Important for % Haze|
|1. Temperature||1. Night Time Soak||1. Abrasion Pretreatment|
|2. Soak Freeze Thaw Pretreat||2. High UV Prereatment||2.|
|3. Oven Pretreatment||3. day Time Spray||3.|
|4. Chemical Pretreatment||4. Irradiance||4.|
Table 7. Interpretation for % Haze
|#1-Least Degradation Predicted||#2-Most Degradation Predicted||Variables Optimized for Cost|
|• No Night Time Soak||• With Night Time Soak||• Low Temperature Exposure|
|• No Abrasion Pretreatment||• With Abrasion Pretreatment||• No Oven Pretreatment|
|• No Soak Freeze Thaw Pretreatment||• With Soak Freeze Thaw Pretreatment||• No Chemical Pretreatment|
|• Low Irradiance||• High Irradiance||• No Day Time Spray|
|• With High UV Pretreatment||• No High UV Pretreatment|
Table 8. Conformation Trials