ENGINEERING CORROSION PREDICTION MODEL

6th Joint FAA/DoD/NASA Aging Aircraft Conference – Sept.16-19, 2002

ENGINEERING CORROSION PREDICTION MODEL FOR AIRCRAFT STRUCTURES M. M. Altynova*, R. G. Kelly**, J. R. Scully**, D. T. Peeler*** Abstract Corrosion of aircraft structures is one of the most costly maintenance problems for the Air Force aging aircraft fleet. To aid maintenance planners in making more efficient decisions, a probabilistic model has been developed to assess corrosion damage and project a structure’s future corrosion condition. The prediction uses two inputs: the current corrosion condition (determined primarily by visual or nondestructive inspection (NDI), such as eddy current, ultrasonic, etc.) and the rate of corrosion growth as a function of the planned Air Force base assignment. NDI data is analyzed and translated into remaining thickness values. Corrosion rates distributions were obtained from direct field measurements for 70 Air Force bases and other operating locations. Both current corrosion conditions and corrosion rates are used in the form of probability density functions. The final predicted corrosion damage is derived from the convolution integral of the initial damage distribution and the corrosion rates distribution where the rate distribution is a function of the assigned basing location. The predicted damage is also presented in the form of a probability distribution function that provides all the necessary data for further structural modeling. This version of the Corrosion Prediction Model (CPM) can be used for corrosion and structural assessment of aircraft lap joints and wings. The software consists of a front end user interface programmed in Visual Basic 6 and a Microsoft SQL Server 2000 Relational Database that stores data about the aircraft history, the aircraft components, the various alloy properties, NDI data obtained from different components, corrosion rates for 70 Air Force bases, etc. The CPM software is connected to the ECLIPSE fatigue prediction software that assesses the remaining fatigue life of the lap joints. For wing structures, the CPM model currently utilizes a database of grindout repairs that includes margins of safety data for the upper wing skin.

* S&K Technologies, Inc. ** University of Virginia *** AFRL Aging Aircraft technology Office Lead Page 1 of 1 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


INTRODUCTION Corrosion of aircraft structures is one of the most costly maintenance problems for the Air Force aging aircraft fleet. In particular, the various forms of localized corrosion that include pitting corrosion, crevice corrosion, stress corrosion cracking (SCC), and corrosion fatigue, are particularly destructive. They frequently occur without any outward sign of damage and are usually discovered coincidentally and severely impact maintenance scheduling, or when left undetected, they can result in sudden and catastrophic structural failures. To develop an effective inspection and maintenance-scheduling program that takes advantage of life extension technologies, it is necessary to predict the evolution of damage as a function of various systems variables. Additionally, the development of effective localized corrosion damage prediction technology is essential for successful implementation of life extension strategies. The deterministic prediction of damage via damage function analysis (DFA) that has been used for estimating corrosion damage is described in [1]. The algorithm developed incorporates methods for defining the chemistry of bulk environment, for estimating the electrochemical corrosion potential of the metal or the alloy, and for mechanistically treating the nucleation and pits growth. This model can be used with any deterministic or empirical equations for pit nucleation rate, pit growth rate, and repassivation rate. This approach can be successfully used to characterize damage to boldly exposed and unprotected material subjected to a well-defined set of environmental parameters assuming that the dependence of deterministic nucleation and growth laws on various variables have been defined. With the constraints of actual aircraft environments and structural configurations imposed, it is necessary to introduce a probabilistic methodology for analysis of localized corrosion because precise deterministic expressions that account for all variables do not exist. The impact of localized corrosion can be predicted from analyzing measured values from several sampling locations within a limited area. Predicted maximum localized corrosion depths can be used to evaluate the residual life of the structure by applying the appropriate corrosion rate equation [2]. Typical rate equations used conventionally to represent localized corrosion are either of the power law or logarithmic law type [3]. Once again, those equations can be successfully used with a known environment and with boldly exposed surfaces. To predict corrosion damage in occluded aircraft structures with an unknown internal microenvironment that can be highly variable, it was determined that mechanistically-based empirical corrosion rate equations employed by this method would not yield the best solution. The probabilistic framework was originally developed for the lap joint configurations [4]. The mathematics and the modeling results are presented below. For the wing structures the model is under current development. The concept and the mathematics of the probabilistic approach for the wing will be discussed in this paper as well. Up to the present time, there has been little quantitative study of either lap joint environmental conditions or lap joint corrosion. There is no fundamental mechanistically based scientific model in existence that describes crevice corrosion within a lap joint for either the As-Built (i.e. pristine) or As-Is (i.e. current ‘aged’) condition. Moreover, the conditions inside these joints are too poorly understood to allow a quantitative determination of the evolution of the corrosion rate given input conditions such as the environment to which the aircraft is exposed. In addition, there is no data available concerning the variability in the geometry of the lap joints within one aircraft, much less across the entire fleet. Faced with such limited knowledge, an “engineering” approach to the modeling of lap joint corrosion was proposed by R. G. Kelly and J. R. Scully (University of Virginia). This is a probability-based approach to Page 2 of 2 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


