[American Institute of Aeronautics and Astronautics 43rd AIAA/ASME/SAE/ASEE Joint Propulsion...

1 American Institute of Aeronautics and Astronautics

Correlation between the Accelerated Aging Test (AAT)

and Real World Storage Temperature

Lien C. Yang* La Canada Flintridge, CA 91011

Constraints on temperature parameters and mathematical formulas used in the current calculations for the accelerated aging test (AAT) are analyzed using the framework of Arrhenius kinetics. This analysis demonstrates that the values currently chosen for the parameters and the formulation are quite reasonable and consistent with the kinetics. Next, the effects of storage temperature are analyzed using typical natural temperature histories at selected geographical locations. It is found that the concept of “average storage temperature” can lead to large inaccuracies in the calculated equivalent AAT test duration that is required. An improved method based on daily temperature extremes is presented. The results indicate that a 18-day AAT test duration at 160oF can support a ~5-year shelf life verification being consistent with AAT equation with a 75oF “average storage temperature”. A ~2.78 times improvement in testing effectiveness over the current 30-day AAT at the same test temperature for a 3-year shelf life is realized. The 50 ± 10% RH @ 160oF currently used in AAT is found to be a good simulation of real world humidity exposure. To preserve this good test feature, RH test level needs be pro-rate increased if the AAT test duration is reduced.1

Nomenclature A = Rate constant in Arrhenius equation AAT = Accelerated aging test d = Thickness of an adsorbed moisture layer Ea = Activation energy ECS = Energetic components and systems F = Reaction rate factor for the exponent in AAT equation HL = Lower shelf life assigned based on F = 3.0 in AAT equation ΔHL = Difference between calculated HL by Arrhenius equation and by AAT equation HU = Upper shelf life assigned based on F = 3.25 in AAT equation HT = AAT test time k = Reaction rate in Arrhenius equation k1 = k @ temperature T1 (oK) k2 = k @ temperature T2 (oK) kB = Boltzmann’s constant K = Correction factor for shelf life calculated by using average daily storage temperature n = Molar fraction of un-reacted material at a given time t no = Initial molar fraction of un-reacted material Δn Molar fraction differential, = n - no

P(T) = Water vapor pressure at temperature T Po(T) = Saturation value of P at temperature T P’ = Water partial pressure in a sealed ETS R = Universal gas constant = 8.314 J/mol-oK= 1.988 cal/mol-oK RH = Relative humidity = P/Po t = Time Δt = Differential time (elapsed time) t1 = Test duration in AAT at test temperature of T1, same as HT t2 = Storage duration at an average or median storage temperature T2 , HL tp = Period in a periodically varying temperature profile T = Temperature T1 = Test temperature in AAT

* Senior Member, AIAA Copyright © 2007 by L. C. Yang, Published by the American Institute of Aeronautics and Astronautics, Inc., with permission

43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 8 - 11 July 2007, Cincinnati, OH

AIAA 2007-5138

Copyright © 2007 by L.C. Yang. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


T2 = Storage temperature used in AAT equation

_T = Average temperature in a periodically varying temperature profile Tmax = Maximum temperature in a periodically varying temperature profile Tmin = Minimum temperature in a periodically varying temperature profile Ti = Initial temperature of a closed ECS at sealing processing Tj = Variable temperature of a closed ECS subsequent to Ti ΔT = Span between temperature extremes = Tmax - Tmin δT = Reference temperature increment in AAT equation θ = Van der Waals’ Constant

I. Introduction

The Accelerated Aging Test (AAT) has been adopted for assessment of shelf life in a variety of industries including pharmaceuticals, food and chemicals. In 1971, it was suggested for aerospace energetic components and systems (ECS)1. This methodology follows the Arrhenius kinetics theory and has the following mathematical form: TTT

TL FHH δ/)( 21* −= (1) Where F = 3.0, or 3.25 δT = reference temperature increment = 20oF (11.11oC)

HL = service life or shelf life (in days), for F = 3.0 HU = service life or shelf life (in days), for F = 3.25 HT = test time duration (in days), 28 days nominal T1 = test temperature (in °F) = 160oF T2 = in-service median storage temperature (in °F)

