This first problem is concerned with the fatigue analysis of a simple “keyhole” specimen. The geometry is shown in Figure 14‑1. All three standard fatigue analyzers (Stress‑Life {S-N}, Strain-Life {-N} and Crack Growth {LEFM}) are demonstrated with three different service load histories and two different materials. The results are then compared to test data accumulated during The SAE Cumulative Fatigue Damage Test Program conducted from 1970-1974. See References (Ch. 16).

In a series of experiments, different constant amplitude cyclic loads were applied to the specimen until it broke into two pieces. To accumulate S-N data, the stress was monitored at the root of the notch (1/2 radius from the hole along the line of direction of the notch) and a stress-life line determined by regression analysis of the scattered points. Two different materials were used for this specimen, MANTEN and RQC100, leading to two S-N data sets as listed in Table 14‑1.

These materials were also tested using a special test specimen under strain control to obtain cyclic stress-strain and strain-life scatter plots. A regression analysis was performed to calculate the local strain parameters listed also in Table 14‑1 as well as the crack growth properties. All of these values are stored in the MSC.Fatigue materials database.

The original FE stresses used in the SAE program were determined using MSC.Nastran. In our example, we use MSC.Patran FEA and validate the results. Therefore, it is advantageous to plot the results of the FE analysis. Figure 14‑2 show maximum principal stress as a function of the distance from the notch. The original MSC.Nastran finite element analysis and actual measured notch root strains were used to describe the relationship between applied load and local notch root strain in the SAE program. The following shows that MSC.Patran FEA can reproduce these same results. The relationship is expressed as

Elastic analysis showed that the relationship between nominal elastic notch root stress, Sn, and applied load, P, can be described by

From the above stress concentration, Kt, for the geometry may be estimated by considering the elastic part of the local notch root strain calibration

and from S = mP

and so

Kt = 203403/(6271.7 x 11.24) = 2.88

With the applied load of 30kN the expected local elastic stress as predicted by the original MSC.Nastran analysis

The equivalent stress predicted by MSC.Patran FEA is 1001 MPa at node 1 and so it is reasonable to assume that the current MSC.Patran FEA model is sufficiently accurate to use in the MSC.Fatigue validations. The reference node (the node which defines the nominal stress) has been chosen to be node 61 since this gives rise to a Kt of 1001/347 = 2.88, which is located at just about one notch root radius away from the notch itself. This reference stress will be called the nominal notch root stress. The MSC.Nastran analysis showed that nominal elastic notch root stress, Sn, divided by the applied load is equal to 11.24 MPa/kN (7.25 ksi/kip). The MSC.Patran FEA analysis gives 347/30 = 11.57 MPa/kN (7.45 ksi/kip). Note that a MSC.Fatigue design optimization analysis carried out at node 181 using a Kt of 1001/87 = 11.5 gives the same answer as an analysis at node 1 with Kt = 1. This illustrates the importance of carrying out a FE analysis to help in estimation of Kt and strain gauge placement. From the above analysis, sufficient confidence is generated by the MSC.Patran FEA model to enable it to be used as part of the MSC.Fatigue global validation procedures.

The materials selected by the SAE Committee were both steels. One was U.S. Steel’s Man-Ten alloy and the other was Belthlehem’s high alloy steel, RQC-100. A summary of the basic smooth (polished) specimen fatigue properties have already been discussed.

The stress-life properties are stored in MSC.Fatigue’s materials database manager, PFMAT, as MANTEN_SN and RQC100_SN. PFMAT can be invoked from within MSC.Patran under the MSC.Fatigue Materials Info form by pressing the Database Management button in the top right corner or directly from the command level by simply typing the symbol pfmat. It is not necessary to actually run PFMAT for to reproduce the results of this problem unless you wish to view the S-N curves.

When invoking PFMAT the main menu allows you to list, search, create, edit, and graphically display existing data sets as well as help to classify welded details. In this case, the datasets for MANTEN and RQC100 are already stored in the standard database, which is held in a read-only location for security reasons. Since you do not need to edit the data, you can use the data stored in the secure database.

