The Repair of Corrosion Damage Holes In Al-Alloy Using SPD

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Final Report

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THE REPAIR OF CORROSION

DAMAGE HOLES IN ALUMIMIUM

ALLOY AIRCRAFT SKINS USING

SUPERSONIC PARTICLE

DEPOSITION BRUNO KAHL: 20272685

SUPERVISED BY: PROFESSOR RHYS JONES

(CENTRELINE TECHNOLOGY 2013)


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SUMMARY The project was carried out to investigate a new method for repairing corrosion damage holes in

alluminium alloy aircraft skins, Supersonic Particle Deposition, that would achieve the repair without

affecting the structural integrity of the skin and protect the damaged site from further corrosion, the

current technique failing to meet this requirement. This was performed by creating computer

designed models of similar dimensions that replicated a damaged and Supersonic Particle Deposition

repaired section of an alluminium alloy aircraft skin. By utilizing Finite Element Methods to model

the specimens such that they simulated the conditions of a typical aircraft skin in flight, a stress

analysis of each model under a typical flight load was then produced. A crack was then input into

the data received from this analysis using a convertor program which outputs data that can be used

within a fatigue crack growth analysis program that defines the growth of the input crack under

cyclic loading and hence when a model will fail. Several models were created of differing

thicknesses and simulated corrosion damage depths to investigate the effect of the repair technique

on differing amounts of removed damaged material. Thus by comparing the amount of cycles each

model undergoes before failure the relative effectiveness of each repair can be determined.

It was found that utilizing the Supersonic Particle Deposition repair technique can significantly

increase the structural integrity of a corrosion damaged alluminium alloy aircraft skin as the

specimens modeled to have been repaired lasted between 2 – 4 times longer than the standard

models. However some issues arose during the analysis of certain specimens which produced

somewhat inconsistent data pertaining to the lower end of the calculated lifetimes. It is suggested

that with more time these issues would have been resolved and the lifetimes determined from the

analyses would be greater, more likely resulting in a 3 – 4 times increase in life produced from the

repairs.

This process was found to achieve the required repair without further damage caused to the aircraft

skin and due to the processes high efficiency it is able to completely protect the damaged site from

additional corrosion damage. As such it is suggested that this method replace the current

mechanically fastened doubler repair technique for repairing corrosion damage holes in alluminium

alloy aircraft skins as it is not only able to protect the damaged site from moisture but also able to

increase the structural integrity of the deteriorated skin.


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TABLE OF CONTENTS

1. INTRODUCTION (4 – 8)

1.1 Corrosion and the Issues it causes to the 4 – 5

Airworthiness of Aircraft

1.2 Current Technique for Repairing 5 – 6

Corrosion Damage and its Shortcomings

1.3 Supersonic Particle Deposition and its 6 – 8

Application to repairing Corrosion Damage

1.4 Project Scope 8

2. METHODOLOGY (8 – 14)

2.1 Creation of the Models in Solidworks 8 – 10

2.2 Processing the Models with FEMAP 10

2.3 Adding the 3D Crack Using the Converter Program 10 – 12

2.4 Simulating Cyclic Loading Using FASTRAN 12 – 14

3. RESULTS (14 – 22)

3.1 Preliminary Stress Analysis 14 - 18

3.2 Crack Growth Analysis 18 - 19

3.3 Crack Growth Comparison and Final Results 19 - 22

4. DISCUSSION (22 – 24)

5. CONCLUSION (24 – 25)

6. ACKNOWLEDGEMENTS (25)

7. REFERENCES (25 – 26)

8. APPENDIX (27 – 30)


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1. INTRODUCTION Any aircraft in service is detrimentally affected by the moisture it encounters within its operational

environment, the most drastically effected region being the skin of the aircraft which is in constant

contact with the atmosphere. As this is an unavoidable issue the damage corrosion causes to

metallic aircraft skins due to moisture is a major hindrance to the continued airworthiness of aircraft

worldwide. This is predominantly due to the extreme costs of repairing such damage and the

potential for catastrophic aircraft failure that accompanies it, which may ultimately result in fatal

accidents. The current procedure for repairing corrosion damage to aircraft skins is somewhat

effective in protecting the damaged site however this process further damages the skin of the

aircraft and introduces new sights for corrosion which has motivated the demand for a new

technique that can achieve the repair without adversely affecting the skins structural integrity.

1.1 Corrosion and the Issues it causes to the Airworthiness of Aircraft Corrosion can effect a number of different materials in differing ways, however as most aircraft skins

are created from metals and the most widely used metal for such an application is aluminium, the

project will concentrate on this material. Corrosion is defined as the degradation of a material as a

result of chemical reactions that take place between the material and the surrounding environment

(Corrosion Technology Laboratory, undated). This degradation is most notably apparent in the

deterioration of the physical properties of the material such as the loss of mass and cross sectional

area of a structure which acts to reduce its strength. The most common form of corrosion that

affects metallic structures is electrochemical oxidation which causes the formation of oxides that

can become concentrated at holes or cracks or can uniformly corrode a surface (Callister 2007). This

loss of mass can be generalized for Aluminum as shown in the figure below along with an example of

a corroded metallic surface.

2Al 2Al3+ + 6e- (Oxidation)

6e- + 6H+ 3H2 (gas) (Reduction) (Callister 2007)

Figure 1: The oxidation/reduction reaction that occurs to Aluminium when in the presence of moisture.

Note that Al – Aluminium, e- - Electrons, and H

+ - Hydrogen and that Al

3+ is the oxidized form of Aluminium.

The Hydrogen atoms present in the above reaction are due to the interaction of Aluminium with moisture

(water), or H2O.

(Ginzel, Kanters 2009)

Figure 2: General widespread corrosion damage to a metallic structure which shows the extent to which

Corrosion can damage a surface.


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Hence corrosion damage is an ever present problem which affects all aircraft and must be constantly

monitored and maintained to prevent any catastrophic damage to the craft. This is extremely costly,

as reflected by the US report to congress from the Department of Defense in 2007 which estimated

that “the cost arising from corrosion damage repair was between 10 and 20 Billion dollars annually”

(Matthews et al, undated). Furthermore the harm caused by corrosion damage can be far worse than

financial loss as the 1988 Aloha Airlines incident exposed. During a routine flight the fuselage of the

Aloha Airlines Boeing 737-200 failed, undergoing explosive decompression which caused one of the

crew members to be ejected into the atmosphere (Wanhill 2002). Upon inspection of the failed

fuselage several corrosion repairs were found in close proximity and it was determined that, along

with general Widespread Fatigue Damage (WFD), these closely spaced repairs were the cause of the

failure (Wanhill 2002).