MIL-STD-15762, Method 3403, incorporated this method and it has since been widely used for evaluation of the shelf life (or service life) of ECS. The provisions in this specification are conservative. It requires a 30-day AAT at 160oF added together with 50 ± 10% RH of humidity, for a three (3) year shelf life verification. This requirement results in a shelf life of 8.76 yrs according to Eq.1 for an “average storage temperature” of 75oF, and it would also correspond to an “average storage temperature” of 94.5oF for three years as shown in Figure 1. As shown in the same figure, a shelf life of 3.5 yrs could be simulated by a 12-day AAT for an “average storage temperature” of 75oF if F = 3 were used in Eq.1. The same 30-day AAT test requirement was adopted in later specifications, e.g., DoD-E-83578A3 and in

several launch vehicle range safety regulations4. In the past few years, there has been considerable discussion of the validity and limitations of this approach5,6. Points of contention include the choice of rate factor, F, the adoption of an universal activation energy for all energetic material, and the selection of test duration and test temperature, all of which appear to be arbitrary. However, after careful considerations, the new 2005 AIAA/SMC Ordnance Standard7 for space and launch vehicle applications has adopted the same formulation and method for AAT of ECS. Confusions were introduced by Eq.1 itself. Since it is an equation modified from the Arrhenius equation (but no derivation was reported), the meaning of physical parameters and their associated constraints are no longer explicitly traceable. This has led to the incorrect impression that all of the parameters can be adjusted and tailored at will. In reality, this is far from the truth, and one of the primary objectives of this paper is to explore these constraints.

Figure 1 AAT Simulated Shelf Life as a Function of “Average Storage Temperature” And F = 3.0


Because the estimated shelf life is dependent upon storage temperature and test duration, an uncertainty results which has to be addressed. The problems associated with defining an “in-service median storage temperature” are multiple. First, the ECS storage temperature has a large variability, ranging from temperature-controlled buildings to direct exposure to the ambient environments in bunkers, magazines and launch sites. The temperature histories for the latter cases are usually not recorded. Second, because Eq.1 is non-linear with respective to the storage temperature, the use of an average temperature cannot properly represent the true temperature exposure effect. It is the purpose of this paper to analyze the temperature profiles at several U. S. geographical locations of interest, using real daily/yearly average and extreme temperatures to estimate the equivalent AAT time that is required. The total required AAT test times are compared with those calculated by the yearly “average temperature”. From these results, the validity of using the yearly “average temperature” can be determined. A final objective relates to the implementation of AAT. Because of its long test duration, it is an expensive test. Therefore, it has always been of interest to explore means and justifications for streamlining the test. Proper alterations of test parameters for shortening the test duration are explored.

II. Correlation between AAT and Arrhenius Equations

The Arrhenius kinetics equation8 is defined as follows,

)/( RTEaAek −= (2)

Where, k = Reaction rate A = rate constant Ea = Activation energy R = Universal gas constant T = Temperature in oK

The simple solution of the differential equation governing the time dependent change is: n = no*e-kt or Δn = - nok*e-kt Δt (3) Where n, no and Δn are the molar fraction respectively at a given time, at the initial time and within the time differential Δt. The condition for the assumption of equal change in the molar fraction at different temperatures is: k1t1 = k2t2 (4)

Where, k1 = A1/ RTEae−

(5)

And, k2 = A2/ RTEae−

Therefore, t11/ RTEae−

= t22/ RTEae−

(6) By substituting t1 and t2 by HT and HL respectively, as used in Eq.1, one obtains:

)/1/1(*)/( 21* TTRE

TLaeHH −−= (7)

Combining Eqs.1 and 7, one obtains the condition of consistency between these two formulations:

Ea /R = -ln [ TTTF δ/)( 21− ] / (1/T1 – 1/T2) (8)

Fig. 2 plots the value of Ea /R (in units of oK) as a function of T2, the “average storage temperature”, for T1 = 160oF and δT = 20oF. It shows that Ea /R is a strong increasing function of T2.


