Net section stress in bending 1

[CamJPete]

Hello all. I'm working a project bound for outer space that has fracture requirements associated with it (NASA-STD-5019). One of these I'm trying to show for my parts is to show "parts have total net-section stresses, e.g., maximum principal or von Mises, whichever is larger, at limit load that are less that are less than 30 percent of the ultimate strength." I've got a finite element model of my assembly that I'll be using to determine what these net section stresses are. There is further explanation later in the section on how to calculate this with a FEM: "For metallic parts addressed in item 6.2.5.a (above), the net-section stresses are to be computed based on strength-of-materials theory. An example of the net-section stress calculation for combined tension and bending stress is detailed in the NASGRO® User’s Manual, Appendix B, in the beginning pages, except no crack or epsilon factor is used for this NFC low-risk application. For complex parts where finite element results are obtained that may include stress concentrations and stress gradients, the net-section stresses are to be computed by integrating the stress distribution and dividing by the area for the sectional area being assessed."

My question is this: how do I treat net section bending stresses? (I've ordered NASGRO, but don't have it yet to know how to do the combined tension and bending stress per their example.) As a simple example, suppose I have a fixed cantilever beam that is FE modeled. If I apply a transverse load at the tip, I'll get stresses due to a bending load on the outer fiber, one side in tension and one in compression. The stress distribution across the net section is assumed linear (although not true), but safe to say there is a region of tensile stress down to the neutral axis and the same for compression. If I take the integral of the stress over this area, it will give me a net stress of zero. I can think of a few ideas on the appropriate way to treat this but wanted to get your thoughts. 1) If I use von Mises stress, it is always a positive quantity, so the net section stress will be positive if using both tensile and compressive stresses. 2) I could use max principal, but need to use the absolute value of stress. 3)I only look at the tensile stress over the tensile stress area and disregard the compressive stress area.

Thanks for your help. I've been mulling this over for weeks and its finally time to tackle the analysis.

 

[rb1957]

if you're "trying to show for my parts is to show "parts have total net-section stresses, e.g., maximum principal or von Mises, whichever is larger, at limit load that are less that are less than 30 percent of the ultimate strength." then that is (possibly) simply the FEA stresses. An example of "Net-section stresses" is the stress in a fuselage skin through a line of rivet holes. The gross stress assumes the holes aren't there so lets say hoop stress, maybe the stress you get from your FEM. The "net section stress" says there's a row of holes, say on a 6D pitch … so there's a net section of 5D between holes, and the net section stress is 6D/5D*gross section stress. You don't need NASGRO for this.

There may be something in NASGRO that says if your Kt is X and your gross section stress is Y then your net section stress is Z = f(X,Y) ? Normally there are two stress concentration factors, depending on which stress is used to normalise the peak stress … gross or net section stress.

If you have a section is bending, smooth, no concentration, no holes, then your net section stress is the same as your gross section stress.

another day in paradise, or is paradise one day closer ?

 

[CamJPete]

Thanks rb1957. I agree that I don't need NASGRO for this. Our company is purchasing it in case we need to actually perform crack growth analysis. What I'm attempting to do with the net section stress analysis is to show that our parts are not fracture critical to begin with and doesn't need a crack growth analysis, which I agree I can do with the FEM. The question I have is how to approach the FEM. (The reason for mentioning NASGRO was simply to say that there apparently is an example on how to treat net section bending in the NASGRO appendix, is all.)

When you say it is just the FEM stress, I still need to integrate that FEM stress over some area to come up with a net section stress. I suppose the requirement is saying that if you're only 30% of ultimate across the net section, then you have plenty of margin against the part breaking off, in case there may be some plastic deformation. What I'm wondering if is how to do this for a part in bending. What I don't think I should do is pick off the maximum von Mises or max principal stress at the outer fiber of the beam and compare that against ultimate. (Unless I'm wrong and it is exactly what I'm supposed to do.)

 

[rb1957]

How do you define "not fracture critical" ? some "ordained" stress value (RF > 2) ?
'cause the calc's to do it are tricky … what crack size ? what crack geometry ? what material toughness ??

another day in paradise, or is paradise one day closer ?

 

[r13]

What is your definition of "net section stress", and "ultimate strength"? And how to compare the maximum (net section) "stress" to the ultimate "strength"? I am at a complete loss here.

 

[rb1957]

"ultimate strength" is ftu, the allowable.
"maximum stress" is the applied stress. I gave an example of the difference between gross section stress and net section.

another day in paradise, or is paradise one day closer ?

 

[r13]

rb,

Thanks for the clarification. Is it correct to say that the yield stress should be considered the upper limit of the applied stress? Sorry, if I've diverted the discussion into wrong way.

