MULTIAXIAL
For multiaxial calculations, the winLIFE MULTIAXIAL module is required in addition to winLIFE BASIC.
From Component Loading to Local Stress/Strain
The knowledge of the local stress (stress, strain) is an essential prerequisite for a fatigue life calculation. There are different problems that need to be solved using different theoretical approaches. On the one hand, the type of component to be analysed (rigid, flexible, multibody system) plays a role, and on the other hand, the type of load.
Loads can be specified as loadtime histories (time series), as load spectra (frequency of load steps) or as spectral density of the load as a function of frequency (power density spectrum). When to use each of these methods is briefly explained here.
Component 
Load given as 
Solution method 
Interface macros / 
Elastic body
Max. excitation frequency < 1/3 of the lowest natural frequency 
Load time history 
Superposition of standard FE load cases by corresponding scaling of loadtime functions 
FEMAP, ANSYS 
Load spectrum 
Superposition of standard FE loading conditions by corresponding scaling of the load time functions 
FEMAP, ANSYS 

Power density spectrum 
Random Fatigue: 
Calculation possible, but requires considerable preparation on the part of the user. 

Multibody systems, partially elastic, large relative movements, inertial forces 
Load is specified in the FEM/MKS system 
Transient analysis: Import of the stress tensor time function from FEM/MKS calculation 
FEMAP 

The loadtime function acting on the component is specified 
The modal stresses and coordinates are calculated and then superimposed using the loadtime function 
RecurDyn / FEMAP 
Transient analysis: Import of the stress tensor time function from FEM/MKS calculation 
FEMAP 

