User’s Manual - Quest Integrity Group User Manual.pdfdiagram (FAD) calculations in accordance with...

User’s ManualVersion 3.0

2465 Central Ave. Suite 110Boulder, Colorado USA 80301

+1 (303) 415 1475www.QuestReliability.com

http://www.questreliability.com/

ContentsContents...........................................................................................................................................2

Installation and Basic Operation......................................................................................................6

Overview......................................................................................................................................6

Minimum System Requirements .................................................................................................6

Installation ...................................................................................................................................6

Licensing.......................................................................................................................................7

Getting Started ............................................................................................................................7

Analysis of Cracks – General Guidelines..........................................................................................9

Geometry Input for Cracks ..........................................................................................................9

Dimensions Window (Crack Analysis)........................................................................................10

Stress Input for Crack Analysis...................................................................................................11

Uniform and Linear Stress Distributions................................................................................11

Weight Function Method.......................................................................................................13

Inferring the Stress Distribution from Internal Pressure.......................................................13

Material Properties for Crack Analysis ......................................................................................14

Parametric Analysis....................................................................................................................14

Crack Analysis Tools...................................................................................................................16

The K Calculator .....................................................................................................................16

The Reference Stress Calculator ............................................................................................16

Fracture Analysis Using the FAD Method......................................................................................17

The Failure Assessment Diagram (FAD).....................................................................................17

FAD Analysis Options .................................................................................................................17

Stress Input for a FAD Analysis ..................................................................................................19

Primary Stresses.....................................................................................................................19

Installation and Basic Operation

User’s Manual Page 3 of 70Signal Fitness-For-ServiceVersion 3.0

Secondary and Residual Stresses...........................................................................................20

Material Properties for a Fracture Analysis...............................................................................21

Tensile Properties ..................................................................................................................21

Stress-Strain Curve.................................................................................................................21

Toughness Parameters ..........................................................................................................21

Charpy Correlations ...............................................................................................................22

Defining Toughness as a Function of Temperature...............................................................23

Master Curve Approach for Toughness.................................................................................23

Assessing a Known Flaw.............................................................................................................24

Assessing Limiting Flaw Size ......................................................................................................24

Assessing Limiting Load .............................................................................................................24

Monte Carlo FAD Analysis .........................................................................................................25

Normal Distribution ...............................................................................................................27

Log-Normal Distribution ........................................................................................................27

Weibull Distribution...............................................................................................................27

Uniform Distribution..............................................................................................................27

Triangular Distribution...........................................................................................................28

Ductile Tearing Analysis.............................................................................................................29

Fatigue Crack Propagation Analysis...............................................................................................32

Crack Growth Options ...............................................................................................................32

Growing a Crack to Failure.....................................................................................................32

Growing a Crack to a Specific Size .........................................................................................32

Growing a Crack for a Specific Number of Cycles..................................................................32

Reporting Units for Fatigue Life.............................................................................................32

Cyclic Stress Input (Constant Amplitude Loading).....................................................................33



Non-Cyclic Stress Input When Growing to Failure ....................................................................34

Material Properties for a Fatigue Analysis ................................................................................35

Material Property Databases for Fatigue ..............................................................................35

Paris Equation (Power Law)...................................................................................................35

Piece-Wise Power Law...........................................................................................................36

NASGRO Equation..................................................................................................................36

User-Defined Fatigue Crack Growth Relationship.................................................................37

Variable Amplitude Fatigue Analysis .........................................................................................39

Cumulative Damage Model ...................................................................................................39

Cycle-By-Cycle Integration.....................................................................................................40

Rayleigh Stress Distribution...................................................................................................40

Tabular Histogram for Cyclic Stresses....................................................................................41

Cyclic Stress Scale Factors......................................................................................................42

Environmental Crack Growth ........................................................................................................44

Creep Crack Growth.......................................................................................................................45

Assessment of Metal Loss and Corrosion Pitting ..........................................................................47

Flaw Type Window.....................................................................................................................47

Dimension Window (Metal Loss Analysis).................................................................................47

Supplemental Loads...................................................................................................................49

Thickness Data Window.............................................................................................................49

Groove or Gouge Data Window ................................................................................................52

Pitting Data Window..................................................................................................................52

Structural Discontinuity Window...............................................................................................54

Brittle Fracture...........................................................................................................................54

Level 1 Crack-Like Flaws ............................................................................................................55



Report ........................................................................................................................................56

Assessment of Creep Damage and Rupture ..................................................................................59

The Geometry Window (Creep Analysis) ..................................................................................59

The Dimensions Window (Creep Analysis) ................................................................................59

The Operating Conditions Window ...........................................................................................59

The Materials Window ..............................................................................................................59

Graphical Output (Creep Analysis) ............................................................................................61

Changing the Variables on the Plots......................................................................................61

Increasing the Number of Plotting Points .............................................................................62

Parametric Analysis (Creep Rupture) ........................................................................................63




OverviewSignal Fitness-For-Service™ is an integrated software package for Fitness-For-Serviceassessment and fracture mechanics analysis. This software performs failure assessment diagram (FAD) calculations in accordance with either API 579 or BS 7910 methodologies. Signal FFS™ also performs assessments of fatigue crack growth, brittle fracture, local metal loss, pitting corrosion, creep damage, and creep crack growth in accordance with both current and upcoming releases of API 579-1/ASME FFS-1 2007 Fitness-For-Service.

A highly flexible parametric study capability allows users to quickly evaluate a wide range of what-if scenarios. For fracture assessments with the FAD approach, a Monte Carlo probabilistic module can be used to quantify risk and the effect of uncertainty in input parameters.

Signal FFS includes extensive material properties databases for fatigue crack propagation and creep rupture. In the case of fatigue crack propagation, the user has a choice of NASGRO (from NASA) or BS 7910 material constants. Material constants for creep analysis are based on the MPC Omega method and were taken from API 579 Appendix F.

An intuitive WindowsTM interface makes navigation through the program straightforward. Of course, this software in not intended for a layman. Signal FFS should be used only by a competent engineer with a working knowledge of fracture mechanics and Fitness-For-Servicemethodology.

Minimum System RequirementsOperating System Windows 2000, XP, or VistaHardware PC with 200 MHz or higher clock speed, 64

MB RAM, 600x800 or higher screen resolution, 50 MB of available disk space

Installation1. We recommend that you exit all programs before installation.