 

[rb1957]

Yield stress (or strength) is one allowable, typically for limit loads (loads expected once in the life of the plane). ultimate load (limit load* 1.5, FoS) are generally compared to ultimate strength, and in bending we can wind that up to plastic bending.

another day in paradise, or is paradise one day closer ?

 

[r13]

rb,

You are correct. Without stating the analytical method and the nature of the applied loads, I don't know what the OP had in mind to compare with the ultimate strength, in hope to derive the relationship ƒ[sub]a (max)[/sub] ≤ 30% of ƒ[sub]ut[/sub]. Either I misunderstood completely, or the OP needs to be more clear on the goal, assumptions, and methodology. Please ignore my comment, if I am way off the topic.

 

[CamJPete]

Thank you all for your replies so far.

I feel like I probably gave you too much information without enough background. The fracture requirements document NASA-STD-5019 has different fracture classifications. Two of them are Non-Fracture Critical (NFC) or Fracture Critical (FC). If a part is classified as FC, a fracture analysis IS required with assumed initial flaw size and growth rates, etc. Within the NFC, there are different sub-classifications, one of which is "low-risk NFC". From the standard: "The low-risk classification is intended for parts that are extremely unlikely to...develop critical flaws because of...large structural margins." One of these "structural margins" they require to be calculated before the part can be considered low-risk is the "net section stress" requirement I stated earlier. It is much easier to show that a part is NFC than it is to do fracture analyses with subsequent inspections on the parts.

With that background, we can expunge from the discussion anything related to fracture, crack growth, or flaw size. Sorry for the initial confusion. My narrow analysis focus for this thread is related only to what area should I use for a net section stress analysis for a part in bending. r13, when you say what is your definition of "net section stress", that's exactly what I'm trying to figure out. Net section stress for a part in pure tension uses the full area being tensioned. But in a beam in bending, only half of the beam is in tension due to the bending load. Should I just use the area in tension from my FEM when calculating the net section stress?

 

[r13]

"The low-risk classification is intended for parts that are extremely unlikely to...develop critical flaws...

I think you can substitute the word "stress" in place of "flaws". So for bending, the critical stress is the one that likely to initiate the failure mechanism, either tension, or compression, would be the net section stress you are looking for.

 

[rb1957]

no, no, no … a "flaw" is not "stress". The point is to protect structure from small imperfections (or flaws) … read up on F111 pivot joint fittings.

ok, what sort of stress concentrations are in your structure ?

This "net section" requirement is quite "olde school" except is areas where it is truly applicable (like along a line of rivets in the fuselage).

What structure is in bending ? Is it a classical beam ? Are there stress concentrations ? Have you done a detailed FEM ?

You want to demonstrate that the structure is not fracture critical due to large stress margins (and avoid all analysis of flaws) … good, smart.
How do you demonstrate a large margin ? What is "large" ? I would do a detailed, very detailed, FEA paying particular attention to regions of stress concentration.
If you have a high margin (RF > 2) for the peak stress then that should be "good enough". They may want a detailed crack growth analysis … put a 0.05" flaw at the critical site (the largest concentration usually) and they'll have to give you a fatigue spectrum.

Is this space or military ? or nuke ??

another day in paradise, or is paradise one day closer ?

 

[CamJPete]

r13, rb is correct, flaw is not the same as stress.

rb, they will not want a detailed crack growth analysis if I can show that it meets the requirements of "non-fracture critical, low-risk". Only parts with a "fracture critical" classification need a crack growth analysis. I'm trying to show that it can meet a non-fracture critical requirement so that I can avoid crack growth analysis. For this discussion, we can safely avoid anything related crack-growth, flaws, etc. I'm wondering specifically about net section.

Yes, rb, I have already created a detailed FEM with stress concentration features included in the high stress areas. I keep going back to the statement in the specification: "For complex parts where finite element results are obtained that may include stress concentrations and stress gradients, the net-section stresses are to be computed by integrating the stress distribution and dividing by the area for the sectional area being assessed." I am hoping to get some insight into what area to use for a generic-cross-section beam in bending. Let's pick any shape for this discussion, say a square cross section beam. It will have some area in tension and some in compression. What area should I use to integrate over and then divide the resultant force by?

Large margin is defined by the net section stress being less than 30% of the ultimate tensile. If net section stress is less than 30% Ftu, it passes this requirement. Thanks all for your time.

 

[r13]

Yea, rb is correct. I was trying to tie the flaw to the initiating stress, as your concern - crack. Fracture frequently occurs on tension members (due to stress concentration on the net area as the example provided by rb),and members subject to repeat loadings with high stress variance, or reversal. The net stress on your example is zero, but if the bending repeats, the net stress change would not be zero, and could lead to crack/failure. I think you should narrow your argument down to certain/specific application, rather than general.