# Fatigue basics

Fatigue basics (stress or strain based)
Fatigue is the failure induced on a material,upon cyclic load action. Unlike a static load failure (e.g.
break under a high tensile load), fatigue failure relates to dynamic loads that are repeated. Fatigue
is really difficult to predict, as its onset is not visible and fatigue failure happens abrruptly and
suddenly. Typically it consists of three stages: crack initiation, crack propagation and fracture,seen in
Figure 1.
Figure 1: Stages of fatigue
Historically, in order to be able to calculate the fatigue life of components, engineers resort to S-n
curves. This curves have been derived from material testing, under constant amplitude fully
reversing loads (tension-compression) under a zero mean stress. Typical examples of S-n curves
are given in Figure 2.
Figure 2: Exemplary S-n curves
The serious limitation of this methodology, relates to the fact that the theory behind it is based on
elastic stresses or equivalently in cases where the irreversible strains (plastic strains) are really
limited. This is found to be accurate in most cases, whenever High Cycle Fatigue (HCF) is studied.
High cycle fatigue can occur when a component is loaded cyclically under loads with amplitudes
lower than the yield of the material (or for Number of cycles >10^5).
However in the Low Cycle Fatigue (LCF) regime, where the load amplitudes are higher, this theory is
not the most accurate. This happens as this higher cyclic loading, will result in plastic strains on the
material locally, especially in areas that include notches (fillets, radii, cross section changes,surface
roughness etc.). What happen locally in those regions, is that due to the presence of the notches,
the stresses will exceed yield, and thus cause permanent deformations locally. Fatigue failure is
always the product of plasticity, therefore some irreversible deformations are required for fatigue
failure to occur.
Therefore, accurately predicting the fatigue life in the LCF regime, requires some assessment over
the strains that develop on the material and a plasticity correction that will consider the change in
fatigue life due to those strains. The fatigue theory developed to incorporate this assessment, is
called strain based fatigue theory. It is not yet so popular, as it requires strain based testing which is
typically more expensive than stress based testing (S-n curves are derived from that). S-N curves
are readily accessible and more engineers are familiarized with the S-n method.
Another important aspect of fatigue related failure, is the type of cyclic loading that acts upon the
structure. We mentioned that the S-N curves are the product of laboratory testing on smooth
structures, uniaxial stresses rarely occur. Additionally, fully reversible loads are rare in modern
engineering components. They occur on some components (axle components, sliding components
of gearboxes etc) but there are many engineering structures that are under load action not fully
reversing but rather fully relaxed (max tension, zero load, max tension etc.) or non-relaxing (rubber
seals).
A graph of two different types of loading, is given below in Figure 3. for the fully relaxing load, the
mean stress ( average of max, min stresses) is tensile. For the fully reversing load, similar to S-N
curve testing), the mean stress is equal to zero.
Figure 3: Fully relaxing and fully reversing cyclic loads
It is well known and proven, that having a tensile mean stress deteriorates fatigue life, compared to a
load history with a zero mean stress. Therefore in order to accurately predict the fatigue life of our
component, given that the load action is not fully reversing, we need to perform a mean-stress
correction that can result in a decreased or increased (when the mean stress is compressive) fatigue
life. For stress based methods, the Goodman diagram is used. This is a graphical method to be used
in conjuction with the S-N curve in order to make a stress-based fatigue assessment of a real life
component. Strain based methods incorporated in fe-safe, can make the plasticity and mean stress
corrections in a more accurate way, compared to stress based fatigue methods. Strain based
methods are available for both LCF and HCF, whereas stress based methods should only be used in
HCF.
Last but not least, strain based methods are crack initiation fatigue theories. This means that a life
prediction is made up till the moment of crack initiation ( crack propagation and failure will follow).
Stress based methods are total fatigue life theories, meaning that they provide a fatigue life
prediction on the entire lifetime of the component and not only up till crack initiation. Of course fesafe can perform fatigue calculations according to both theories (stress based and strain based).
The software addtionally includes extensive material libraries, wherein corresponding S-N curve data
and strain based test data are readilly available for the user.
Fe-safe Case Study
FEA model and case study details
Fe-safe can calculate fatigue life from both elastic and elastic-plastic FEA if needed. The latter is
supported only as a dataset sequence loading and it is meaningful when there is contact taking
place in an FEA model as well as when gross plasticity is occuring, modifying the load paths.More
information on how/when to use elastic plastic FEA with fe-safe can be found in the knowledge
article (QA00000029000).
For the damage accumulation, caused by different load histories, fe-safe uses Miner's rule.
As an exemplary case study, a planar notched plate of 50x30 mm (notch radius=3 mm), will be put
under static unixaxial tension. The fea model is linear elastic. The respectful loads and BCs of the
model , can be seen in Figure 4. It is noted that a unit stress of 1 MPa is applied on the plate. The
unit stress will be scaled up and assigned a load history (a sinusoidal fully reversing signal) within fe
safe. When the Abaqus job for the linear elastic model is complete, we can append the *.odb as
input into fe -safe.
Figure 4: Loads and BCs of fea model
Figure 5, shows contour stresses at the end of the static step in Abaqus. Although the loading and
boundary conditions are unidirectional for the model, a resulting bidirectional stress state is evident,
due to the presence of the notch. Fe-safe uses the tensorial stresses to calculate fatigue (and not
the von Mises stress shown).
Figure 5: Stress measures at the end of static step analysis in Abaqus
Fe-safe supports various loading methods.The most commonly used (but not only ones available) ,
are shown in Figure 6 below.
From top to bottom in Figure 6:
Single load history (scale and combine)
Multiple load history (scale and combine)
For our case study, a single tensile unit stress was applied in the fe model. Infe-safe we will need to
scale this unit stress up to almost yield levels (300 MPa) and to couple it with a sinusoidal signal, in
order to produce our fully reversing load cycle. We will need the single load history option in fe-safe.
If we had additional loads acting on the plate, having the same or even different directions, we would
be able to calculate the fatigue life via the multiple load history option in fe-safe.
The process that was described above, is shown graphically, in the following figures.
Figure 7: Append to fea results
Figure 10:algorithm selection tab
The predicted log lifes using, biaxial stress life with plasticity correction, uniaxial stress life (normal
stress) with no plasticity correction and biaxial strain life will be demonstrated for the notch plate.
The predicted lifes are written as *.odb and can be directly post processed in Abaqus. Figure 11
shows comparative results of the fatigue life prediction in log scale. The results have been produced
by different algorithms (strain and stress based).
Figure 11: Fatigue life predictions notched plate
Algorithm used
Lowest Predicted
life
Repeats
Brown Miller strain
based
2.86 (node 549)
724
Biaxial stress life
(normal stress) with plasticity
correction
2.9 (node 549)
794
Uniaxial stress life no plasticity
0.22 (node 549)
correction
1.65
As a reminder, the external load level in our case study is high, almost at yield levels, therefore this
is a case study of Low Cycle Fatigue (LCF).
In terms of accuracy, the Brown miller strain based algorithm is the most advanced strain based
algorithm within fe-safe, for assessing ductile metals.
A biaxial stress based algorithm with plasticity correction is a stress based algorithm . This should
only be used for HCF, however the plasticity correction that is not included in a typical S-N curve
fatigue analysis, seems to give a reasonable prediction in terms of repeats until failure, compared to
the Brown miller algorithm. We need to always keep in mind, that stress methods predict life to
fatigue failure whereas strain based methods (such as the Brown miller) predict life to crack
initiation.
Last but not least, if we assess the fatigue life of the notched plate with a traditional uniaxial S-N
curve method (available in fe-safe but advised to be used only for HCF), we can immediately see
the effect on the predicted life. Stress based methods (S-N curve) on the LCF regime, are always
too conservative (underpredict) fatigue lifes as they lack the plasticity correction (thankfully fe-safe
can account for this), effectively leading to oversizing of components in order to account for fatigue.
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Topics: fatigue, fe-safe, Abaqus
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Simuleon blog topics related to Finite Element Analysis like; Structural Analysis and CFD analysis
performed with SIMULIA Abaqus FEA, XFlow CFD, Isight Simulation Automation, Tosca Topology
Optimization and Fe-Safe accurate Fatigue.
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