1.2 Current Technique for Repairing Corrosion Damage and its

Shortcomings The most common method of repair to the skin of an aircraft that has been damaged significantly

enough by corrosion to necessitate action involves blending out the damage and riveting a

mechanically fastened doubler over the site. The doubler acts to transfer any present forces around

the damaged site; however this creates stress concentrations at the corners of the doubler and at

the holes required for the rivets and additionally the introduced rivet holes will act as new sites at

which corrosion will be concentrated (Net Composites 2013). Furthermore this method fails to

prevent moisture present in the vehicles operational environment from entering the repaired site

and hence stop any additional corrosion damage. As this damage can occur over a relatively large

area several repairs may be necessary in close proximity to one another which will effectively reduce

the strength of the already deteriorated aircraft skin which can cause structural failure as the Aloha

Airlines incident revealed. A typical diagram of such a repair is shown below to illuminate the

shortcomings of the current repair technique along with an actual example.

(Net Composites 2013) (CycloContractor 2010)

Figure 3: On the left is a diagram of a repair carried out utilizing a mechanically fastened doubler and on the

right a real life example of such a repair. Note the high number of rivets and hence holes that are

introduced to achieve the repair.


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Hence while this method may prevent the damaged area from taking the full load applied at the site

it also acts to reduce the structural integrity of the skin of the aircraft and in turn detrimentally

affects the airworthiness of the vehicle. This has prompted research into new methods of repair

that will not damage the aircraft skin any further and will be able to successfully remove any

corrosion damage; a very promising method is that of Supersonic Particle Deposition.

1.3 Supersonic Particle Deposition and its Application to repairing

Corrosion Damage Supersonic Particle Deposition (or SPD as it will be referred to hereafter) involves the high speed

deposition of microscopic particles onto a sample, in which the particles ultimately impact the

substrate of the specimen and adhere to the surface. This process is also known as Cold Spray which

is indicative of the fact that the particles, typically 1-50 μm in diameter (Matthews, et al 2010), do not

melt during the procedure but instead undergo plastic deformation which provides the energy for

bonding between the target material and the micro-particles (Leyman 2004). A strong pressure field

is required at the point of impact to overcome the typical strain hardening rate involved with plastic

deformation and as such the particles must be accelerated beyond a critical velocity, which is

dependent on their size, shape and material (Singh et al, 2012). Hence the particle must impact with

enough energy that high strain rate deformation occurs and the particle gains ductility which results

in a viscous flow, rather than losing ductility as is the norm under plastic deformation (Callister 2007).

This is achieved by accelerating the particles in a compressed supersonic gas jet and specifically

designed nozzle to velocities of 300 – 1,000 m/s, thus the Kinetic Energy of the micro-particles

imparted by the expansion of the supersonic gas jet is converted to plastic deformation during the

process of bonding (Matthews, et al 2010). Currently the bonding process between the target

material and the micro-particles is poorly understood but what is known is that the impact of the

particles with the substrate at such high velocities causes adiabatic shear instability which leads to

thermal softening at the substrate being dominant over the typical strain rate hardening (Matthews,

et al 2010). This leads to the required viscous flow of the SPD material for bonding, at very near the

materials melting point temperature (Singh et al, 2012), a typical animation of the bonding

mechanism (at the current level of knowledge) is shown below.

(Singh et al, 2012)

Figure 4: A generalized animation of the bonding process believed to be responsible for the SPD particles

adhering to the surface of samples. Note a) 5ns after contact, b) 20ns, c) 35ns, d) 50ns. In the last two


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images jetting of the material begins as the particle nears its melting point and begins to flow outwards like

a viscous liquid due to the pressure field at the point of impact, however it does not in fact melt.

A typical SPD apparatus is made up of a Gas Control Module which houses the compressed gas,

either Helium or Nitrogen, typically under 1.3 – 3.5 MPa of pressure (Matthews, et al 2010). The gas is

then passed through a Powder Feeder that supplies the microscopic particles of the desired material

and is subsequently heated to 200 – 500 oC to increase the gases rate of expansion before entering

the specifically designed nozzle (Matthews, et al 2010). As mentioned the micro-particles do not melt

but will typically reach 100 – 300 oC, depending on the SPD material (Leyman 2004). The Supersonic

Nozzle then accelerates the gas and particles further, directing the particles onto the target

specimen and the nozzle is able to scan the desired area allowing a layer of uniform thickness to be

deposited. A simple of diagram of such an apparatus is shown below.

Figure 5: A standard set-up for the Supersonic Particle Deposition process

The particles utilized may be metallic, ceramic or polymer however the ‘powder’ (collection of

microscopic particles) used in SPD for repairing alluminium alloy aircraft skins is generally required

to be of the same type of material as the target specimen. As the micro-particles act to fill in the

blended out material the properties of the applied SPD are desired to have similar properties to the

specimen to be repaired, such as Modulus of Elasticity and Poisson’s ratio, such that the stress

distribution within the repaired sample be consistent and there is no thermal mismatch. As the

particles can be deposited in thick layers in a relatively short amount of time, the process able to

deposit up to 20 kilograms of material an hour (Leyman 2004), any repair can effectively fill the entire

blendout of damaged material and hence ensure no moisture can enter the repaired site. In

addition, as R. Jones and N. Matthews have shown by testing 1.27 mm thick 2024-T3 clad

alluminium alloy specimens that have been repaired by SPD; the method is also able to increase the

structural integrity of the deteriorated material. The non-repaired specimen was found to fail at

approximately 35,000 cycles while the repaired specimen showed no evidence of crack growth after

60,000 cycles (Matthews undated). As the procedure is capable of repairing corrosion damage

without adversely affecting the target substrate and protects the damaged site from further

corrosion damage SPD is an effective and efficient method that may be able to replace the outdated

mechanically fastened doubler technique.


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1.4 Project Scope To test the capability of repairing corrosion damage holes in alluminium alloy aircraft skins using SPD

several models were created in a Computer Aided Design (CAD) program and subsequently imported

into a Finite Element Methods (FEM) analysis program to be pre-processed. During the procedure

loads and constraints were applied to the model to simulate the typical pressure and conditions that

a section of the skin of an aircraft would experience in flight. The use of FEM provides a process to

reduce the infinite number of degrees of freedom of a continuous structure into a discrete model

that can be numerically solved. The complexity is overcome by breaking the geometry up into

smaller elements and continually solving for each region of interest and thus as the element size

becomes smaller and the geometry goes towards that of a continuous structure, “the accuracy of

the results will invariably converge on that of the exact solution” (Felippa 2004). A three dimensional

crack was then input into the data received from the FEM stress analysis that simulates a naturally

occurring defect and the models simulated to undergo cyclic stresses by using the Fatigue Structural

Analysis program (FASTRAN). Fracture mechanics then define the growth of the input crack under

the simulated cyclic loading and ultimately determined when the models failed. This occurred once

the crack was found to be of a sufficient size, which was verified by the relative stress intensity

factors calculated within each specimen exceeding the critical fracture toughness of the material

applied to the models. The model is then simulated to fracture at this point and the amount of

cycles and relative growth of the crack during the ‘life’ of the specimen output from the program.