corrosion problems described in [2]. Such an approach was used for the development of the As-Is to To-Be corrosion prediction model described in this paper, where As-Is means the current condition and To-Be – the predicted condition of the lap joint. The framework developed will use databases that either exist or need to be created. To predict the corrosion damage to the lap joint in a given time period, two major components should be available: 1. Information on the As-Is corrosion condition of the specific aircraft assembly from NonDestructive Inspection (NDI). 2. Corrosion rate measurements of As-Is lap joints as a function of environmental parameters (chloride concentrations, humidity, temperature, time of wetness, etc. - indexed as the ESI – Environmental Severity Index ). The framework developed uses the distributions of the initial damage depths and corrosion rates. To predict the To-Be corrosion damage of a lap joint subjected to a particular corrosive environment (ESI), the initial damage depths from NDI as well as the possible range of corrosion rates should be processed in the form of Probability Distribution Functions (PDF). Figure 1 schematically represents how the distribution of corrosion rates might depend on the ESI of a particular Air Force base or geographic location.

Figure 1. An illustration of the probabilistic framework for the corrosion growth model.

The proposed model would then take these data and perform the following tasks: Page 3 of 3 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


(a) Select planned aircraft basing location and station time. (b) Look up the relevant distribution of corrosion rates from the database for this basing location. The next step in the model would be to apply the selected corrosion rates distribution to the initial corrosion depth distribution from the NDI image (Figure 1) to calculate: (a) The final damage depths distribution after some time interval ∆t, and; (b) how long it would be before the tail of the distribution would hit the specified defect size (for fatigue) or thickness loss (for residual strength). This output could be fed into a structural model assuming that this specific damage size could be considered as the initial crack. BACKGROUND 1. Lap Joint Model Frequency of Occurrence rate (FOR) for Different Corrosion Conditions The FOR (Frequency of Occurrence of Rate) function is the Probability Density Function (PDF) for different values of damage propagation rate p. The physical meaning is described as: Probability (p is in the range p o to p o +dp) is = FOR (po )*dp. It is typical to describe rate information as PDFs. Examples include [2]: - SCC fracture lives - Pit depths - SCC crack depths - Incubation times to pitting or cracking. Values of p are defined only in the range of

0 ≤ p ≤ +∞

(1)

The total integral of any PDF: +∞

∫ PDF ( p)dp = 1

(2)

0

The following section presents several examples of corrosion problems relevant to the effects of corrosion on structural integrity of aging aircraft. Number of Sites of Given Depth (NSD) at Time Moment to . The NSD is the Probability Density Function for corrosion site depth values h, as recorded from the NonDestructive Inspection (NDI) of an aircraft in service at the moment of time to . It describes the distribution density of damage depth values. The expressions (1) and (2) also apply to h. Problem Statement Predict the values of damage depths at a time moment t= to +∆t. Example of Idealistic Solution Let us assume that the FOR (p)=δ(p - p o ) (Dirac’s delta-function). This means that all the measurements of damage penetration rate equal p o . Let us assume that NSD (h)=δ (h - h o ) as well. This means that all the measured values of damage depth at a time moment to were found to be h o . Page 4 of 4 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


In this case the solution for the problem is simple. At a time moment t= to +∆t the predicted depth values of any specific damage will be: h(to +∆t)=h o +p o ∗ ∆t

(3)

General Solution The solution when FOR and NSD are general functions is more complicated. Final depth values will be described by another PDF. For convenience, let us call it Predicted Number of Sites of Given Depth (PNSD). By definition, for any PDF, the probability that the original depth of the damage was in the range of ho ≤ h ≤ ho + dh is NSD( ho ) * dh (4) Likewise, the probability that the damage penetration rate is in the range of p o ≤ p ≤ po + dp is FOR ( po ) * dp . (5) Given the above values of initial damage depth and damage penetration rate, the predicted final damage depth at time (t o + ∆t ) will be h f (t o + ∆t )

h f (t o + ∆t ) = ho + po * ∆t

(6) f

From here it is obvious, that h o is defined in the range of 0 to h f . Corresponding values for p o are

h and 0. ∆t

The probability of such an event (that the final damage depth is h f ≤ h ≤ h f + dh , when the values of h o and p o are in the corresponding intervals (defined by Equations 4 and 5) is given by the multiplication of corresponding probabilities: Probability ( h f ≤ h ≤ h f + dh ) = NSD( ho ) * dh * FOR ( po ) * dp

(7) f

However, more than one specific value of po and ho will result in the value of h . Actually, any combination of p and h that satisfies the equation (6) will result in the same final damage depth. All these combinations will contribute to the final probability of having the final damage depth value of h f . Therefore, the most general expression for the probability that the final damage depth is h f ≤ h ≤ h f + dh is described by the integral of (7) over all the values p and h that meet the requirement of (6): h= hf

Probability ( h ≤ h ≤ h + dh ) = f

f

∫ NSD(h) * d (h ) * FOR ( p) * dp

(8)

h =0

The derivation of the final predicted distribution function for damage depth values has been presented in [4]. The PNSD function is a convolution of two distribution functions FOR (p) and NSD (h): po =

PNSD( h f ) =

hf ∆t

∫ NSD(h

f

− po * ∆t ) * FOR ( po ) * dpo

(9)

po= 0

The probability distribution function PNSD (hf ) carries the significant information about the predicted corrosion condition in the lap joint after time ∆t. It may be used to determine answers for many specific questions about future corrosion condition of the aircraft structural detail. For example: Problem 1: NDI?