Now you can look at the S-N curves graphically. First use the Load menu to load MANTEN_SN and RQC100_SN datasets into the database manager memory locations for material 1 and material 2. Then choose the graph option from the main menu. Note that RQC100_SN gives longer lives at all stress ranges. The key to determining this is to pick a certain stress level and go across horizontally until you hit the S-N curves. The more spread apart two S-N curves are in the horizontal direction the longer lives the one further to the right will give relative to the other.

Use the following keystrokes to perform the above task (note that most of these commands can also be accomplished with a mouse):

Three load histories were selected by the SAE Committee for use in their evaluation. It is important to emphasize that these sequences are not intended to represent standard loading spectra in the same way that Carlos or Falstaf have done. However, they do contain many features which are typical of ground vehicle applications and, therefore, are useful in the evaluation of life estimation methods.

The first load history has a predominantly tensile mean which reflects sudden changes in mean such as occur from transmission torque measured on a tractor engaged in front-end load work and is referred to as the TRANSMISSION history. The second load history has a predominantly negative mean obtained from the bending moment on a vehicle suspension driven over a proving ground and is referred to as the SUSPENSION history. The last is a load history representing a vibration with nearly zero mean load obtained from a mounting bracket, referred to as the BRACKET history. All of these histories contain uncalibrated values scaled to +/- 999 and are stored in files saetrn.dac, saesus.dac, and saebrackt.dac, respectively.

For the purposes of the global validation the three time histories have been scaled by MSC.Fatigue’s time history database manager, PTIME to provide a set of data which correspond to the local load levels used in the actual laboratory tests. The loading levels are given in Table 14‑2.

An example of how to use PTIME to scale the above mentioned time histories is given here. Once PTIME has been invoked, (either from the command level by typing the symbol ptime or from within MSC.Patran from the MSC.Fatigue Loading Info form by pressing the Database Management button), use the following operations. The instructions shown below need to be repeated for each of the scaled time histories in Table 14‑2, if you desire to investigate all of them. Only the first is shown.

After this PTIME session a file called saetrn15.dac will exist in your directory as well as the ptime.adb and ptime.tdb files. This session assumes you are invoking PTIME for the very first time and you are working in a clean directory. Most of these commands can also be performed with the mouse.

To set up the MSC.Fatigue job for an S-N component fatigue analysis of the keyhole specimen, invoke MSC.Patran or MSC.Fatigue Pre & Post and fill out the MSC.Fatigue forms as shown below. In order for the fatigue analysis to be performed correctly you will need the files key.out and key.txt which can be found in the examples directory delivered with your MSC.Fatigue system.

<install_dir>/mscfatigue_files/examples

The file key.out contains the geometry of the specimen and key.txt contains the FEA results which must be translated into binary format before proceeding. This is done with a special utility program called RESTXT delivered with your MSC.Fatigue system. (It can be invoked by simply typing the symbol restxt at the system prompt.) After translation the new file is called key.res. (In most instances FE results will be stored in and accessed from the database.)

Unless stated otherwise, parameters not specifically specified should retain their default values.

Results for all load history and material combinations are tabulated in Keyhole Results, 1207. For our specific example here, the results can be seen by opening the Results form. From this form, you can read results into the database for making contour plots or enter a separate program (PFPOST) for listing the results in tabular form. This latter method is convenient for quickly identifying the life at our reference node 61. To quickly assess the damage:

The analysis at node 61 predicted life of approximately 20,000 repeats of the time history. When using component S-N curves, it is only necessary or valid to evaluate the fatigue life at the reference location. The stress plotted on the S-N curve corresponds to the stress at node 61, however, we know that failure will actually occur at node 1 (at the notch). Therefore the actual fatigue life at node 1 is what is reported at node 61 in this example. Life or damage contour plots of S-N component results will be meaningless and therefore the results are not necessary to be read into the MSC.Patran database.

Now to answer some of the objectives of this problem, you must set the action to Optimize from the MSC.Fatigue Results form. This will invoke a separate MSC.Fatigue module called FEFAT from which we can answer these questions. Remember you want to investigate the effect of the S-N scatter via the design criterion, the effect of mean stress, and the difference between the two materials under investigation:

Note at this point that the same exact result is presented for Node61 (i.e., ~20,000 repeats). Now change the design criterion.

For a 96 percent certainty of survival you can expect the life to decrease to approximately 12,000 repeats. Now investigate mean stress.

