**Oil and Gas Industry Application**

AFGROW includes many capabilities that may be used to assess the fitness for service requirements of the oil and gas industry. The following sections contain information about API-579 K-solutions, crack growth rate models and other useful tools and features designed to assist the user in this effort.

# API 579-1 Pipeline Crack Models

API 579-1, Part 9 (Annex 9B) stress intensity solutions have been implemented in AFGROW for several cracked pipe geometries.

These solutions are divided into three loading categories.

## API-579 Pressure Based Models

All pipeline pressure-based models require the input loading spectrum in terms of internal pipe pressure. In Imperial units, pressure is given in Ksi and in the Metric system, pressure is expected in MPa.

All user input values in the Spectrum Dialog will be related to internal pipe pressure when any of the pipeline pressure-based models are selected. The Spectrum Multiplication Factor (SMF) is a scaling factor applied to the maximum and minimum values in the input spectrum. The resulting values will reflect internal maximum and minimum internal pressure values. The Residual Strength Requirement and Preload values are assumed to be internal pressure values and are not scaled by the SMF.

## API-579 Polynomial K-Solutions

All pipeline polynomial K-solution models require the input loading spectrum in terms of the stress at the crack origin. In Imperial units, stress is given in Ksi and in the Metric system, stress is expected in MPa.

The fourth order polynomial representation of the stress distribution in the thickness direction acting at the crack plane are expected to start at the crack origin and is a function of the normalized distance from the crack origin in the pipe thickness direction (y/t). The polynomial coefficients (S0 – S4) are entered in the Polynomial Stresses dialog as shown. In the case of internal cracks, internal pipe pressure (crack face pressure) should be entered in the dialog. The pressure entered will be scaled by the spectrum maximum and minimum values after they are scaled by the SMF. This can be simplified using a normalized input spectrum where the highest maximum value is 1.0.

All user input values in the Spectrum Dialog will be related to the stress normal to the crack plane at the crack origin when any of the pipeline polynomial-based models are selected. The Spectrum Multiplication Factor (SMF) is a scaling factor applied to the maximum and minimum values in the input spectrum. The resulting values will reflect maximum and minimum stress values at the crack origin. The Residual Strength Requirement and Preload values are assumed to be normal stress values normal to the crack origin and are not scaled. by the SMF.

## Polynomial Based K-Solution Example

This polynomial based solution can be used to model an internal surface crack in a pipe under internal pressure and the resulting solution will be compared to the pressure-based solution for the following conditions.

Outside Diameter: 20 inches

Inside Diameter: 19.5 inches

Internal Pressure: 1 Ksi

Crack Dimensions: a = 0.05, c = 0.05

The axial stress normal to the crack plane is assumed to be constant through the thickness and may be determined as:

The polynomial function will be reduced to the single coefficient, S0 (constant term). It is useful to normalize the polynomial to the stress at the crack origin so that the constant term will be set equal to 1.0. In that case, the SMF value will be equal to the normalization value, or 19.75 for this example. The loading spectrum will need to be defined relative to this load case. In this case, it will simply consist of the internal pressure (Ksi). The crack face pressure value entered in the Polynomial Stresses dialog is scaled by the SMF value, so it must be divided by SMF. In this case, the crack face pressure will be 1/19.75 = 0.0506. The polynomial dialog will be completed as shown below:

The K-solution for this model is:

Kc = 6.3244

Ka = 5.3134

The corresponding pressure-based K-solution is:

Kc = 6.1731

Ka = 5.1864

These solutions agree within 3%.

## API-579 Weight Function Models

All pipeline weight function K-solution models require the input loading spectrum in terms of the stress at the crack origin. In Imperial units, stress is given in Ksi and in the Metric system, stress is expected in MPa.

These models are used when there is a known unflawed stress distribution through the pipe thickness at the proposed crack location.