Figure 2 Activation Energy as a Function of Average Storage Temperature for an AAT Test

Temperature of 71.11oC (160oF)

It is important to note that both AAT and the Arrhenius formulation deal with the relative change of a given property or characteristic instead of its absolute value because the constant A in Eq.2 is not specified. This is considerably different from high explosive decomposition kinetics in which the value of A is available for most energetic materials9. This may be considered a deficiency, or alternatively an advantage. In any event, the AAT does not give absolute values of the possible changes. The shelf life verification is largely dependent on the function test performed after the accelerated aging. Throughout the history of AAT, both for non-ECS and ECS, the concept was strongly influenced by a

simple “rule of thumb” methodology; something like “Equivalent age doubles for each 10oC rise in AAT test temperature.” Therefore, the choice of an F factor other

than e = 2.7183, leads to a deviation from the Arrhenius formulation. From Fig. 2, it can be seen that the AAT formula manifests itself in a variable activation energy, Ea , which ranges from 8693 R-Ko at T2 = 0oF to 10962 R-Ko

at T2 = 120oF with a median value of 10111 R-Ko at T2 = 75oF (F = 3.0). They are equal to 17.3, 21.8 and 20.1 kcal/mol respectively. The high-end value corresponds to F = 3.25 and T2 = 160oF is approximately 25 kcal/mol. It is well-acknowledged in the AAT references 1, 5, 6, that the range of AAT should be distant from the decomposition kinetics of the energetic materials themselves (including high explosives and common pyrotechnics) which have typical activation energies ranging from 40 to 60 kcal/mol9. For thermal energy to be significant in relation to these high energies, elevated temperature in proximity to the ingredient melting temperatures is required10– a condition that is not justifiable for natural storage. Therefore, one may ask: Can the activation energies in the range implied by AAT cover major modes of ECS aging failure? To help answer this question, the following table summarizes activation energies for some known possible ECS failure modes:

Table 1 Examples of Possible ECS Failure Modes Substances Mode Ea , kcal/mol

Water Adsorption11 10.50 KNO3 Dissolution12 8.34 KClO4 Dissolution12 12.20 PETN Sublimation9 29.10 RDX Sublimation9 31.10

RDX Crystal Fusion under residual cyclohexanone solvent13

<30.0? as it can occur at 200oF of temperature

Many other degradation mechanisms are not quantifiable and their assessment is subject to judgment calls. For example, the activation energies for metal oxides are very high, in the hundreds kcal/mol range. However, under the influence of high moisture levels, oxides can be readily formed at ambient temperatures implying much lower activation energies. Some common ECS degradation mechanisms involve stress relaxation in press-loaded powder matrices. These may occur in insensitive high explosives at mild temperatures and require very small thermal mechanical activation energies or they can be affected by low temperature phase changes9. A variety of plastics, polymers and lubricants with upper temperature limits rated at ~160oF are used in various ECS. Thus adopting 160oF as AAT test temperature and an activation energy of ~20 kcal/mol appears to be reasonable and can adequately cover most failure modes. From the point of view of physics, one expects that the activation energy of degradation for a given ECS, despite the fact that it may contain multiple ingredients, is a rather constant parameter, or at least that it is not highly variable according to the test conditions. Thus, if we choose Ea = 10111 R-Ko as the constant value, the accuracy in applying the AAT formula with different F values (3.0 versus 3.25) can be evaluated and compared with Arrhenius kinetics. Figure 3 shows the predicted shelf life by AAT and the Arrhenius equation (Ea = 10111 R-Ko) with T1 = 160oF and HT = 30 days. It can be seen that the F = 3.0 case follows closely with the Arrhenius prediction, especially in the temperature range of interest, 70o – 90oF. Larger deviations would result if F = 3.25 is used. The magnified deviations are showed in Figure 4, which plots the difference between predictions by the Arrhenius equation (Ea =


10111 R-Ko) and the AAT equation as a function of the average storage temperature. The inaccuracy in the F = 3.25 result is not acceptable as it represents a large AAT over-prediction in the temperature range of interest, 70o – 90oF. For comparison, accuracies of AAT relative to Arrhenius equation using variable activation energies obtained via Eq.8 with T2 = 75oF and variable F values, were determined. The features of ΔHL are similar to that showed for F = 3.0 in Fig. 4 and the results are summarized in Table 2. It can be seen that the AAT over-prediction inaccuracy is an increasing function of F and that using F = 3.0, results in improved accuracy over that obtained by using F = 3.25.

