Machine Design

# How to get a better handle on fatigue

A finite-element-analysis program can pinpoint high stresses in a part or assembly, but that location might not be where cracks first initiate or failure occurs.

A finite-element-analysis program can pinpoint high stresses in a part or assembly, but that location might not be where cracks first initiate or failure occurs. The problem is that FEA often considers only static loads as a simplifying assumption. In the real world, most parts experience cyclical loads which makes them fail from fatigue. Calculating a life or fatigue value is a way to consider cyclical loads along with a stress analysis to predict how long a part might last.

Fatigue analysis isn't new. Most engineering curriculums introduce students to theories of material failure and SN curves, as a way of conducting fatigue analyses. The technology is more recently turning up in programs aimed at designers and engineers who are less expert with FEA methods. DesignSpace 6.0 is one example. It provides a look at how fatigue calculations have been implemented and what they tell about designs.

Stress analysis is a critical first step in the process because fatigue depends on microfractures or small cracks that generally grow with tensile stress more than compressive. "Users import models into the software just as they would for a stress analysis," says Tim Pawlak, a research fellow with Ansys Inc., Canonsburg, Pa. "And models are readied for a fatigue analysis in a manner similar to a stress run: Users apply boundary conditions and mesh, apply a fatigue load, and solve." The difference is that users must supply a cyclic-load description and a failure theory. The software calculates life in terms of cycles and damage to the part in terms of fraction of available life.

Engineers can apply loads for a fatigue analysis several ways. "So-called fully reversed loads, for example, are sinusoidal with the neutral position at zero and oscillating equal amounts in positive and negative directions," says Pawlak. Actually, the sine-wave description can be located anywhere on a load chart so that the midpoint is the median stress.

For many real-world conditions, loading will not be a constant amplitude over time. SAE has sponsored several publications (AE-6 and AE-14) dedicated to understanding and analyzing this type of loading in detail. For standardized real-world loading, SAE provides several sample histories.

These represent loading such as vibration signals taken from an average roadway. Sample loads were collected from strain gages on parts. One such file contains 20,000 points, but larger data files are certainly possible.

Modifications could let sinusoidal loading vary between zero and some positive or negative value, so it would not be fully reversed, and that would change results. The software allows using a sequence of oscillations, such as those from the SAE.

Selecting one of several possible failure modes requires a bit more study. "For instance, the Soderberg failure mode requires identifying the material yield strength. It provides the most conservative results," says Al Hancq, a development engineer with Ansys. It's best applied to standard steel parts. The Gerber theory works better for ductile materials. And the Goodman model works best on brittle materials such as cast iron.

An SN-None condition can be applied to check the results. "It ignores mean stresses," says Hancq. "It's useful after you've completed an analysis using one of the fatigue models and you'd like to know if the mean stress is important. Rerun the analysis using the SN-None condition instead of a failure model and compare results. If results are close, then mean stress is less influential and you have more confidence in the results."

Lab test data is also useful. It usually reports a cyclical load and cycle count at failure. This ideal information can be modified with a reduction factor to produce more accurate or real-world values.Take the example of a U-joint. A fatigue strength-reduction factor of 0.5 applied to the analysis introduces the effects of heat, wear, or corrosion. The example also uses the Gerber theory for a ductile material.

Torsion in the shaft produces pure shear where the shaft joins the U-section. Results indicate that the U-joint will survive a modest 7,500 cycles with reversed loading. From this information an engineer might try to increase the joint's life by reducing the load, redesigning the part, or increasing the fatigue strength-reduction factor to raise the cycle life of the part. For example, perhaps putting a boot around the U-joint to protect it from the weather would justify increasing the factor. A second run with a factor of 0.8 produced a life of 86,000 cycles, and a safety factor of 9.

Another attempt to model accurate loads raised the mean stress of the cyclical load. The software then predicts a life of 59,000 cycles for the U-joint and a factor of safety of 2.7. Applying the Goodman theory for a cast-iron joint lets the software calculate a more conservative life of 21,000 cycles for the same loading.

The fatigue software can perform a slightly more complex output. "For it, the software finds the different alternating stresses and mean stresses and puts them into bins called a Rainflow matrix," says Hancq. Using a 32 32 Rainflow matrix for this problem, a minimum life was found to be 652 loading blocks. A larger matrix would allow for greater precision but would increase computational time. Thus, if the input loading history represents the loading from one week, then the part will last 652 weeks.