Service Life Prediction Models
Xenon Arc Weather-Ometers and Proper DOE Offer a Powerful Tool to Weathering Researchers
by Kelly Hardcastle, Atlas Material Testing Technology LLC
Introduction
Manufacturers can easily build service life prediction models for weathering studies using xenon arc Weather-Ometers and proper design of experiment (DOE). These models can then be used by inputting environmental data from the outdoor exposure location for which you wish to predict service life. This article describes a weathering service life prediction model built in the lab for yellowing of unprotected polycarbonate. Atlas Material Testing Technology used it to predict weathering service life in South Florida and Arizona. The results showed good agreement between predicted and observed service life.
Building the Model
The first step was to perform a simple design of experiment (DOE) in Ci4000 and Ci5000 xenon arc Weather-Ometer instruments. For this DOE, all exposure trials utilized quartz inner, borosilicate outer filters with no spray or dark cycles. The ultraviolet (UV) light irradiance settings, black panel temperature (BPT) settings and relative humidity (RH%) settings were adjusted to a variety of levels for seven trials as shown in Table 1. In each trial, the amount of exposure required to cause a change in the yellowness index1 (delta Y.I.) of 6 units was determined for each exposure condition. For example, the irradiance, BPT and RH% conditions of trial 1 required 1427 KJ/m2 at 340 nm exposure to reach a delta Y.I. of 6 while the conditions of trial 6 only required 829 KJ/m2 at 340 nm to produce the same yellowing.
The second step in building the SLP model was to use multi-linear regression analysis2 to obtain a predictive equation. In order to do this, the duration, irradiance, BPT and RH% variables had to be converted into the appropriate form for the Arrehnius relationship; Ln (life estimate in KJ/m2 at 340 nm), UV irradiance intensity in W/m2 nm, 1/°K BPT, and RH%. Once in Arrhenius form, the 73 data points from the DOE were used in the regression analysis to calculate the predictive function shown in Table 2. Thus, the xenon arc Weather-Ometer DOE data and regression analysis produced a predictive model describing the polycarbonate yellowing as a function of the UV intensity, BPT and RH% variables. Figure 1 shows the model function for two of the three variables.
Using the Model
The first step in using the SLP model was to obtain the variable levels that occur in the outdoor weathering environment where the polycarbonate was to be exposed. Atlas researchers obtained environmental variable measurements in south Florida and central Arizona for UV irradiance, BPT and RH%. This environmental data was in 30-minute time increments, yielding 48 data points per day for a year. An example of a single day's outdoor data for irradiance and BPT is shown in Figure 2.
The second step to use the predictive model was to enter each 30-minute combination of outdoor environmental variable observations into the predictive function. This gave a prediction of the polycarbonate yellowing for each 30-minute duration of outdoor exposure. All contributions for which the light intensity was zero (night time) were disregarded. Researchers continued to sum the degradation from each 30-minute exposure interval throughout the year until the degree of yellowing reached failure (delta Y.I. of 6). This sum represented the service life prediction for this study. The calculations predicted a service life of 332 MJ/m2 total ultra-violet radiation (TUVR) in south Florida and a service life of 408 MJ/m2 TUVR in Arizona with service life being defined as the amount of UV radiant exposure before the polycarbonate yellowed to 6 delta Y.I. units.
Considerations Using the Prediction
One important consideration discovered in this case study was that significant differences existed in weathering variable measurements in the xenon arc laboratory instruments and the outdoor variable measurements. In xenon arc exposures, the light intensity variable is measured in W/m2 at 340 nm while outdoors, light intensity is measured in W/m2 from 295 to 385 nm or TUVR. BPT measurement devices used in outdoor exposures also differ significantly from the BPTs used in xenon arc exposures. Ideally, both the model measured variables and the outdoor measured variables should be measured in the same way with devices of identical response. In order to obtain comparable irradiance data, the outdoor TUVR irradiance data was simply multiplied by ten in order to obtain a proportional approximation for the 340-nm xenon intensity data. The outdoor BPT data was used directly as measured with the outdoor style sensors.
Figure 2. Example of single-day black-panel temperature and irradience values in Florida.
Click to enlarge
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Another important consideration is that weathering is highly material dependent. Different formulations and even different batches of a single formulation may weather differently. The information presented in this case study is not meant to address service life prediction of polycarbonate but only to study the methodologies for applying SLP to exposure data. Use of this information for any other purpose is not recommended.
Comparing Predicted and Observed Data
Actual outdoor exposure of the polycarbonate were performed at Atlas's outdoor exposure laboratories in south Florida and Arizona in order to confirm the utility of the SLP model. Five independent exposures of the polycarbonate material were performed in Miami, Florida and Phoenix, Arizona at outdoor reference laboratory exposure facilities. All exposures were conducted at an angle of 5° facing south in an un-backed configuration. The 5 exposures started in different years and at different seasons of the year at the different locations. Changes in Y.I. as a function of total UV exposure for the different tests are shown in Figure 3. One observes the service life of the polycarbonate as approximately 380 and 450 MJ/m2 TUVR in Miami and Phoenix, respectively for these exposures.
The model-predicted estimates for service life are compared to the actual observed values in Figure 3. In both exposure environments, the model-predicted service-life estimate differed from the observed outdoor service life by less than 15%. Given the differences in variable measurement and the crude approximations undertaken in the calculation, this level of agreement was unexpected for a first approximation.
Summary
Figure 3. Observed reference exposure results compared to model predictions. Click to enlarge
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This case study on polycarbonate offered researchers a good opportunity to gain experience and insights in SLP methodologies. The model developed here within showed reasonable agreement between predicted and observed service life. One way researchers may improve the methodology is to use the same type environmental variable measurements outdoors as used in the laboratory. Building SLP models with xenon arc Weather-Ometers in the laboratory and using the models by inputting outdoor environmental variable data appears to offer a powerful tool for the weathering researcher's toolbox.
References
1. ASTM E 313-96 Practice for Calculating Yellowness and Whitness Indicies from Instrummentally Measured Color Coordinates. 1996 Annual Book of ASTM Standards, vol. 6.01. Philadelphia: American Society of Testing and Materials, 1996
2. James T. McClave et al. Statistics for Business and Economics, 8th ed., Prentice-Hall, NJ, 2001
For more information, contact Kelly Hardcastle, director, R&D, Atlas Material Testing Technology LLC at khardcastle@atlas-mts.com or by phone at 623-465-7356.