Table 2 Difference of Shelf Life, ΔHL = HL by Arrhenius Eq.2 – HL by AAT Eq.1 for Different F Values (Different Ea Values by Eq.8 with T2 = 75oF are used in the Arrhenius Eq. 2)

F 2.25 2.5 2.75 3.0 3.25 3.5 Ea* , R-oK 7463.7 8433.4 9310.7 10111.5 10848.2 11530.3

T2, for Minimum ΔHL , oF 92 92 89 89 88 87

Minimum ΔHL , yrs -0.106 -0.171 -0.262 -0.386 -0.550 -0.762 HL @T2 by Eq. 1, yrs 1.30 1.94 2.98 4.06 5.72 7.96

ΔHL/HL , % 8.15 8.81 8.92 9.51 9.62 9.57 * Ea is calculated from Eq.8 with T2 = 75oF

A similar under-prediction discrepancy for results using F = 3.25 also appears in Figure 5, which is the reverse plot (using Eq.9) of the required AAT test duration for one single day at a given storage temperature. We thus conclude that an F value of 3.0 is a more accurate choice than 3.25. The results also indicate that the inaccuracy at lower storage temperature regimes (<70oF) has less of an impact on the equivalent AAT test time than that at higher storage temperatures.

Figure 3 AAT Simulated Shelf Life (F = 3.0, 3.25)

as Compared to Arrhenius Predicted Life With Ea/R = 10111 oK

Figure 4 Difference in Predicted Shelf Life, ΔHL , Arrhenius Minus AAT

Figure 5 Required AAT Duration per Single Day as a Function of Average

Storage Temperature

Figure 6 Activation Energy as a Function of Average Storage Temperature for an AAT

Test Temperature of 100oC (212oF)

ΔHL = - 0.386 yrs T2 = 89oF


Figure 7 Plot of a Typical Daily Temperature Data for Southern AZ

Equation 8 indicates that the increase of the test temperature, T1 is equivalent to an increase in the effective activation energy to levels much higher than that warranted by T1 = 160oF. Large inaccuracy in AAT prediction would result. Figure 6 shows Ea as a function of T2 for T1 = 100oC (212oF). It can be seen that the upper end of Ea in the case of F = 3.00 reaches approximately 27.5 kcal/mol, a level too high for AAT validity and accuracy. In addition, too high a test temperature can induce unrealistic failure modes not covered by AAT (this assessment is not included in our current study as it requires quantitative values of A in Eq. 2). In Ref. 14, it was reported that when a PETN based composition was subjected to 80o- 100o C AAT, failure mode due to PETN sublimation did occur.

III. Proper Handling of Storage Temperature Effect ECS storage for aerospace applications adopts methods that are unique to aerospace systems:

• For safety, the primary method is to use bunkers and magazines in which the components are more or less subjected to natural temperature conditions. This is similar to many other applications.

• Due to the relatively small amount of explosive used in aerospace ECS, some ECS suppliers have adopted the practice of indoor storage. Therefore, depending on the work shift planning in the facility, the temperature is partially controlled by air conditioning.

• Aerospace systems, e.g., launch vehicles and missiles, are generally considered delicate. Therefore, the system level assembly, transportation and storage are performed in assembly buildings or transporters which have temperature controls of around 75oF.

• Due to the large size of the launch vehicles, they are not under temperature control once placed on the launching pad, i.e., they are subjected to natural temperature conditions.

The situation is made more complicated because ECS suppliers, assembly and launch facilities usually are located at different geographic locations and ECS are therefore processed in different time frames, to such an extent that a systematic temperature record for a given ECS is usually not available. Local temperature history available on several web-sites15, 16 for most U.S. locations may be used to represent the worst-case temperatures for our study. The maximum, minimum and average temperatures on each day are tabulated on these web-sites. Fig. 7 plots this information for typical records from southern Arizona (AZ). It can be seen that the day-to-day variation is very large, and a seven-day moving average cannot smooth out the curves. A six-degree polynomial fit appears to be more effective in smoothing out the record. For the benefit of later discussion, a multiple-year average of daily average

temperatures is shown along with their 6-degree polynomial trend lines in Fig.8, for four typical U. S. locations. Initially, it was thought that the data could be used for the AAT test duration calculation. However, it was found that the calculation could not be accurately performed by using the daily average temperature. The more accurate method, using daily maximum and minimum temperatures, will subsequently be formulated and reported. The figure nevertheless provides a good characterization of the yearly temperature profile at these locations. We now proceed to formulate a new approach for the required equivalent AAT test duration calculation based on Eq.9, the inverse of Eq.1 and the daily Tmax and Tmin.