2. Insert the CD into the drive. If auto-run is enabled on your PC, an installation menu will appear. Click the button labeled Install Signal FFS to begin the installation. If auto-run is not enabled, you can run SignalFFS_Setup.exe from the CD directly to initiate the installation.

3. The installation wizard will guide you through the installation.



4. Select a destination directory and program group when prompted, or use the default. NOTE: do not install Signal FFS to multiple different locations on your hard drive. This could cause problems with future updates or cause the program to not function correctly.

5. You may need to restart your computer in order to complete the installation process. The install program will tell you if this is necessary.

LicensingThe demonstration version of Signal FFS will allow you to access and view all of the available features, and run several of the API 579 Examples. With the demonstration version you will be unable to run custom analyses.

Once you have purchased Signal FFS, to unlock the full functionality of Signal FFS, you will need to apply your license key to the installation directory (typically, c:\Program Files\Quest Reliability\SignalFFS). Detailed instructions will be provided at time of purchase.

Note: if you are upgrading from Fracture Graphic™ or PetroFit™, a new license key is required. Please contact us at [email protected] or +1-303-415-1475.

Getting StartedSignal FFS is launched like any other Windows program. You can find the Signal FFS shortcut in the Programs item in the Start menu under the program group specified during installation (by default, this is “Quest Reliability”). Alternatively, you can open the application directory with Windows explorer and double-click on the SignalFFS.exe executable.

After startup, a Home window is displayed. At this point, the user selects the type of analysis (brittle fracture, corrosion/metal loss, cracks/crack-like flaws or creep rupture) and selects the system of units. , and various options associated with each type of analysis. At subsequent windows, the user inputs information about geometry, dimensions, loading, and material properties.

Depending on the type of analyses, there are additional input windows, some of which have multiple tabs. Navigation through the input windows is easy, and can be accomplished in one of three ways of ways. The forward and reverse arrows (which point to the right and left, respectively) move the user to the next and previous step. The tabs on each window offer a second means of navigation. Finally, clicking on the buttons on the navigation bar along the left-hand side of the screen allows the user to move quickly between input windows. Note that the available options on the navigation bar will vary depending on the type of analysis selected.

Clicking on the Data Sheet button will advance the user to a tabbed window that contains all of the input data that have been previously entered. Data are displayed on a spreadsheet grid, and values can be edited directly in the spreadsheet. All data grids are fully functional spreadsheets

mailto:[email protected]



that support Excel formula syntax, as well as Cut, Copy, Paste, Copy Down and Copy Rightcommands. These commands are available in the Edit menu.

Clicking the Run button executes the analysis. Results are displayed graphically and in tabular form.

Signal FFS files have a .ffs extension, but files from Fracture Graphics (.fgr) and PetroFit (.pft) can also be opened. New, Open, Save, and Save As commands are available in the File menu, as with most WindowsTM programs. File opening and saving commands can also be accessed from the tool bar along the top of the window as well as from standard keyboard shortcuts (e.g. Ctrl-S to save and Ctrl-O to open).

Home window

Analysis of Cracks – General Guidelines



Geometry Input for CracksThe Geometry window is shown below. At the first tab, the component geometry, crack location/orientation, and the crack shape are selected. At the second tab, information about the weld (if applicable) is input. This latter set of inputs is used to estimate weld residual stresses for the fracture analysis. It has no effect on the crack propagation rates for fatigue and environmental cracking analyses.

The main Geometry window



The Weld tab of the Geometry window

Dimensions Window (Crack Analysis)The dimensions of the component and the crack are input at this window. In the case of a crack propagation analysis (fatigue or environmental cracking) the crack dimensions may be the initial, final, or both, depending on the type of analysis.



The Dimensions window for crack analysis.

Stress Input for Crack Analysis

Uniform and Linear Stress DistributionsA stress gradient can be treated by inputting a linear, or up to a 4th order polynomial stress distribution. A linear stress gradient can be input in one of three ways. A membrane and bending component can be defined or the minimum and maximum values at either end can be specified. Alternatively the coefficients of a linear equation can be input. The coefficients on the polynomial have units of stress.

The origin (x = 0) of the stress distribution is defined at the crack mouth in the case of a surface-breaking crack, at the surface nearest the crack in the case of a buried flaw, or by the internal/external orientation chosen in the case of through-wall cracks in components such as cylinders and spheres.

It is important to note that the stress distribution to be input corresponds to the stress at the flaw location in the absence of the flaw. The redistribution of stress that results from the introduction of a crack is taken into account in the K solution.



Linear stress distribution input.

Polynomial stress distribution input.



Weight Function MethodThe weight function method uses the Principle of Superposition to calculate stress intensity factors for arbitrary loading. For geometries where weight functions are available, stresses obtained directly from finite element results can be input into Signal FFS.

The weight function option is selected at the Stresses window for each of the stress types (primary, secondary, etc.). An input window, as illustrated below, will be displayed. IMPORTANT NOTE: you must input the stress distribution that corresponds to the uncrackedcondition. The origin (x = 0) is defined at the crack mouth, and distances are absolute (inches or millimeters) rather than dimensionless (x/t). The full through-thickness stress distribution should be input rather than a partial distribution.

A graphical display of the weight function or any of the stress distributions that have been input can be displayed by selecting the Show Stress Distribution option from the Analysis menu on the main window.

Input window for weight functions.

Inferring the Stress Distribution from Internal PressureFor cylindrical and spherical shells, the through-wall stress distribution can be determined automatically by inputting the internal pressure. When the ratio of the inside radius, Ri, to wall thickness, t, is less than 5, a weight function is used to determine the stress intensity solution corresponding to the hoop stress. For larger Ri/t, the hoop stress distribution is represented by a cubic polynomial. For internal cracks, the pressure loading on the crack is included in the KI



calculation. The methodology for computing hoop stress can be modified by selecting Analysis Options from the Analysis menu.

Material Properties for Crack AnalysisThe Material Properties window is shown below. For a fracture analysis, the tensile properties and fracture toughness must be input. For a fatigue analysis, the appropriate material constants for the crack growth law must be input. In the latter case, two material property databases are available.

The Material Properties window for a crack analysis.

