While trying to verify some AFGROW solutions for the Single Corner Crack at Hole in bending, I was comparing the Stress Intensity Factors (SIFs) that I compute in a separate Excel spreadsheeet (VBA). My VBA program computes the SIFs from the original Newman Raju curve fits in Chapter 9 of Computational Methods in the Mechanics of Fracture, 1986. I am using version 4.11.14.0 06/29/2006, which I think is last version before AFGROW got really big (since it didn’t include the Fawaz curve fits for corner crack(s) at a hole)—I am running AFGROW on an old computer which is severely RAM limited compared to 2010 computers.

There are actually 3 references given in the AFGROW help for this crack scenario and the bending load, The first one can be downloaded from the AFGROW site, http://afgrow.net/downloads/ddownload.aspx, the 2^nd can be downloaded from a NASA website, and the third is unavailable.

1) Newman, J.C., and Raju, I.S., "Stress Intensity Factor Equations for Cracks in Three-Dimensional Bodies Subjected to Tension and Bending Loads," Chapter 9, Computational Methods in the Mechanics of Fracture, Elsevier Science Publishers B.V., 1986

2) Zhao, W., J. C. Newman, Jr., M. A. Sutton, X. R. Wu, and K. N. Shivakumar, "Analysis of Corner Cracks at Hole by a 3-D Weight Function Method with Stresses from Finite Element Method," NASA Technical Memorandum 110144, July 1995.

3) Zhao, W. and Newman, Jr., J. C., Electronic Communication, Unpublished NASA Langley Research Center Results, 24 February 1998.

I noticed substantial differences between what I was computing with my VBA (20% or more) and what AFGROW was computing, suggesting that whatever equations were in Ref. 2 and 3 were affecting my results:

My configuration was double (n=2) or single corner crack (n=1), so I show results for both:

                         VBA          VBA                            AFGROW               AFGROW

n                        SIFc           SIFa                                SIFc                         SIFa

1                     3.95091       3.6774                             3.952                        3.678

2                     4.01409       3.73621                           4.112                        3.736

SIFc is the SIF for crack “c” and SIFa applies to crack “a.” VBA are my spreadsheet solutions. Geometry was 2 inches wide, thickness 0.25 inches, hole diameter 0.25 inches, and both crack dimensions are 0.05 inches. Bending stress is 10 ksi, no tension (BSR=1, TSR=0, no bearing). Interesting that all these SIFs are close except for the double corner crack, SIFc.

After double checking all of my equations, I contacted AFGROW support to try to resolve the differences. Turns out there is a 4^th reference not mentioned in Help that summarizes the equations used to modify the bending SIFs from the Ref. 1 above that you can download from AFGROW’s site:

Modification of Stress Intensity Factor Equation for Corner Cracks From a Hole Under Remote Bending by Zhao and Newman.

Jim Harter gave me this document, which contains modifications to 3 sub-equations in the Newman Raju curve fits, coded those into my VBA; still had a difference. I went to another computer that had a more recent version of AFGROW, 5.1.5.16 07/26/2010, which gave me the following comparison:

                                                                                AFGROW               AFGROW

                         VBA          VBA                              5.1.5.16                    5.1.5.16

n                        SIFc           SIFa                                SIFc                         SIFa

1                     3.95091       3.6774                             3.9509                      3.6774

2                     4.01409       3.73621                           4.0141                      3.7362

Turns out there is a small undocumented bug in this old version of AFGROW; mystery solved.

Several Users have asked me to post some helpful "rules of thumb" that may be useful when performing life prediction tasks. While I am happy to do it, I must first state that while I have found this information to be useful, each user must take full responsibility for their own life predictions. Neither I nor LexTech take any responsibility for how this information is used.

Typical Retardation Parameters

Willenborg SOLR

Aluminum (2.5 to 3.0)

Titanium Alloys (2.2 to 2.7)

Steel (1.8 to 2.2)

Closure Model

Aluminum (3.8 to 4.2)

Crack Growth Rate Data

Aluminum Alloys

Threshold @R=0 (1 to 2) Note, while this is the typical range, I have seen reputable data as high as 3 in a few cases. Always look at data for a similar alloy if there are no reliable data for the alloy of interest.

A typical crossing point for most aluminum alloys is approximately 1.0 E-5 in/cycle at Delta K = 10 Ksi-sqrt(in) for R=0

Also, note that a "double-knee" is typical for aluminum alloys tested in air. The first "knee" generally ocurrs at approx. 4.0E-07, and the second around 2.0E-8 in/cycle.

As we approach the first commercial release of AFGROW, it makes sense to do a little "code cleaning." Based on user input (or lack thereof), it appears that the bonded repair analysis capability is not being used. Therefore, we are planning to remove the capability from the new release.

We are asking for input from anyone who would be adversly affected by this decision.

We added an Installation Notes document on our Documentation and Supporting Information Page.

If you are experiencing problems saving or reading an AFGROW input file, you need to download and install MSXML 4.0 Service Pack 3 (Microsoft XML Core Services), as described in the AFGROW Installation Notes document.

The following suggestions have been made for ways to improve AFGROW and the AFGROW Web Site:

AFGROW Improvements:

• Add Residual Strength Plotting Capability
• K-Solution for an Offset Loaded Lug
• Stress-Life Crack Initiation Model
• Expand Multi-Crack Capability
• Include the Bending Stress Fraction in the Bearing Stress Fraction Calculator Option
• Ability to Model Cracks in a Bonded Metallic Repair Patch
• Ability to Edit Parameters by Selecting an Item in the Status View
• Include Warning to Save Data Before Closing AFGROW

Web Site Improvements

• Publish AFGROW Tips and Tricks
• Retardation Parameter "Rules of Thumb"
• Add Material Data/Documentation

This will allow users to adjust spectrum tension and compression values independently. The primary purpose of this capability is to allow users to model interference fit pins as a pre-load which may be considered to be a function of crack length. The modifications will be in either equation or tabular form. The general capability will allow for a number of input parameters to be used in order to make the capability as flexible as possible.

Compression Factors for Stress Intensity Solutions

Stress intensity solutions for the crack opening mode are applicable under tensile loading conditions. Examples include a crack at an open hole, and a crack at a hole under bearing load. In the first case, the stress field in the assumed crack plane under remote tension, is quite different in magnitude under remote compression. In the second case, the crack will not see any compression due to the geometry. Although K is not defined under compression loading, the K-values calculated under compression use the same solution as the values calculated under tension loading. These values are then used to determine a crack growth rate for the resulting R-value. The ability to correct this situation may help improve crack growth life predictions for load spectra that includes significant amount of compression loading.

Beta Correction for Advanced Through-the-Thickness Cracks

AFGROW currently allows users to apply beta correction factors to classic models and corner cracked advanced models. The capability will be added to the advanced through crack cases. This will provide additional modeling flexibility for these cases.

K-Solution for an Edge Notch in a Plate

A new advanced solution for corner or through crack at an edge notch in a plate is being developed. This will permit users to continue life predictions for continuing damage cases in which a crack has grown from a hole to the near edge, and another crack was growing simultaneously on the opposite side of the hole. Some have reported using an edge crack to simulate this continuing damage condition, but the result will be extremely conservative since the hole radius will tend to reduce the actual K-value for this geometry. The availability of this new solution will provide better accuracy for these types of problems.

Comments/suggestions are welcome