Low Ductility of a Beam Working Primarily in Shear 3

[Logan82]

Hi,

I have received the results of a Charpy Impact Test on a steel beam made of A7 steel. The test indicates that the steel is brittle (8 J at 0°C). My beam is utilized mostly in shear, and slightly in bending. CSA S16-19 31.1.1 indicates that "Brittle fracture is a fracture mechanism taking place in the presence of tensile stresses and accompanied by limited or no plastic deformation before fracture at a stress level significantly lower than the yield point of the material".

Does having a low ductility also have an impact if a beam works primarily in shear?

 

[CDG31]

My thoughts are that you can compare it, in terms of shear, to a concrete beam without reinforcement. Concrete is a brittle material yet it has its own shear capacity and definitely needs reinforcement to help with tensile forces. I think your case is similar. I would make sure the beam has plenty of capacity for tensile forces developed due to the moment since brittle failures are definitely not desired, since they don't provide any warning before failure.

 

[Lomarandil]

Mohr's circle means that shear stresses in one orientation are tensile stresses in another orientation.

So yes, a low-ductility steel like A7 would be more likely to experience a brittle failure than a high-ductility steel (although most shear failures are considered fairly brittle anyway, excluding those related to element slenderness).

That said, low-ductility material is not inherently prone to fracture -- that would require some other root cause like a material flaw, crack initiation, impact, etc. They are two phenomenon, sometimes but not necessarily linked.

Typically, this all gets handled just by using a lower working stress limit (higher factor of safety before yield) for A7 steel. Is that appropriate in your case, or do you have a specific reason to dig further into this?

----
just call me Lo.

 

[dhengr]

Logan82:
A7 steel was has been around for a long time and performed quite well under many normal conditions. I agree with Lomarandil that this issue is more a matter of engineering experience and judgement as regards any special details or loading conditions, than an issue with A7 steel itself. Using an appropriate FoS, not working it right up to yield, paying attention to any impact loading, inspecting for any cracking or damage during usage, and in particular good clean design and detailing so as not to cause any stress raisers, and the like, is probably the most important consideration. Look back at the early AISC manuals (or like CA codes) to see what allowable stresses and design criteria they worked with and kinda try to live within that design regimen.

 

[Logan82]

Sorry for the delay, I was away in a remote location.

Thank you all for your replies!

In my case, the standard allowable stress criterias are met, and from my understanding there are no wrong details in the design. However, I think the standard allowable stress criterias are not sufficient, since brittle fracture can happen at "[...] a stress level significantly lower than the yield point of the material" (CSA S16-19 31.1.1). But I have no clue how to determine that.

Typically, this all gets handled just by using a lower working stress limit (higher factor of safety before yield) for A7 steel.

Where can I find such higher factor of safety for A7 steel?

Is that appropriate in your case, or do you have a specific reason to dig further into this?

Thank you Lomarandil, your answer is really appropriate, but I think I have to dig further, in the sense that I have to determine the specific factor of safety required. In my case, I have low temperatures, impacts, primary members in shear at the end of the members and bending in the center (so tension).

 

[Lomarandil]

Logan, does it meet today's allowable stress provisions, or do you mean the historical working stress limits? (13ksi allowable shear, as I recall). The latter is what I referred to previously.

To dig further into this would be to perform fracture analysis based on a known or assumed maximum flaw.

----
just call me Lo.

 

[Logan82]

It meets today's code allowable stress provisions, using the historic yield strength of steel at the time of construction, that is Fy = 30 ksi. This yield strength was validated using samples in a lab.

I think I found where your 13 ksi comes from:

In the allowable stress theory, a reduced maximum allowable stress is compared to a non factored applied stress. I can compare that maximum allowable stress with the limit state design of the CSA S16-19 by working the equations like that:
For pure shear, the allowable stress in steel would be:
Reduced_resistance > Factored_load
0.9 * 0.6 * Fy > 1.5 * Live_load (here I have taken the maximum factor of 1.5 for building loads, which is for live loads)
0.9 * 0.6 * Fy / 1.5 > Live_load
0.36 * Fy > Live_load

For Fy = 30 ksi:
0.36 * 30 ksi > Live_load
10.8 ksi > Live_load

In my case, it would be more conservative to use the new standards than 13 ksi. I would get 13 ksi if I replaced 1.5 by 1.25 in my equations.

"[...] perform fracture analysis based on a known or assumed maximum flaw."

How can I do that? I know about Charpy V-Notch test, but I have not heard about this test.

 

[Lomarandil]

It isn't a test per-se, it is an analysis procedure -- mostly performed in the mechanical/aerospace world.

Again, without a known/assumed flaw size or stress raiser in the detailing, fracture analysis may at best provide a lower-bound analysis, or might not provide any real valuable information. Fair warning. We don't know the full story, but in most cases, as long as the shear stress is under the allowable, and there isn't any significant change in the function of the beam -- I'd be content without running fracture analysis.

Essentially (as I recall from my course 15 years ago!), using some complex (literally) math on a given problem geometry, a critical stress intensity factor (K) can be defined at which the flaw (assumed elliptical or crack-like) will grow essentially unrestrained through the material -- a fracture failure. Your Charpy test result can be correlated to a material fracture toughness parameter(K_IC). If the material toughness exceeds the critical stress intensity factor, fracture will not occur in that circumstance.

This website gives a pretty reasonable overview of the basics of fracture mechanics. I'll have to look for my course notes sometime to see if they are any more practical, but they're buried at the moment.


----
just call me Lo.

 

[Logan82]

It is very interesting that we have the science to go in such depth regarding crack analysis. However, in my case, I would close this structure if I had found any crack in the primary members, and I would repair it / replace it.

Your Charpy test result can be correlated to a material fracture toughness parameter(K_IC).

This is something I have already looked for, but I could not find much in the litterature.

[...]without a known/assumed flaw size or stress raiser in the detailing, fracture analysis may at best provide a lower-bound analysis.

How can I perform a fracture analysis without an existing crack? Could it be by assuming a very small crack (for instance 1 mm)?

 

[Lomarandil]

Right, in the aerospace world, rather than analyzing an existing crack (say in the case of a new airframe), they would assume the maximum size flaw that would not be detected by whatever QC measures were in place.

----
just call me Lo.

 

[Logan82]

https://www.fracturemechanics.org/history.html[/URL]]The quandary addressed by fracture mechanics is that on the one hand, linear elastic solutions for stresses at crack tips in structures predict they should immediately fail under any(!) load, no matter how small. Of course this doesn't actually happen. On the other hand, the stress concentrations can be responsible for failures occurring at crack lengths much shorter than what would be necessary for yielding failure of the remaining uncracked portions (think of glass). It is these 'issues' that make the field of fracture mechanics so challenging, and intriguing.

I think this theory is more for research than real life structural application currently, since we don't know:
[ul]
[li] Where the crack will be[/li]
[li] The future crack size[/li]
[li] The future crack geometry[/li]
[li] The exact steel grain configuration[/li]
[li] Taking into account the fact that the steel in my structure is brittle, we don't know if a large crack could develop suddenly (similar to glass) [/li]
[/ul]

 

[Lomarandil]

It's a niche case.. sometimes applicable in "real life structural design" (I've done it), but uncommon for sure. Most structural engineers wouldn't know about it.

Now, the steel grains don't come into play in any meaningful sense at the scale we are discussing. And while your steel is brittle in the relative scheme of steel -- it's nowhere near as brittle as glass.

Only you (or your EOR) can make the final decision of whether any fracture analysis is merited.

----
just call me Lo.