History of Bending Fatigue, Part III

The History of Bending Fatigue, Part III
When creating a model simulation for gear and rolling element fatigue, a disciplined approach is the only way to get it right.


In rotating machinery, bending and contact fatigue life is a principle concern in design life. In all wrought and powder metal gearing and mechanical power transmission components, the interactions of forces, time at load, environmental concerns, geometry, and specific material selection — in addition to processing and treatments and inclusive residual stresses — make for a complex process of analysis. Therefore, the investigation of the factors impacting bending fatigue is crucial in order to build a reasonable predictive model of design life.

Having mentored many newly graduated engineers over the years, one question I always ask — and none have ever grasped the concept the first time — is this: “How do you know if you have the right material, or good lubrication, or the appropriate analysis, or all of the right factors in your model; and how do you know for sure?” The question is so fundamental, and the answer is utterly profound — “You make sure.” Then, as always, the response is, “How do I do that?” Again — you make sure of it. Consult subject matter experts, do research, and gather your resources.  Always verify and validate results. Perform conformation runs, if possible. You are the one wholly responsible to make sure you get it right. I cannot emphasize this enough. Quick screening tests and simulated data are extremely helpful in building a robust process and analysis. Then, look at the data and ask, “Is this right? Is it near what was expected? Does the result seem reasonable?” And by the way, the reality is that when the testing is finalized, we discover — much to our missed expectations — ­that we have just learned how to do the test and take the right data in a manner of control and accuracy appropriate to the task. We also discover, upon creating the model and analyzing the results, that more control and discipline were needed to eliminate outliers and variation. Because of this, 80 percent of creating the fatigue model needs be the upfront work of strategy, planning, and executions of the experiment before the first data point is measured. A disciplined approach is the only way to get it right the first time (Figure 1).

Figure 1: Worm gear fatigue.

A significant part of the upfront 80 percent is determining the appropriate design life model discussed previously in Part-II and designing the experiment. These next two parts in the series will be identifying the impending factors that will be crucial to defining the theoretical design life of the component or product in question.

Factors That Impact Fatigue Design Life


Most published fatigue data for steel is based on reversed bending endurance of special polished specimens. Some published data is based on reverse axial cycling and correlated to reverse bending. It is very important to understand what standard published data is and then be able to translate those “general” results to the component or system you wish to model.

In literature, cast iron endurance strength limits for polished RR Moore specimens are often given as 40 percent of its ultimate strength. Wrought steel is taken as 50 percent before any other derating factors are considered. This may be acceptable for the “first cut” thinking of endurance suitability, but certainly not for a more refined model. Published monotonic tensile properties and fully reversed bending of un-notched endurance limits of selected steels give varying ratios of Sn/Su depending on the specific composition of material. In fact, typical wrought steels used in power gearing range from Sn = 35% of Su for Annealed 1020 to Sn = 60% of Su for 4130 Q&T. This is a very large difference. General design texts provide the assumption of Sn = 50% of Su for steel based on polished fatigue specimens. Refining values of fatigue data can significantly enhance the accuracy of design life estimation.
It is recommended that the technologist find simple and unique ways to ascertain the cycle life of critical geometric sections or the component itself. This is done by accelerated or application testing rather than relying on published fatigue data or approximations of tensile strength whenever possible.

However, there is a true benefit of utilizing standard powder metal materials for gearing and mechanical power transmission products. The Metal Powder Industry Federation (MPIF) has done extensive testing of standard fatigue samples on hundreds of material combinations and published the results in MPIF-35. Even so, the technologist still has to ascertain the difference between minimum mechanical properties and “typical” PM properties and the reliability levels at which these were established. In addition to these issues, the data of the polished and standard specimen data must be correlated into values connected to your application. This is why critically analyzing these impending factors is so important.


