More Than You Ever Wanted To Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating

More Than You Ever Wanted to Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating Stresses

There’s one last complication to consider with fluctuating stresses. When we looked at the case of fully reversed stresses (that is, σ_m = 0, σ_a ≠ 0) we found a fatigue stress concentration factor based on the stress concentration factor for a static situation.

With a fluctuating stress, the situation is a little different. Since the mean stress is non-zero, the part is always under some kind of load. We can consider the effects of this constant mean stress separately from the effects of the momentary alternating stress and assign them a separate fatigue stress concentration factor, which we’ll call K_fm.

Let’s think about what’s actually physically happening to a part being subjected to a fluctuating stress. Let’s say we’re dealing with a plate with a slot in it subjected to fluctuating tension.

More Than You Ever Wanted To Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating

There’s obviously a large stress concentration at the slot that we’ll have to take into account.

There’s three different scenarios which can occur here. The first is that the maximum stress the plate sees (the largest value of combined mean and alternating stress, taking stress concentrations into account) never approaches the yield strength of the material. The plate just stretches and contracts elastically. This isn’t really any different from our previous situation with fatigue stress concentration factors - we can use the K_f factor we got earlier here.

More Than You Ever Wanted To Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating

But suppose the yield strength is exceeded. What happens then? If the maximum stress is greater than the yield strength, then the plate must deform plastically at that point of maximum stress - the slot must widen. If the slot is wider, then the stress concentration is relieved - there’s more room for movement before the geometry stops you. If other words, the fatigue stress concentration factor is lessened.

If it’s just your maximum stress that exceeds the yield strength but your minimum stress is still below it, this localized yielding will be one-sided - you’ll get a slot that’s widened on one side, but you’ll still have some overall mean stress. If this is the case, you base your stress concentration factor on the relationship of the mean and alternating stresses to the yield strength.

More Than You Ever Wanted To Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating

If both your minimum and maximum stresses exceed the yield strength of the material, you get a situation where you’ve widened the slot as far as you can without actually breaking the part on both sides and you’re experiencing a stress of magnitude equal to the yield strength at either extreme of the fluctuation. Since you now have a fluctuation with equal and opposite extremes, your mean stress is zero - the mean fatigue stress concentration factor is zero. The scenario is now one of fully reversed loading and the mean stress drops right out of it.

More Than You Ever Wanted To Know About Mechanical Engineering, Part 33: Stress Concentrations With Fluctuating

More Posts from T-sci-eng and Others

7 years ago

coolest physics thing that u know??

The coolest physics thing that I know keeps changing over time. But here is one that is extremely fascinating ( and also exaggerated for the effect ; but true! ):

Person living at the top of a skyscraper experiences time faster than one at the bottom

It is a known fact that the higher you are in the earth’s ** atmosphere, the lesser the effect of gravity is.

But the lesser the effect of gravity is, the faster the time ticks.

image

By how much you ask? Even if you live on the top floor of the Burj Khalifa  your entire life, you would have aged more only by a few milliseconds than your friends at the bottom. 

( Sure, doesn’t seem like much, but hell would break loose if we don’t consider this on the bigger scale of things )

This is known as Gravitational time dilation and is at the foundations of General Theory of Relativity. (More about this in an upcoming post)

Have a great day and thanks for asking!

EDIT: ** Lets just say hypothetically the earth is not spinning( just to ignore special relativistic effects) and we are looking at only the effects of height.

7 years ago
Ceramics: Aluminum Nitride
Ceramics: Aluminum Nitride
Ceramics: Aluminum Nitride
Ceramics: Aluminum Nitride

Ceramics: Aluminum Nitride

First synthesized in the late 1800s, aluminum nitride’s potential wasn’t realized until a hundred years later in the late 1900s. AlN is a ceramic with high thermal conductivity but is an electrical insulator. It is classified as a covalent compound, the only stable compound in the binary Al-N system. 

AlN is similar in properties to beryllium oxide (BeO), but is cheaper and has less of a potential to be toxic. In addition to the properties mentioned above, this ceramic also has high chemical resistance and exhibits piezoelectric properties. 