How many damage sites will have depth values exceeding h cr after time period Page 5 of 5 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference

∆t after


∞

N ( hcr ) =

Answer 1:

∫ PNSD(h )dh

(10)

h = hcr

Problem 2: What is the time period ∆t after which 99% of all the damage sites will still be not deeper than h cr (this ∆t estimate may be used to assign next NDI interval)? Answer 2:

∆t is a solution of equation below: hcr

0.99 =

∫ PNSD(h )dh

(11)

h= 0

This equation shall be solved numerically using a computer program. Problem 3: What average mass loss could be expected at the lap joint area of 3x3 in 2 after time period ∆t at given environmental conditions? Answer 3: ∞

∆M = ρ* 9 * N *

∫ h * PNSD( h)dh

(12)

h= 0

where

ρ is material density and N is total number of corrosion damage sites.

Suggested Forms of Distribution Functions NSD and FOR At this point it is assumed that both functions NSD (h) and FOR (p) would be given in analytical or numerical form. Both functions are determined only for positive parameters (h and p respectively). Both functions are non-symmetrical. The best candidate for such a distribution function will be a two- or three- parameter Weibull Distribution function, which is becoming an extremely useful and popular tool of reliability analysis in the aerospace industry. In various forms of corrosion, Gumbel and Weibull distributions are often observed [2]. The Weibull Cumulative Distribution Function (CDF) is written as [5]:

x − xo β ) ] , while Weibull PDF is the derivative of CDF and determined as: η β x − xo β −1 x − xo β PDFW ( x) = ( ) exp[ −( ) ] η η η F ( x) = 1 − exp[ −(

Where,

(13)

β is the shape parameter, η is the characteristic life (for life-data) or scale parameter (for other data, such as strength, or dimension), x o is simple shift of the origin; for two-parameter Weibull function xo =0. For some systems xo ≠0 makes physical sense. In such cases using third parameter is justified. In many cases, however, a two-parameter Weibull distribution is sufficient and preferable for this model.

2. Wing Model Corrosion conditions in the upper wing of KC-135 aircraft were reported to have contributions from multiple damage modes, for example, environmentally assisted cracking (EAC), exfoliation, intergranular Page 6 of 6 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


corrosion (IGC), pitting corrosion (PC), crevice corrosion, and general surface attack. Multiple mechanical, electrochemical and metallurgical factors have signific ant effect on the rate of corrosion, and, as a result, on the structural integrity of the upper wing skins. The current state of the art does not allow engineers to perform fundamental evaluation of all these factors and prediction of corrosion condition for wing components. Therefore the probabilistic approach developed for the lap joints can be expanded for upper wing skins. Defining the Initial Conditions for the Wing The initial (As-Is) conditions of the corrosion damage on the wing can be obtained from different sources: 1. Results of visual inspection, 2. Grindout data, 3. NDI images showing exfoliation and/or previously performed grindouts. In case of visually detected exfoliation damage, the diameter of the damage can be supplied as an initial condition to the analysis. An example of a visually inspected exfoliation site is shown in Figure 2.

Figure 2. Example of exfoliation damage on KC-135 upper wing skin. When the visual inspection is performed, the depth of exfoliation is not known. One of the ways to estimate how deep the damage could be (without performing a grindout) is to use a “library” or a database of depth data collected from metallographic sections of corresponding damaged areas of other aircraft. Another source is the database of maintenance records of the grindouts and other repairs performed on the upper wing skins. Such a database was developed at Tinker Air Force Base. The Tinker Grindouts database contains corrosion grindout information from more than 500 aircraft including their basing history and specific corrosion damage repair information. The depth and diameter of each grindout are recorded along with the exact location on the individual wing panel identified by a unique WUC (Work Unit Code). It has 20,000+ records overall collected over a period of more than 10 years. The CPM can query the Grindouts Database, pull all the grindout records for the certain WUC over the entire fleet of KC-135, find the grindouts with the diameter more or less equal to the diameter of the visually inspected exfoliation and plot the depth distribution or a shape factor distribution for this diameter. The depth distribution for a 2.0 inch diameter grindout is shown in Figure 3 (the data is from the Tinker Grindout Database). To estimate the depth of the exfoliation damage within a certain level of confidence the user can take the mean value or the 95% percentile of the distribution shown in Figure 3. Page 7 of 7 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


