- What is the modification ouput "testcourse distance" good for?
- What does FEMFAT has to do with STATISTICS?
- How can I combine FEMFAT results in the "Results Manager"?
- How do I evaluate a failure probability and range of dispersion?
- How can FEMFAT results be retrospectively exported to an *.odb file?
- What can the Formula Editor in the Results Manager be used for?
- What is the meaning of the entries in the *.rfm file?

**Test course distance**

The test course distance is used for the recalculation of the damage for a damage value over a certain distance. This means that if the load spectrum used refers, for example, to a 5 km test course, then 5 can be entered here to calculate the damage result for a one kilometer test course. The reciprocal of the damage then provides information about how many test course kilometers can be completed until the damage value of 1 is reached. Thus, the damage result is divided by the value in the "Test Course Distance" field.

**CAUTION****:** The scaling of the damage only takes place in the FEMFAT result file (*.dma)!

Lets assume that FEMFAT produces a damage value of 0.8 from a calculation; how should this value be interpreted? First of all a couple of details need to be cleared up. If, for example, the value has been produced at an FE-node subject to a singular load (e.g. force application, center node of a parabolic element with beam, rod or RBE connection), then this must be excluded from the usual assessment.

Suppose you need to look at an "assessable" FE-node with value D=0.8, then the material file used in FEMFAT is the point from which to proceed. The material file contains a percentage for the survival probability. This survival probability (Pü) of e.g. 97.5% (typical for most FKM materials), indicates that for the specified load, and assuming a Gaussian normal distribution, 97.5% of samples will take a larger number of load cycles before crack initiation. Remember: the S/N curves used in the FEMFAT materials are "crack initiation S/N curves".

In statistics, a Gaussian distribution is uniquely described by the mean value and the standard deviation. In the Haibach method, the ratio of the number of load cycles N90% at which 90% of the samples are cracked to N10% the number of load cycles at which only 10% of the samples are cracked, is used as the range of variation TN. The standard deviation s and the range of dispersionTN are related by the equation:

This equation is obtained because the 90% and 10% quantile for a standard normal distribution lie 1.28*s to the left and right of the mean value. FEMFAT processes the range of variation TS, which describes a similar behavior but only for the vertical direction i.e. the amplitude stresses. In the low-cycle region before the fatigue cycle limit, the two ranges are related by the gradient k of the S/N curve:

Thus a damage value of D=0.8 means that 80% of the possible load cycles up to fracture for 97.5% survival probability have been reached. In order for FEMFAT to be able to process materials with different survival probabilities, and also make predictions for a definable survival probability, the fatigue strength is corrected using the statistical influence factor. If "u" is the standardized random variable of the Gaussian normal distribution with mean value=0 and standard deviation=1, then for a material with Pü=97.5% and a selected survival probability of 99.9%, the fatigue strength is now just 90.312% of the original value (ignoring other influencing factors):

Pü [%] | u | f (50%) | f (90%) | f (97,5%) |
---|---|---|---|---|

50 | 0,0000 | 1,0000 | 1,12250 | 1,19330 |

90 | 1,2816 | 0,89087 | 1,00000 | 1,06308 |

97,5 | 1,9600 | 0,83801 | 0,94065 | 1,00000 |

99 | 2,3263 | 0,81079 | 0,91011 | 0,96752 |

99,9 | 3,0902 | 0,75682 | 0,84953 | 0,90311 |

99,99 | 3,7190 | 0,71511 | 0,80271 | 0,85334 |

99,999 | 4,2649 | 0,68076 | 0,76415 | 0,81235 |

99,9999 | 4,7534 | 0,65143 | 0,73123 | 0,77735 |

For endurance-limit safety factors the procedure is as follows: take a material with 90% survival probability and range of Dispersion TS =1.25 (samples have a distribution which sufficiently approximates the standard normal distribution); if the FEMFAT result now gives a safety factor SD=1.4 for constant mean stress in a FE-node, it would be theoretically possible to increase the amplitude stress by 40% or one reads from the following graph (see FEMFAT basic user manual) the increased component survival probabilities (lower failure probability), i.e. 99.99999 % - generally quite adequate for components in the automobile and passenger transport industry.

The "Results Manager" allows FEMFAT results to be scaled and combined, and the results of several analysis runs to be amalgamated to form a single result. Any number of FEMFAT results (fps files) can be imported into the "Results Manager" and combined.

Overall, there are three different options available for combining the data:

Fig. 1: "Result Manager" input

1. Using the "critical" setting the respective extreme value from the main results (safety factor, damage, degree of multiaxiality,…) is exported to the result file together with the corresponding secondary results (1/safety factor, stresses, gradient,…).

2. Using the "Linear" setting the values or their reciprocals are combined linearly, depending on the analysis method. The mean of the secondary results is formed using a weighting factor derived from the main results.