The stress distribution in the crack plane is entered in the thickness direction starting at the crack origin. It is highly recommended that the distribution be normalized to 1.0 at the crack origin since the input spectrum is expected to represent the stress at the crack origin. If the stress distribution and input spectrum are normalized, the SMF value in the Spectrum dialog will represent the stress at the crack origin for the spectrum value that has been normalized to 1.0.

# Crack Growth Rate Models

Users may choose between any of the five following crack growth rate models.

## Forman Equation

The Forman equation is an enhancement of the Paris equation which includes a mechanism to shift crack growth rate data as a function of stress ratio (R) and account for increasing crack growth rate as the applied stress intensity approaches the failure limit (Kc) for a given material. AFGROW also includes some additional features for the Forman equation that may allow it to more accurately model raw test data. These optional features include:

Up to 3 segments to follow material behavior in region I, II, and III

Additional controls for data shifting as a function of stress ratio.

## Walker Equation

The Walker equation is also a derivative of the Paris equation, but it includes the ability to model R-shift behavior with an additional parameter (m) which controls the amount of data shifting as a material property. The allowable range for the m-value is [0 – 1], where m = 1 results in no data shift and m = 0 results in the maximum possible data shift.

## NASGRO, Version 3 Equation

The NASGRO equation is also built upon the Paris equation but uses multiple parameters to obtain a closed-form equation to model material crack growth rate data through all regions of crack growth. The implementation of the NASGRO equation in AFGROW is from the last publicly available version of the NASGRO crack growth life prediction program developed by NASA (NASGRO, Version 3). A database of NASGRO equation parameters for 361 materials are available in AFGROW.

## Harter T-Method

The Harter T-method is a tabular crack growth rate model that applies the Walker equation on a point-by-point basis for 25 crack growth rates. This model uses crack growth rate data obtained for two stress rations (R1 and R2). A straight line in logarithmic scale is assumed between each point for any stress ratio, and m-values are calculated at each growth rate based on data available for each stress ratio. The resulting data shifting is a function of the m-value at each growth rate. This allows the shifting to reflect the actual behavior observed in the raw crack growth rate data. The method is represented as a 25x3 material property matrix of crack growth rates, DK, and m-values.

## Tabular Look-Up

The tabular look-up model provides the most accurate and flexible option to represent raw crack growth rate data. The tabular matrix includes an unlimited number of crack growth rates and corresponding stress intensity values for up to 10 stress ratios. A straight line in logarithmic scale is assumed between each rate value at each stress ratio and interpolation between stress ratio is based on the Harter T-method. AFGROW currently includes referenced tabular fits for more than 90 materials and fits for additional materials are being added on a regular basis.

The tabular look-up model also includes options for crack growth direction dependance and the ability to account for the effect of changes in environment effects over the life of a component.

# Crack Growth Material Database

An extensive material database is available for crack growth life predictions using the tabular look-up method or NASGRO, V3 equation.

## Tabular Lookup Database

## NASGRO, V3 Equation Parameter Database

# Failure Criteria

AFGROW includes several failure criteria options:

A user may select any or all available criteria and AFGROW will terminate on the first occurrence.

# Through Thickness Transition

There are also several options for transition from part-through to through-the-thickness cracks

When using appropriate API-579 solutions, the CorLAS burst model may be used to predict failure for a part-through crack in a pipe.

# Crack Initiation Capability

A strain-life based crack initiation capability is available to estimate the time to crack formation for geometries with local stress concentrations.

A large Cyclic Stress-Strain and Strain-Life equation parameter database us available along with the ability to input tabular material data.

## Crack Initation Material Parameter Database

# Load History Generation

AFGROW includes a load history generation tool (**Spectrum Manager**) that allows the user to import loading information to create and/or edit loading spectra for the life prediction process.

The capabilities of the new Spectrum Manager include visual spectrum design, spectrum statistics at a glance, user-defined spectrum tags, clipping, truncation, spectrum reversal, spectrum level/sub-spectra reordering/randomization, and copy-paste from MS Excel. Loading spectra may also be generated from load exceedance information.

# Context Sensitive Help

Help is available for all AFGROW features and capabilities using the F1 key.