X 95% of the Distribution = 0.05 in

Figure 3. An example of a Statistical Depth Distribution for a 2.0 inch diameter grindout (lognormal PDF) When a grindout is performed, the diameter and the depth are known but additional exfoliation damage can still progress over time. End grains may be exposed to the environment due to protection system flaws and imbedded active corrosion may have been missed. Predictions can be made if the corrosion rate distributions in the long, long-transverse and short-transverse directions are available. Ultrasonic NDI scans that show exfoliation damage on the upper wing skins can be analyzed in a way similar to NDI scans of lap joints. This data can be used for the predictions of future damage states and structural analysis as well. The following information will be used as an input data for the Wing Model: FOR(p) frequency of occurrence of rate – distribution of corrosion rate, as a function of depth penetration rate SFD(s) -

Corrosion area shape factor distribution, as a function of shape factor: s=L/h Weibull, or other functions, i.e. lognormal, may be used to describe these distributions. An example of the shape factor distribution function is shown in Figure 4. It was calculated with the data from the Grindouts Database. Corrosion rate distribution in short-transverse or long-transverse directions is required for future predictions. This data is not available right now, but an initial estimation can be made with the data from the same Grindout Database. Basing location, station time and the diameter and depth of a grindout that was performed after being stationed at a particular base can be used to calculate the rate distribution. As an example, the corrosion rate distribution in the short-transverse direction for Kadena Air Base is shown in Figure 5. Additional refinements will be made to the rate distribution when more data is available (e.g., field exposure coupons or metallographic data, etc.).

Page 8 of 8 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


Probability Density Function 0.01

Lognormal Data 1 P=2, A=MLE-S F=25087 | S=0

Probability Density Function

8.00E-3

6.00E-3

4.00E-3

2.00E-3 Marina Altynova SKT 3/26/2002 3:27:21 PM

0 0

60.00

120.00 180.00 Shape factor (L/h)

240.00

300.00

µ=4.59, σ=1.05

Figure 4. An example Probability Density Function of a grindout shape factor derived from Tinker Grindout database (lognormal PDF)

Probability Density Function 2000.00

Normal Data 1 P=2, A=MLE-S F=25311 | S=0

1600.00

PDF

1200.00

800.00

400.00 Marina Altynova SKT 3/26/2002 4:37:38 PM

0 0

2.00E-3 4.00E-3 6.00E-3 8.00E-3 0.01 Exfoliation Rate in ST direction, in/year

µ=3.02Ε−3, σ=2.33Ε−4



Figure 5. An example of an exfoliation rate distribution in the short-transverse direction for Kadena AFB derived from Tinker Grindout data Target Results of Wing Corrosion Prediction Model As a result of visual or NDI inspection performed on the wing there could be one or two input characteristics available: L – diameter of the exfoliation damage ho – depth of the exfoliated damage The engineer needs to know how wide and how deep corrosion the damage will be after one deployment between depot cycles at a specific Air Force Base if the area is left untouched without any repair. For a given ESI (Environmental Severity Index) the rate distribution function is represented as FOR (p), in the same way as with the Lap Joint Model. The difference is that here could be rate distribution functions in the long-transverse and short-transverse directions as well. These functions can be provided from the field data and are represented as FORLT (p) and FORST (p). Given the current damage data and distribution functions described above, it is possible to estimate the probability distribution function for the corrosion area at some future point in time: PDD(h,t o +∆t) -

Predicted depth distribution at time to +∆t

(14)

PLD(L,t o +∆t) -

Predicted length distribution

(15)

“Average”, “Most likely”, “90-percentile”, and “99%-percentile” values of corrosion depth and area may be calculated from these distributions. In the situation when both initial parameters – the diameter of the damage and its depth − are known, the prediction scenario is straightforward. The predicted distribution of the probability that the corrosion area will have depth value of h1 at a point in time t1 = to +∆t, where ∆t=60 months (one depot cycle): PDD(h1 )*dh, is the probability that the final depth has a value in the range (h1 , h1 + dh). It is equal to the probability that the exfoliation rate in ST direction pS T is in the range (pST , pST + dpST ), where pST =

h1 − h0 ∆t  h1 − h0    ∆t 

which is defined as FORST (pST)= FORST 

 h1 − h0   * dp ST  ∆t 

PDD(h1 )*dh= FORST 

 h1 − h0  dp ST  h − h0  1 = FOR ST  1 * *  ∆t  dh  ∆t  ∆t

PDD(h1 ) = FOR ST  In general form:

 h − h0  1 *  ∆t  ∆t

PDD(h) = FOR ST 


(16)


PLD(L)*dL is the probability that final diameter(length) has value in the range (L1 , L1 + dL) It is equal to the probability that the exfoliation rate pL (in LT direction) is in the range (pL , pL + dpL ),

 L1 − L0  1 *  ∆t  ∆t

PLD(L)= FOR L 

(17)

