Abstract
An operating life analysis is the backbone of managing structural durability successfully and, thus, the focus of this chapter. Therefore, the understanding of the component’s strength behavior as well as of the loads to the structure is necessary. The stress–strength interference is introduced which equally relies on the analysis of the loads and the characteristics of the structure. Hence, load and stress analyses are described in this chapter as well as fundamental strength behavior and fatigue are introduced. We will learn to bring the results into a consistent form and to perform a damage calculation that answers the question as to whether the design is safe and durable enough.
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Notes
- 1.
We learned that about 82% of the population in Germany has bicycles: Do we believe that this number does not include heavyweight people?
- 2.
A truly heavyweight gentleman may ride his bike off-road though it is designed for city roads only: What does that mean for the loads to the structure and finally to the structural stresses? And does it make any difference when that gentleman repeats that regularly?
- 3.
Just before Apple introduced its first iPhone in 2007, the market leader at that time presented the new Nokia N95 slider phone which came with a 21-mm-thick body and a 2.6 in. display. In April 2019, Samsung planned to introduce the world’s first smartphone with a foldable OLED display which is then 7.3 in. in size. According to the manufacturer, the folding mechanism should work more than 100,000 times and they started a final trial with testees who quickly reported about failures. Mark Gurman from Bloomberg sent a Twitter statement (@markgurman) on April 17th: ‘The screen on my Galaxy Fold review unit is completely broken and unusable just two days in. Hard to know if this is widespread of not. The phone comes with a protective layer/film. Samsung says you are not supposed to remove it. I removed, not knowing you’re not supposed to (consumers won’t know either).’
- 4.
The first downhill mountain biking race took place at Fairfax, California, in 1976—and today, it is pretty popular riding a bike at a speed of car on a steep, muddy or rocky slope of a mountain.
- 5.
Hence, the probability of failure has it own density function—and that is what we can see in II and III of Fig. 2.5.
- 6.
The larger the interference region is, the more likely a failure occur—hence, it is more likely for III than for II.
- 7.
August Wöhler performed pioneering work during 1860–1870 when he examined fatigue failures by applying controlled load cycles under constant amplitudes [5].
- 8.
We have to consider that this is the number of load cycles which lead to internal forces—stresses—because of the rotating mass. The obvious source of forces applied to a crankshaft is the product of combustion chamber pressure acting on top of the piston as well as the piston acceleration.
- 9.
Loads are different from stresses and strains—that is something we assume that the reader knows.
- 10.
Residual stresses occur without external loads and are an important factor of the fatigue life of structures.
- 11.
When talking about speed change related to straight driving, that implies both acceleration and deceleration. For the sake of simplicity, here is only acceleration noted, but it is anyway correct because deceleration means a negative acceleration as well.
- 12.
It is quite easy to find lower power three-axis MEMS sensors for max. accelerations of ±16 g at a price of less than 1 €. In one of the biggest manufacturing site, every day more than 4 million MEMS sensors are produced (according to press release of BOSCH Sensortec GmbH—2015).
- 13.
Other designs may use a complex circuitry of numerous strain gages applied to specific locations of the wheel structure that makes it possible to rely on the original wheel structure instead of having a specific design to which the load cells are attached to.
- 14.
About 90% of all strain gages which have been applied at my lab for automotive applications are 3 mm gages, but few others are significantly smaller to catch local strains at locations which have a huge gradient and need more attention to the variation in strain.
- 15.
That is pretty much the same than in finite element analysis (FEA): Once you face a huge strain or stress gradient, you may want to reduce the size of your elements at least in that region and recompute the analysis to get a better idea of the numbers you are computing. The smaller the element size is, the better is the geometrical approximation as well as the nodal interpolation becomes more accurate—and that typically results in an increasing computational strain or stress at the point of interest. Without diving deeply into the theory of math modeling using FEA, it can be said that a standard element with a linear shape function is a ‘constant strain element’—just similar to a strain gage. To get a proper correlation between gage readings and computational strain, the element size should be really small too. Alternatively, the results accuracy of FEA can be improved by using a quadratic shape function which then means that the strain or stress can vary linearly within an individual element. However, it needs to be taken into consideration that a correlation study between computational and experimental strain analysis is not trivial and relies on careful specifications for FEA element type and mesh size as well as strain gage configuration and placement.
- 16.
In 1928, General Motors Company stated about the rationale behind its Milford proving ground: ‘No other industry has gone forward so swiftly with so few basic facts—facts that are needed if the motor car is to be of increasing usefulness to a greater number of people. If the industry is to continue its rate of progress it must know more facts about the material used, the economics of design and what happens as the car is being operated mile after mile upon the road in the hands of the use. To get these facts, General Motors five years ago decided to establish a proving ground and to make it the most comprehensive undertaking of the kind the world.’
- 17.
Here, the dwell time is shown by colors and goes up from blue to light blue, then green, yellow, orange, red and finally black. Such a qualitative information is often fine enough, because even that small region in red color means that the original time history offers many different individual events which then accumulate to such a total time.
- 18.
According to the diagram, there are verticals at roughly 12,500 N which come together with lateral forces from −600 to +1000 N.
- 19.
Although those values have to be different from lap to lap, they are not too much different: It would be unlikely to have huge force differences, since it is the same PG track and the vehicle drivers do know what they do. Hence, we often assume to see a probability density for those values which satisfy a Gaussian distribution representing a real-valued random variable.
- 20.
The Benard-van Elteren test from 1953 is an extension of the Friedman test (1937) which utilizes the method of m rankings.
- 21.
The computer performance today allows many more equidistant levels than the small number used for the example in Fig. 2.15, so this type of inaccuracy is not necessarily a big issue nowadays.
- 22.
‘Driving on poor roads with deteriorating conditions costs motorists roughly $67 billion in additional operating and repair costs annually’ says a policy analysis of the Committee for Economic Development in the USA in May 2017.
- 23.
Dislocation density in metals can be measured by using X-ray diffraction (XRD) analysis.
- 24.
Beachmarks are sometimes called clamshell marks too.
- 25.
Keep in mind that in such a diagram at least the abscissa is in logarithmic scale—hence, the space with regard to the number of cycles between different points is much bigger than expected.
- 26.
Actually, aluminum is the most abundant metal in the world and the third most common element, comprising about 8% of the earth’s crust which makes it today the most widely used metal after steel.
- 27.
Going much beyond 106 and even up to 1010 cycles means to be in the giga-cycle regime, which is another word for VHCF.
- 28.
Actually, that material is often referred to by its old name 18/8 which is derived from its nominal composition with 18% chromium and 8% nickel.
- 29.
Although high-load amplitudes may be introduced, the static load carrying capacity is not exceeded.
- 30.
When using amplitudes, the term Nf actually means the number of reversals-to-failure: Since one reversal is just half of a cycle, so, pretty often we can read the term 2.Nf.
- 31.
As it often happens with name assignment in science and engineering, Anglo-Saxon people do prefer to see their guys as the most important. Hence in English literature, the damage accumulation is often referred to as ‘Miner’s rule.’
- 32.
At that time, it was the majority view to accept an endurance limit for steel and cast iron—hence, the modification was related to the original Palmgren–Miner’s rule which assumed to has a horizontal line below nothing happened in terms of partial damage. When today using Sonsino’s rule of having a 5–10% decrease in fatigue strength per decade, for the modified damage accumulation that does not make any difference: Haibach’s rule reflects on the progressive changes within the material’s structure when having a mix of cyclic stress amplitudes.
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Heim, R. (2020). Operating Life Analysis. In: Structural Durability: Methods and Concepts. Structural Integrity, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-030-48173-5_2
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