Power density spectrum 
Random Fatigue: 
Calculation possible, but requires considerable preparation on the part of the user. 
SUPERPOSITION OF FE UNIT LOAD CASES: RIGID BODIES UNDER THE INFLUENCE OF TIMEVARYING LOADS
If a rigid body is subjected to one or more load variables (force, moment), the locally occurring stresses and strains can be calculated by combining the (measured) loadtime function with statically determined unit load cases.
The stress tensors obtained from the unit load cases are scaled with the measured loadtime functions and superposed for each time step. The result is a stress tensortime function which is used as the basis for the damage accumulation calculation. This method is applicable if the deformations of the body are small relative to its dimensions.
For this example (figure) we therefore need:
 The curve of the forces as a function of time (time series): F1(t),F2(t),F3(t)
 The results of the associated FE unit load cases.
In each case, a force FFE1, FFE2, FFE3 acts with the same line of action and point of application as the associated force. The results of the FE calculation are the stress tensors in each node of interest (the surface) for each load case.
NONLINEAR, TRANSIENT ANALYSIS: VARIABLE COMPONENT GEOMETRY AND TIME AND/OR DIRECTIONVARYING LOADING
If a body changes its geometry significantly or if the directions of the acting forces change or if inertial forces occur, the superposition method described above is no longer suitable for the calculation. An example of this is an excavator (Fig.) whose bucket is moved in such a way that the three angles alfa, beta and gamma change over time. In addition, the external load changes due to the moving load. In this case, the behaviour of the excavator can be calculated using a MBS/FEM simulation. The forces and stresses at each point of interest can be calculated for each point in time. The stress tensor, which fully describes the stress state, can also be specified.
If you now export the stress tensors for the nodes of interest k for each time step t, a fatigue life calculation can be performed with winLIFE based on this. In this way, other geometrically nonlinear variable components and vibration states can also be analysed.
Components under the Influence of Rotating Principal Stresses (Multiaxial Stresses)
The calculation of components in which the principal stress directions rotate is considerably more complex than the calculation of components in which the principal stress direction does not change. This case, known as a multiaxial problem, usually has a larger number of external loads, but at least 2 external loads, e.g. a shaft under torsion and bending.
However, there are often dozens or even hundreds of independent loads, usually defined by measured time signals. Such problems can be found in various areas of mechanical engineering, such as car bodies, axle components, crankshafts, rotating hubs in wind turbines, etc.
The following figure shows an example of a dynamically loaded axle guide. It is loaded by a horizontal and a vertical force group F_{1} and F_{2}. As the groups of forces are not proportional to each other, the direction of the principal stress can change (multiaxial problem).
The calculation time for multiaxial problems is considerably longer than for uniaxial or biaxial problems. Therefore, only the nodes on the surface are considered. Since damage usually originates from the surface, this restriction does not limit the solvability. As there is a planar stress state on the surface, the calculation is further simplified.
If the angle f or the ratio of the two principal stresses s2/s1 is variable over time, it means that we are dealing with a multiaxial case. Mohr’s stress circle can also be used to decide.
Because it is possible to calculate a multiaxial problem in a simple way without disadvantages if the change of stress direction is only small, the grade of multiaxiality must be determined at the start. For this purpose WinLIFE shows the angle f and the principal stress ratio s2/s1 for characteristic time steps presented by a point ().The location of the points helps to identify whether a multiaxial problem really exists or if a simplified calculation can be done by assuming that the case is biaxial.
Damage Parameter
Since the stress situation in the cutting plane consists of normal and shear stresses, these must be used to ascertain a damage equivalent size. The following equivalent stress hypotheses or damage parameters are possible:
 Normal stress  , shear stress and modified von Mises criterion,
 Findley
 Smith Watson Topper, P. Bergmann, Socie and Fatemi Socie,
Fatigue Life Calculation Depending on the Direction / Welded Joints
Particularly in the field of wind energy and ship building, structure stress concepts are common since very large components can hardly be calculated in any other way. In winLIFE several variations of structure stress concepts have now been included. You will need an entry file with the stress tensors extrapolated on the weld and the normal unit vectors.
How a fatigue life calculation is carried out
Using static FEA and superimpose according to (measured) load time histories
The calculation is carried out in the following steps as can also be seen in a simplified manner.
 Firstly, a FE loading condition must be calculated for each effective load. This must be done with a “unit load”.
 A material SN curve must be defined in the same way as a stress SN curve for a uniaxial case. In the case of Local Strain Approach an eNcurve must be created.
 The time needed for the calculation can be considerably reduced if critical nodes are preselected. This selection can either be made by the user entering node numbers, or winLIFE can perform an automatic analysis to find the nodes that are most likely to be the critical ones.
 If a hysteresis is carried out and if you only take into consideration the reversals in common, then the loadtime function can be reduced to the events relevant to the damage. This considerably reduces the time needed for the calculation.
 The stress tensor for each selected node and each time step is calculated based on the unit load cases and the loadtime functions.
 Then, according to the critical cutting plane method, the shear stress and the normal stress is calculated for each node and time step for every plane. With this data, an equivalent stress or a damage parameter can be calculated. There are several hypothesis and damage parameters available, which the user has to select.
 The equivalent stress available for each node, time step and cutting plane is classed according to the rainflow method and a damage calculation is carried out. The plane with the greatest damage is the critical one. This result is taken as the damage for the node.
Modale Superposition
You can analyse properly dynamically loaded components by static superposition as described before only if the frequency of the excitation is less than 1/3 ot the first natural frequency of the system. If the condition is not met you need to decompose the signal in single shares for each natural frequency (modal coordinates). Furthermore you need to calculate the stress tensor for each natural fequency.
To performe the modal superposition you have to calculate two charateristic quantities:
 The natural frequencies and the related stress tensor
 The modal coordinates. These represent the share of the signal which excites the structure in the related frequency
This procedure is formally identical to the static superposition.
Using Strain gauges
When strain rosettes are used and the strain is measured, a fatigue calculation based on this data can be carried out. The data can be read directly and a flexible readin tool is available (see next figure).
A fatigue prediction can be done for that point, where the measurement has been done.
How to reduce the calculation time
The extensive possibilities for interactively processing the loadtime function are also available in the multiaxial module. It is therefore possible to process the loadtime function interactively.
Analysis of the results
In a multiaxial case it is possible to analyse the results in the following ways:
 Mohr’s circle showing the critical cutting planes for each node and all considered time steps. The arising stress conditions can then be seen (diagram 6).
 largest principal stress vector for each node and all considered time steps
In addition there are numerous possibilities of showing the sum of damage with the FEA program postprocessor.
The accuracy of the results for multiaxial problems will generally not be as good as those for uniaxial or biaxial problems. For this reason a conventional calculation should be carried out whenever possible in addition to the multiaxial calculation.
Reliable information can be ascertained regarding the critical places where a tear can be expected. Combining test results and the Relative Miner’s Law, it is also possible to make helpful forecasts regarding the quantity.
Partial load analysis
If several loads are acting on a component it is often interesting to know what influence the individual loads have on the damage sum. This can be ascertained with the partial load analysis.
We will now examine the following three alternatives. (To distinguish the alternatives, we use symbols recognisable from the set theory.)
 ∃ (= it only exists once) Only one of the existing loads is taken into account. The others are all set at Zero.
  ∃ (=it does not exist exactly once) one of the acting loads is set at = 0 while all other loads remain unchanged.
 ∀∃ (as required) the user can select combinations as required.
For each existing loadtimefunction a column L1, L2, .. is created for the multiplicator. If this =1, then the loadtimefunction is used unchanged. If it is =0 the corresponding loadtimefunction will be set at =0.
The index column relates to the matrix line number.
Rotating Loadings / Load File Split
The calculation of rotating components is possible with a static superposition of scaled unit load cases. A rotation is observed in several equidistant splayed windows and the loadtime function is broken up into individual loadtime functions which only correspond to the value when within the splayed window. Outside the splayed window, they are equal to Zero.
Under the menu item Extras /Tools / Split Load an input mask opens. The contents of the file are shown in the window.
If there are any commentary lines, these will have to be skipped over. Enter the number of commentary lines in the designated box. In the example here there are no commentary lines (=0).