TTT

LT FHH δ/)( 12* −= (9) If the daily temperature variation is assumed to be a sinusoidal function between Tmax and Tmin as shown in Fig. 9, then,

T = (TMax + TMin )/2 + [(TMax - TMin )/2] Sin (2πt/tp) = −

T + (ΔT/2)*Sin (2πt/tp) (10)


Where, _T = Average Temperature (daily) = (TMax + TMin )/2

ΔT= TMax - TMin And, tp = period in the day = 24 hrs

The required equivalent AAT test duration for a single day is the integral over the 24-hrs period,

Δt = ∫ − dtT 20/)160(0.3

= ∫ − dtT 20/)160(0.3 * ∫ Δ dtpttSinT 20/)/2()*2/(0.3 π

= ∫ − dtT 20/)160(0.3 * K (11)

K = ∫ Δ dtpttSinT 20/)/2()*2/(0.3 π (12)

Thus K acts as a correction factor, the value of which depends only on ΔT. It is a multiplier of the result based on daily average temperature

_T (The integral in Eq.11). Its numerical integration result is shown in Fig. 10.

For a giving year, we now have three different methods for calculating the required equivalent AAT test duration: 1. Use the average yearly temperature and Eq.9, as commonly assumed in the references. 2. Use the average daily temperature and Eq.9, then sum up all calculated daily values for the entire year. 3. Use Eq.11 for each day, then sum up all of the calculated daily values for the entire year.

Cases for selected U.S. locations and years were evaluated and the results are summarized in Table 3. It can be seen that significant errors exist in the results obtained using methods 1 and 2. As expected from Eq.11, the estimated required AAT test duration by Method 2 is longer than that estimated by Method 1. Similarly, the estimated duration by Method 3 is longer than that estimated by Method 2 (especially in the case of southern AZ,

Figure 8 Multiple-Year Average of Daily Average Temperature


where the daily ΔT is higher, as is characteristic of a typical desert climate). Method 3 is more accurate, and therefore the results are more valid for AAT shelf life estimation. They are extrapolated for the estimation of the AAT test duration required for three and five years of shelf life (Columns 7 and 8). Unlike the daily temperature, variation in results calculated from one year to another are very small. One interesting thing to note is that due to cold winter temperatures in several locations, the calculated yearly required AAT test days are less than that required for the case in which the ECS temperature is maintained at the relatively high and constant value of 75oF. In other words, for shelf-life efficiency, providing cooling of ECS via air conditioning during hot weather is more important than the heating during cold weather. Method 3 can be used for accurate evaluation of ECS shelf life if detailed storage temperature history is available. However, because of ECS storage is not always subjected to extreme natural temperatures such as those exist in southern AZ and the Eastern FL coasts, results in Table 3 indicate that an 18-day AAT generally can support a maximum of ~5 yrs of shelf life for multiple-location storage. This is consistent with 18-day AAT prediction of 5.25 yrs at a constant T2 = 75oF but with the benefit that justification of an “average storage temperature” of 75oF is not required. If this approach is adopted, elaborate case-by-case evaluation may be unnecessary. It represents a (5/3)*(30/18) = 2.78 times improvement in testing effectiveness over the current 30-day AAT for 3-year shelf life. Similarly, a 12-day AAT can only support an ECS shelf life of ~3.5 yrs. As will be covered in a separate paper17, provisions for a longer shelf life beyond 3.5 yrs for a 12-day AAT, based on trend line analysis can be evaluated.

IV. Humidity Test Requirement per AAT Humidity effect on ECS due to storage as simulated by AAT is a much more complicated problem than its counterpart, temperature effect. In addition to difficulties in defining the time-dependent environment, the effects also depend on the adsorption/absorption characteristics of the ECS ingredients, the initial absorption condition and the leak rate. From the following Table 4, it can be seen that the 30-day test condition at 160oF and 50±10% RH included in AAT is by far the most stringent test on this parameter. It is apparent that the face values of the equivalent moisture exposure of various tests cannot simulate more than one year of the natural humidity. Coincidently, assuming a 10-6 cc/s/atm leak rate for ECS, the total leak = 365*24*3600*10-6*10 mmHg/760 mmHg = 0.42 cc–– a level too large for most small sized ECS. In order to clarify the situation, the adsorption of moisture by the energetic powder matrix needs be considered. Due to the fine particle size of the powder, the resulting large surface area can entail significant moisture adsorption. The relative humidity in a typical ECS loading room is usually controlled to approximately 50% at 75oF for safety. Depending on the powder, a maximum of 0.2%wt of moisture adsorption is generally allowed. The powder, after staying on the bench, is loaded and the closure disc is welded on. Normally, no bake-out or back-fill with dry inert gases is performed. Thus, the sealed ECS roughly maintains the initial condition of 50%RH at 75oF (11.036 mmHg). The subsequent change of the partial pressure of moisture in the ECS will be governed by the adsorption law, the so-called “Frankel-Halsey-Hill equation21:

