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June 20, 1999

10 Min Read
Short-term ESC data for long-term predictions

Editor's note: Plastics that come in contact with acids, solvents, or sterilization environments are at serious risk for environmental stress cracking (ESC). The problem lies in testing-it isn't feasible to perform long-term tests, but short-term results can be misleading. Clinton Haynes and Douglas Marriott of Stress Engineering Services (Mason, OH) offer the following method for converting short-term ESC data to accurate long-term predictions. The company specializes in integrated approaches to product, package, and equipment system development using a variety of testing and analysis techniques. You may recognize their work from an earlier contribution on closure analysis.

ArticleImage1873.jpg
Example of a part with environmental stress
cracking, which remains one of the most
significant design challenges for injection
molded parts.

Environmental stress cracking (ESC) remains one of the most significant design challenges for injection molded parts. ESC is likely to be a problem for products or containers that will contact aggressive materials such as bleach, acids, solvents, hard surface cleaners, and fragrances, or for autoclaved medical components. To date, there is little or no quantitative data available to make realistic, physics-based design calculations and life predictions. Because of the wide range of contact materials or environmental conditions that exist, resin manufacturers can not effectively develop data to help solve this problem.

In general, manufacturers will develop accelerated testing protocols to evaluate the performance of their product designs. Tests attempt to simulate worst-case conditions and accelerate the aging processes that may take place. For example, a typical test for an injection-molded cleaning device used in industrial cleaning solutions may be to place the product in an elevated concentration of solution at elevated temperature for several weeks.

If the product does not exhibit any cracks or dramatic reductions in strength, the assumption is that it will survive, without failure, in the field. The hope is that this test in some way represents a worst-case scenario.

But this approach does not represent the service environment or the time- scale in which the product is typically used. If the accelerated test is negative, the product will likely survive in service-but what if the test leads to a failure? In the case of a home-use cleaning device, the question is, "How does the average usage cycle of 30 minutes per day in a dilute concentration of cleaning fluid at room temperature relate to the assumed accelerated testing conditions?"

Ideally, we would like to learn enough about ESC from the accelerated test to quantitatively predict how long a component will survive under more realistic conditions. Inferring material behavior under one set of conditions from tests done under other, more severe conditions is known as extrapolation.

There are two critical elements needed to make accelerated ESC programs meaningful:

  • A clear understanding of the service loads and conditions.

  • A reliable extrapolation method, if possible, with a sound basis in physics or chemistry.

Our current knowledge about ESC says that the driving force is a combination of material type, chemical environment, and a sustained stress (or strain). In plastic materials, unlike many metals, the terms "stress" and "strain" are not interchangeable because of material creep. At this time, science is uncertain whether it is stress or imposed deformation that triggers the cracking mechanism. These two possibilities need to be considered when planning an ESC test.

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Figure 1. Stress and strain levels can be calculated using computer-based simulation tools such as this finite element model of a part.

Calculating Stress and Strain Levels
Service loads are derived from the use of the product. Generally, designers calculate or measure the range of forces or imposed deformations acting on the product. Once reasonable estimates for these forces are made, the stress and strain levels can be calculated either analytically or computationally using computer-based simulation tools such as finite element analysis (Figure 1). Calculated stress values define the target range for the extrapolation technique. This means that the test conditions are invariably more severe, on average, than this range.

Extrapolation Methods
Several methods exist for extrapolating long-term plastic behavior from short-term accelerated tests. Although there are invariably objections to the use of extrapolation techniques in general, this does not solve the problem that extrapolation must be used to get any solution at all. Stress Engineering Services (SES) has built a useful experience base with available techniques to predict the performance characteristics of environmental stress cracking in the field of plastics.

After trying other methods, SES has come to rely on a simple, well tested approach to predict environmental stress cracking based on the so-called Arrhenius relation. The Arrhenius relationship is empirical. It was developed by a Swedish chemist who won a Nobel prize for his work on reaction rates.

Arrhenius observed that when a process such as material creep, cracking, certain chemical reactions, or diffusion is driven by temperature, the process progresses through a gradual state change. For example, this state might be a series of milestones along the path of an uncracked plastic component to a fully cracked component. The state at any time depends on both the temperature and the time at temperature.

Arrhenius found that he could correlate the state reached in any process after some time t at temperature T, by

Equation (1)
Amount of state change =
F[(t)exp (-Q/RT)]

where:
Q = activation energy, a constant expressed as energy per unit mass
R = the Universal Gas constant

The rate-of-change of the process can be derived by differentiating (1) as

Equation (2)
Rate-of-change ArticleImage3873.GIF
{dF[(t)exp (-Q/RT)]}/dt

In words, equations (1) and (2) say that the state reached in a process at one temperature T1, after time t1, is the same as the state reached after a different time t2, at a different temperature T2. In other words, the state history for all temperatures can be collapsed onto a single master curve by replacing the time axis by a temperature-corrected time axis.

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Figure 2. Schematic diagram of process at two different temperatures shifted to master curve.