3. Using the "Formula" setting, the FEMFAT results can be combined with great flexibility by means of a uses-defined equation. Equation input can be performed using the buttons in the menu or via the keyboard.

Example: different total damage for a Load spectra

In this case, the stresses over a crank angle of 720 degrees were analyzed by means of the dynamic simulation of a conrod. The damage at five different engine speeds (1,000 to 5,000 rpm) was combined (Figure 1) by means of modal superposition and participation factors in ChannelMAX.

Using Method 2 - "Linear", the individual partial damages arising from the various speeds can be added to a defined number of load cycles to form the overall damage:

The ensuing fps file can now be represented in VISUALIZER (Figure 2) and exported in any postprocessor Format.

Fig. 2: Visualization of the combined results

If the Option 3 equation was used for combining, the results are available as "User-defined results" (can be edited).

Instead of the standard deviation s common in statistics, FEMFAT works with the load-related range of dispersion . The load cycle-related range of dispersion is determined from the load cycle number N90%, at which 90% of specimens are cracked to the load cycle number N10%, at which only 10% of samples are cracked. The following simple relationship exists between and , where k is included as the slope of the S/N curve:

The range of dispersion can be specified for separate node groups by the user on the FEMFAT GUI. This value may vary between 1.1 and 1.6 depending on the component, material and manufacturing process. For example, in FEMFAT a value of 1.5 (after Radaj) may be specified for analyzing a welded joint in structural steel.

The default range of dispersion is defined as 1.26. This value corresponds (after Haibach) to chip-forming machining of steel components with low to medium notch effect or of notched cast iron components.

How are survival probability and failure probability related?

Fig. 1 shows the relationship between survival probability PU on the top and the failure probability on the bottom of the diagram for various ranges of dispersion. The diagram was compiled using the Gaussian distribution (log N) usual for FEMFAT, the rated survival probability is 90%.

One type of failure probability can be determined from

where represents the failure probability identified using the simplified method, because statistical data, e.g. on dispersion ranges for operating loads from several measurements, are often not available.

can be used in simplification in place of the true failure probability if the dispersion ranges for operating loads are small compared to the dispersion ranges of dynamic strength, or the ratio of standard deviations of the normal distributions of load/strength is small. If this is not the case, the true failure probability approaches the failure probability of a very unfavorable load, which is rarely achieved or exceeded. In many cases, the simplified failure probability may be adopted.

The fatigue safety factor required for a durability assessment with a specified failure probability and range of dispersion can be read from the abscissa of figure 7.

It is sometimes necessary to prepare FEMFAT results for additional postprocessors. When using the *.odb output format for the ABAQUS Viewer a small trick needs to be applied, because the FEMFAT result must always be appended to an existing *.odb file.

Procedure:

1. Import the FE-structure for appending the FEMFAT result by means of the *.odb file.

2. Import the *.fps file (internal FEMFAT result file, also required by FEMFAT visualizer)

3. Define the *.odb output file using a new name.

4. Press the "Write" button!

Using the “Results Manager” (RM), you can manage, or, more accurately, process your results from one or several FEMFAT analysis runs to form a processed results data record.

Let’s assume your company policy requires the investigation of a component for several levels of a stepped load spectrum, however not with respect to the endurance limit as in FEMFAT, but instead with a 2-deflection-point S/N curve.

The 2nd deflection point should be at 70% of the local endurance limit and the 2nd slope should be (2*k-1), as in Miner modified.

SOLUTION: The fps files of the damage analyses of individual collective levels are loaded in the RM and a “formula” is defined for each fps file: if( [File_1:Stress_Ampl.] < [File_1:L ocFatigLim]*0.7),0,[File_1:Damage_ M|mod])

Up to 10 results can be generated in the new fps file this way. Depending on the number of levels, you will get several such fps files which can be processed in another pass to form a single end result. The “linear combination” approach can be used here in which the individual damage results are added up weighted according to their frequency of occurrence.

One of the numerous useful outputs of a MAX analysis is an ASCII file with the extension .rfm.

It contains information about the rain-flow matrix at the critical node.However, if you open this file in an edi-tor, you will see that it contains more than just one 64x64 matrix. But let’s take one thing at a time:

At the very top, you will find 2 lines with the class limits for amplitude stress and mean stress.

Then there are a total of six 64x64 blocks; three each for the closed and open cycles.

The first block contains the number of closed cycles and the second block contains the share (in percent) of the respective matrix entries relative to the total damage.

Analogous to this, the blocks for the number of open cycles follow with their share (in percent) of the total damage.

The fifth and sixth matrix contain the damage referenced to the number of cycles for the closed and open cycles.

These, by the way, are also the same six matrices which you can have displayed in FEMFAT using the rainflow matrix viewer from the Visualization menu.