The most typical situation is when the diameter of the exfoliation is the only given characteristic of the damage (as a result of visual inspection or in some cases, NDI). In this case the current and the future depth of the exfoliation can be estimated by applying the Shape Factor Distribution SFD(s). The predicted depth of exfoliation can be estimated using PLD(L) from equation (17) and the experimentally determined shape factor distribution SFD(s). The probability for the diameter to be “near” L2 is PLD(L2 )*dL. For specific value of the shape factor

s2 =

L2 h

(18)

the depth of exfoliation damage is h. The probability of such a specific combination of s2 and L2 is:

 L  dL SFD( s 2 ) * ds * PLD( L2 ) * dL = SFD 2  * * PLD( L2 ) * dL  h h

(19)

The total probability that the final depth size has a value of h is the total sum of probabilities (equation 19) for all possible combinations of L2 and s2 that satisfy equation (18): ∞

∫

 L2  dL * * PLD( L2 ) * dL =  h  h

Probability (h, h+dh) = SFD 0

y=∞

 y  dy = ∫ SFD  * * PLD( y ) * dy = h h y=0

y=∞

 y  dy  y − L0  1 SFD  * * FOR   * dy h h  ∆t  ∆t y= 0

∫

Per the definition of the probability distribution function for the predicted depth h: y=∞

PDD(h) =

 y 1  y − L0  1 SFD  * * FOR   * dy h h  ∆t  ∆t y= 0

∫


(20)


RESULTS AND DISCUSSION Corrosion Prediction Model (CPM) Software The mathematical model described in the previous section was numerically implemented in to the Corrosion Prediction Model Software. The CPM software consists of two parts: (1) a Relational SQL Server 2000 Database and (2) a Graphic User Interface – CPM interface connected to the database. 1) The CPM Relational Database stores an information about different tail numbers, their basing histories, geometry and material properties of different structural details, NDI data, grindout data for the wing structures, corrosion rates data for different basing locations, maintenance information and the cost data associated with it. The database is developed with the SQL Server 2000. 2) CPM interface is developed with Visual Basic 6 and is connected to the SQL Server 2000 database via ADO (ActiveX Data Objects). The screens and functionality of the CPM software are briefly described below. The complete description of the Graphic al User Interface can be found in [6]. The user can select an aircraft tail number from the entry screen (Figure 6).

Figure 6. Tail Number Selection screen, Corrosion Prediction Model. After the selection is made the user should select either the fuselage or the wing map (Figure 7 a, b respectively).



(a)

(b)

Figure 7. Maps of the (a) fuselage and (b) upper wing of the KC-135. The user can select a component for analysis, for instance, Stringer 29 (red label) or Stringer 25 (pink label) on the fuselage map, or Stringer 17, wing stations 320-360 on the wing map (yellow labels). The color labels on the map identify the region where NDI or a visual inspection data was collected and is available for analysis. After the selection of the structural detail is made the user can proceed to the As-Is Corrosion Damage Analysis.

The As-Is Corrosion Damage Analysis When the user clicks on the selected structural detail for the selected tail number, the most recent NDI image for the selected structural detail is pulled from the CPM Relational Database. The user now can select an area of interest, draw a box around it and analyze it. The analysis is similar to a typical NDI image analysis. The program will plot a histogram of calibrated thickness loss values within this box, then finds the best fit of Weibull probability distribution function for this histogram. Weibull parameters η and β for the selected area are displayed on the screen along with a graph of the As-Is Weibull distribution function. For a particular structural detail, the Weibull statistics of the entire bay and of the critical fastener row can be obtained separately by similar image analysis or obtained from the database if the image was preprocessed. An example of the developed screen of the interface is shown in Figure 8. The area of interest is selected for damage assessment. The thickness loss distribution histogram of the selected area is plotted and fitted into the Weibull Probability Distribution Function.



Figure 8. The As-Is Damage Analysis screen, Corrosion Prediction Model. This resulting parameters η and β of Weibull Probability Distribution Function NSD (h) are used in a Corrosion Prediction Model:

NSD( h ) =

β h β −1 h * ( ) * exp( −( ) β ) η η η

(21)

For the wing damage analysis, the results of visual or NDI inspection in the form of damage diameter and the related shape factor distribution can be supplied for further analysis. Corrosion Rates Data The corrosion rates distributions were obtained from direct field measurements for 70 Air Force bases. Battelle [7] has been conducting studies to determine corrosion rates in outdoor exposure and to establish relative severity levels at a series of military bases. This method provided a first cut at ranking more than 70 bases around the world with respect to aluminum corrosion. Table 1 shows the mass loss data collected on the AA 2024 lap joints for some of the base locations.