Hence by comparing the amount of cycles undergone by each model up until fracture occurs, a

measure of the success of each SPD repair can be obtained.

2. METHODOLOGY To investigate the real life application of SPD for repairing corrosion damage holes in alluminium

alloy aircraft skins computer designed models were created using a CAD program, Solidworks, and

then processed using a FEM program, FEMAP, and finally passed through a fatigue crack analysis

program, FASTRAN. The models were designed to reflect the loads and conditions that an actual

section of an aircraft skin would experience in service and hence replicate the behavior of both a

blended out baseline and SPD repaired section of an aircraft skin under typical cyclic flight loads.

2.1 Creation of the Models in Solidworks The constant dimensions applied to the models were 300mm long and 40mm wide sections and to

observe the effect of the SPD repair on the thickness of the skin, both 10mm and 5mm thick models

were created in Solidworks. To then investigate the effect of the depth of the blendout applied to

the structure an elliptical cutout was added to the models of differing depths, but constant lengths

of 50mm and spanning the width. Hence a 3mm and 1.5mm deep blendout were applied to

separate 10mm thick models and a 2mm and 1mm deep blendout applied to the 5mm thick models.

As such 4 base models were created and then subsequently altered to simulate the structure as

having been repaired by SPD. This was achieved by creating the SPD parts separately, utilizing the

geometry of the base models to determine their dimensions, and then merging the two parts

utilizing the CAD program. The 10mm thick models had an SPD section of constant thickness above

the base models of 1.5mm and the 5mm thick models included a 1mm thick SPD section and in

addition for each model the ends of the SPD parts were chamfered. These dimensions were chosen

as they are similar to that of the actual specimens of damaged alluminium skins, both SPD repaired

and standard base models, which were tested by R. Jones and N. Matthews. Thus eight models


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were created, four baseline and four simulated to be repaired via SPD, the only difference between

each model of the same thickness and blendout depth being the added section that replicates the

SPD repair, below each base model is shown alongside its SPD repaired model.

Figure 6: 300mm x 40mm x 10mm Solidworks models with 3mm deep blendouts. The base model is shown

on the left and the SPD repaired model on the right.

Figure 7: 300mm x 40mm x 10mm Solidworks models with 1.5mm deep blendouts. The base model is

shown on the left and the SPD repaired model on the right.




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2.2 Processing the Models with FEMAP Each model then underwent pre-processing in FEMAP in which they were constrained such that no

translation or rotation occurred, which mirrored the conditions of a section of an aircraft skin. A

constant pressure of 160MPa was then applied to either end of the specimens, this pressure chosen

as it is typical of a standard flight load. The properties of the differing materials applied to the

models was also defined here, the base specimen made up of a standard alluminium alloy had a

young’s modulous E= 70,000 MPa, a shear modulous G=26,000 MPa and a possions ratio, v= 0.3.

Due to the fact that in the process of depositing the particles the material undergoes some stiffening

as a result of compressive stresses imparted during the procedure the properties of the SPD repaired

sections were chosen to be E=73,000 MPa, G=28,000 MPa and a poisons ratio of 0.33. Note these

were taken from R. Jones and N. Matthews work in which they compared the force vs. deflection

curve of the SPD material with other known materials to determine its properties (Peng et al,

undated). However an important and rather odd occurrence must be noted at this stage, as although

the models were designed in Solidworks in the units of millimetres once they were imported into

FEMAP the geometry reverted to metres. As such the values applied to each model were Pa not

MPa.

The models were also meshed; to a relatively fine degree for preliminary work as the finer the mesh

the longer the computational time required to complete the analysis, and were re-meshed at a later

time once all the processes required to achieve the final results could be streamlined. At this time a

preliminary stress analysis was carried out to observe the maximum principal stress at the site

where the 3D crack is to be input for each model and additionally to display the stress distribution in

both the repaired and baseline specimens. Unfortunately the only files that can be run with the

FASTRAN program are output from the NEI Nastran analyzer and as such an analysis of all the

models was then exported to NEI Nastran. The files were then opened in the new analyzer and

certain output and result processor parameters altered to allow the correct file types to be output

which could then be utilized to obtain the files to be run in FASTRAN.

2.3 Adding the 3D Crack Using the Converter Program With the grid point stress file output from the analyzer the converter program, along with the ascii

Input file, was then utilized to add a 3D crack to the very center and at the surface of the applied

blendouts of the models. This process, however, does not add a physical crack to the FEM models

but instead uses the stress field of the uncracked bodies to produce a new set of stress fields that

have been recalculated as having a user defined crack input into the data. That is the original stress

field of the models output by the analyzer is altered to simulate the behavior of the same stress field


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with a crack applied, thus a new set of stress fields are calculated which can be utilized in the

FASTRAN program. To be consistent with the current Damage Tolerance Standards design paradigm

a 0.1mm x 0.1mm semi-elliptical (or in this case semi-circular) surface flaw was input into the data,

this type of crack and the relative dimensions were chosen to simulate a naturally occurring defect.

A diagram of such a crack is shown below.

(Jones, Pitt 2013)

Figure 10: A simple diagram of a semi-elliptical surface flaw. Note c is the major axis crack length and in the

models to be tested is applied to run parallel to the width and a is the minor axis crack length and is applied

to run parallel to the thickness.

The philosophy behind this design viewpoint is that in any structure there exist initial flaws or

damage sites introduced during manufacture or naturally occurring, and “that this damage will not

grow to a size that would endanger flight safety for the service life of the aircraft” (Jones et al,

current). As such the discipline of Fracture Mechanics is utilized to determine whether a crack within

a structure will grow under the loads and conditions applied and ultimately whether the structure

will fail. Indeed fracture mechanics is utilized within the FASTRAN program to determine the growth

of the crack under the simulated cyclic loading and when eventual failure of the models will occur.

As such an input file was generated for each model in which the node where the desired crack is to

emanate can be defined along with the relative coordinates for the major and minor crack length

axes. In addition the type of crack is defined within this file, for our models this was chosen to be

semi-elliptical, and a set of nodes and elements selected to be recalculated as the new stress field.

By selecting the set of nodes and elements desired to be analyzed the computational time required

for each analysis can be significantly reduced by choosing only certain parts of the model as defined

by the user, the selected area obviously centered on the site of the input crack. With each input file

set up and the necessary stress fields obtained the converter program can then be run which

outputs two new files that define the new stress fields with the addition of the semi-circular flaw.