Parametric AnalysisTo perform an analysis while systematically varying one or more input values, select the parametric analysis option under the Analysis menu. A window will be displayed that offers a list of variables. Check the items that you wish to include in the analysis. Enter the values for each case in the spreadsheet. When you click the Run button, the analysis will be performed with the input values in the first row, repeated for the values in the second row, and so on. You may use spreadsheet formulae to link variables to one another. For example, suppose that you wish to vary flaw size but maintain a 5:1 ratio between flaw length and flaw depth. You could enter flaw length values in the first column and enter



= A1/5

in the first row of the second column, and then use the Copy Down command in the Edit menu to paste this formula in subsequent rows.

The number of cases that can be run in a parametric study is limited only by the number of rows in the spreadsheet (approximately 16,000).

Selection of variables to include in the parametric analysis.



Inputting values for the parametric analysis. Variables can be related through spreadsheet formulae.

Crack Analysis Tools

The K CalculatorSelecting K Calculator from the Tools menu reveals a tabbed window at which the user can view stress intensity values for a range of crack sizes. In order to use the K calculator, the user must first input the geometry, dimensions and stresses.

The Reference Stress CalculatorSelecting Reference Stress Calculator from the Tools menu reveals a tabbed window at which the user can view stress intensity values for a range of crack sizes. In order to use the reference stress calculator, the user must first input the geometry, dimensions and stresses.

Fracture Analysis Using the FAD Method



The Failure Assessment Diagram (FAD)This is a two-criteria failure model that considers the full range of behavior from brittle fracture to ductile overload. For a given structure that contains a crack-like flaw, a toughness ratio, Kr, is computed and plotted, along with a stress ratio (Lr). The failure assessment diagram (FAD) is a locus of points that correspond to critical combinations of toughness ratio. If the assessment point for the structure of interest lies inside the FAD (i.e., below the failure locus curve), the structure is considered safe. The analysis predicts failure when the point falls outside of the FAD.

FAD output. The assessment point falls inside the FAD curve in this case.

FAD Analysis OptionsThe fracture analysis can be performed with either the API 579 or BS 7910 FAD methodologies. In both cases, there are three choices for the FAD curve. The standard FAD curve can be used (API 579 Level 2, which is equivalent to the BS 7910 Level 2A FAD), or a material-specific FAD



that requires a stress-strain curve can be selected. Alternatively, a user-defined FAD curve can be input (see below).

Note that both the API 579 and BS 7910 procedures use the same FAD curves. However, there are subtle differences in the way in which the two methodologies compute the assessment point. In the Signal FFS software, the KI and reference stress solutions from API 579 are used irrespective of the analysis procedure that is selected. The reason for this is that the compendia of KI and reference stress solutions in API 579 are far more extensive and up to date than the limited collection of solutions in BS 7910.

The FAD analysis can be performed either with a single toughness value or with a resistance curve.

Fracture Analysis tab on the Home window.



Input window for User-Defined FAD.

Stress Input for a FAD Analysis

Primary StressesPrimary stresses are the result of externally applied forces and moments. Stated another way, primary stresses are load-controlled stresses. An example of primary stress is the shell membrane stress due to internal pressure in a vessel or pipe.

In an FAD analysis, primary stresses are used to calculate the load ratio, Lr, which is the horizontal axis of the FAD.



Primary stress input.

Secondary and Residual StressesSecondary stresses are displacement controlled and may relax with plastic deformation. Residual stresses due to welding and other sources are treated the same as secondary stresses in a FAD analysis. Secondary and residual stresses are not included in the calculation of the load ratio, Lr.

While most pressure vessel and piping design codes treat all thermal stresses as secondary, it is not necessarily appropriate to do so in a FAD calculation. For example, thermal expansion loads in a piping system are indistinguishable from primary loads as far as a crack is concerned. When the “gage length” over which a displacement is imposed is long, such as in the piping system example, there is virtually no difference between load control and displacement control. Local thermal stresses, such as those due to a through-wall temperature gradient, can be treated as secondary in an FAD analysis. Long-range thermal loads should be treated as primary.

On the Primary Stress tab, there is an option for selecting either the default weld residual stress distribution, or a user-defined distribution, which may include secondary stresses, residual stresses, or both. Both API 579 and BS 7910 provide recommended residual stress distributions for common welded joint configurations. Both sets of distributions have been programmed into Signal FFS, and the appropriate residual stress distribution will automatically be selected if the Default option is selected for the secondary/residual stress input.



Some of the API 579 expressions for weld residual stress are a function of the heat input of the final pass. The Heat Input Calculator, which can be selected from the Tools menu or the Weldtab of the Geometry window, computes heat input given voltage, current, and travel speed.

Material Properties for a Fracture Analysis

Tensile PropertiesYield strength and tensile strength are required to define the x axis of the FAD. Tensile properties also form the basis of the default assumptions for weld residual stresses.

Stress-Strain CurveThe material-specific FAD, which is one of the Level 3 options in both API 579 and BS 7910, requires that the stress-strain curve be specified. In Signal FFS, the user can define the stress-strain curve with Ramberg-Osgood coefficients or he/she can enter the curve in tabular form. Spreadsheet formulae can be used to enter a stress-strain relationship other than Ramberg-Osgood. A true stress – true strain curve should be input.

Stress-strain curve input for a material-specific FAD.

Toughness ParametersFracture toughness data can be specified in terms of critical crack tip opening displacement (CTOD), J integral, or stress intensity factor (K). Alternatively, several Charpy correlations are available to infer toughness.



Input of tensile and fracture toughness values.

Charpy CorrelationsWhen fracture toughness data are not available, Signal FFS offers a choice of correlations between Charpy data and fracture toughness. For ferritic steels in the ductile-brittle transition region there is a choice between API 579 lower-bound correlations or the Barsom-Rolfe two-step correlation. There are actually two API 579 lower-bound correlations: one for normal situations and one for dynamic loading or hydrogen-charged steels. For upper shelf behavior, or for materials that do not exhibit a ductile-brittle transition, the Rolfe-Novak correlation may be used.

For Monte Carlo analyses, a correlation between the 20 ft-lb (28 Joule) transition temperature and the toughness Master Curve index temperature (To) is available.



Charpy correlations to fracture toughness.

Defining Toughness as a Function of TemperatureAt the first tab of the Material Properties window, the user has the option of specifying toughness as a function of temperature. To take advantage of this feature, click on the appropriate check box and then click the Define Eqn. button. For toughness based on Charpy energy, the temperature dependence is defined by a hyperbolic tangent equation. For other toughness parameters, the Fracture Toughness Master Curve defines the temperature dependence. Both equations are appropriate only for ferritic steels.