For a most conservative answer, you would want to select Goodman mean stress correction answer of ~8000 repeats at 96% certainty of survival. Now investigate the other material.

Note that at 50% certainty of survival, RQC100 does better with a life of ~47,000 repeats (~20,000 repeats for MANTEN) than it does at 96% (~7400 repeats, ~12,000 repeats for MANTEN) even though earlier we determined that RQC100 was a better material at all lives based on the S-N curves. This fact is due to the statistical nature of S-N curves where the scatter in the S-N data for RQC100 is much more variable than for MANTEN.

The exact same finite element analysis results are used in this example as were used in the previous S-N example of the keyhole specimen. The finite element analysis was performed with a static loading of 30kN and the results stored under the jobname KEY.

In case you skipped the previous example, the results are stored in the file key.txt and must be translated from a text format to a binary format using the MSC.Patran’s utility program called RESTXT delivered with your MSC.Patran system. After translation the new file is called key.res. (It can be invoked by simply typing the symbol restxt at the system prompt.) In order for the fatigue analysis to be performed correctly, you will also need the file key.out. Both can be found in the examples directory delivered with your MSC.Fatigue system. The file key.out contains the geometry of the specimen.

<install_dir>/mscfatigue_files/examples

The same materials as in the previous S-N analysis example are again used in this example. One is U.S. Steel’s Man-Ten alloy and the other was Belthlehem’s high alloy steel, RQC-100. The specimen was polished, and the surface was untreated. A summary of the basic smooth (polished) specimen fatigue properties have already been discussed.

The strain-life and cyclic stress-strain properties are stored in MSC.Fatigue’s materials database manager, PFMAT, as MANTEN and RQC100. PFMAT can be invoked from within MSC.Patran under the MSC.Fatigue Materials Information form by pressing the Database Manager button or directly from the command level by simply typing the symbol pfmat. It is not necessary to actually run PFMAT for this problem unless you want to view the strain-life, or cyclic stress-strain curves.

In this case, the datasets for MANTEN and RQC100 are already stored in the standard database, which is held in a read-only location for security reasons. Since you do not wish to edit the data, you can use the data stored in the secure database.

You can look at the strain-life curves graphically. First use the Load menu to load MANTEN and RQC100 datasets into the database manager memory locations for material 1 and material 2. Then choose the Graphical display option from the main menu. Then choose to graph the strain-life curves. Note that RQC100 gives longer lives at all strain levels except in the transition zone. The transition zone is where the elastic and plastic lines that make up the strain-life curve cross each other. To the right of the transition zone is known as the high-cycle regime where elastic effects dominate. To the left is the low-cycle regime where plastic effects dominate. Plot also the cyclic and monotonic stress-strain curves for the two materials. Can you tell which one exhibits cyclic hardening and which exhibits cyclic softening? (MANTEN is hardening and RQC100 is softening.)

Use the following keystrokes to perform the above task (note that most of these commands can also be accomplished with a mouse).

The specimen was loaded with three random time histories corresponding to typical histories for transmission, suspension, and bracket components at different load levels.

The three load histories were selected by the SAE Committee for use in their evaluation and are the same as those used in the previous S‑N analysis of the keyhole. The same scaling was used as already discussed and shown in Table 14‑2. Use step three from the previous example to obtain the appropriately scaled time history. It is assumed that you are starting from a fresh, empty directory.

To set up the MSC.Fatigue job for a crack initiation fatigue analysis of the keyhole specimen, enter MSC.Patran or MSC.Fatigue Pre & Post and use the following keystrokes shown below. It is assumed that you are starting from a fresh, empty directory. If a parameter is not specified, accept its default.

Results for all load history and material combinations are tabulated in Keyhole Results, 1207. For our specific problem, the results can be seen by opening the Results form from the MSC.Fatigue main form. You can either read results into the database for making contour plots or you can enter a separate program (PFPOST) for listing the results in tabular form. This latter method is convenient for quickly identifying which node has the shortest life. To quickly assess the most damaged nodes:

From this, we can see that Node 1 has the most damage associated with it and a fatigue life of approximately 6200 repeats.

For a quick contour plot of the log of life in repeats of the time history, do the following:

You may want to zoom-in on the critical area to see it better.

