Ever design a device that failed under stresses far below what you thought were "safe?" If so, the likely cause of the failure was fatigue. Materials under long-term cyclic loading can fail at significantly less than yield strength. Although this may seem puzzling and even counterintuitive, 60 to 80% of engineering failures are caused by some form of fatigue.
Fatigue typically arises in products such as steel rails, beams, girders, and rotating stepped shafts where materials oscillate through a range of stresses. Typically, fatigue-life data is most readily available for various grades of steel and for certain grades of aluminum. However, you can study any material for which you have tensile properties and strain-life data.
Cyclic stresses can reverse or modulate in intensity. Over time (months to years, depending on frequency), these stresses weaken the material. And the greater the amplitude of stress variations, the greater the effects of fatigue on the material, and the shorter the product life.
Materials that fail by fatigue usually show a unique pattern of crack propagation.A split appears relatively smooth shaped at its initiation point and gradually widens over time until it tears catastrophically. In contrast, materials that fail under stresses greater than yield (instantly or soon after applying the load) usually show jagged tears and are fragmented throughout.
Computer-Aided Fatigue Analysis
Hand calculations, engineering handbooks, and Goodman diagrams all predict the fatigue life of products. But hand calculations are limited and may not be accurate for complex geometry and assemblies. Early fatigue-analysis software computed stress-based fatiguelifecalculations and provided more detail-and accuracy. But the programs, generally tools for "guru" analysts, were expensive and cumbersome.
More-recent fatigue-analysis software, such as FatigueWizard from the United Kingdom and distributed by Algor Inc., is more manageable and affordable. Through an innovative wizard interface, the software makes it easier to perform sophisticated and accurate stress and strain-based fatigue-life calculations.
The fatigue software needs an FEA program to handle static-stress analysis of models because stress or strain results are input as the basis of the life calculations. The software interface guides users step by step to set up a fatigue analysis. A stepped shaft intended for rotating machinery such as a conveyor roll will provide an example of how to set up a fatigue problem.
Users select between either a strain (recommended default) or stress-based analysis. The strain-based method is more recent, allows for plasticity, and is suitable for low and high-cycle fatigue problems. The stress-based method is more traditional, but should only be used on high-cycle fatigue problems.
Fatigue life is influenced by the peakto-peak amplitude of the load variation and also by the mean strain or stress level. For the stepped shaft, the mean strain and stress are zero since the stress magnitude reverses from tension to compression. When the mean strain/stress level is not zero, the Morrow or Smith-Watson-Topper methods (strain-based computations) and the Gerber or Goodman methods (stress-based computations) can be used to properly determine the effect on fatigue life.
Next, apply material properties from the editable material database or by typing in values for the elastic modulus and tensile strength. The software generatesa strain-life curve, which can verify the material data entry.
The number of load cycles to failure for any given material should increase as the amount of strain decreases. This is not a linear relationship, but rather a curve with a decreasing slope — typically plotted using a log-log graph. Improperly entered strain-life data will more likely be detected by seeing a graph as opposed to simply seeing data in tabular form.
Users can enter a multiplier to simulate local stress concentrations not explicitly modeled, such as welded connections. And because surface roughness influences calculations, users select a surface-finishing process, such as polished, machined, or forged.
The next step defines the load history by specifying values for the load multiplier over time. Since the FEA stress/strain data is static and represents the result of a specific, instantaneous load condition, you must define the history of how the stress or strain varies over time.
For the rotating shaft analysis, the multiplier varies from zero to 1.0 to 1.0 and back to zero sinusoidally. This occurs in a rotating object subjected to bending forces. Though the load may be constant, the shaft is continuously being bent in a different direction due to its rotation.
Users can also examine more complex conditions such as transient analyses and multiple-load cases. The software uses stress or strain values from the preceding linear-static analysis. Users then specify a number of repetitions for the loading cycle and have the software calculate either a safety factor or the number of cycles to failure. This example asks for a target life of at least 10 million cycles.
The software presents a summary that indicates whether the design hits its target or not. It also predicts the number of cycles to failure.
Good News, Bad News
Although the preceding linear-static stress analysis for the shaft indicated stresses far below the material yield point, the fatigue analysis indicates the design is unsafe based on the supplied parameters. The software predicts the number of cycles to failure at far less than the required 10 million.
FatigueWizard and the FEA package displays results such as life or safety-factor contours. A customizable, HTMLbased report can be quickly generated in the fatigue software. This report, a requirement by many engineering groups, summarizes the durability results and lets engineers easily share the results with others.
If the design is determined to be unsafe, a bulleted list of suggestions for resolving the fatigue life problem is provided. Suggestions include verifying the accuracy of specified parameters, ensuring that the poor life result isn't due to stress exaggeration (e.g., at a constrained node or a single point of force application), and altering the design of the component if necessary to decrease the stress level.