# Fatigue calculation using Abaqus Viewer

The present day design goal tends to be “Design for Warranty”. Warranty describes about life of component or at least the timeline within which the component will provide optimum efficiency or maintenance free functioning for the desired life. Fatigue is a phenomenon which occurs due to repetitive loading. Fatigue analysis is a method which can predict components life in hours or in terms of factors.

As FEA software’s reduces time, effort and cost by reducing the need for prototyping, there has been a steep rise in their demand and hence price. At times there might be unavailability of fatigue software’s due to licensing or budget issues, but it is still possible to predict the components life using our static analysis results and basic fatigue equations. Stress life (S-N Curve), Strain Life (ɛ-N Curve), Crack Propagation (fracture Mechanics) and Vibration approach (Frequency response) are four widely used FEA methods for calculating Fatigue. For metals and High Cycle load cases, Stress life approach is used for hand calculation of Fatigue factor.

#### Good man curve and equation are as follows

(σa /σen )+ (σm /σuts) = 1 ————– Good Man Equation

(σa /σen )+ (σm /σyield) = 1 ————– Soderberg Equation

(σa /σen )+ (σm /σuts)2 = 1 ————– Gerber Equation

σa = Alternating Stress σm = Mean Stress

σen = Endurance Limit σuts = Ultimate Strength

σyield = Yield Strength

From the above shown curve, it is observed that Goodman line falls between Soderberg and Gerber line. Hence fatigue factor calculation using Good man should yield conservative result. In the graph, we can plot a point using Stress amplitude and Mean stress and if the point lies within Goodman line then the component is assumed to have infinite life and anything outside the region is assumed as finite life or failure.

#### Sample S-N Curve

#### Effect of Prestress in Mean Stress Calculation

In most cases we tend to ignore the assembly stress or prestress and directly calculate the fatigue factor or safety factor. As this might result in wrong prediction it is better to include the assembly stress or prestress in mean stress calculation. Prestress will be present in models due to assembly process like bolt tightening and manufacturing process like rolling, stamping etc,. Except pure alternating load, mean stress will be present in components throughout the loading cycle. The effect of prestress due to bolt tightening and other manufacturing processes will have influence in the mean stress, as this might lead to tensile or compressive mean stress, where the former decreases life and latter increase life. Hence the effect of prestress should be included in mean stress calculation.

#### Fatigue Factor Calculation

A Linear or Non Linear (without material nonlinearity) FEA model can be solved using Abaqus solver for any static load case and stress and displacements can be viewed using Abaqus viewer. As Abaqus viewer allows user to create a cycle between different load steps, loading cycles can be approximated using the following options

Abaqus Viewer » Tools » Create Field Output » From Frames

The Abaqus viewer can calculate the stresses for newly created loading cycle or load step by using the raw stresses. The Max and Min stresses viewed from these steps indicate stress range.

From Abaqus viewer we can get following values assembly stresses and stress range. From these two values mean stress and stress amplitude can be calculated as shown below.

Mean Stress, **σ**m = Prestress + (Stress range/2)

Stress Amplitude, **σ**a = Stress range/2

Now Fatigue factor can be calculated by rearranging Goodman equation

Fatigue factor = (**σ**a /**σ**en) + [1- (**σ**m /**σ**uts)]

#### Conclusion

From the Goodman equation, if the fatigue factor is greater than 1 then the component is said to have infinite life or life more than the specified cycles obtained through S-N Curve. The above method holds good only for ductile materials and high cycle fatigue (HCF) cases.

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