Now to answer some of the objectives of this problem you must change the action to Optimize on the Results form in MSC.Fatigue. This will invoke a separate MSC.Fatigue module called FEFAT from which we can answer the questions. Remember we wish to analyze the effect of different surface finishes and treatments and also investigate the effect of mean stress as well as evaluate the two different materials.

Note at this point that the same exact result is presented for Node 1 (i.e., ~6200 repeats). Before answering the above questions, look at the damage distribution. Press the End button to continue.

This Cycles/Damage histogram capability gives you an idea of where the majority of the damage is coming from. In our example, we can see that there are a lot of cycles with a low stress range and fewer with a high range. We would expect the high stress ranges (this means a broader hysteresis loop on the stress-strain plane) to give us most of the damage. When you toggle the cycles histogram to a damage histogram you see that this is indeed the case. There is, however, a fairly wide damage distribution at the higher ranges which means we cannot point to a single event causing damage. Now to see the effect of surface treatment and finish.

Each time you do a recalculation, you are presented with a table listing the various surface finishes or treatments and the corresponding lives. From these tables, you can see that there is at least a factor of 2 difference better or worse when using various surface finishes and treatments. This means the effect is worth considering as a way to improve or reduce the life depending on your design life requirements. Now for the effect of mean stress:

You can see that the two mean stress options, Smith-Watson-Topper (SWT) and Morrow give lives less than that achieved using no mean stress correction (~6200, ~9100, ~10500 repeats, respectively) with the SWT method being the most conservative. This is to be expected since the time history we are using (SAETRN) has a predominantly tensile mean. If the time history had a predominantly compressive mean (SAESUS), then we would expect to see the two mean stress correction methods giving longer lives than no correction. If the time history had a roughly zero mean (SAEBRAKT), then all three methods would give approximately the same answers. This is indeed what the results show in Keyhole Results, 1207. Now change the material to RQC100.

It is clear that RQC100 is a superior material using all mean stress methods.

The exact same finite element analysis results are used in this example as were used in the previous two examples of the keyhole specimen. The finite element analysis was performed with a static loading of 30kN and the results stored under the jobname KEY.

In case you skipped the previous examples, the results are stored in the file key.txt and must be translated from a text format to a binary format using the MSC.Patran utility program called RESTXT delivered with your MSC.Patran system. After translation the new file is called key.res. (It can be invoked by simply typing the symbol restxt at the system prompt.) In order for the fatigue analysis to be performed correctly you will also need the file key.out. Both can be found in the examples directory delivered with your MSC.Fatigue system. The file key.out contains the geometry of the specimen.

<install_dir>/mscfatigue_files/examples

In addition, you will need to define a shape factor, K solution, sometimes known as a Y-compliance or beta function. MSC.Fatigue contains a library of compliance functions which contain the means to calculate the fracture mechanics stress intensity factor, K. Please see Crack Growth (Ch. 7) for a discussion of the K Solution Library.

The geometry of our keyhole specimen is similar to the compact tension specimen for which there is an entry already in the K Solution Library. To define the particular dimensions of the keyhole you must invoke PKSOL by typing the symbol pksol at the system prompt or you may access is during the MSC.Fatigue setup in the Solution Parameter form when the Analysis Type is set to Crack Growth. Once in the PKSOL module, enter the following keystrokes to define the proper K solution. A file called keyhole.ksn will exist in your directory at the conclusion of the PKSOL execution.

The dimensions can be set up in any units as long as the units used when defining the initial and final crack lengths and any notch dimensions are the same as defined in the compliance function. Initial and final crack lengths are defined in the MSC.Fatigue setup mode. If you wish you can plot the Y function vs. crack ratio using MSC.Patran’s XY plot application from the Solution Parameters form.

The same materials as in the previous S-N and -N analyses examples are again used in this example. One is U.S. Steel’s Man-Ten alloy and the other was Belthlehem-s high alloy steel, RQC-100. The specimen was polished, and the surface was untreated. A summary of the basic smooth (polished) specimen fatigue properties have already been discussed.

The da/dn curves are stored in MSC.Fatigue’s materials database manager, PFMAT, as MANTEN and RQC100. PFMAT can be invoked from within MSC.Patran under the MSC.Fatigue material form by pressing the Database Manager button or directly from the command level by simply typing the symbol pfmat. It is not necessary to actually run PFMAT for this problem unless you want to view these da/dn curves.