The Master Curve approach defines not only the temperature dependence, but also the statistical distribution of toughness. Consequently, the user must specify the desired probability level (e.g. median, 10% lower bound, etc.). The user must also specify an upper shelf cut-off for the equation.

Master Curve Approach for ToughnessThe temperature dependence of fracture toughness as well as its statistical distribution can be defined by the master curve approach, which is described in a new ASTM standard. This approach applies only to ferritic steels in the ductile-brittle transition region.

The Master Curve is defined entirely by a reference temperature, To, which indexes the relative position of the ductile-brittle transition region. This approach can be applied in a probabilistic analysis such as the Monte Carlo method. The Master Curve can also be used to define a toughness-temperature relationship in a deterministic analysis.



Assessing a Known FlawThis option is specified at the first tab of the Geometry window. The user specifies flaw dimension as well as stress and material properties. The program then computes a point on the failure assessment diagram to determine whether or not the specified flaw is acceptable.

Assessing Limiting Flaw SizeThis option is specified at the first tab of the Geometry window. The user specifies stress and material properties but not flaw dimensions. The program computes and plots the combinations of flaw length and depth that correspond to assessment points that lie on the failure assessment diagram.

Limiting flaw curves. (The legend was edited by right-clicking on the graph and selecting Edit Chart Data.)

Assessing Limiting LoadThis option is specified at the first tab of the Geometry window. The user specifies a base stress distribution, material properties and flaw dimensions. The program computes a scaling factor for the given stress distribution which would cause a flaw of the given length and depth to produce an assessment point that lies on the failure assessment diagram.



Monte Carlo FAD AnalysisInput data for a fracture analysis typically contain a high degree of uncertainty. Signal FFS allows the user to input the probability distribution of a given property which is then varied over a series of Monte Carlo trials. The results of this trial can then be displayed both numerically and graphically.

The user chooses the parameters to be varied in the analysis by selecting the Monte Carlo option from the Analysis menu and then checking the desired input values. The user then defines the statistical distribution for each variable. Signal FFS supports five types of probability distributions:

Normal (Gaussian)

Log Normal

Weibull

Triangular

Uniform

These distributions are described below.

Signal FFS permits two types of Monte Carlo analysis. The standard analysis permits the user to link variables in the data spreadsheet. Suppose, for example, that operating temperature is chosen as a random variable. Spreadsheet formulae can be used to express material properties as a function of temperature. A random temperature is then inserted into the spreadsheet on each Monte Carlo trial, and the corresponding temperature-dependent values are then read from the spreadsheet.

The fast Monte Carlo analysis does not permit these spreadsheet links. While the same parameters can be varied in both, the fast analysis checks the data spreadsheet only once for the initial values to be used in the analysis. However, when temperature and toughness are both random variables, and the toughness distribution is characterized by the Master Curve approach, the fast Monte Carlo analysis will account for the random temperature in the toughness variation.



Variables to be included in the Monte Carlo Analysis.

Statistical distribution input for Monte Carlo analysis.



Normal DistributionThe normal or Gaussian distribution has a characteristic bell curve shape. The probability density function for a variable x is given by

p xx

( ) exp

1

2

1

2

2

where and are the mean and standard deviation of x, respectively.

Log-Normal DistributionThe logarithmic normal distribution is virtually identical to a conventional normal distribution, except that the variable x is replaced by its logarithm. The probability density function is given by

2

10log

2

1exp

2

1)(

x

xxp

where and are the mean and standard deviation of log10 (x), respectively. The latter quantity is also known as the log standard error (LSE). Note that the above distribution is written in terms of Base 10 logarithms, and thus the LSE specified by the user must be Base 10.

Weibull DistributionThe cumulative probability function for the three-parameter Weibull distribution is as follows:

P xx x

x xo

1 exp min

min

where xmin is the minimum, xo is the Weibull mean, and is the Weibull slope. A two-parameter Weibull distribution corresponds to the special case where xmin = 0. The above expression reduces to an exponential distribution when = 1.

Uniform DistributionThe probability density function for the uniform distribution is illustrated below. The variable xmust lie between xmin and xmax, and all values in this range are equally likely.



Xmin

PROBABILITYDENSITY

Xmax

X

The uniform distribution.

Triangular Distribution

The probability density function for the triangular distribution is illustrated below. The variable x must lie between xmin and xmax, with xmode being the most likely value.

Xmin XmaxXmode

PROBABILITYDENSITY

The triangular distribution.



Output of a Monte Carlo analysis on the FAD

Ductile Tearing AnalysisDuctile materials whose toughness is defined by a resistance curve exhibit stable tearing prior to final failure. The analysis of such behavior involves plotting a series of points on the failure assessment diagram corresponding to various amounts of crack growth. If all points fall inside the FAD, no tearing is predicted. If the assessment point corresponding to the initial crack size falls outside of the FAD but points corresponding to finite amounts of crack growth lie inside the FAD, the analysis indicates some stable tearing. Instability is predicted when all points are outside of the FAD and the locus of assessment points is tangent to the FAD curve.

The ductile tearing analysis option is selected on the Fracture Analysis tab of the Homewindow. The crack growth resistance curve is entered on the Material Properties window.



R curve input.

Kr

Lr

Increasing

Crack Size

J

a

Plotting the R curve on the FAD.



Kr

Lr

Stable Crack Growth

Ductile Instability

No Crack

Growth

Interpretation of ductile tearing analysis results.

Fatigue Crack Propagation Analysis



Crack Growth OptionsAn end-point of a fatigue analysis can be based on reaching a failure condition, a specified crack size, or a specified number of cycles. These various options are selected on the Crack Growthtab of the Home window.

Growing a Crack to FailureThe initial crack dimensions are specified, and the number of fatigue cycles required to reach failure is computed, along with the final crack dimensions. This option involves performing a fracture analysis (using the FAD method) in conjunction with the crack growth calculation. Consequently, the user is required to specify tensile properties and fracture toughness for the material of interest, as well as the appropriate primary and secondary loads.

After each increment of crack growth, the FAD coordinates corresponding to the current crack size will be computed. If the assessment point falls inside the FAD, the crack growth analysis will continue. If the point falls outside of the FAD, an iterative calculation will be performed to determine the critical crack dimensions and the cycles to failure.

Growing a Crack to a Specific SizeThe initial crack dimensions are specified, together with the final depth or final length. The number of cycles required to reach this crack dimension is then calculated. Note that the final depth and final length cannot both be specified; one can be specified and the other calculated.

