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emon11
Post  Post subject: Mechanics of Materials  |  Posted: Sun Jan 29, 2012 1:03 pm

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Hello,

I am an Asst. Prof. of Mechanical Engg. Department and I take classes for the subject Mechanics of Materials. While going through the complex stress and strain chapter I had to give my students an example of the concept of Principal Stress and Principal Plane. I gave them the example of cutting a Birthday Cake with a knife vertically at an angle 90 degrees to the cake surface or slicing a bread toast horizontally where direct stress(compressive in nature in this case) is maximum but shear stress is zero.

I was earnestly looking for some more interesting examples which can be related to day-to-day life. Google couldn't help. Seeking for some help. Thank you.


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marnixR
Post  Post subject: Re: Mechanics of Materials  |  Posted: Sun Jan 29, 2012 1:22 pm
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i seem to remember that 3-dimensional stress/strain was involved in the failure mechanism of the Liberty ships, resulting from sharp angles in a welded structure (+ the lack of appreciation of brittle fracture in welded structures)

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iNow
Post  Post subject: Re: Mechanics of Materials  |  Posted: Sun Jan 29, 2012 3:09 pm
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My immediate thought goes to precision wire saws used in semiconductor manufacturing or in the making of thin film solar panels on glass. This is precise within a few nanometers, and feeds everything from iPhones to tablets to rooftop cells.


Btw - Welcome to the site. Hope to see you around in the various discussions of the community.

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bunbury
Post  Post subject: Re: Mechanics of Materials  |  Posted: Sun Jan 29, 2012 5:23 pm
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How about considering a cylindrical vessel under internal pressure. A domestic hot water tank is an everyday example.


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Ophiolite
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 01, 2012 12:43 pm
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Was the fatigue failure of the hull of the Comet airliners around the windows not an example of this?


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marnixR
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 01, 2012 5:30 pm
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Ophiolite wrote:
Was the fatigue failure of the hull of the Comet airliners around the windows not an example of this?


because they didn't have rounded corners, which then acted as stress raisers

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SkinWalker
Post  Post subject: Re: Mechanics of Materials  |  Posted: Sun Feb 05, 2012 12:26 am
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@ emon11

As our 100th member, I want to say WELCOME!!

I hope you'll stay on board with us for more discussions!


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DrRocket
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 08, 2012 2:23 am
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emon11 wrote:
Hello,

I am an Asst. Prof. of Mechanical Engg. Department and I take classes for the subject Mechanics of Materials. While going through the complex stress and strain chapter I had to give my students an example of the concept of Principal Stress and Principal Plane. I gave them the example of cutting a Birthday Cake with a knife vertically at an angle 90 degrees to the cake surface or slicing a bread toast horizontally where direct stress(compressive in nature in this case) is maximum but shear stress is zero.

I was earnestly looking for some more interesting examples which can be related to day-to-day life. Google couldn't help. Seeking for some help. Thank you.


Max principal stresss is commonly used as a failure criteria in rubbery mateials.

More abstractly the stress tensor is symmetric hence diagonalizable and the associated basis is that in which principle stress is expressed. So one sees that shear is, in a sense, due to a selection of a coordinate system, and is not an invariant.

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DrRocket
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 08, 2012 2:26 am
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Ophiolite wrote:
Was the fatigue failure of the hull of the Comet airliners around the windows not an example of this?


No. That has essentially nothing whatever to do with principal stresses, as opposed to stress in any other set of coordinates. Fatigue failure is the result of repeated load cycles with full reversal of the applied stress, and strain beyond the elastic limit. There are in fact , for various materials handbook data that gives expected lifetime in terms of the number of cycles imposed.

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DrRocket
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 08, 2012 2:28 am
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marnixR wrote:
Ophiolite wrote:
Was the fatigue failure of the hull of the Comet airliners around the windows not an example of this?


because they didn't have rounded corners, which then acted as stress raisers


Stress risers increase l ocal stress as opposed to the far field stress levels, but beyond that they are not a cause of fatigue failure. Fatigue requires cyclic loading.

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marnixR
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 08, 2012 7:40 am
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the following article seems to imply that only low-cycle fatigue was involved, but the investigations clearly highlighted the stress raiser from the design as the crucial factor in making the structure prone to fatigue

"This [the relevant piece of the fuselage] was recovered within a few hours of searching and showed, in the language of the coroner, the ‘unmistakable fingerprint of fatigue’. The fatigue crack was associated with the stress concentrations of the rather square rear ADF window cutout (stress of 315 MPa at edge of window), and with a bolt hole around the window"

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DrRocket
Post  Post subject: Re: Mechanics of Materials  |  Posted: Wed Feb 08, 2012 8:00 pm
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marnixR wrote:
the following article seems to imply that only low-cycle fatigue was involved, but the investigations clearly highlighted the stress raiser from the design as the crucial factor in making the structure prone to fatigue

"This [the relevant piece of the fuselage] was recovered within a few hours of searching and showed, in the language of the coroner, the ‘unmistakable fingerprint of fatigue’. The fatigue crack was associated with the stress concentrations of the rather square rear ADF window cutout (stress of 315 MPa at edge of window), and with a bolt hole around the window"


A stress riser, as I said, can dramatically reduce fatigue life. But it is not in and of itself a cause of fatigue failure -- a cyclic load is required for fatigue.

What I see in the report is that after some 3057 combined flight and test cycles a crack was formed near the escape hatch, and repaired. After another 546 cycles the fuselage failed catastrophically. This is consistent with a poor crack repair, increased stress near the failure initiation point, and final fatigue failure.

I see a statement by a "coroner", but I do not see any clear statement of a microscopic analysis of the material by a metallurgist. Perhaps something is lost in the translation from British English to American English.

A crack is the quintessential stress riser. Ordinary stress analysis is not adequate for structural analysis in the presence of cracks and specialized fracture mechanics, with associated empirically derived fracture allowables for the material, are required for a proper analysis. I note that the report states that stress levels near the crack were only 70 MPa (about 10 Ksi) which is quite low. This suggests to me that there must indeed have been a very significant stress riser at the failure point. A sharp crack might well be the culprit.

Another effect of a crack is to form a point that is particularly vulnerable to corrosion. This can also be severe and in the presence of high stress in appropriate directions and a corrosive environment (a little moisture with free ions to give conductivity) can be quite rapid, as in the case of stress corrosion cracking of high strength aluminum alloys.

Nevertheless in order for fatigue failure a reversing cyclic load is needed. The higher the amplitude of the applied load (which a stress riser will influence dramatically) the lower the number of cycles required to induce failure. http://en.wikipedia.org/wiki/Fatigue_(material)

A stress riser can also cause failure by simply causing the local stress to exceed the allowable stress for the material. This is not fatigue failure, but the difference will be of little importance to a passenger on the plane that is now plummeting to the ground.

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emon11
Post  Post subject: Re: Mechanics of Materials  |  Posted: Thu Feb 09, 2012 2:11 pm

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Ok. The discussion helped me a lot. Thanks to all of u.


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