These files can then be run in FASTRAN with additional user defined files that dictate the growth and

the properties applied to the crack and additionally the relevant properties of the models. The

created input file for one of the models has been supplied in the appendix for clarity. As the crack

applied is to be similar for every specimen several properties within these files will remain constant

throughout the entire analysis with only the node where the crack is to be placed and the relative

crack axis coordinates differing for each model. However due to merging the SPD models in


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Solidworks, when imported into FEMAP they were no longer centered and had varying geometrical

positions which further necessitated the calculation of each crack axes coordinates. A task that was

much simpler for the base models which were perfectly centered and required only a brief

observation to determine the correct coordinates for each crack axis.

2.4 Simulating Cyclic Loading Using FASTRAN After obtaining the files for the new stress fields from the converter program the user defined LIFE

and PROP files were set up for each individual model. However as the analysis undertaken by the

FASTRAN program is dependent on Fracture Mechanics and hence this discipline regulates the

outcome of the analysis it is convenient to review the important factors that will define when

fracture occurs in each model. The FASTRAN program continually calculates the stress intensity

factors, K, which the models experience due to the simulated input crack. Hence as the crack grows

the program utilizes the convertor output crack-included stress files to determine the relative stress

intensity factors around the crack site. K is defined as shown below

K= limr->0 ((2πr)^(1/2))σ equ. 1

(Jones, Pitt 2013)

Where r – The distance from the crack tip, σ – The Local Stress

As the models are simulated to undergo cyclic loading this value will constantly change as defined by

the R ratio which is shown below.

R= σmin/σmax= Kmin/Kmax equ.2

(Jones, Pitt 2013)

Where σmin is the minimum stress applied in the cycle and σmax the maximum applied stress. As such

Kmin is the stress intensity factor associated with the minimum applied stress and Kmax the maximum.

Hence the values of the stress intensity factors will cycle from a maximum value to a minimum value

along with the applied stress. However for any material and applied crack there exists a fatigue

threshold, ΔKthr , for which any stress intensity factor range exceeding this value will cause the

imbedded crack to grow, the definition of these values is shown below.

ΔK= Kmax - Kmin > ΔKthr The crack will grow. equ. 3

(Jones, Pitt 2013)

Furthermore if the calculated stress intensity factors are larger than the materials critical fracture

toughness, Kc, then the structure in question will fracture.

K > Kc The structure will fracture. equ. 4

(Jones, Pitt 2013)

Thus in general the stress intensity factor range determines whether or not the crack within a

structure will grow, depending on the cyclic loads applied. Then once crack growth is initiated there

will be a point at which the stress intensity factors within the structure will be large enough to cause


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failure. As such the FASTRAN program is dependent on these definitions; however the associated

crack growth can be characterized in differing ways, defined by the LIFE and PROP files. This is due

to the fact that a crack does not grow evenly throughout its life, in fact once a crack reaches a

certain length the behaviour of the crack alters and begins to grow at an increasing rate. The

geometry of a crack also determines its growth behaviour during a structures lifetime and as such

there are several different equations that define the growth of a crack within a structure pertaining

to different crack geometries. For the tested models a semi-elliptical crack was placed within the

central region of the specimens and each crack axis defined to grow to 80% of the relative model

dimensions during their life. That is the major crack axis, c, had a constant final crack length of

16mm for all specimens and the minor crack axis, a, changed with the thickness and blendout depth

of each model, being 80% of the local thickness at the crack input, this is standard practice for an

analysis of this type. Due to their complexity the LIFE and PROP files to be utilized during the

analysis were supplied with several characteristics already defined that would reflect the conditions

of the created models and the geometry of the applied crack. As such only certain values were

altered in these files throughout the analysis, a sample of the PROP and LIFE files used in one such

analysis has been provided in the appendix for clarity. As the thickness is the smallest dimension for

each model it is clear that the length of the minor crack axis, a, will mostly contribute to the fracture

of the specimens and from the LIFE file the equation defining this growth is as such.

da/dn = C1*( ΔKeff )^C2 equ. 5

(Peng 2010)

Where n – Number of Cycles, C1 – a constant, C2- a constant and ΔKeff – is the effective stress

intensity factor range.

ΔKeff = ΔK - ΔKop equ. 6

Where ΔKop = Kop – Kmin equ. 7

(Jones, Pitt 2013)

And Kop – The value of the stress intensity factor at which the crack opens for a given load cycle.

Within the LIFE file the dimensions of the model and applied crack are defined along with several

other values that will effect the constants in equation 5 which determine the behavior of the crack,

however as mentioned these values have been previously set up for the models to be tested with

only the thickness of the structure and the minor crack axis altered in the LIFE files between models.

The PROP file designates the properties of the material of the specimens and the general crack

growth rate, in this file one is able to define the growth of the major crack axis and for the models in

question this is set to da/dn = dc/dn, thus the major and minor crack axes should grow evenly. The

relative constants applied to equation 5 are also defined within this file along with the loading

conditions. However the most important part of this file is the inclusion of the Spectrum file which

dictates the cyclic loading that the models will undergo. This file contains flight load history data

taken from an actual aircraft over the course of its life, the specific craft spectra utilized in the

analysis was from an AP3C-Orion. Hence the LIFE and PROP files characterize the behavior of the

crack as defined by the properties of the material within which the crack is applied and the relative


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crack growth law selected. The spectrum file then applies the cyclic loading which the models

undergo until the crack grows to a size that causes fracture. Again the PROP file was supplied with

the important values already set up and the only changes made to this file between each model

were the relative differing dimensions of each model.

As such with the LIFE and PROP files set up for the different models and the relative stress field files

obtained from the convertor program the data was run with the FASTRAN program which output the

growth of both crack axes and the amount of cycles taken until the models fractured. This data

could then be compared and the relative success of the simulated SPD repairs quantified.

3. RESULTS

3.1 Preliminary Stress Analysis After creating the geometry of the models in Solidworks and subsequently applying the properties,

loads and constraints in FEMAP a preliminary maximum principal stress analysis was carried out on

all models to observe the stress distribution within each. This provided feedback on whether the

models had been pre-processed correctly by observing the stress distribution within each model and

comparing it to the expected profile. Additionally the reduction in stress at the site at which the 3D

crack is to be input was verified which provided insight into the expected results which would later

be compared with the final findings to determine their relative accuracy. As such the results of each

analysis have been shown below.

300mm x 40mm x 10mm Models with 3mm Deep Blendouts

Figure 11: 300mm x 40mm x 10mm Base Model with 3mm deep blendout. Maximum principal stress at site

where crack is to be input = 234.5 MPa.


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Figure 12: 300mm x 40mm x 10mm SPD repaired Model with 3mm deep blendout. Maximum principal

stress at site where crack is to be input = 143.6 MPa.

The profile of the analysis for the 10mm thick models with 3mm deep blendouts was as expected,

however it was noted that there was a sharp rise in stress at the chamfered ends of the SPD repaired

section, although this was somewhat predicted due to the steep slope of the chamfer. However

there is a marked drop in stress at the initiation of the chamfer which should offset the

concentration and hence the effect of these regions should be negligible on the final results.

However what is most notable when comparing the two is the relatively large reduction in stress

within the blended out area, the addition of the SPD section produces an even distribution of the

applied load and a clear reduction in the local stress at the crack site. By utilizing the query

command in FEMAP the maximum principal stress at the exact site around where the crack is to be

placed can be determined for each model and has been shown along with the analysis result. For

the 300mm x 40mm x 10mm models with 3mm deep blendouts a 61.2% reduction in stress was

determined at the site of the crack in the SPD repaired model.

300mm x 40mm x 10mm Models with 1.5mm Deep Blendouts

Figure 13: 300mm x 40mm x 10mm Base Model with 1.5mm deep blendout. Maximum principal stress at

site where crack is to be input = 191.1 MPa.


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Figure 14: 300mm x 40mm x 10mm SPD repaired Model with 1.5mm deep blendout. Maximum principal

stress at site where crack is to be input = 144.5 MPa.

The stress profiles produced from the analysis of the 10mm thick models with 1.5mm deep

blendouts was very similar to the previous models, containing the same interesting characteristics

and a 75.6% stress reduction determined in the SPD model at the crack site.




Figure 16: 300mm x 40mm x 5mm SPD repaired Model with 2mm deep blendout. Maximum principal stress

at site where crack is to be input = 136.8 MPa.


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Due to the reduction in thickness the 5mm thick models with 2mm deep blendouts had a somewhat

different stress profile. This was apparent mainly in the SPD repaired model as the base specimen

resembled the previous two except with a much larger concentration of stress within the blendout.

This was again predicted as this model contained the largest percentage of removed material and

hence would contain the highest concentration of stress. A most unusual aspect here, however, is

that the resultant stress in the SPD repaired models was lower at the site where the crack is to be

placed then in either of the 10mm thick models. This may be explained by the fact that the

specimen is half the thickness of the 10mm thick models and as such the SPD section incorporates a

larger percentage of the entire geometry. So while the stress at the crack site is smaller than that in

the thicker models the average distributed stress may be higher throughout the entire model. In

addition the SPD repaired section was modeled to have slightly higher properties then the base

model and as it retains a higher percentage of the geometry in the 5mm thick models it may explain

the unexpected stress distribution. The reduction in stress at the site where the flaw is to be input

for this SPD model was found to be 50.7%.




Figure 18: 300mm x 40mm x 5mm SPD Model with 1mm deep blendout. Maximum principal stress at site



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The results of the analysis of the 5mm thick models with 1mm deep blendouts were very similar to

the previous 5mm thick models, again having very similar stress profile characteristics, the relative

reduction in stress at the crack site in the SPD model found to be 68.3%.

As the preliminary stress analysis showed no anomalies it was concluded that no significant errors

had been made during the modeling process and the specimens could now undergo further

processing to produce the correct files to be used in FASTRAN. Hence with all the relevant files

created each model individually underwent the analysis procedure which provided the crack growth

history within each model and the number of load cycles the specimen underwent before fracture.

A sample of this output has been provided in the appendix for one of the tested models for clarity.

3.2 Crack Growth Analysis The relevant crack growth data output from FASTRAN was then observed to establish whether the

crack had been modeled correctly, which was determined from the characteristics of the crack

growth in both the major and minor axes. As such the size of both the major and minor crack axes

for each model was plotted against the number of cycles and has been shown below, with the

results from the models of the same thickness and blendout depth grouped for comparison.

Figure 19: The growth of each crack length axis in both the Base and SPD Repaired Models for the 300mm x

40mm x 10mm Models with 3mm deep blendouts.


40mm x 10mm Models with 1.5mm deep blendouts.


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By observing each of the above figures it is clear that the crack has grown as expected in each of the

specimens. Both the major and minor crack length axes grow at relatively the same rate which is

consistent with a semi-circular flaw that is growing symmetrically. In addition it is clear that the SPD

repaired models have a much longer lifetime then the baseline models and that the growth of the

cracks within the SPD models is much slower. However this analysis simply ensures that the crack

has grown in the desired fashion and that no unusual behavior has occurred within the models.

3.3 Crack Growth Comparison and Final Results To further investigate the effect of the SPD repair the growth of the major axis crack length in the

SPD repaired model has been compared to that in the baseline model and in addition this has been

reproduced for the minor axis crack lengths and is shown below.


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Figure 23: A comparison of the growth of both the major and minor axis crack lengths between the Base and

SPD Repaired 300mm x 40mm x 10mm Models with 3mm deep blendouts.

By observing the above figures of the crack growth in the 10mm thick models with 3mm deep

blendouts it is clear that the growth in both the major and minor axis crack lengths is much slower in

the SPD repaired models than the baseline models. Failure was found to occur in the baseline model

at 4,227,068 cycles and in the SPD repaired model at 16,508,330 cycles which is a significant

improvement.


SPD Repaired 300mm x 40mm x 10mm Models with 1.5mm deep blendouts.

The growth of each crack axis in the 10mm thick models with the 1.5mm deep blendouts was very similar to

the previous model, failure occurring in the baseline model at 5,431,358 cycles and in the SPD model at

16,719,121 cycles.


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It is apparent that there was little difference between the crack growth within the 5mm and 10mm

thick models, the cracks again growing at a much slower rate in the SPD repaired models than the

baseline models. For the 5mm thick models with the 2mm deep blendouts failure was found to

occur in the baseline model at 2,499,748 cycles and in the SPD repaired model at 7,771,675. As such

it appears that the increase in life between the two was much smaller than expected, as this

specimen had the largest amount of material removed to simulate a blended out damaged region it

was predicted that this model would have the greatest increase in life. In addition this model had

the highest percentage of maximum principal stress reduction which supports this expectation.



Once again the growth of the crack lengths within the 5mm thick models with 1mm deep blendouts

was consistent with the previous models, the baseline model failing at 3,881,021 cycles and the SPD

repaired model at 8,124,990. Hence it is clear that this SPD model had the lowest increase in life by

a significant amount, this is again inconstant with the amount of material removed from each model

and the corresponding reduction in stress determined from the preliminary analysis. The 300mm x

40mm x 10mm models with 1.5mm blendouts had the lowest percent of material removed and as

such should produce the lowest increase in life after SPD repair. As this issue has seemingly affected


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both of the 5mm models, the increase in life for both being lower than expected, it is suggested that

some issue has arisen during the modeling of these specimens.