In this case, the datasets for MANTEN and RQC100 are already stored in the standard database, which is held in a read-only location for security reasons. Since you do not need to edit the data, you can use the data stored in the secure database.

You can look at the da/dn curves graphically. First, use the Load menu to load MANTEN and RQC100 datasets into the database manager memory locations for material 1 and material 2. Then choose the graph option from the main menu. Then choose the Graphical display option to plot the effective and/or apparent K plots. Note that the apparent K plot is non-linear whereas the effective K plot is linearized. The effective K plot has taken into account and correctly modeled all correction effects such as environment, history, closure, etc., and linearized the apparent K plot.

The specimen was loaded with three random time histories corresponding to typical histories for transmission, suspension and bracket components at different load levels.

The three load histories were selected by the SAE Committee for use in their evaluation and are the same as those used in the previous two examples of the keyhole. The same scaling was used as already discussed and shown in Table 14‑2. See step 3 from the first example for an explanation of the loading histories and their proper scaling. It is assumed that you are starting in a clean, empty directory.

To set up the MSC.Fatigue job for a crack growth analysis of the keyhole specimen, enter MSC.Patran and enter the following keystrokes shown below. Unless specified, accept all defaults.

Before completely filling out the Materials form, we need to digress a bit to create a special MSC.Patran group which contains the node or nodes of the specimen which define where the nominal or far field stress occurs since this is the stress that a crack growth analysis expects. (The stress that would be there if no crack were present including the notch.) To do this follow these instructions without closing down the MSC.Fatigue forms.

Now that the new group is created you can continue to fill out the MSC.Fatigue forms.

The following notes are made about the job setup:

Results for all load history and material combination are tabulated in Keyhole Results, 1207. For our specific example here, the results can be seen by opening the Results from the MSC.Fatigue main form.

From the results summary page, we can see that the crack grew to final length of a little over 0.2 inches in approximately 1400 repeats of the time history. The mode of failure was by exceeding the fracture toughness of the material.

Now to answer some of the objectives of this example you must change the Action on the Results form to Optimize. This will invoke a separate MSC.Fatigue module called PCRACK from which we can answer these questions.

This essentially reruns the analysis and puts up the summary report page again except that this time we are allowed to see the crack grow graphically. The same exact results are had as before. Now introduce a residual stress.

The job stops after only approximately 58 repeats with no significant growth. The residual stress has retarded/stopped the crack growth. Now change the material to RQC100. Since we know from the previous example that RQC100 is a superior material, we might expect that the life will be extremely enhanced.

Surprisingly, RQC100 has a longer crack initiation life but a shorter crack propagation life than MANTEN. Apparently RQC100 is more ductile that MANTEN by the fact that the crack grew to a length of about 0.6 inches as opposed to MANTEN, which only grew to about 0.2 inches, even though it lasted longer.

The results tabulated, starting with Table 14‑3, indicate the comparison between the actual measured lives and those calculated by MSC.Fatigue. For the purposes of validation, the MSC.Fatigue lives listed below will be taken to be the definitive answers. Any significant deviations from these results must be considered to indicate regression of the analysis code.

Plots of measured vs. predicted lives for the Crack Initiation and Crack Growth comparisons of the tabulated data are also presented, starting at Figure 14‑3. For the Crack Initiation comparisons only, the Smith-Topper-Watson (STW) results are plotted. The solid straight line on each plot represents the one to one correspondence if predicted life exactly equaled measured life. The two straight dotted lines represent a three times factor indicating a goodness band. A point lying above the solid line represents a conservative life estimate in comparison to test results. Generally, the correlation is well within the expected scatter band.

The results for the crack growth problem can not be consistently reproduced using this model without experimenting with the initial crack size and mean stress. The crack growth analysis is very sensitive to the initial crack size, the indicated mean stress and also the far-field stress chosen to do the prediction. The results table shows the mean stress and initial crack size chosen for each case. This is deemed acceptable since during the SAE study of the keyhole specimen, the mean stresses and initial crack sizes were not consistently or properly monitored.

The following conclusions can be drawn from this example: