This chapter on multiaxial life prediction consists mainly of a description of the multiaxial fatigue analysis module FEMLF. This module can be accessed from Analysis on the Main Fatigue form (Analysis > Multiaxial FOS or Multiaxial CI).

This analysis module allows fatigue life predictions and safety factor calculations to be made, even when the loadings are complex and multiaxial, including both proportional and non-proportional loadings. It should be kept in mind that if you are dealing with proportional or near proportional loadings, you may find the standard MSC Fatigue options give sufficiently good results.

The programs normally used during the execution of a multiaxial fatigue analysis are as follows:

The actual programs necessary to complete a global multi-node or element crack initiation analysis are:

Most of the options in this module require surface resolved stresses, i.e. results either from thin shells or using the surface normal extract option for solid models. The exception is the Dang Van method which accepts 2-D or 3-D stresses.

The results may be reviewed using PFPOST, by reading them back into the pre-/postprocessor for postprocessing, or by using the graphical options in FEMLF.

In summary, to run a multiaxial fatigue or safety factor analysis:

The analysis should produce a jobname.fef or jobname.fos result files.

The Multiaxial Analysis options are selected from the main MSC Fatigue form as shown in Figure 6‑1.

On the Solution Parameters form select the Analysis method. If Dang Van is selected the Users is required to input a hardening parameter.

The Dang Van method is a complex method which defines the endurance limit in terms of the microscopic shear stress amplitude and the hydrostatic stress. For details of the method, see the theory on Dang Van Method, 396 in this chapter. The required parameters are the Torsional Fatigue Endurance (or fatigue limit) and the hydrostatic stress sensitivity factor. The Dang Van fatigue limit criterion says that:

where τ is the microscopic shear stress, a is the hydrostatic stress sensitivity, ph is the hydrostatic stress and t is the torsional fatigue limit (fatigue or endurance limit in a pure torsion fatigue test). You may not have access to parameters a and t. However, these may reasonably be estimated if you have some uniaxial data available. For instance, if you know the bending fatigue limit f, t can be estimated from t = 0.577 * f. (For most materials the factor is somewhere between 0.5 and 0.6). The bending fatigue limit may be around 1.25 times the uniaxial tension-compression fatigue limit.

Now, consider the conditions at the bending fatigue limit, where the shear stress amplitude τ will be 0.5 * f and the hydrostatic stress amplitude f/3. We can therefore rewrite equation (6‑8).

which gives a = 0.23.

The hardening parameter has a default value of 0.05. The Dang Van method is an iterative method which converges to a solution. The hardening parameter determines the rate at which convergence occurs. A value of 0.05 is a reasonable compromise between accuracy and speed.

When this form is complete, click OK, complete the Materials and Loading form, and submit the job from the job control menu. Processing will begin and progress can be monitored using the monitor job function under job control.

When the job is complete a listing of the ten worst safety factors is presented.

If you have only selected one node or element for analysis, the program will show you the following graphical output:

It is converted when using the Dang Van Criterion to define a safety factor which may be used to compare the worst loading condition to the fatigue limit criterion.

The definition of safety factor used in FE-Fatigue is:

except when the denominator is less than or equal to zero, when the life is predicted to be infinite, and the safety factor is effectively infinite. For the purposes of contour plotting, an upper limit for safety factors is used in results files, with the default being 100, but which can be set as a preference.

In addition to the safety factor, the following parameters are calculated and written to the results file:

- the value of the microscopic shear stress corresponding to the critical time-history point at which the safety factor is determined

- the value of the hydrostatic stress corresponding to the critical time-history point at which the safety factor is determined

- the projection of the most critical point on the Dang Van diagram onto the t axis, parallel to the Dang Van criterion line.

DF - the "Danger Factor", defined as (A-B)/B in the following figure, i.e.:

If the McDiarmid Method is selected no further input is required on the Solution control form. The only requirement is that stresses be surface resolved.

The McDiarmid criterion can be expressed.

Under uniaxial conditions at the fatigue limit, so if the method is to give the correct answer for uniaxial conditions.

By default, the UTS of the material is taken to be that of the material mentioned in the .fes file, which can be different for different groups in the job. When the analysis is complete, a form lists the 10 worst safety factors.

When Multiaxial Crack Initiation Life Analysis option is selected from the main form Figure 6‑1, the Solution Control lists the available analysis methods. Select the desired analysis method, keeping in mind that the first 4 methods (Normal Strain, SWT-Bannatine, Shear Stress, Fatamie-Socie) are critical plane methods while the Wang Brown method employs a multiaxial rainflow counting algorithm. An explanation of the methods is given below. Mutiaxial properties that have the correct Fatemie-Socie and Wang Brown parameters are available in the materials database parameter for a few materials. Users may add multiaxial data with reference to the rules in Problem 4: Ten Simple Notched Geometries (Ch. 14).

The cyclic plasticity model, necessary for the notch correction procedure, is the Glinka model.

Complete the Materials and Loading forms as per the other solution sequences and submit the Job.

Options 1 to 4 are conventional critical plane models which resolve stress and strain components onto particular planes. Options 1 and 2 make multiple fatigue calculations on planes inclined at 90 degrees to the free surface (X-Y plane) at 10 degree intervals, making 18 planes in all. Options 3 and 4, which are based on shear strain, also consider planes inclined at 45 degrees to the surface, making 36 planes in all. The critical plane is considered to be the one with the largest value of predicted damage. The equations of these methods are as follows:

Multiaxial fatigue is a current research area, so there is still a lot of discussion about what the best methods are, and when they are applicable, and new models are still emerging. We have attempted to provide a sample of what we consider to be the better models. We will also attempt to provide some guidelines as to which models should be used when.

The next question on the form is the equivalent units. By default, the software will give a fatigue life prediction in Repeats of the loading history. If some other units are defined or desired, enter the number of units in one repeat of the history and the name of the units. FEMLF will then give an answer in the equivalent units.

The next two fields are only used for the Fatemi-Socie method and the Wang-Brown method. Sensible defaults are provided if this information is not available. Apart from these parameters, the only other material information required for these methods is the normal uniaxial cyclic parameters.

When this form is complete, click OK to initiate the job. When the job is complete, a form will appear, summarizing the result for the (up to) ten most damaged nodes.

When initial calculations are complete, the results may be reviewed in the following ways:

The options on this form have the following function:

The program FEMLF may be operated in Batch mode. The batch keywords and their meanings are as follows:

femlf /opt=s/inp=jobname/out=y/dammod=N/anareg=all