XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> Concluding Remarks
This exercise has served to introduce the Crack Initiation method which uses local strain and is mostly accredited to Manson and Coffin; the material parameter, c, is named after Coffin. The cyclic stress-strain curve and the strain-life curve have been introduced as well as the Neuber notch correction method.
Other Notch Corrections
Other elastic-plastic correction methods are available in MSC Fatigue which are valuable to use for very low cycle fatigue where the Neuber method tends to break down and not be as accurate. To use the other methods (Seeger-Beste or Mertens-Dittman) you need to define a parameter, αp. These methods, as αp tends to infinity, revert to the Neuber method.
This parameter, αp, is known as a shape factor or a limit load ratio (Lu/Ly). Ly is the yield limit and Lu is the limit load where you assume elastic-perfectly plastic behavior yield stress (+ or -) across the whole section. To determine Lu it becomes a simple integration (if you have a simple geometry). If you also have a small notch, the Kt of the notch will reduce the yield load but not the limit load (much) so the shape factor goes up. These ratios generally fall somewhere between 1.5 and 3. See the MSC Fatigue User’s Guide for a more detailed definition of αp and its value for some standard shapes.
The diagram above compares an elastic-plastic FE analysis to the Neuber and other notch
correction methods.
Stresses vs. Strains
In this example we used stresses from our FE model. We could have just as easily selected the strains to use instead. We would expect to get exactly the same answers, however there are a few things to be
aware of.
1. Young’s Modulus must be the same as that used in the FE analysis and that defined in the material BS4360-50D. Otherwise the strains reported in the FE model will be different than the ones calculated by MSC Fatigue when converting stresses to strains.
2. The number of rainflow bins can influence the accuracy between using stress vs. strains. Try this as an exercise to see the influence of the number of bins on the fatigue life prediction.
From the Results... form select Re-Analyze and enter Node 981 2314 3650. These are the nodes with the highest stresses. This will run FEFAT for you. When FEFAT appears accept all the defaults except change the Matrix size to 64. Then do it for 128 bins. Note that the fatigue life predictions increase to over 14,000 cycles. Now go back to the original job setup and change the General Setup Parameter, FE Results: to Strains, and go to the Loading Info... form and select the Strain Tensor in the Load Case ID column. Re-run the analysis and do the same Re-Analyze operation as you did when using the stress FE results. Note that for 32 bins, the same exact results are determined for all three nodes. Even for a higher matrix size, the strain FE results are less conservative than when using the FE stresses. This is because the resolution of the bins is better when using stresses.
3. You should be very careful using FE strains from plate models. Because many FE codes do not calculate or do not include the out-of-plane strain (εz), which is needed to determine the proper strain combination parameter (max. abs. principal, signed von Mises, etc.), it is safer to use the stresses from the FE analysis.
4. One final thing to be aware of using FE strains: the strains that are usually stored in the database when imported from a typical analysis code such as MSC Nastran are stored as strain tensors, not as engineering strain. MSC Fatigue multiplies the three shear strain components by two to convert them to engineering strain before using them in a fatigue analysis. This does not happen when external result files are used.