Growing a Crack for a Specific Number of CyclesIn this type of analysis, the number of cycles is input, along with either the initial or final crack dimensions. If the initial crack dimensions are input, the final dimensions corresponding to the specified number of cycles are computed. If the final crack dimensions are specified, the crack growth analysis is run “backwards” to infer the initial dimensions.

Reporting Units for Fatigue LifeThe default units for a cyclic fatigue analysis are cycles. Alternatively, the user may specify a number of cycles per unit time and view the results in terms of that unit of time.



Fatigue crack growth options.

Cyclic Stress Input (Constant Amplitude Loading)The cyclic stress is defined as the maximum minus the minimum stress in a fatigue cycle. Uniform, linear, polynomial, and weight function stress inputs may be input, depending on the geometry. When there is more than one stress term (i.e., linear and polynomial cases), all terms are assumed to be in phase with one another. For example, if there are both membrane and bending cyclic stresses, both loads are assumed to cycle at the same frequency.

The R ratio is input on the Cyclic Stress tab. This value is used only if the user selects the NASGRO or BS 7910 fatigue properties. The R ratio is used to estimate the threshold stress intensity range for both the NASGRO and BS 7910 databases, and it has an influence on other crack growth constants in the case of the BS 7910 properties. If the user inputs his/her own fatigue properties, the R ratio input has no effect on the analysis.

When estimating the R ratio, be sure to consider all stresses, including primary, secondary and residual. For example, non-stress-relieved welds typically have a high R ratio in fatigue because of yield-magnitude residual stresses.

The Reference Stress Scale Factor allows the user to apply a factor of safety to the reference stress calculated during an analysis. A factor of 1.0 leaves the reference stress unchanged.



Cyclic stress input window.

Non-Cyclic Stress Input When Growing to FailureWhen growing a crack to failure in a fatigue analysis, it is necessary to input information required for the FAD calculation, including primary, secondary and residual stresses, as well as fracture toughness. For static loads such as weld residual stress, the input is handled no differently than in a standard FAD analysis. For loads that are cyclic, the peak value should be input for the FAD calculation.

In the simplest case of constant amplitude fatigue with only cyclic primary membrane stress (no secondary or residual stress), the peak primary stress is related to cyclic stress as follows:

( ) 1r m mS P R

When other stresses are present, or there is variable amplitude loading, the above expression does not apply. Consequently, Signal FFS does not assume any relationship between cyclic stress and primary stress. These values are treated as being completely independent of one another. Although the R ratio is input on the Cyclic Stress tab, it is not used to relate cyclic stress to primary or secondary stresses.



Material Properties for a Fatigue Analysis

Material Property Databases for FatigueSignal FFS provides two sets of material constants for fatigue crack propagation analysis. NASA has compiled an extensive database of fatigue properties for use in its NASGRO software. In addition, BS 7910 tabulated several sets of material constants for steel weldments in air and sea water environments.

When the user selects the database and material from the drop-down lists, the corresponding material constants are filled in automatically. The input fields are locked when one of the database options is selected. However, to change one or more of the coefficients, simply unselect the database option.

Selection of a material from the NASGRO database.

Paris Equation (Power Law)The crack growth rate in this case is assumed to follow a power law:

da

dNC K m

where C and m are material constants that can either be input by the user or taken from one of the databases. A threshold stress intensity range can be specified, below which crack growth will not occur.



Piece-Wise Power LawThe crack growth rate can be specified as a piece-wise power law, where the coefficients of the Paris equation vary over the range of the data. The user specifies up to three exponents (m1, m2, and m3) and the first pre-exponential coefficient, C1. The other coefficients (C2 and C3) are computed automatically. A threshold stress intensity range can also be specified.

NASGRO EquationThe following fatigue crack growth expression was developed by NASA Johnson Space Center and is used in their NASGRO software:

q

c

pth

m

K

K

K

K

KCdN

da

max1

1

The above equation is actually a simplification of the NASGRO model, and does not account for retardation due to crack closure.

NASA has compiled a materials database that contains coefficients for a large number of materials. When the NASGRO database option is selected in the Materials window, the appropriate material constants are input automatically, and the da/dN – K curve is tabulated in a spreadsheet grid (see below).



The NASGRO fatigue crack propagation equation.

User-Defined Fatigue Crack Growth RelationshipThe user can enter an arbitrary growth law by selecting the appropriate option on the Fatigue Growth tab in the Materials window. The input grid is a working spreadsheet, so the user can enter the growth equation as a spreadsheet formula and use the Copy Down (CTRL-D) command in the Edit menu. Alternatively, crack growth data can be pasted into the input grid from a spreadsheet application such as Microsoft Excel.

Spreadsheet grid for user-specified growth equation.



Typical output from a fatigue analysis.



Variable Amplitude Fatigue Analysis

Cumulative Damage ModelThis option is set at the Home window. This model is a modified version of Miner’s rule that accounts an arbitrary growth law which may include a fatigue threshold. This methodology is very fast and efficient, and gives results that are virtually identical to those obtained with cycle-by-cycle integration. However, neither of the currently available variables amplitude fatigue models in Signal FFS account for history effects such as retardation and crack closure.

The diagram below illustrates how the cumulative damage model works. The loading spectrum can be input either as a tabular histogram or a Rayleigh distribution. The cyclic stress histogram is converted to a K histogram using the current flaw dimensions and the stress intensity solution. A da/dN histogram is then computed from the growth law. Finally, the crack growth rate is averaged for the current increment:

1i

itot

da daN

dN N dN

This process is repeated for each crack growth increment.



da

dN

K

FATIGUE CRACKGROWTH LAW

da

dN

Ni

CRACK GROWTHRATE HISTOGRAM

FLAW DIMENSIONS

STRESS INTENSITYSOLUTION

K HISTOGRAM

Cyclic Stress

STRESSHISTOGRAM

K

Ni

Ni

Cumulative damage model for variable amplitude fatigue.

Cycle-By-Cycle IntegrationThis option is set at the Home window. Loading can either by random or deterministic when the stress spectrum is given in the form of a tabular histogram. This method is very time-consuming, and the cumulative damage model is recommended.

Rayleigh Stress DistributionThe Rayleigh statistical distribution is commonly used to describe cyclic loading spectra. The form of the distribution is as follows:

px

Sx

rd

1011 1

22.

exp



where

xS S

Sr r

rd

min

and Sr is the cyclic stress, Srmin is the minimum value, and Srd is the deviation. The user is required to input Srd and Srm, which is the modal value, equal to Srmin + Srd.