Additionally it is clear from all of the above images that the major axis crack length never reaches its

maximum length as defined in the LIFE file, which is consistent with the prediction that the minor

axis crack length would affect the models to a greater degree as it is applied within the models

smallest dimension.

Finally all of the relevant data has been tabulated below to depict the success of each repair.

Table 1: Final Results for each Model

Model

Cycles to Base

Model Failure

Cycles to SPD Model

Failure

SPD/No SPD

Lives

300mm x 40mm x 10mm /

3mm Blendout 4227068 16508330 3.905

300mm x 40mm x 10mm /

1.5mm Blendout 5431358 16719121 3.078

300mm x 40mm x 5mm /

2mm Blendout 2499748 7771675 3.109

300mm x 40mm x 5mm /

1mm Blendout 3881021 8124990 2.094

As such it is clear that SPD is able to repair corrosion damage holes effectively, increasing the lives of

the tested models by between 2 – 4 times the lives of the baseline models. This was achieved, as

reflected by the preliminary stress analysis, by the added SPD sections ability to lower the stress

within the models which effectively reduced the calculated stress intensity factors around the crack

site and hence decreased the crack growth rate, improving the lifetime of the specimens.

4. DISCUSSION Although the results output from the FASTRAN program have shown the effectiveness of the SPD

procedure there is some inconsistency between these results and those received from the

preliminary stress analysis. The analysis undertaken with NX Nastran within FEMAP indicated that

the 5mm thick models with 2mm deep blendouts would have the greatest increase in life when

modeled to have been repaired by SPD. The reduction in the maximum principal stress at the site of

the crack was almost half the value determined in the baseline model while the 10mm thick models

with 1.5mm deep blendouts had roughly a three quarter reduction in maximum principal stress at

the site of the crack, yet the increase in life for these specimens was practically the same. In

addition the fact that the two models had similar increases in life although the 10mm thick, 1.5 mm

deep blendout models had the smallest percent of material removed out of all the specimens and


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the 5mm thick, 2mm deep blendout specimens had the largest percent suggests the results are not

completely accurate. In addition the 5mm thick models with 1mm deep blendouts had the lowest

increase in life out of all the models, yet these specimens again had a greater percent of material

removed than the 10mm thick, 1.5mm deep blendout models. Thus it seems that some problems

have occurred during the FASTRAN analyses which have reduced the relative lifetime of the two

5mm thick SPD repaired models. Indeed there were some issues involved with the NEI Nastran

analysis of these specimens as when analyzed several warnings were received about the skew angle

of the elements within the models exceeding the nominal level. These warnings were not present in

the analysis of the 10mm thick SPD repaired models and in addition did not occur in the analysis of

any of the base models. It is suggested that the problem in question is due to the fact that the SPD

section of the 5mm thick models were much thinner and hence the geometry became irregular with

sharper gradients throughout. As such there may have been difficulties with analyzing these

regions, which were not present in the NX analysis, and the grid point stress file output from NEI

Nastran may not have contained an accurate measure of all of the elements within the model. Due

to the skew angle issue these elements may have been ignored during the analysis which would

affect the output grid point stress file which was subsequently used to obtain the FASTRAN related

files. As the pre-processing that each model underwent was identical this issue was most likely

introduced during the creation of the geometry of the models within Solidworks. Unfortunately due

to several problems with the files that were utilized with the FASTRAN program the amount of time

spent on the 5mm thick specimens was much less than the 10mm thick models. All of the 10mm

thick models were analyzed before the other specimens and during the process several issues arose

which required a lot of time to resolve. As mentioned, due to the complexity of the FASTRAN

program and the associated user defined files, several files were supplied which were supposedly

pre-defined for the models to be tested and the properties and conditions applied to the specimens.

However after several time consuming analyses, which resulted in clearly incorrect output data, it

was determined that several of the defined values within the PROP file were incorrectly set up for

the models in question. Once this was corrected the 10mm thick models were analyzed with no

apparent errors, however little time was left to allow for an accurate analysis of the 5mm thick

models. As such the analysis was undertaken even though there appeared to be some irregularity in

the elements within the 5mm thick models which has most likely produced the inconsistent results.

Hence if more time were allowed a comprehensive study of the mesh applied to the 5mm thick

models could have been undertaken to determine a mesh size that would allow an accurate analysis.

By altering the mesh size within the SPD region of these models and carrying out several analyses a

correct refinement could have been determined that would have produced more accurate results. It

is suggested that with more time, or less time wasted using the incorrect files, all of the specimens

could have been modeled accurately which would have increased the SPD lives of the 5mm thick

models and the final results would have more likely shown a 3 – 4 times increase in life between the

SPD repaired and base models.

The project itself had some limitations, as only baseline and SPD repaired models were compared. It

would have been relatively simple to create a further set of models from each base specimen that

replicated a repair of a skin using the mechanically fastened doubler method. The baseline models

could then have been compared against both an SPD repaired and a mechanically fastened doubler

repaired model and the relative success of the two different techniques contrasted. This would then

clearly show the capability of each method and reinforce the need for a move to a new repair


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technique. In addition the use of the FASTRAN program was not entirely necessary; a similar

procedure can be done by hand that does not involve the high level of complexity of FASTRAN. The

stress intensity factors around the crack tip could be manually computed from the NX Nastran

analysis and the corresponding crack growth then determined, which would be repeated iteratively

until the stress intensity factors associated with the crack tip exceeded the materials critical fracture

toughness, at which point failure would be siumlated. This procedure would be much clearer than

using FASTRAN as any irregularities would be obvious when computing the data, on the other hand

when utilizing the program it was found that when any issues arose it would simply shut down

without alerting the user as to why. Hence the mentioned problems that arose with FASTRAN were

impossible to define with the limited knowledge of the program possessed as eventually these issues

were resolved by observing the FASTRAN process in dos.prompt, which is out of the author’s skill

level. However as some of the models contained over 500 data points this method would have most

likely proved too time consuming, although this process may be suitable for models of smaller

thickness, which would fail at a quicker rate and hence produce less data points that require

computing.

Finally a further investigation could have been carried out during the project on the interfacial layer,

which is the extremely thin layer between the SPD material and the base material. As mentioned

the bonding process involved with SPD is relatively poorly understood, however several studies have

been done on the contact layer that exists at the boundary between the SPD material and the target

material. Metallurgical images show an apparent mixing of the two materials which has prompted

questions into the properties of the interfacial layer. By modeling this layer between the base and

the created SPD repaired section a comprehensive observation of the behavior of this material

under the applied stresses could be obtained which would further the knowledge of this relatively

unknown phenomenon.