Table 1. Field Mass loss data for AA2024-T3 Battelle lap joints. Base Dover AFB, Deleware Ramstein AB, Germany Seymour Johnson AFB (Goldsboro), North Carolina Osan AB, South Korea Homestead ARB, Florida McChord AFB (Tacoma), Washington Travis AFB (Fairfield), California Hickam AFB, Hawaii Mildenhall (RAF), United Kingdom Charleston AFB, South Carolina Gabreski AP/ANG (West Hampton, NY) Lajes Field, Azores MacDill AFB (Tampa), Florida Kadena AB, Japan Yokota AB, Japan Moffet Field, California Pease ANGB (Portsmouth), New Hampshire Robertson Army Base (Australia) Tyndall AFB (Panama), Florida Wright Patterson AFB (Dayton), Ohio

Mass Loss Data ( µg/cm2) 4 mths 6 mths 9 mths 12 mths 802.5 935 989.5 1006.5 1462 1489 1954 2027 2307 2470 2617 4317 4333.5 7224.5 967 1165 870 1344 1824.5 1220

This data was converted into the corrosion rates distribution functions required for the Corrosion Prediction Model. 12 month mass loss data was assumed to be the mean value of the rate distribution for the particular basing location. Having this value as a mean, and assuming that shape factor β= 2 , the scale factor, η was calculated numerically, so the rate distribution function FOR(p) was created for each base location:

FOR ( p ) =

β p β −1 p * ( ) * exp( −( ) β ) η η η

(22)

This data has been used to populate the CPM database of corrosion rates. The relative ranking of the bases according to their severity is shown in Figure 9.



Figure 9. Relative Base Ranking graph based on the mass loss data. For the wing structures the rate data in both directions – longitudinal, long transverse and short transverse can be estimated from field exposure coupons. An example of a wing skin exposed at Pease AFB for 1 year is shown in Figure10. This data will populate the database of corrosion rates and will be used for the corrosion prediction model. The data is being collected at this time.

Figure10. Wing skin exposed at Pease AFB for 1 year.



PREDICTIONS Predicted Number of Sites of a Given Depth, PNSD- Lap Joint Model The Weibull Probability Density Functions NSD describes the As-Is state of the lap joint specimen. Function FOR characterizes corrosion rates for this particular specimen exposed to a specific environmental index (ESI). Based on Equation (9), these functions can be used to predict the corrosion damage of the analyzed area of the lap joint panel after a specified period of time, ∆ t, since the last NDI. The CPM interface solves equations (9, 10) numerically. The input parameters are: Weibull distribution parameters β and η of NSD and FOR functions, ∆ t, and critical corrosion site depth h cr. PNSD (h) Calculation The CPM program calculates the PNSD function, and for a multi- ESI (multi-base deployment plan) case, the calculated PNSD from a previous ESI is treated as the NSD for the current calculation. Predicted PNSD can be further used in solving equations (10)-(12) to provide more practical results, such as predicted averaged mass or thickness loss. The corresponding interface screen is shown in Figure 11.

Figure 11. Results of the corrosion prediction: Predicted Lap Joint Sheet Thickness Distribution after 5 years at Davis-Monthan AFB, followed by 5 years at Hickam AFB, HI.

Result Expression: Graphically shown NSD and PNSD functions and the As-Is and To-Be mean thickness losses and the values of mean plus 1 to 3 standard deviation values after 60 months consecutive exposures Page 17 of 17 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


to the environment of Davis-Monthan AFB, AZ and followed by Hickam AFB, HI. The rework limit is also shown, so a repair decision can be made in advance. As –Is and To-Be Topography Evaluations - Lap Joint Model The developed probabilistic model can be easily applied to any specimen configuration as long as it is possible to obtain the distribution of initial damage for this configuration and the distribution of corrosion rates for the exposure environment. The predicted result can be presented in the form of a probability distribution function, average mass or thickness loss, or a percentage of area corroded more or less than certain corrosion criteria. For instance, the maximum allowable thickness loss for the structural detail can be displayed. To relate the corrosion prediction model with the fatigue crack growth analysis the current and predicted topography must be evaluated. The topography measurements cannot be performed directly in the field, only in the laboratory environment. That is why the concept of the catalog was created. Lap joint samples were scanned with field NDI equipment to identify and quantify the corrosion damage areas, then the specimens were taken apart and laser profilometry or X-Ray were performed on those corrosion areas for topography evaluation. To model the evolution of topography the following approaches can be used: -

Use 2- or 3-D remaining thickness data obtained from laser profilometry or X-Ray. Use the Probability Distribution Function (FOR) of corrosion rates for the expected environmental conditions (ESI) Generate the “Most Likely” geometrical profile or remaining thickness map to be used in fatigue analysis.

The developed corrosion prediction model can take any Weibull or any other distribution of corrosion rates and apply them to the remaining thickness map/profile. The topography that results from applying those corrosion rates for a given time can then be calculated. Average remaining sheet thickness can also be derived. Finally, any slice through the structure (to obtain the surface profile) can also be extracted. Different scenarios of applying corrosion rates to the initial thickness map or profile can be considered: A. Corrosion Scenario 1(previous attack predicts future attack = perfect memory): The rate of attack for a given region will scale linearly with the initial thickness loss, i.e., the areas most severely attacked previously will have the highest corrosion rates. The limits of the corrosion rates considered would be the lowest and highest rates observed in the Weibull distribution for the considered ESI. The same rate will be applied to a given area throughout the entire five-year simulation. B. Corrosion Scenario 2 (random attack at all time = no memory): The rate of attack for a given region will be "randomly" selected using the Weibull probability distribution for the ESI considered. For each year, the rate of attack for the region will be "randomly" selected again. This scenario will lead to an eventual leveling of the attack, but it may not do so over the small number of cycles we are using. C. Corrosion Scenario 3 (initial random attack, then perfect memory): The rate of attack for a given region for the first year will be "randomly" selected using the Weibull probability distribution for the ESI considered. The rate of attack for a given region will scale linearly with the initial thickness loss, i.e., the areas most severely attacked previously will have the highest corrosion rates. Page 18 of 18 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


D. Corrosion Scenario 4 (initial perfect memory, then no memory): The rate of attack for a given region for the first year will scale linearly with the initial thickness loss, i.e., the areas most severely attacked previously will have the highest corrosion rates. For subsequent years, the rate of attack for a given region will be "randomly" selected using the Weibull probability distribution for the ESI considered. Some examples of topography evolution, where the thickness profiles were obtained from laser profilometry, are shown below. In the present analysis, two specimens are used: 1) SM2SP4 – from Boeing 707, and 2) SM10SP1- from C-135. The profiles across the most heavily corroded areas on those specimens were measured using laser profilometry. The rate distribution was retrieved from the CPM relational database. The results of the conducted analysis are shown below. The As-Is profile is displayed as a blue line and the predicted To-Be profile is in red. The Mean Thickness Loss is calculated for the As-Is and To-Be conditions and is shown beneath the combo box. Each scenario was applied for two consecutive periods of 8 months each. The graph shows the As-Is and To-Be thickness profiles for two scenarios. Beneath the profiles there are two histograms that show how the remaining thickness distribution changes in time. Again, blue is the As-Is histogram, red is the To-Be histogram. Since the remaining thickness decreases, the histogram moves to the left.

a)

b)

Figure 12. Scenario A applied to specimen a) SM2SP4 (Boeing 707), b) SM10SP1 (C-135). The rate applied was that from Brindisi Air Force Base, Italy.



a)

b)

Figure 13. Scenario B applied to the specimen a) SM2SP4 (Boeing 707), b) SM10SP1 (C-135). The rate applied – Brindisi AFB.

a)

b)

Figure 14. Scenario C applied to the specimen a) SM2SP4 (Boeing 707), b) SM10SP1 – C-135. The rate applied was that from Brindisi Air Force Base, Italy.



a)

b)

Figure 15. Scenario D applied to the specimen a) SM2SP4 (Boeing 707), b) SM10SP1 (C-135). The rate applied was that from Brindisi Air Force Base, Italy. The structural models will determine the most likely location for a crack to be initiated due to the corrosion topography. The complete results on the topography predictions were included in [8]. Structural Analysis The structural analysis of the corroded lap joint or wing is performed by ECLIPSE (Environmental and Cyclic Life Interaction Prediction Software ). The two software – the CPM and ECLIPSE are interconnected, so the output from corrosion analysis and predictions is fed into the structural analysis performed by ECLIPSE. The output from CPM to ECLIPSE consists of the As-Is and To-Be thickness loss distributions of the selected area, of the entire bay and critical fastener row of the lap joint, geometry and materials data for the analyzed structural detail retrieved from the relational database. ECLIPSE is a fatigue prediction tool for imposing age-based or time-based structural degradation effects (such as corrosion) onto traditional cyclic damage tolerance (a.k.a. crack growth) analyses. The software accounts for the independent and the interdependent effects of structural degradation in the time domain as that degradation interacts with cyclic loading. The ECLIPSE process works across many different classes of age degradation and types of structure; this software has been tailored to be specific to fuselage lap splices that undergo (predominantly) constant amplitude fatigue loading due to fuselage pressurization. ECLIPSE is built and compiled (using Microsoft COM technology) as a ‘wrapper’ around the freely available damage tolerance code AFGROW. ECLIPSE predicts the holistic structural life from the As-Manufactured Initial Discontinuity State (IDS) to the final state when the structure can no longer serve its intended function. This final state is somewhat subjective, as ‘failure’ is a complicated notion in complex structure such as aircraft systems. Care has been taken to remain conservative yet reasonable during the predictions, with the primary goal being to treat corrosion as a quantifiable structural issue rather than simply an economic problem that must be fixed when detected. The complete description of ECLIPSE can be found in [9]. ECLIPSE Output An ECLIPSE Age Degradation analysis currently consists of four parts: •

A pristine crack growth run (for comparison) Page 21 of 21 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


•

An age degradation analysis (for the ligament, one fastener pitch)

•

A center-cracked panel ‘additional life’ run (for the pristine case)

•

A center-cracked panel ‘additional life’ run (for the corroded case)