Input window for the Rayleigh distribution

Tabular Histogram for Cyclic StressesThe tabular input option enables the user to define a cyclic stress histogram. For the cumulative damage model, cyclic stresses must be input in increasing order. The number of binned cycles for each Sr is relative and need not correspond to the absolute number of cycles in the analysis. For example, if the relative total binned cycles is 100 and a given cyclic stress is specified as occurring once, this stress will occur 1% of the time. The relative binned cycles need not be integers in the case of random loading. For example, fractional cycles can be entered such that the total relative cycles add up to unity.

When the fatigue analysis is to be performed by cycle-by-cycle integration, the user has the option of specifying a deterministic sequence of loading. In this case, the sequence is entered inthe order it occurs. The number of cycles for each Sr has an absolute meaning in this case, and must be entered as an integer. A repeating loading sequence need only be entered once. Consider for example a loading sequence that occurs over 100 cycles. If the total number of cycles in the analysis is 100,000 the sequence will be repeated 1000 times.



The input grid is a fully functional spreadsheet. A mathematical relationship between cyclic stress and cycles can be entered using standard spreadsheet syntax. The Copy Down (Ctrl-D) command in the Edit menu can be used to paste the formula into multiple rows.

Cyclic stress histogram.

Cyclic Stress Scale FactorsWhen performing variable amplitude loading using either the Rayleigh distribution or the tabular histogram, one of more scale factors must be entered on the Cyclic tab of the Stresses/Loads window. For uniform membrane loading, this scale factor is normally set to 1.0, in which case the histogram values or Rayleigh coefficients will be used directly. When there are multiple stress components (e.g., membrane + bending or polynomial), a series of scaling coefficients must be entered.

For example, suppose that the magnitude of the cyclic bending stress is half that of the membrane stress. The membrane stress distribution could be entered as a histogram or as Rayleigh coefficients, and scaling factors of 1.0 and 0.5 would be entered for membrane and bending stresses, respectively. Note that only a single histogram or Rayleigh distribution can be defined irrespective of the number of stress components. The analysis assumes that the ratio of the components remains fixed.

Although it is customary to define the histogram or Rayleigh distribution with absolute stress values and use dimensionless scaling factors for the various components, there is an alternative approach. The scale factors for the stress components can be entered as absolute stress values and the histogram can be defined as an amplitude table. Since the scale factor and loading



spectrum are multiplied together to obtain the cyclic stress values, it does not matter which input is dimensionless and which has units of stress.

This latter approach is advisable when performing variable amplitude fatigue analysis using a weight function solution for K. That is, the tabular stress input for the weight function should be a reference stress distribution, and the histogram should be an amplitude table that scales this stress distribution.

Cyclic stress scale factors, which are multiplied by the stress values in the histogram or Rayleigh distribution

Environmental Crack Growth


Environmental Crack GrowthAn environmental crack growth analysis is very similar to a fatigue crack propagation analysis. The key difference is that the growth rate is a function of static loads rather than cyclic loads. Crack growth laws for environmental cracking have the following form:

I

daf K

dt

Power law, piece-wise power law, and user-defined growth expressions are available. The NASGRO equation is grayed out because it is not suitable for environmental cracking.

Input window for environmental cracking material constants.

Creep Crack Growth


Creep Crack GrowthCreep crack growth rate is assumed to obey the following relationship:

qt

daHC

dt

where Ct is a creep crack growth driving force parameter, and H and q are material constants. The value of Ct is a function of the applied stress intensity factor, the reference stress, and the creep rate. Traditionally, steady-state creep rate has been assumed to follow a power law in stress:

nA

where A and n are material constants. The above expression is referred to as the Bailey-Norton creep law.

The constants H, q, A, and n can be input by the user along with temperature. Alternatively the Omega creep model, which is described in API 579 Appendix F, can be used. In the latter case, the necessary material constants are provided in a database for a range of steels.

Unlike the Bailey-Norton Law, the Omega model accounts for creep damage and the resulting acceleration of creep rate, especially near the end of life. Consequently, the Omega expression for creep rate is not a simple power law. The Omega model is used in the Signal FFS creep rupture module described elsewhere in this manual. In the case of creep crack growth, the Omega material constants are used to infer the parameters H and q.

Creep Crack Growth


User-specified creep crack growth material constants.

Using the Omega material properties database for creep crack growth coefficients

Assessment of Metal Loss and Corrosion Pitting


Assessment of Metal Loss and Corrosion PittingThe assessments of general metal loss, local metal loss, and pitting corrosion are in accordance with API 579. The specific type of metal loss or corrosion (general metal loss, local metal loss, pitting, groove-like loss, etc) can be selected on the Home window.

If general metal loss is selected, the software will perform only an API 579 Section 4 analysis. If local metal loss is selected, the software will perform both Section 4 and Section 5 analyses if possible. API 579 does not provide precise definitions to distinguish between general metal loss and a local thin area (LTA). The local metal loss assessment (Section 5) is generally less conservative, particularly if the wall thinning is confined to a small area. If a groove-like flaw is selected, only a Section 5 assessment will be performed.

Flaw Type WindowAfter selecting the type of structure (pressure vessel, piping component, or storage tank) on the Home window, click on the forward arrow to display the Flaw Type window. A variety of information is input at this window, including the flaw location, material, and design temperature.

The user may input the allowable stress value. Alternatively, there is an allowable stress database for the ASME Boiler and Pressure Vessel Code, Section VIII, Division 1, as well as the ASME B31.1 Piping Code.

The default remaining strength factor (RSF) for pitting and metal loss is 0.9. This default can be overridden by entering the desired RSF on the Flaw Type window.

Dimension Window (Metal Loss Analysis)At the Dimensions window, the user enters the diameter and thickness of the component of interest along with the design pressure. The uniform metal loss (past corrosion) and the future corrosion allowance is also entered. The minimum design thickness, tmin, can be computed automatically if desired, or it can be input by the user. In certain cases, however, automatically calculated tmin values may not be displayed on the Dimensions window because more information is required. If, for example, supplemental loads are specified on the Flaw Typewindow, tmin cannot be calculated until these loads are entered at the appropriate window. In such cases, the computed value of tmin will be shown on the report.



The Flaw Type window.