5. CONCLUSIONS The project was undertaken to verify the ability of SPD to repair corrosion damage holes in

alluminium alloy aircraft skins and was found to be capable of improving the life of modeled aircraft

skins simulated to have been repaired by SPD by between 2 and 4 times the life of the baseline,

unrepaired models. The maximum increase in life was found to be 3.905 times greater for the SPD

repaired model compared to the corresponding baseline model and the minimum increase, 2.094

times greater. However it was apparent that some problems occurred during the analysis of certain

models and these correspond to the lower end of the calculated lifetimes, suggesting that a more

accurate analysis would in fact likely show a 3 – 4 times increase in the lives of the SPD models. This

would then reflect the work of R. Jones and N. Matthews who have undertaken experiments on

actual specimens that have been repaired by SPD and compared them to non-repaired specimens

and found a significant increase in the life of the SPD models. Due to the limited time allowed for

the analysis only a comparison between SPD repaired and baseline models could be undertaken, a

further comparison between the baseline models and a new set of mechanically fastened doubler

repaired models is recommended which would clearly show the difference in the ability of each

repair technique. In addition an investigation into the interfacial layer that exists at the boundary

between the SPD and target material would illuminate the characteristics of this poorly understood

region.


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6. ACKNOWLEDGEMENTS I would like to acknowledge Professor Rhys Jones for his guidance throughout the project.

In addition I would also like to acknowledge Dr. Daren Peng for his help, guidance and unwavering

patience.

7. REFERENCES Callister W.D Jr, 2007, Materials Science and Engineering an Introduction, 7

th Edition, John Wiley & Sons Inc.,

New York, United States, pp. 623 – 624.

Centreline Technology 2013, Cold Spray Coatings, Supersonic Spray Technology, viewed 03 October, 2013,

http://www.cntrline.com/en/technology_full.php?page=CE43000&rp=4.

Corrosion Technology Laboratory undated, Fundamentals of Corrosion and Corrosion Control, NASA Kennedy

Space Centre, viewed 03 October, 2013, http://corrosion.ksc.nasa.gov/corr_fundamentals.htm.

Felippa, C.A, 2004, Introduction to Finite Element Methods, University of Colorado, Boulder, Colorado.

Ginzel, R.K, Kanters, W.A, 2009, Pipeling Corrosion and Cracking and the Associated Calibration Considerations

for Same Side Sizing Applications, Eclipse Scientific Products Inc., viewed 09 October 2013,

http://www.ndt.net/article/v07n07/ginzel_r/ginzel_r.htm.

Jones, R, Chiu, W.K, Pitt, S, Peng, D, Current, Structural Integrity and Damage Tolerance Design, Rail CRC.

Jones, R and Pitt, S 2013, Damage Tolerance and Airworthiness, MAE4408 Lecture Notes, Monash University

Melbourne.

Leyman F. Phillip 2004, Supersonic Particle Deposition (Cold Spray), Research Laboratory Weapons and

Materials Research Directorate US Army, viewed 14 August, 2013,

http://www.asetsdefense.org/documents/Workshops/24thCadmiumPlatingMeeting/14.%20Leyman%20HCAT

%20Cold%20Spray%20Presentation.pdf.

Mathews N 2010, Design Engineering in a SRP Environment, Roseband Engineering, viewed 10 August, 2013,

http://www.defence.gov.au/dgta/Documents/DAVCOMP/SDE%20Symposium/2010/Supersonic%20Particle%2

0Disposition.pdf.

Matthews, N, Jones, R, Elston, J, Cairns, K, Baker, J, Wadsley, B, Pitt, S, undated, ‘SPD Repairs to Thin

Aluminium Structures’; International Congress of the Aeronautical Sciences, vol. 28, pp 1 – 9.

Net Composites 2013, Types of Repair, Abaris Training Resources, inc, viewed 03 August, 2013

http://www.netcomposites.com/guide/types-of-repair/70.

Newman, J.C Jr, 1992, FATRAN-II A Fatigue Crack Growth Structural Analysis Program, NASA Technical

Memorandum 104159, Langley Research Centre, Hampton, Virginia.

Peng, D, Walmsley B, Matthews, N and Jones R, undated, FATIGUE ASSESSMENT OF SPD REPAIRS TO

CORROSION DAMAGE, Rosebank Engineering and Monash University Australia.

Singh, H, Sidhu, T.S, Kalsi, S.B.S, 2012, Cold Spray Technology: Future of Coating Deposition Processes, Guru

Nanak Dev University, Shaheed Bhagat Singh College of Engineering and Technology, Amritsar College of

Engineering and Technology.

http://www.cntrline.com/en/technology_full.php?page=CE43000&rp=4

http://corrosion.ksc.nasa.gov/corr_fundamentals.htm

http://www.asetsdefense.org/documents/Workshops/24thCadmiumPlatingMeeting/14.%20Leyman%20HCAT%20Cold%20Spray%20Presentation.pdf

http://www.asetsdefense.org/documents/Workshops/24thCadmiumPlatingMeeting/14.%20Leyman%20HCAT%20Cold%20Spray%20Presentation.pdf

http://www.defence.gov.au/dgta/Documents/DAVCOMP/SDE%20Symposium/2010/Supersonic%20Particle%20Disposition.pdf

http://www.defence.gov.au/dgta/Documents/DAVCOMP/SDE%20Symposium/2010/Supersonic%20Particle%20Disposition.pdf

http://www.netcomposites.com/guide/types-of-repair/70


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CycloContractor 2010, 1963 Airstream Safari: Patching Holes, Wiring, Insulation, viewed 08 December,

2013,http://cyclocontractor.wordpress.com/2010/03/02/1963-airstream-safari-patching-holes-wiring-

insulation/.

Wanhill, R.J.H, 2002, Milestone Case Histories in Aircraft Structural Integrity; National Aerospace Laboratory

Peng, D, 2010, Running the Fatigue Life Estimating Code, Monash University, Melbourne.

http://cyclocontractor.wordpress.com/2010/03/02/1963-airstream-safari-patching-holes-wiring-insulation/

http://cyclocontractor.wordpress.com/2010/03/02/1963-airstream-safari-patching-holes-wiring-insulation/


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8. APPENDICES Files used and output for 300mm x 40mm x 10mm SPD Model with 3mm deep blendout, provided

for clarity.

Input File

spd103 !Nastran Name

3 !flag_dim

no !ANALYSE ALL THE ELEMENTS (Y/N)

nodes !node list exported from FEMAP

ele !element ids LIST EXPORTED FROM FEMAP

m !unit

1 !HOW MANY CRACKS ARE IN THE STRUCTURE.

28698 !THE LIST OF NODES WHERE A CRACK EMINATES

0.013725 0.010217 -0.0094144 !input x, y and z coord. of the ith crack at major axis.