Metals are classically described as homogenous and isotropic, possessing linear strain behavior within the material yield limit. But on the micro level these behaviors may or may not exist. In a perfect and homogenous material they would. However, heat treatments, cold working, inclusions, point dislocations and discontinuities and other point defects impart variation and may change assumed metal behavior significantly. It is well known that heat treatment, chemistry, alloy and cold working can have significant effects on tensile strength. The extent of that effect must be individualized with all the variables involved because generalizations based on published data may not be all that accurate in any individual case.

Fine grain structures (Figure 2) generally do give greater fatigue resistance over coarse grains (Figure 3).

Figure 2: Fine grain of bronze.
Figure 3: Course grain of bronze.

The mechanics of slip strain show that localized yielding along slip bands can reduce the amount of slipping. Also, crystalline cracking has more opportunity for arrest when an increasing numbers of grain boundaries act to impede crack propagation. Therefore: porosity, material inclusions, delaminating along with the aggregate distribution and shape and orientation of grains all work together to impart variance in fatigue life. Again, this is a significant reason to do a series of screening tests on the material and if possible, on the geometry to be used for critical designs.

Size Effects

Size matters. Fatigue failure results from the interaction of a stress and a critical flaw such that the concentration of stress exceeds the material strength limit and begins the process of crack propagation. The essence is that fatigue failure migrates to the weakest link in the material. Again, size matters. In reversed bending, smaller diameters or thicknesses have more favorable stress gradients projecting from their neutral axis than their larger counterparts. When the neutral axis grows larger, surface stress increases given a constant value of deflection.

Historical fatigue testing has shown for diameters or thicknesses less than 10.0 mm: fatigue behavior in un-notched specimens in reverse bending is largely unchanged. However, the fatigue limit of the 10.0 mm specimen decreases 20 percent to 30 percent as the size of the specimen increases to 50.0 mm. This behavior continues as the specimen gets even larger. The reason: as the geometry increases, the stress gradient distributes over a smaller area ratio and results in larger stress on the surface. Also, statistically-larger diameter or thicknesses, having greater surface area, have a greater probability or (opportunity), of discontinuities, voids and point defects in the regions that enable micro cracking.

Surface Finish

Surface cracking is common for heat rated materials that do not have the quench rate optimized for the material process. Microscopic cracks appear at the surface and failure begins immediately during the design life. Subsurface cracking on the other hand, exists when defects or various heat treatments or surface processing results in a change of microstructure relative to the surface material. However, most fatigue failures occur at the surface where tensile stresses are generally highest. This is always true unless there is subsurface case separation as in plated, clad or carburized metals. Machining causes geometrical irregularities in the metal surface. Surface texture is also introduced in the molding and sintering of powder metal materials. These surface irregularities are in effect multiple stress concentrations whose influence is dependent on the magnitude of finish roughness (Figure 4).

Figure 4: Subsurface cracking.

One of the reasons RR Moore test bars are polished is to take this factor out of the pure fatigue test results so that the difference between a mirror finish relative to whatever the component has, can be accounted for. Mirror polished surfaces are given a derating factor of unity (1.0) and rough surfaced castings can have a factor of 0.20 for an 80% reduction in the endurance limit. Surface effects are generally pronounced over long cycling where many cycles are needed for crack nucleation leading to failure. One of the major problems in gear grinding is grinding burn. The overheating (burning) of the metal surface under coolant quench can cause micro-cracking from the machining process itself. Heat treating can result in quench cracks. In these cases crack nucleation may begin immediately under load leading to infant failure of the component. In addition to these, concentricity and run out is an often overlooked but critical variable. These alone can overwhelmingly define the endurance limit. Eccentric induced bending stresses are superimposed on whatever loading conditions exist and are simply additive to reversed bending. For rotating and axial beams; the farther the neutral axis is away from the surface (i.e. the larger the diameter), the greater the additional surface stress due to eccentricity. Dynamic hysteresis energy can significantly increase surface thermals and opportunities for surface cracking, in some cases greatly diminishing endurance life (Figure 5).

Figure 5: Bending fatigue.

Still to come in Parts IV and V

• Effects of frequency
• Stress concentrations – notch effects
• Residual stresses
• Plating and fatigue
• Environmental concerns
• Fretting and pitting

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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.