The output columns in the output window, Figure 16, display the values of various structural parameters at each time-cycle increment. The crack lengths "a" and "c" start from the IDS size and progress due to both cyclic and age-based degradation. The thickness changes as corrosion affects global area loss on the section. Currently, the width, Tension Stress Ratio, Bearing Stress Ratio, and multi-site damage factor are not time dependent variables. The multi-site damage factor is hard-coded to 1.0, representing a severe MSD scenario and a critical crack length of about a half a fastener pitch. The final two output columns present Residual Strength Margins of Safety (M.S.) for Kcrit (critical Stress Intensity) and for Net Section Yield. The input criteria Pxx (Residual Strength Requirement) multiplies the computed residual strengths before the Margin of Safety computation to provide safety against an overload condition. The output of Age Degradation Analysis provides the following results: 1)

the holistic life (As-manufactured to Failure) for the ligament analysis;

2)

the result of the pristine run is output next;

3)

the ‘additional life’ results of the two center-cracked panel analyses;

4)

How safe is this structure today? (As-Is Static Margin of Safety)

5)

How safe will this structure be at its next scheduled maintenance? (To-Be Static Margin of Safety)

6)

How long before the structure is unsafe? (Corrosion-fatigue cycles remaining)

Figure 16. The output of the Age Degradation Analysis for the KC-135 aircraft with the planned basing locations at Davis-Monthan AFB for 5 years followed by 5 years at Hickam AFB.



The output from ECLIPSE includes a worksheet with the pristine (no corrosion) crack growth outputs ("Pristine_output"), the corroded ECLIPSE age degradation with crack growth analysis ("ECLIPSE_output"), the "A vs. Cycles Chart" and the "C vs. Cycles Chart". The Pristine_output sheet is straightforward. It includes traditional damage tolerance parameters, the crack lengths "a" and "c", where "a" is the dimension of a part-through crack through the thickness and "c" is the dimension of a part-through crack along the surface (along a line drawn between fasteners) or the dimension of a through crack. The beta factors used in the crack growth analysis are output, and the elapsed fatigue cycles are shown. The ECLIPSE_output worksheet displays a copy of the information that was last output to the ECLIPSE Output window. The worksheets “A vs. Cycles Chart and “C vs. Cycles Chart are the Excel Plot Windows of the crack length “a” or “c”. A sample is shown for the “c” dimension, Figure 17.

Figure 17. Corroded ECLIPSE age degradation with crack growth analysis (“ECLIPSE_output”) After the corrosion and structural predictions are completed the user can review the available maintenance operations for the analyzed structural detail, select the appropriate repair option and then perform the Cost Analysis for the recommended repair options. The Cost Analysis based on a Markov model is integrated into the software. The Cost Screen contains a maintenance option matrix for user selection and a list of the best maintenance options based on the lowest long-term maintenance cost as shown in Figure 18. The expected average cost per damage event for the user’s selection and the best maintenance option are shown on the screen. The user can manipulate the maintenance option matrix to check the cost changes due to available maintenance options.



Figure 18. Results of Cost Analysis, Corrosion Prediction Model. The results of corrosion and structural predictions can be summarized and saved as a text file or printed directly (Figure 19).

Figure 19. Summary Screen, Corrosion Prediction Model. Page 24 of 24 M. Altynova, et al 6th Joint FAA/DoD/NASA Aging Aircraft Conference


Conclusion The Corrosion Prediction Model based on a probabilistic approach has been developed during the Corrosion Maintenance Improvement (CMI) period of performance. It allows the user to analyze current corrosion damage and to determine the future damage state depending on the aircraft’s basing location. The Corrosion Prediction Model has been closely integrated with the ECLIPSE fatigue prediction software to perform structural analysis of the current and projected conditions of lap joints and is currently being modified to include wing components under the Corrosion Effects on Structural Integrity (CESI) program. Both the CMI and the CESI programs were sponsored by the Air Force Research Laboratories (AFRL) at WrightPatterson Air Force Base, Ohio.

LIST OF REFERENCES 1. “Deterministic Prediction of Pit Depth Distribution”, G. Engelhardt, D. D. Macdonald, Corrosion, 54, 6, pp. 469-479 (1998). 2. “Introduction to Life Prediction of Industrial Plant Materials”, by M. Kowaka, Allerton Press, Inc. New York, ISBN 0-89864-073-3 (1994). 3. “Pitting Corrosion of Metals”, Z. Szklarska-Smalowska, NACE, Houston, TX,p. 113, (1986). 4. “Lap Joint Corrosion Prediction Model”, M. M. Altynova, R. G. Kelly, J. R. Scully, X. Zheng, G. R. Cooke, D. T. Peeler, Aging Aircraft 2000, St. Louis, MO, (2000). 5. “The New Weibull Handbook” by Dr. Robert B. Abernethy, 2nd Edition. Distributed by SAE International. 6. Corrosion Maintenance Improvement (CMI) Final Report, February 20, 2002. 7. Final Report on “Field Site Reactivity Monitoring”, submitted to AFRL/MLS by William H. Abbott, July 27, 2001. 8. “Combining Probabalistic and Database Approaches to the Prediction of Corrosion Damage in Aging Aircraft”, by R. G. Kelly, J. R. Scully, M. M. Altynova, D. T. Peeler. 9. Corrosion Maintenance Improvement (CMI) Final Report, February 20, 2002, Appendix 3.
