# History of Bending Fatigue, Part II

In Part I, we outlined a brief but historical synopsis of mechanical fatigue. Here, in Part II, the next step is to define the appropriate design life model for the application.

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Safety factors cannot replace appropriate evaluation of impending dynamics in fatigue design. Determining the design life model is where the process must begin. Using the best and most complex calculations in strain life, crack propagation, and classical fatigue theory can be for naught if all of the critical contributing factors are not accounted for and examined for their root cause fatigue impact. There are many factors. What these factors are and how you might select them for your application is the topic of this series of articles. However, the first step in this process is to evaluate the appropriate application of the “Life Model.”

Mechanical failures involve interactions of time, load, and environmental conditions. Mechanical forces impacting design life can be cyclic, steady state, fluctuating, shock, monotonic, axial, torsion, compressive, uniaxial, or multi-axial and can also be any combination thereof. By definition, a monotonic test load is applied in sequential increments until the desired state or failure occurs. The duration of critical loads can be a few milliseconds or range over long periods of time as in the case of statically preloaded gears. The interactions of forces, time at load, environmental, thermal parameters, geometry, and specific material selections — in addition to processing, treatments, and induced residual stresses — make for a complex process of building a predictive model of fatigue design life.

Therefore, before an investigation of factors can begin, it is necessary to determine the best design-life model, what testing will be done, and the type of analyses that will be employed to determine the component or system design life.

Regardless of how intense and complex the analytical models of fatigue life are, fatigue is still only moderately understood and the results of analytical and statistical analysis are at best an approximation of design life even in the most defined models. Therefore, it is incumbent on the engineer to do these critical things:

• Define the appropriate design life model.
• Fully define the impending factors impacting design life by specific application.
• Identify and plan the proper analyses for a predictive survival model before data is taken.
• Design an appropriate test plan upfront.
• Be flexible once fatigue results accumulate and make adjustments to the test plan based on error analysis, the residuals of variation, and the critical statistics (to be discussed in later sections).
• Take the right data, in the right amount, according to an understanding of the statistical power of the test and additional reliability metrics.
• Use the best statistical methods for estimating survival life.

Also consider the following:

### Choose the right design life model

• Infinite application Life model.
• Safe-life model.
• Fail-safe model.
• Failure tolerant model.

### Design for infinite application life

These criteria can mean different things to various applications. The goal here is to design the component such that it never fails, hence, the component or system is designed for infinite life. When it comes to industrial components that accumulate millions of cycles such as valve springs or high speed gears and shafts, designing for infinite life might be a good thing; and economical, as well. This is particularly true in machine design where failure may incur personal injury or great financial distress. Sometimes, in commercial power-gearing, a very small upsize in shafting can make the difference between premature failure and infinite application life. In powder metallurgy gearing, a small 6.0% increase in density can result in as much as a 50% increase in bending fatigue strength. However, infinite design life is not always the goal. In the cases where minimum mass and minimum volume are desired, the excessive weight or packaging of an aerospace or automotive component might not be cost effective or justified, and a different design life model should be chosen.

### Design for the safe-life application model

Safe-life design is established on the number of cycles, amplitude, and spectrum of loading. The design is for a specific, yet finite, life that meets or exceeds a predetermined application life expectancy. One common example of a safe-life application is an internal and external spline assembly connection. Fretting corrosion over time and cycles tends to wear and tear away the contact surfaces under repeated cyclic loading. If the connections are designed properly, fretting occurs, but never leads to premature failure. We can call the connection “damage tolerant.” Safe-life design will incorporate a strength margin for the residuals or scatter of failure data about the mean survival and confidence intervals. Appropriate factors of safety must also be intelligently specified for unknown application factors or events the component may encounter. One of the most prevalent applications for safe-life design is rolling elements, particularly for bearings.

Many years ago, I worked on a coupling design a for a tunnel boring machine. The component was required to transmit 13,000 HP and last a minimum of three-weeks at full power. When a failed coupling came back for inspection, we all marveled at the classic surface contact fatigue damage that had accumulated in the most profound way. The coupling was made of Nitralloy in a 50.8 module (0.5 DP). After three weeks of operation, the toothed contact surfaces were infused with spider cracking along the entire 20-inch gear face. It was the best example of contact stress induced crack propagation and plastic flow I have ever seen. Forensic failure analysis is the best education and experience most engineers will ever receive. In the testing phase, we really want to see failures in a controlled and predictable manner. However, in the safe-life application model, the specified allowable design life must be less than tested or simulated results. In the safe life design, the goal is to obtain advance notice by physical or sensorial means to identify components nearing end of life without enduring an actual failure.

### Design for fail-safe application life

This mode of design life is prevalent throughout the aerospace industry since catastrophic failure cannot be tolerated. The durability of a component or system is rigorously tested to determine its design life under many complex loading variables. When the survival life and probability models have been determined, a fail-safe design life is established. When a fail-safe component reaches a certain number of cycles, hours or events, it is taken out of service or replaced. An example of fail-safe thinking is crack growth retarders bonded to integral metallic aircraft structures to enhance fatigue life and in some cases, to heal micro breaches. Fail-safe thinking also requires redundancy so that if one component in the system fails, the whole system does not fail.

### Design for failure tolerance

Damage tolerant design allows for fatigue failure damage that can be tolerated should it occur. For example, if a pinion shears teeth before or after the end of its design life, it may be inconvenient, but it is repairable or replaceable. In addition, the application will involve negligible risk to life and limb. This model says that a system failure is manageable such that extraordinary or uneconomical countermeasures are not needed or warranted. An example might be of gears, bearings, or other mechanical elements in a commercial, industrial, or consumer application. A failure may be sudden, gradual, or inconvenient, but the tolerance for failure is acceptable by design when all the risk factors have been analyzed. If downstream machinery or life and limb are not endangered by the failure or an unsustainable loss of production encountered, then warranty or maintenance becomes the primary factor generally considered in this type of fatigue design model.

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is a senior technical specialist in the development of gearing, drive motors, and power closure devices in the automotive industry. He currently serves on the AGMA Plastic and PM Gearing Committees. Eberle is a master six-sigma black belt and has authored many papers on gearing, measurement system analysis and process statistics. He can be reached at Fred_Eberle@hci.Hi-Lex.com.