This ability to collapse state histories onto a single curve by a simple shift in the time axis is an important feature of using the Arrhenius relationship in predicting the effects of ESC degradation (Figure 2).

Using the Method
Using the Arrhenius relation as a method of extrapolating ESC data offers a significant opportunity to dramatically reduce the risk of product failures. The nature of product testing when using this extrapolation method is different from traditional methods. Product designers must calculate stress levels in the component so rational test conditions can be established.

The following example contributes to confidence in the Arrhenius relation as a practical design tool for plastics designers. It provides quantitative evidence of the predictive capabilities of the relationship.

ArticleImage5873.jpg

Figure 3. Strips of material from a new HDPE component that would be in contact with a cleaning fluid in service are tested before market introduction to determine risk of cracking.

Designers wanted to determine the risk of cracking in an HDPE component that would be in contact with a cleaning fluid in service using the environmental test program that preceded product launch. Strips of HDPE material were wound around mandrels of specified radii, to produce the same defined levels of strain in the HDPE that were expected to be seen in service (Figure 3). Two sets of specimens were then immersed in the cleaning fluid of interest at temperatures of 60C and 71C respectively. The surfaces were examined visually at intervals until cracks were observed.

Curve Fitting Short-Term Data
First, a short-term accelerated aging experiment was conducted in the cleaning fluid for a period of about two days. The purpose of this initial experiment was to create the curve fit to short-term data using the Arrhenius relation equation (1). Table 1 summarizes the stress levels and actual time a sample was immersed in cleaning solution before a crack was observed. In this table, strains are converted to nominal strains by multiplying by the short-term tensile modulus at the test temperature. These data were used to generate a curve fit with the Arrhenius equation.

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Table 1 in the last column summarizes both the experimental data and the corresponding calculated time-to-crack for this same period. The correspondence is good, indicating that the Arrhenius model adequately represents the data over this exposure time period. The goal, however, is to demonstrate the capability of the method to predict time-to-failure for periods of time much longer than what was measured during a short term test.

Extrapolating to Longer Times
To evaluate the adequacy of the method, a second ESC test was conducted at a lower temperature, 60C, for approximately 11 days. Table 2 summarizes the experimental results for both temperatures.

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Using only the short term data (Table 1 data only), the Arrhenius equation (1) was used to extrapolate the short term data and predict the time-to-crack for the 11-day test at lower temperature. The extrapolation was made by fitting the experimental data with an expression of the form

Equation (3)
Time-to-crack (t) =
kcArticleImage8873.GIF-n exp(Q/RT)

where:
n = 2.53
Q/R = 20130
T = temperature (°K)
kc and n are constants obtained from a least squares fit of selected data

The resulting table (see last column, Table 2) offers a comparison of the extrapolated data with the long-term test data. It illustrates that for modest levels of extrapolation-a factor of about 10-the predictions are good.

Rule of Thumb
In the plastics field, the Arrhenius relation has proven to be useful in predicting ESC performance. There are other candidate methods, but these are invariably a variation on the Arrhenius theme. For instance, there is a well known rule-of-thumb used in estimating reaction rates that states, "Rate doubles for every [10 deg F] increase in temperature."

This is a rough rule, and is intended only for guidance. The 10 deg F is in brackets because, in reality, it varies around this value. It is good enough to identify the magnitude of the likely change going from one set of conditions to another. It is not surprising, therefore, that it is not "right." It is a theory, albeit a very simple one. How good is it? There is some justification for the concept of a doubling increment, which can be demonstrated over a limited temperature range using the Arrhenius relation.

From equation (2), it is easy to show that the ratio of two rates at temperatures T1 and T2 is given by

r1/r2 = e -(Q/R) [(T2-T1)/(T1T2)]

Setting T = T2-T1 and assuming that DT is small compared with T, the ratio between the rates r1 and r2 becomes approximately

r1/r2 = e -(Q/RT2)DT

which states that for moderate changes in temperature, the rate increases by a fixed ratio for a defined increment in temperature.

The Arrhenius relation should not be used indiscriminately for all time/temperature-related extrapolations, but it does seem to work well with ESC and creep. No matter what the application, care always has to be exercised that the material state under the extrapolated conditions is basically the same as those in the test used to collect the data.

For example, you can't extrapolate reliably from conditions above the glass transition temperature to conditions below it. This automatically places limits on the amount of extrapolation possible.

It is possible to reduce test times by increasing both the temperature and the stress. However, raising the temperature is limited by the obvious problem that the polymer will melt at very high temperatures.

Furthermore, raising the temperature also tends to limit what extrapolation can be achieved by increasing the stress, because the strength also decreases dramatically with increasing temperature. In practice it appears that three orders of magnitude is about the practical limit for this extrapolation method.

Contact Information
Stress Engineering ServicesMason, OH
Clinton Haynes
Phone: (513) 336-6701
Fax: (513) 336-6817
Web: www.ses-oh.com

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