0.013725 0.010117 -0.0094244 !input x, y and z coord. of the ith crack at minor axis.

2 !type of crack: [1]-Embedded,[2]-Semi-ellpitical,[3]-Corner.

0 !symmetrical about Major axis of the crack (1 symmetry and 0 unsymmetrical)

0 !symmetrical about Minor axis of the crack (1 symmetry and 0 unsymmetrical)

0 !symmetrical about Plane in which the the crack exists, eg z=0 (1-symmetry and 0-

unsymmetrical)

Life File

0

0.0001 0.016 5 <-- MAXIMA OF THE CRACK

0.0001 0.0056 5 <-- MINIMA OF THE CRACK

-666 <-- ENTER outer RADIUS FOR CIRCUMFERENTIAL CRACK OR -666=INFINITE

-666.0 <-- ENTER outer RADIUS OF LACING MEMBER -666 IF NONE

1.007 <-- ENTER WALL THICKNESS

0.04 <-- ENTER WALL WIDTH


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1.000 1.000 <-- ENTER NOTCH RADIUS

1.000 <-- ENTER CURVATURE

1 <-- 1-TENSION 2-BENDING 3-NEWMAN NOTCH 4-DAREN NOTCH

2 <-- 1-mm 2=m

0 0 0 0 0 <-- ENTER A RESIDUAL STRESS IN MPA (0 IF NONE)

1 <-- STRESS SCALE FACTOR

0.0 <-- INITIAL MESH REGION TO IGNORE

0.02D0 <-- TOLERANCE CLOSE TO A/C=1

0 <-- (-1 or 1)-(SADDLE POINT) 0-(NO SADDLE POINT)

0 <-- (1) DISPLACE K SURFACE PLOT (0) TURNS PLOT OFF

0 <-- (1) NONSYMMETRICAL CRACK GROWTH (0) SYMMETRICAL

1 <-- (1) EXTERNAL (2) INTERNAL CRACK IN A PIPE

0 <--=1: da/dn=c1*(dkeff-threshold)^c2,=0:da/dn=c1*(dkeff)^c2, =2: Mod. Forman's

100 <-- k-lowerkvalue

1. <-- Constant a (mm)

1.788 <--threshold MPa(m)^0.

0 <--N value Keff^(1-N)*Kmax^N

0.000102 <--a0

Prop File

P3C Spectrum Loading

361RU.s

Al 7010-T73651

434.0 510.0 70000.0 0.30 1.80 0 0 1.0

1

1.86e-9 2 0.11 0 111 111 0.0 0.01

0 0


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10 10 1 0 0.01

4 0 200 1 8 0 0

0.04 0.007 0.0001 0.0001 0.0001 0.0001 0.0 0.0

0.016

52 8

0 0.0

977 977 0 0

0.675

0.0 0.0 0.0 0.0

FASTRAN Output (shortened)

BLOCK C A/T CYCLES ALP KO/KMAX DKC DC/DN DKA DA/DN

25 0.1006E-03 0.0144 29319 0.000 2.37 0.143E-09 2.15 0.108E-09

57 0.1016E-03 0.0145 67431 0.242 2.37 0.581E-10 2.15 0.418E-10

89 0.1025E-03 0.0145 105638 0.371 2.37 0.120E-11 2.15 0.302E-12

119 0.1036E-03 0.0147 142082 0.249 2.37 0.803E-10 2.15 0.588E-10

150 0.1046E-03 0.0148 179202 0.097 2.37 0.213E-09 2.15 0.163E-09

182 0.1055E-03 0.0149 217314 0.264 2.37 0.224E-10 2.15 0.147E-10

213 0.1063E-03 0.0149 255484 0.246 2.37 0.512E-10 2.15 0.362E-10

245 0.1071E-03 0.0150 293791 0.263 2.37 0.140E-09 2.15 0.105E-09

276 0.1080E-03 0.0151 330549 0.306 2.38 0.000E+00 2.15 0.000E+00

307 0.1089E-03 0.0152 367836 0.369 2.38 0.268E-11 2.15 0.104E-11

338 0.1098E-03 0.0153 405021 0.241 2.38 0.112E-09 2.15 0.828E-10

369 0.1107E-03 0.0154 441935 0.239 2.38 0.122E-10 2.15 0.723E-11

401 0.1115E-03 0.0155 480338 0.232 2.38 0.782E-10 2.15 0.565E-10

431 0.1123E-03 0.0156 516229 0.250 2.38 0.378E-10 2.15 0.259E-10

460 0.1130E-03 0.0156 551655 0.193 2.38 0.106E-09 2.15 0.776E-10


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490 0.1140E-03 0.0157 587989 0.194 2.38 0.148E-11 2.15 0.401E-12

521 0.1148E-03 0.0158 624575 0.246 2.38 0.152E-09 2.15 0.114E-09

13477 0.5218E-02 0.6621 16171830 0.258 15.86 0.618E-08 15.24 0.566E-08

13497 0.5280E-02 0.6701 16194867 0.184 15.97 0.126E-08 15.33 0.115E-08

13516 0.5346E-02 0.6788 16217708 0.234 16.08 0.905E-09 15.42 0.820E-09

13536 0.5404E-02 0.6864 16241785 0.247 16.18 0.121E-07 15.51 0.111E-07

13553 0.5475E-02 0.6955 16262076 0.251 16.30 0.937E-08 15.61 0.854E-08

13571 0.5540E-02 0.7040 16284822 0.257 16.41 0.113E-07 15.70 0.103E-07

13590 0.5607E-02 0.7127 16307196 0.273 16.52 0.403E-08 15.80 0.365E-08

13610 0.5679E-02 0.7220 16331306 0.000 16.64 0.147E-07 15.90 0.134E-07

13629 0.5759E-02 0.7324 16353915 0.126 16.78 0.133E-07 16.01 0.121E-07

13649 0.5828E-02 0.7412 16377917 0.261 16.89 0.907E-08 16.10 0.819E-08

13668 0.5904E-02 0.7510 16400380 0.328 17.02 0.835E-09 16.21 0.743E-09

13686 0.5971E-02 0.7597 16422107 0.253 17.13 0.114E-07 16.30 0.103E-07

13704 0.6070E-02 0.7723 16444143 0.240 17.29 0.824E-08 16.43 0.739E-08

13723 0.6152E-02 0.7828 16466554 0.268 17.43 0.928E-08 16.55 0.830E-08

13743 0.6229E-02 0.7926 16490019 0.144 17.56 0.132E-07 16.65 0.118E-07

USER DEFINED FINAL CRACK SIZE REACHED:

CRACK LENGTH = 0.0063 CRACK DEPTH = 0.0056 TOTAL CYCLES = 16508330