-kB*ln(P/Po)T = 3dθ

(13)

Where, Po is the saturation pressure of moisture at temperature T (oK), d is the thickness of the adsorbed moisture layer and θ is the van der Waals’ constant of the powder matrix. The exponent factor of 3 has been verified by the

Figure 9 An Example of Single Day Temperature

Variation and the Required Equivalent AAT Time (Tmax = 100oF and Tmin = 60oF)

Figure 10 Correction Factor K as a Function of ΔT


Table 3 Equivalent AAT Test Duration in Days as Estimated from Real Temperature Data

1 2 3 4 5 6 7 8

Location Period _T by

Period

HT for HL = 1 yr, by Column 3

HT for HL = 1 yr, by

_

T per Day

HT for HL = 1 yr, by Tmax/Tmin per Day

HT for HL = 3 yrs, = 3* Column 6

HT for HL = 5 yrs, = 5* Column 6

2004 69.9 2.59 3.51 4.10 12.30 20.50 2005 70.2 2.62 3.57 4.12 12.36 20.60 2006 70.9 2.73 3.86 4.42 13.26 22.10 Southern

AZ 2004-2006 70.3 2.65 3.54 NA NA NA

2003 72.4 2.96 3.32 3.55 10.65 17.75 2004 72.4 2.97 3.34 3.60 10.80 18.00 2005 72.4 2.98 3.37 3.60 10.80 18.00

Eastern FL

Coasts 2003-2005 72.4 2.97 3.28 NA NA NA

2002 61.4 1.63 2.26 2.50 7.50 12.50 2003 60.4 1.54 2.07 2.29 6.87 11.45 2004 62.0 1.68 2.07 2.34 7.02 11.70 2005 61.8 1.65 2.23 2.44 7.32 12.20

Northern AL

2002-2005 61.4 1.62 2.11 NA NA NA

2000 52.2 0.98 1.59 1.72 5.16 8.60 2001 53.2 1.03 1.64 1.78 5.34 8.90 2002 53.0 1.02 1.73 1.87 5.61 9.35 2003 50.9 0.91 1.47 1.59 4.77 7.95 2004 51.8 0.96 1.49 1.61 4.83 8.05 2005 52.8 1.01 1.76 1.90 5.70 9.50

Great Lakes Area

2000-2005 52.0 0.98 1.51 NA NA NA

2003 57.6 1.32 1.38 1.52 4.56 7.60 2004 59.3 1.45 1.53 1.69 5.10 8.50 2005 58.8 1.40 1.43 1.58 4.74 7.90

Southern CA

Coasts 2003-2005 58.6 1.39 1.43 NA NA NA

Table 4 Equivalent Moisture Exposure under Various Test Conditions

Test Method Test Condition Equivalent Moisture Exposure, mmHg-day

Natural 1 yr, 365 days, 10 mmHg average moisture 3650

AAT 30-day at 122 mmHg (50%RH at 160oF) 3660

MIL-STD-1344A, Condition D18

1344 hrs at 49.8 mmHg (90%RH at 40oC) 2789

MIL-STD-33119 192 hrs at 158.6 mmHg (95%RH at 160oF) 1269

ITOP 4-2-82020, 4.1 Steady State, High

Humidity Test

360 hrs at 83.65mmHg (95%RH at 49oC) 1255


author in previous work22, 23. Fig. 11 shows the adsorption isotherm at a constant temperature of 75oF. Note that when P/Po = 50%, the value of d is fairly stable, i.e., it does not change much with the P/Po values. If the temperature is changing, d is then governed by the universal adsorption curve22 shown in Fig. 12 in which d is plotted against the temperature normalized partial pressure (P/Po)T. Once again, in the range of variation for this parameter of interest, d is rather constant. Under this condition, the following relation holds:

iT

io

i

TPTP

⎥⎦

⎤⎢⎣

⎡)()(

=

jT

jo

j

TPTP

⎥⎥⎦

⎤

⎢⎢⎣

⎡

)()(

(14)

Because of the known condition of:

iT

io

i

TPTP

⎥⎦

⎤⎢⎣

⎡)()(

= 0.5297.05 (15)

and using the well-established saturation vapor pressure equation11 as a function of temperature (oK) for water: ln (Po) = 20.611 – 5203.3/ T (16) P(Tj) at Tj can be calculated. The differential between the ambient moisture pressure and the “internal” moisture pressure in the ECS, P(Tj), is the effective humidity pressure affecting the moisture leak flow.

