Better material and load models make fatigue analysis more useful.

The fatigue-life contour plot of an aluminum suspension component was generated by fe-safe from Safe Technology Ltd., and a finite-element computer model. The software correctly predicted failure locations with good correlation to physical tests. |

**John Draper**

Managing Director

Safe Technology Ltd.

Sheffield, England

www.safetechnology.com

By one estimate, premature fatigue fractures in structural components annually cost Europe and the USA about 4% of their gross domestic product. Manufacturers pay the price through long prototype-development cycles, overweight components, unpredictable warranty claims, and loss of customer confidence. The challenge for software developers has been to deliver reliable fatigue-analysis tools because over designing components is no longer a viable option.

In a nutshell, fatigue failures stem from small cracks that initiate in weaker grains or grain boundaries in metals under repeated stress cycles. These cracks may propagate, because of cyclic stresses, until the material fractures. However, accurately calculating fatigue life requires considering every significant load in the service life. Loading complexity and resulting stress states mean fatigue analysis is more challenging than simply designing a component to withstand maximum loads. In addition, it is too computationally intensive to use finite-element software to model the stress-strain response for every event in a long load history.

Several recent developments have transformed fatigue analysis into a capable computer-aided design tool with an accuracy at least equal to other analysis software. For instance, fatigue analysis now takes a single set of FEA results, scales stresses by a loading history, and calculates plasticity at each node on the model. This is done by more computationally efficient fatigue software. Multiaxially loaded components, difficult to analyze in previous software, are now handled by simply superimposing elastic results before estimating plasticity.

Initial design costs are higher when durability assessment is built into the design process because the analysis is more sophisticated. Compensation, however, comes by removing metal from areas that are overdesigned. Lower weight may reduce dynamic forces and produce further benefits in other components. There will also be immediate savings in materials. |

Until recently, these methods could only be applied to uniaxial stress states because of the complexity of calculating cyclic-plasticity effects for multiaxial stresses. Techniques that deliver acceptable accuracy are now available, and it has become common practice to treat all components as multiaxially stressed. Principal stresses that change orientation are handled using critical plane analysis, a search technique that finds the direction of crack initiation at each node on a model.

Another welcome trend: fatigue software that interfaces with FEA programs includes a database of fatigue properties. The fatigue software calculates where and when fatigue cracks will occur (fatigue hot spots), determines factors of safety on working stresses (for optimizations), and finds probabilities of survival at different service lives. Results are presented as contour plots of fatigue lives, stress-safety factors, and probabilities of failure, and are plotted using standard FEA viewers and graphics software.

Other benefits from the technology are less obvious. For example, fatigue-analysis software can identify which loads are important at the predicted-failure points, so prototype testing can be simplified and include important loading. In addition, the software can produce what amounts to warranty-claim curves. These would show the effect of different user profiles on a calculated in-service failure rate, and from this where designs could be refined. The curves might also guide the marketing department if it needs to write exclusions in the warranty. Either way, the information is available to assess both options and make a cost-effective decision.

Our own fatigue-analysis software is being extended into the complex areas of high temperature and time-dependent creep fatigue. These features are applicable to engine design, for example. The capability of the software, fe-safe, now includes:

Fatigue-analysis software develops curves that help estimate warranty claims and, in particular, how they might vary for different users. The curves are generated by fe-safe software from Safe Technology Ltd. |

•The phase relationship between stress and temperature, which can vary from cycle to cycle.

•The bulk relaxation of stresses with time. This temperature dependent effect changes the mean stresses in a component.

•Strain-aging of the material, which progressively reduces the material's fatigue strength over time

Engineers have long struggled with the question: If a cycle starts cold, peaks hot, and finishes cold, what fatigue data do I use? Simulating the four thermomechanical effects listed provides an answer to the question and to those dealing with more complex stress and temperature cycling.

Results of high-temperature fatigue analysis of a prototype automotive piston show a failure as calculated by fe-safe. One design change to make the piston more fatigue resistant increased the radius of the fillet where the crack initiates. |

### A little history on fatigue

Engineers have recognized for over 150 years that metals can fail in fatigue. In 1850s the Institution of Mechanical Engineers in the U.K. discussed results of fatigue tests on wrought iron which was cyclically loaded to simulate 90 years of railway service on an axle. Engineers concluded that the raised shoulders used to locate wheels on the axle contributed to the failures, and there would be no failures if the stresses did not exceed the material's elastic limit.

Three essential axioms of fatigue design were discussed in that period: Failures are caused by cyclic loading, stress concentrations at changes of section reduce the fatigue life, and there is a safe, working stress below which failure will not occur. (The current definition is not as simple as that proposed in 1850.)

Modern fatigue analysis came to life in the 1980s when in-vehicle load measurement became available with analysis software and low-cost computers. Early software analyzed the measured strain histories and was used for prototype assessment and post-failure investigations. Local stress-strain or critical-location fatigue analysis uses a mathematical model of the material's response to each loading event, including the effects of nonelastic stresses that may occur locally in stress concentrations such as fillet radii. This integrated approach works equally well for high-cycle components and those in which some fatigue damage is caused by less frequent high loads. This development eliminates the necessity of separating fatigue into high and low cycles.