The Continuum Engineering

Introduction:  Fatigue and Damage Tolerance (F&DT) analysis is often required for certification purposes.  Damage Tolerance (DT) is also referred to as Crack Growth or fracture analysis.  For certification of aerospace components 14 CFR 25 requirements - referred to as Federal Aviation Regulations (FAR) - require aerospace components be qualified by testing or analysis when subjected to fatigue (repetitive) loads.  The fatigue loads are based on an aircraft’s intended use for which it is certified.  It comes from the plane manufacturer and flows down to component manufacturers.  There is again the Advisory Circulars (AC) to the FAR that also need to be complied.  Typically the customer specification would specify the following:

(i)                  AC25.571: F&DT analysis to meet Design Service Goal (DSG) fatigue loads

(ii)                AC25.24: F&DT analysis to meet Main Engine Fan Blade Out (MEFBO) fatigue loads

(iii)               RTCA-DO160F: Fatigue analysis for certification of airborne equipment

Fatigue Analysis:  Fatigue analysis is a fairly simple exercise that used to be performed by hand before computers were introduced.  Then simple classical methods were used and parts were bulky.  With the introduction of Finite Element (FE) method in structural analysis, parts are represented by tens of thousands nodes and elements and it is not practical to do hand analysis of a few locations.  So, spreadsheet based fatigue analysis became popular.  There are several fatigue analysis codes in the market and some large companies have their own codes.  Though all the codes basically do the same thing, the format of the data, the classification of the disturbances and computation methodologies are not identical.  Most of these fatigue codes use spreadsheets for input and output.  But the computations are performed internally through macros and it is very difficult for the user to see or test intermediate steps.  This EXCEL based procedure saves all intermediate steps, and allows users to deviate and implement their own computation steps.  If the events do not need to be re-sequenced, then no macro needs to be run.  Optionally, the user may re-sequence events by hand or using a separate code.  This code can perform fatigue assessment per AC25.571, AC25.24 and RTCA-DO160F.

Damage Tolerance Analysis:  DT analysis, like fatigue analysis, involves closed form solution and can be performed by hand.  There are several codes in the market that perform DT analysis.  NASGRO is a fairly popular and inexpensive code to use.  Also, NASGRO has a built-in database of materials with crack growth properties.  DT analysis goes hand-in-hand with fatigue analysis.  While fatigue analysis is performed with the assumption that the part has no cracks, DT analysis assumes the existence of cracks and checks the growth of crack size as a function of cycles.  DT analysis requires a stress spectrum, and this EXCEL based procedure will generate a stress spectrum in a format that NASGRO accepts.

Random Vibration:  RTCA-DO160F requires equipment be test verified.  But before subjecting the equipment to the operation or endurance environment of RTCA-DO160F, user would like to perform fatigue check to see if the equipment would survive the test.  The standard procedure is to use a FE code like MSC/NASTRAN or NX/NASTRAN and use frequency response based (Solution 111) to apply the random vibration environment represented by PSD.  The FE output would give the 1-sigma stresses and the expected frequencies, which along with the duration of test are used to compute fatigue damage.  The EXCEL based procedure allows three distributions: Rayleigh, normal or equivalent sinusoidal to obtain the loading spectrum.  An alternative more efficient method is to perform frequency response solution in MSC/NASTRAN and perform the random vibration analysis in MSC/PATRAN.  FEMAP cannot perform random vibration analysis.

Rain Flow:  The disturbance loading events often do not have the same amplitude or mean.  At issue is how do you obtain the cycles?  There are different methods of obtaining the cycles.  The ASTM E-1049 has different methods and the one most widely used is referred to as simplified rain flow method.  Other rain flow methods may give slightly different results.  In the simplified rain flow method:

-         there are no half cycles

-         the method starts with the largest load point

-         the first (i.e. largest) load point is added to the end

The EXCEL based procedure has a macro that obtains cycles by the simplified rain flow method.  Given a vector representing stress or strain points, the MACRO will give a new vector where the points are re-arranged.

Stress Ratio:  The S-N curve is most often given for stress ration (R= max stress/min stress) of -1.0.  When the stress ratio is different, then one would need to look for appropriate S-N curve or use some correction like Goodman or Sodderberg.  The EXCEL based procedure can perform Goodman or Sodderberg correction.

Stress Concentration:  The S-N curve is most often given for stress concentration ratio (Kt) of 1.0.  At notches and corners there is stress amplification, and one has two choices.  Look for an S-N curve with appropriate Kt.  When S-N curve of appropriate Kt is not available, one can make detailed FE model to capture the amplification or use analytical expression for Kt to capture the peak stress and then use S-N curve of Kt=1.0.  The EXCEL based procedure does not make any correction for Kt and it is left to the user to use the correct S-N curve and make any adjustments to input stresses.

Stress Components:  The typical S-N curve is for uni-axial stress.  But since the generic stress is a tensor quantity, the user often has the dilemma as to which stress component to use.  The EXCEL based procedure supports principal stress and component stress.  The user can easily modify it to handle VM-stress.  The EXCEL based procedure allows input of stress tensor associated with each interface load to compute the stress tenor at a point when all interface loads are active.  Principal stresses are computed and the maximum of the absolute principal stresses is used.  This approach is conservative and the user can modify it at his will.

Finite Element Code: Any FE code can be used to determine the component stress state under unit load at any loading interface while fixed at the boundary interfaces.  MSC/NASTRAN with MSC/PATRAN and NX/NASTRAN with FEMAP were used to generate the stress states.  While MSC/NASTRAN and NX/NASTRAN are the FE codes, MSC/PATRAN and FEMAP are the pre- and post-processors used to generate the FE model and post-process the output to obtain stress tensor at critical locations.  Again, MSC/NASTRAN Solution 101 was used to obtain the interface forces on the component when it is treated as a mass point (and the internal forces represent interface forces) in the system model under unit acceleration in system X, Y and Z directions.  The component stress state from disturbances (in terms of system X, Y and Z-direction accelerations) is obtained by multiplying the amplitude of the disturbances with unit system level acceleration based internal (interface) forces with the component stresses under unit interface forces.

Benefits: Following are some of the benefits of using our code that you should consider:

(1)   Our F&DT code stands out as it is simple and shows the intermediate steps

(2)   Our code allows you to modify the procedure for your convenience

(3)   There is no restriction on size of problem

(4)   You learn fatigue analysis as you use our code

(5)   We provide guidance on the interfacing programs (NASTRAN, PATRAN, FEMAP)

(6)   This code is a procedure based on MicroSoft EXCEL that is readily available

(7)   We give you lifetime usage rights and rights to make changes

(8)   Very reasonable price (no comparable product in market at this price)

(9)   Can be used to verify other F&DT codes

Who should buy: Following are people who can benefit:

(1)   Small companies that need a powerful F&DT code without spending a fortune

(2)   Stress engineer wants to have a handy F&DT code

(3)   Student of structural analysis

(4)   Engineer new to F&DT

(5)   Want to verify results from other F&DT code

Files: The following files are available for user to download and use:            

Cost: The following table provides the costs.