The websites15, 16 mentioned previously also provide humidity records for U.S. locations in a format similar to the temperature records: daily maximum, daily minimum and daily average RHs or dew points. As an example, a plot of a typical record of the average humidity in mmHg is shown in Fig. 13 for year 2002 at a northern Alabama location. The day-to-day humidity variation appears to be more prominent than its temperature counterpart. Once again, a seven-day moving average trend line was not totally effective in accounting for the data points and a six-degree polynomial trend line appears to be more effective for the purpose. Fig. 14 shows the concept of using the daily average moisture pressure, P, and the daily average pressure internal to the ECS, P’, to obtain the difference between them, i.e., the effective moisture pressure differential P - P’, in this case for a northern Alabama location.

• P is the value taken from the average of daily average pressure from 2002 to 2005, followed by a seven-day floating average.

• P’ [=P(Tj)] is the value calculated from Eqs.15 and 16 using the average of daily average temperature from 2002 to 2005, followed by a seven-day floating average.

• The pressure differential is obtained by P – P’. It can be seen that the procedure drastically reduces the effective pressure to a level with an average value of 3.46 mmHg over the course of the year. A total yearly moisture exposure of 365*3.46 mmHg = 1263 mmHg-day is in effect. Therefore, the 3660 mmHg-day exposure by the 30-day AAT is equivalent to about 2.9 yrs of yearly exposure at this location. An interesting situation predicted by this analysis is the effect of temperature control. For the majority of cases in storage, the temperature of ECS is maintained at 75oF for an ECS internal moisture pressure

Figure 11 Frankel-Halsey-Hill Predicted Adsorption Isotherm atT=75oF (297.05oC)

Figure 12 Temperature-Normalized Frankel-Halsey-Hill Adsorption Isotherm

P/Po (P/Po)T


of 11.036 mmHg. Therefore, in the cold months, the ambient moisture pressures are actually lower than that inside the ECS. A “reverse” exposure condition is in effect. If this effect is taken into consideration, the 3660 mmHg-day moisture exposure can equal or exceed that imparted by natural moisture exposure for five years. Therefore, it is likely a valid simulation for a long-term storage condition of five years.

Figure 13 Daily Average Moisture Pressure, 2002, Northern AL

Based on the foregoing discussion, we conclude that measurement of the humidity portion of AAT is a sound approach. If one reduces the AAT test duration, the test humidity level needs be increased accordingly to preserve the total intended 3660 mmHg-day total exposure (e.g., if 18-day AAT is adopted, the humidity level would need be increased from 50%RH to 83.3%RH).

V. Conclusions

1. A detailed analysis correlating current accelerated aging test (AAT) formulation with the Arrhenius kinetic theory has been performed. The results indicated :

a. Using the factor F = 3.0 leads to more accurate results than using F = 3.25.

b. The choice of 71.1oC (160oF) as the test temperature in conjunction with the temperature increment of 11.1oC (20oF) is consistent with the failure mode activation energies of interest. Higher temperatures may produce undesirable or inaccurate results.

2. The concept of “average storage temperature” used extensively in AAT interpretation is not well-defined. A detailed method based on the integration of daily maximum, daily minimum

and daily average temperatures has been derived and proven to be more accurate. 3. A detailed evaluation of the AAT equation based on real temperature history has been performed for

illustration. 4. The evaluation results support an 18-day AAT for validation of approximately five (5) yrs of shelf life. 5. A 12-day AAT is only sufficient for validation of 3.5 yrs of shelf life. Additional allowance may be attained via

trend line analysis. 6. The 50±10% RH used in the AAT test is a good simulation for five-years of natural humidity exposure.

Therefore, if the AAT test duration is reduced, the humidity test level needs to be increased to preserve the equivalent total of 3660 mmHg-day humidity exposure.

Acknowledgements

The author acknowledges S. Goldstein of the Aerospace Corporation and D.L. Jackson of ATK, Inc. for many

Figure 14 An Example of Differential Moisture Pressure Concept


helpful discussions on the topic in recent years; M. Dao-Randall of Northrop Grumman for earlier exploration of websites availability for the local temperature and humidity data; T.L. Graham of Ohio State Univ., E. Yang of Univ. of Pennsylvania and S. Yang of Case Western Reserve Univ. for reviewing this paper; J.D. Glass and D. Farotto of PSEMC for sharing of Ref. 1.