Thanks to its thermal and electrical conductivity properties, AlN is useful in microelectronics. It is used in microelectronic packaging, surface acoustic wave sensors, in RF filters, as a crucible for the growth of gallium arsenide crystals, in piezoelectric MEMs applications, and many more. In addition, the wurtzite phase of aluminum nitride, w-AlN, is a wide band gap semiconductor material, with potential applications in deep ultraviolet optoelectronics. 

Because AlN is a covalent compound, high pressures or sintering aids are required to assist densification during production. Typical additives include rare-earth or alkaline-earth oxides, such as yttrium compounds. The additives and sintering conditions used can alter the properties of commercially available grades of AlN.

Sources: ( 1 ) ( 2 - images 2 and 3 ) ( 3 - images 1 and 4 ) ( 4 )

7 years ago
Does One Of These LEGO Men Look Bigger Than The Other? They’re Actually The Exact Same Size, But Are

Does one of these LEGO men look bigger than the other? They’re actually the exact same size, but are in an Ames room - a false-perspective illusion room that tricks your brain into thinking things are smaller, or larger, than they really are.

You can make one of these models to try this for yourself. Download our free template from here. And it even works in full size, if you can make one large enough!

Does One Of These LEGO Men Look Bigger Than The Other? They’re Actually The Exact Same Size, But Are
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Chances Of Hypersonic Travel Heat Up With New Materials Discovery

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Hypersonic travel means moving at Mach five or above, which is at least five times faster than the speed of sound. When moving at such velocity the heat generated by air and gas in the atmosphere is extremely hot and can have a serious impact on an aircraft or projectile’s structural integrity. That is because he temperatures hitting the aircraft can reach anywhere from 2,000 to 3,000 °C.

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But, at present, even conventional UHTCs can’t currently satisfy the associated ablation requirements of travelling at such extreme speeds and temperatures. However, the researchers at The University of Manchester’s and the Royce Institute, in collaboration with the Central South University of China, have designed and fabricated a new carbide coating that is vastly superior in resisting temperatures up to 3,000 °C, when compared to existing UHTCs.

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Apparently One Whale Years Ago Was Observed Doing This For Hours And Now More And More Whales In The

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Instead of expending any energy actively hunting, the whale just holds its mouth open wherever fish are being hunted by birds. To escape the birds, the fish try to hide in the whale’s mouth because it’s a darker area that looks like shelter. …They’re turning into giant, sea-mammal pitcher plants.

https://onlinelibrary.wiley.com/doi/epdf/10.1111/mms.12557?referrer_access_token=bXLTS5BeSw_vlIKHkM0bYIta6bR2k8jH0KrdpFOxC654HjreJ8D19K86UreR5JPsSRb0CuGhiJSV1L1ht-N1Gf_K_1a9MREFzQGU9oJDNctsKDin_HXcYEdsLg3EbcTl

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Møbius Donut.

Møbius donut.

7 years ago

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2. It is mathematically possible to build an actual time machine - what’s holding us back is finding materials that can physically bend the fabric of space-time.

3. Siberia has a colossal crater called the ‘doorway to the underworld’, and its permafrost is melting so fast, ancient forests are being exposed for the first time in 200,000 years.

4. The world’s first semi-synthetic organisms are living among us - scientists have given rise to new lifeforms using an expanded, six-letter genetic code.

5. Vantablack - the blackest material known to science - now comes in a handy ‘spray-on’ form and it’s the weirdest thing we’ve seen so far this year.

6. It’s official: time crystals are a new state of matter, and we now have an actual blueprint to create these “impossible” objects at will.

7. A brand new human organ has been classified, and it’s been hiding in plain sight this whole time. Everyone, meet your mesentery.

8. Carl Sagan was freakishly good at predicting the future - his disturbingly accurate description of a world where pseudoscience and scientific illiteracy reigns gave us all moment for pause.