The dimensions window for metal loss analysis.



Supplemental LoadsIf supplemental loads are specified at the Flaw Type window, the Supplemental Loads input window will appear after the Dimensions window. Both primary and secondary supplemental loads can be entered on this window.

Supplemental loads input window.

Thickness Data WindowThe Thickness Data window will appear when either general metal loss or local thin area (LTA) is selected in the Flaw Type window. If general metal loss is selected, three types of thickness data can be entered:

1. A single minimum thickness reading, tmm.

2. Thickness readings at random locations.

3. Thickness readings on a rectangular grid.

If local thin area is selected, only the first and third options listed above are available. Note that if thickness data are entered at random locations, a local metal loss (Section 5) analysis cannot be performed. If only a minimum thickness value, tmm, is entered, the LTA will be assumed to have a rectangular thickness profile. Such an analysis is conservative relative an assessment based on a more accurate thickness profile.



An assessment based on a thickness grid is recommended if such data are available. Signal FFSallows the user to specify the number of longitudinal (or meridianal) and circumferential inspection planes. A spreadsheet grid with the requisite number of rows and columns will appear. Note that the first row and first column are reserved for the longitudinal and circumferential distances. If the grid spacing is uniform, the user need only specify the spacing and the first row and column of the spreadsheet will be filled in automatically.

Input of a minimum thickness measurement.



Input of thickness data at random locations.

Input of a thickness grid.



Groove or Gouge Data WindowThe length and width of a groove-like flaw can be entered directly on the Groove or Gouge Datawindow. Alternatively, a thickness profile can be entered, similar to local thin areas. If the groove-like flaw is not oriented in the longitudinal or circumferential direction, the thickness grid follows the groove orientation.

Groove data input window.

Pitting Data WindowThe Pitting Data window provides inputs for both Level 1 and Level 2 pitting assessments.

For Level 1 assessments, pitting charts are provided to compare with the observed degree of pitting on the component. Several pre-defined pitting damage levels are provided in a drop down list, which correspond to the pitting charts in API 579. When using the predefined pitting charts, the only required user input is the maximum pit depth.

For Level 2 assessments, pit couple data must be entered. Required data for each pit couple include the depth and diameter of each pit, as well as the spacing and the orientation angle with respect to the principal axes.

For localized pitting, enter the axial and circumferential extent of the region of pitting. The remaining strength factor (RSF) computed from the pit couple data will be used to define an equivalent local thin area (LTA), which will be assessed according to Section 5 of API 579.



Level 1 pitting charts.

Level 2 pit couple data.



Structural Discontinuity WindowAt the Flaw Type window, the user can specify that metal loss occurs at a structural discontinuity such as a nozzle or piping branch. The Structural Discontinuity window will appear if this option has been selected. At this window, the local dimensions are input, along with materials of construction and allowable stress values.

Structural discontinuity input window.

Brittle FractureAt the Home window, the user can specify a Brittle Fracture assessment. The Brittle Fracture window provides the user with a series of questions, the answers to which are used to compute the Critical Exposure Temperature (CET) for a component.



Brittle Fracture input window.

Level 1 Crack-Like FlawsFor cases where the detailed analysis of an FAD assessment is not possible or required, a more simple Level 1 assessment of crack-like flaws can be done. This selection is done at the Homewindow, and the required information is input in the Crack Data window.



Level 1 Crack Data window.

ReportClicking on the Run button will cause a report to be generated and displayed on the Results tab of the Data Sheet window. The report is divided into 3 major sections. The first section lists the input values and the second section summarizes the results. The third section provides more details of the calculations, including intermediate values. This latter section outlines each step in the assessment. The steps correspond to those in API 579. This section of the report is useful for checking the calculations and understanding the assumptions Signal FFS has made.

With the Results tab visible, select Save Report from the File menu to save a copy of the report in Rich Text format (*.rtf). A copy of the report is automatically saved whenever the main Signal FFS file (*.ffs) is saved. These *.rtf files can be opened and edited in Microsoft Word or other word processors. The report can also be printed directly from Signal FFS.



Report header and input data.



Results summary and detailed step-by-step results.

Software License Agreement


Assessment of Creep Damage and Rupture

The Geometry Window (Creep Analysis)Three types of loading can be analyzed: uniaxial, pressurized tube, and multiaxial. In the latter case, the ratio of the second and third principal stress to the maximum principal stress must be input. These ratios are assumed to be constant throughout the life of the component.

The Dimensions Window (Creep Analysis)When evaluating a boiler tube, the user must input the wall thickness and outside diameter. If corrosion is to be considered, the user must also input information about the corrosion rate. The corrosion rates can be input directly, or the user can input thickness readings. In the former case, the user inputs the corrosion rates at two temperatures, and an Arhennius law is used to infer corrosion rate at other temperatures. In the case of thickness readings, the user must input the measured thickness at the end of each exposure. The user may use these thickness readings directly in the calculation or these data can be used to fit an Arhennius law for corrosion rate.

The life assessment can account for corrosion on the ID, the OD, or both. When both ID and OD corrosion are considered, two sets of corrosion rates must be specified. If the corrosion is quantified by thickness readings, both the measured thickness and OD must be input.

The Operating Conditions WindowAt the Operating Condition window, the user inputs the time increment, temperature and pressure for each exposure. If thickness readings were input at the Dimensions window, the time increments will be carried forward to this window. The corrosion rates and thicknesses are computed automatically with spreadsheet formulae, based in the information provided in the Dimensions window.

The Materials WindowAt the Materials window, the user can choose one of the materials in the Omega database. Alternatively, he/she can access a user-defined materials database. Once the material is specified, the user must input a rupture strain. He can also specify a prior damage level with the top slide bar.

The two lower slide bars pertain to the relative creep strength and ductility of the material. For example, moving the strength slide bar to the right corresponds to selecting a material at the lower end of the scatter band for creep rate in the alloy of interest. One unit on the slide bar corresponds to one log standard error.



Geometry input window.

Dimensions window.



Operating conditions window.

Graphical Output (Creep Analysis)The output data are plotted on 6 graphs. The appearance of these plots can be modified through a series of items under the Graph menu. To change the scale of a graph, double click on the axis of interest.

Changing the Variables on the PlotsThe default settings result in six output variables plotted against time. However, the user can have a high degree of flexibility in defining the variables to be plotted.

To change any or all of the graphs, choose the Select Plot Variables item under the Analysismenu. A window like that shown below will appear, and then the user can change the x and y plotting variables for any of the six graphs.