References1

1 Moses, S.A., “Accelerated Life Test for Aerospace Explosive Components,” pp 11-3-1 thru 11-3-8, Proceedings of the

Seventh symposium on Explosives and Pyrotechnics, Franklin Institute Laboratories (Now is Frankin Applied Physics, [email protected]), Philadelphia, PA, 1971.

2 MIL-STD-1576 (USAF), “Electroexplosive Subsystems Safety Requirements and Test Methods for Space Systems,” 31

July 1984. 3 DoD-E-63578A (USAF), “Explosive Ordnance for Space Vehicles,” October, 1987. 4 Eastern and Western Range Safety Requirement (USAF EWR 127-1), 45th Space Wing and 30th Space Wing, 31 march,

1997. 5 Russakov, L.S. and Whalley, I.A., AIAA 2000-3646, “Accelerated Aging Testing of Energetic Components–A Current

Assessment of Methodology,” 36th AIAA/ASME/SAE/ASEE joint Propulsion Conference, July 17-19, 2000, Huntsville, AL. 6 Glass, J.D., AIAA 2004-3419, “Uses and Abuses of Accelerated Age Testing of Pyrotechnic Devices,” 40th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 11-14, 2004, Ft. Lauderdale, FL. 7 Criteria for Explosive Systems and Device on Space and Launch Vehicles, AIAA S-113-2005, AIAA, 10 Nov. 2005 8 Cook, M. A., The Science of High Explosives, Robert E. Krieger Publishing Co., Malabar Drive, Malabar, FL, 32950,

1958. 9 Gibbs, T.R. and Popolato, A., “LASL Explosive Property Data,” Univ. of California Press, Berkeley, CA, 1980. 10 Yang, L.C. and Do, I.P., AIAA 99-2420, “Key Parameters for Controlling of Function Reliability in ‘Nonel Tube’

Explosive Transfer System,” 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 20-24 June 1999, Los Angeles, CA. The same paper also appeared on AIAA Journal, Vol. 38, No 12, pp 2260-2267, 12 May 2000.

11 Gray, D.E., “American Institute of Physics handbook,” 3rd ed. McGraw-Hill Book Co., New York, N.Y., 1972. 12 Handbook of Chemistry and Physics, 47th Ed., pp D-53, the chemical Rubber Co., Cleveland, OH, 1966-67. 13 GIDEP Alert No. 8C-A-88-01, “RDX Core Linear shaped charge Failure,” Dec. 01, 1988. 14 Loyola, V.M. and Klassen, S.E., “Materials and Performance Evaluation of Accelerated aged XTX8003,” SAND97-

2721C, Sandia National Lab., Albuquerque, NM, March 1998. 15 http://www.wunderground.com/ 16 http://www.almanac.com/weatherhistory/locations/index.php 17 Yang, L.C., AIAA-2007-5135, “Practical Problems and Solutions in Age Trend-line Analyses for Energetic

Components,” 43th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 8-11 July 2007, Cincinnati, OH. 18 MIL-STD-1344A, U.S. DoD, “Test Methods for Electrical Connectors,” 15 December 1993. 19 MIL-STD-331B, “Fuse and Fuse Components, Environmental and Performance Tests for (please see change notice 8),”

Armament Research, Development and Engineering Center, U.S. Army Armament, Munitions and Chemical Command, Attn: SMCAR-AEF-C, Picatinny Arsenal, Dover, NJ, 28 November 2000.

20 International Test Operation Procedure (ITOP) 4-2-820, “FR/GE/UK/US Temperature and Humidity tests of

Ammunition,” U.S. Army Test and Evaluation Command, AMSTE-T, Aberdeen Proving ground, MD 21005-5055. 21 Young, D.M. and Crowell, A.D., “Physical Adsorption of Gases.” Butterworths, London, 1962. 22 Yang, L.C., “Quartz Microbalance studies on Unsaturated Helium Films,” Dissertation, University of California, Los

Angeles, 1973. 23 Yang, L.C., Vo, T.D. and Burris, H.H., “Nitrogen Adsorption Isotherms for Zeolite and activated Carbon,” pp 625-634,

Cryogenics, December 1982.

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