9. A single giant neuron that wraps around the entire circumference of a mouse’s brain has been identified, and it appears to be linked to mammalian consciousness.

10. The world’s rarest and most ancient dog isn’t extinct after all - in fact, the outrageously handsome New Guinea highland wild dog appears to be thriving.

11. Your appendix might not be the useless evolutionary byproduct after all. Unlike your wisdom teeth, your appendix might actually be serving an important biological function - and one that our species isn’t ready to give up just yet.

12. After 130 years, we might have to completely redraw the dinosaur family tree, thanks to a previously unimportant cat-sized fossil from Scotland.

13. Polycystic ovary syndrome might actually start in the brain, not the ovaries.

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17. Human activity has literally changed the space surrounding our planet - decades of Very Low Frequency (VLF) radio communications have accidentally formed a protective, human-made bubble around Earth.

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7 years ago

If you trace the orbits of Earth and Venus over 8 years, this is the pattern that emerges

7 years ago

That Time We Flew Past Pluto…

Two years ago today (July 14), our New Horizons spacecraft made its closest flyby of Pluto…collecting images and science that revealed a geologically complex world. Data from this mission are helping us understand worlds at the edge of our solar system.

image

The spacecraft is now venturing deeper into the distant, mysterious Kuiper Belt…a relic of solar system formation…to reach its next target. On New Year’s Day 2019, New Horizons will zoom past a Kuiper Belt object known as 2014 MU69.

image

The Kuiper Belt is a disc-shaped region of icy bodies – including dwarf planets such as Pluto – and comets beyond the orbit of Neptune. It extends from about 30 to 55 Astronomical Units (an AU is the distance from the sun to Earth) and is probably populated with hundreds of thousands of icy bodies larger than 62 miles across, and an estimated trillion or more comets.

image

Nearly a billion miles beyond Pluto, you may be asking how the spacecraft will function for the 2014 MU69 flyby. Well, New Horizons was originally designed to fly far beyond the Pluto system and explore deeper into the Kuiper Belt. 

image

The spacecraft carries extra hydrazine fuel for the flyby; its communications system is designed to work from beyond Pluto; its power system is designed to operate for many more years; and its scientific instruments were designed to operate in light levels much lower than it will experience during the 2014 MU69 flyby.

What have we learned about Pluto since its historic flyby in 2015?

During its encounter, the New Horizons spacecraft collected more than 1,200 images of Pluto and tens of gigabits of data. The intensive downlinking of information took about a year to return to Earth! Here are a few things we’ve discovered:

Pluto Has a Heart

image

This image captured by New Horizons around 16 hours before its closest approach shows Pluto’s “heart.” This stunning image of one of its most dominant features shows us that the heart’s diameter is about the same distance as from Denver to Chicago. This image also showed us that Pluto is a complex world with incredible geological diversity.

Icy Plains

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Pluto’s vast icy plain, informally called Sputnik Planitia, resembles frozen mud cracks on Earth. It has a broken surface of irregularly-shaped segments, bordered by what appear to be shallow troughs.

Majestic Mountains

image

Images from the spacecraft display chaotically jumbled mountains that only add to the complexity of Pluto’s geography. The rugged, icy mountains are as tall as 11,000 feet high.

Color Variations

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This high-resolution enhanced color view of Pluto combines blue, red and infrared images taken by the New Horizons spacecraft. The surface of tPluto has a remarkable range of subtle color variations. Many landforms have their own distinct colors, telling a complex geological and climatological story.

Foggy Haze and Blue Atmosphere

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Images returned from the New Horizons spacecraft have also revealed that Pluto’s global atmospheric haze has many more layers than scientists realized. The haze even creates a twilight effect that softly illuminates nightside terrain near sunset, which makes them visible to the cameras aboard the spacecraft.

Water Ice

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New Horizons detected numerous small, exposed regions of water ice on Pluto. Scientists are eager to understand why water appears exactly where it does, and not in other places.

Stay updated on New Horizons findings by visiting the New Horizons page. You can also keep track of Pluto News on Twitter via @NASANewHorizons.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

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