Signal FFS will “remember” these saved settings and will create six graphs according to thesepreferences each time the program is run.



Selection of variables to plot on the 6 graphs.

Increasing the Number of Plotting PointsAt its initial default setting, Signal FFS will output and plot information only at the beginning and end of each exposure. This sometimes results in unattractive plots. For example, the strain versus time curve may have a jagged piece-wise linear shape rather than a smooth exponential shape. To remedy this situation, additional plotting points may be added.

To add plotting points, select Analysis Options from the Analysis menu and change the Number of Intermediate Analysis Points on the first tab of the window. (The default is zero.) The graphs below compare creep strain plots with 0 and 4 intermediate points.



No Intermediate Points:

Four Intermediate Points:

Parametric Analysis (Creep Rupture)Sensitivity studies can be performed by varying one parameter and keeping other variables constant. To run a parametric analysis, you must first input information required to perform a deterministic analysis. Next, select Parametric Analysis from the Analysis menu. A list of



variables will then appear. The list below pertains to a pressurized tube; this list varies somewhat depending on the geometry being considered.

All variables other than the quantity to be varied parametrically remain constant. If temperature is the parametric variable, as in this example, the corrosion rate can be linked to temperature through spreadsheet formulae on the Input Data tab.

Parametric analysis inputs for a creep rupture analysis.



Note that the parametric analysis assumes a fixed temperature and pressure for each case. The total exposure time and the plotting interval are specified on the window shown on the previous page.

The six creep rupture graphs will be plotted with a series of curves corresponding to the parametric cases. The graph below illustrates creep curves at 5 temperatures.

To change the legend text:

1. Click on the legend with the right mouse button and select Edit Chart Data.

2. Double click on the column headings you wish to change and type in the appropriate label(s).



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11.2 Third Party Software. If Third Party Software included with the Software is subject to additional terms and conditions imposed by Quest’s third party licensors, such terms and conditions will be contained in the “About” pages of the Software and are deemed incorporated herein by reference. Client agrees to comply with all such applicable terms and conditions.

11.3 Publicity. Quest may, subject to Client’s approval of content, not to be unreasonably withheld or delayed, (a) create a general contract announcement press release indicating that the parties have entered into this Agreement, (b) use Client’s business name and logo in written materials identifying Quest’s Clients and in other appropriate promotional materials; (c) identify Client in applicable case studies; and (d) identify Client as a reference for prospective Clients and the media (provided that Client shall not be obligated to comment in any way).

11.4 Compliance with Laws. Each party will comply with all applicable export and import control laws and regulations in its use of the Software and, in particular, Client will not export or re-export the Software without all required government licenses and Client agrees to comply with the export laws, restrictions, national security controls and regulations of the all applicable foreign agencies or authorities.

11.5 Assignment. Neither party may assign or transfer, by operation of law or otherwise, any of its rights under the Agreement (including the license rights granted to Client to the Software) to any third party without the other party’s prior written consent, which consent will not be unreasonably withheld or delayed; except that Quest may assign this Agreement, without consent, to any successor to all or substantially all its business or assets to which this Agreement relates, whether by merger, sale of assets, sale of stock, reorganization or otherwise. Any attempted assignment or transfer in violation of the foregoing will be null and void.

11.6 Force Majeure. Except for any payment obligations, neither party shall be liable hereunder by reason of any failure or delay in the performance of its obligations hereunder for any cause which is beyond the reasonable control of such party.

11.7 U.S. Government End Users. If Client is a branch or agency of the United States Government, the



following provision applies. The Software is comprised of “commercial computer software” and “commercial computer software documentation” as such terms are used in 48 C.F.R. 12.212 and are provided to the Government (a) for acquisition by or on behalf of civilian agencies, consistent with the policy set forth in 48 C.F.R. 12.212; or (b) for acquisition by or on behalf of units of the Department of Defense, consistent with the policies set forth in 48 C.F.R. 227.7202-1 and 227.7202-3.

11.8 Notices. All notices, consents, and approvals under this Agreement must be delivered in writing by courier, by electronic mail (email), by electronic facsimile (fax), or by certified or registered mail, (postage prepaid and return receipt requested) to the other party at the address set forth beneath such party’s signature, and will be effective upon receipt or when delivery is refused. Either party may change its address by giving notice of the new address to the other party.

11.9 Governing Law and Venue. This Agreement will be governed by and interpreted in accordance with the laws of the State of Colorado, without reference to its choice of laws rules. Any action or proceeding arising from or relating to this Agreement shall be brought in a federal or state court in Denver, Colorado, and each party irrevocably submits to the jurisdiction and venue of any such court in any such action or proceeding.

11.10 Interpretation. This Agreement is in English and shall be interpreted according to the commonly understood meaning of the words and phrases in the United States of America.

11.11 Remedies. Except as provided in Sections 6and 7, the parties’ rights and remedies under the Agreement are cumulative. Client acknowledges that the Software contains valuable trade secrets and proprietary information of Quest, that any actual or threatened breach of Section 2 will constitute immediate, irreparable harm to Quest for which monetary damages would be an inadequate remedy, and that injunctive relief is an appropriate remedy for such breach. If any legal action is brought by a party to enforce the Agreement, the prevailing party will be entitled to receive its attorneys’ fees, court costs, and other collection expenses, in addition to any other relief it may receive.

11.12 Waivers. All waivers must be in writing. Any waiver or failure to enforce any provision of this Agreement on one occasion will not be deemed a waiver of any other provision or of such provision on any other occasion.

11.13 Severability. If any provision of this Agreement is unenforceable, such provision will be changed and interpreted to accomplish the objectives of such provision to the greatest extent possible under applicable law and the remaining provisions will continue in full force and effect. Without limiting the generality of the foregoing, Section 8 will remain in effect notwithstanding the unenforceability of any provision in Section 6.2.

11.14 Construction. The headings of Sections of this Agreement are for convenience and are not to be used in interpreting this Agreement. As used in this Agreement, the word “including” means “including but not limited to.”

11.15 Entire Agreement. This Agreement (including all exhibits and attachments) constitutes the entire agreement between the parties regarding the subject hereof and supersedes all prior or contemporaneous agreements, understandings, and communication, whether written or oral. This Agreement may be amended only by a written document signed by both parties. The terms of any purchase order or similar document submitted by Client to Quest will have no effect.

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