STRESS CONCENTRATION FACTORS & STATIC STRESSES

[StressMan2506]

Ladies & Gents:

The conventional approach in the office in which I work is that we calculate net static stresses as gross stress times the ratio of gross area to net, i.e. no stress concentration at the edges of holes. I do not believe this approach to be correct and I cite section 17.1 of Roark, 7th edition. This section is entitled "Static Stress & Strain Concentration Factors".

Comments etc are invited.


Regards,
Louis

 

[edbgtr]

StressMan2506,
As I don't have the advantage of a copy of the 7th Edition, please share with us how the book proposes to calculate the ultimate tensile rupture stress (or load) of say a long plate strip with a centrally located hole in it, with a strip width to diameter ratio of say, W/D = 4.
Thanks
Ed

 

[StressMan2506]

Hi edbgtr:

I quote from Roark:-

"If the load on a structure exceeds the value for which the maximum stress at a stress concentration equals the elastic limit of the material, the stress distribution changes from that within the elastic range. Neuber ['Theory of Stress Concentration for Shear Strained Prismatic Bodies with Nonlinear Stress-Strain Law', J. Appl. Mech, Series E, vol. 28, no. 4, pp 544-550, 1961]presented a formula which includes stress and strain. Defining an effective stress concentration factor, Ksigma=(sigma max)/(sigma nom), and an effective strain concentration factor, Kepsilon =(epsilon max)/(epsilon nom), Neuber established that Kt is the geometric mean of stress and strain factors. That is, Kt=sq. root of Ksigma*Kepsilon, or Ksigma=[(Kt^2]/Kepsilon. In terms of the stress and strains, this can be written as (sigma max)*(epsilon max)=[(Kt)^2]*(sigma nom)*(epsilon nom)

Kt and sigma nom. are obtained exactly the same as when the max stress is within the elastic range. The determination of epsilon nom. is found from the material's elastic stress-strain curve using the nominal stress."

That's the best I can do right now. I hope it is helpful.


Louis

 

[rb1957]

i think your approach is funny ... which is not to say it is Wrong.

you may be in a different engineering design space than i'm used to, eg steel, very low gross stress. your approach may be that if the net stress is less than 1/3 of yield then you don't get plasticity at the holes (you are effectively accounting for the Kt as the hole by having such a low net stress).

 

[StressMan2506]

Hi rb1957:

What you refer to as "your approach" is what I manually copied from Roark. In my opinion there is a rationale to it but it is not what is conventionally done in our office. Here we pro-rata gross-to-net and then make a plasticity correction if the resulting stress is over the elastic limit.

I work in an aircraft stress office where the great bulk of our work involves Al. alloy...I used to do structural steel work.

Regards,
Louis

 

[Kwan]

Here's my 2 cents. Given a plate with a hole and the criteria is for the part to withstand ultimate loading (the part can yield). I check the net section stress against ultimate and ensure a positive margin. This is static stress analysis. What happens as the load increases is that in the location of the stress concentration the material yields and the stress redistributes. A similar method is used when using plastic bending.

 

[rb1957]

sorry, i just read the word "static" in your thread. i think it is quite reasonable to consider the net section stress without a stress concentration factor for static analysis. the logic is that under ultimate loading localised yielding (from the stress concentration) is negligible since the whole (net) section is assumed to be working at yield stress.

what's happening is the the peak stress due to the stress concentration is balanced by a slightly reduced stress on the remote section (away from the hole) ... since the overall force balance must be maintained. so the local side of the hole starts to yield first, but plasticity bluntens the stress concentration (the peak stress won't achieve the linear peak stress if this is beyond yield). You could do a complete non-linear analysis but i think the result would be within a "gnat" of this approximation.

mind you i've also seen people want to see a positive margin on the linear stress concentraion peak stress ... VERY conservative design.

 

[StressMan2506]

Hi rb1957 & Kwan:

The method presented in Roark does knock the stress down from a notional greater-than-yield value because the sigmas & epsilons are calculated from the Ramberg-Osgood equation.

My interpretation is that this method permits an estimate of peak stress when limit stresses are moderate. I would also suggest that you take a look at pages 36 & 37 of the 2nd edition of "Peterson's Stress Concentration Factors" where the concept of "effective stress concentration factor" is also put forward. Here it is shown how the ratio of peak to general falls off as general rises. This effect is born out in the application of Neuber's method as presented in Roark.

Kwan's approach follows the convention used in the office in which I work. My purpose hear is to debate the merits (or otherwise) of Neuber's method as presented in Roark.

Louis

 

[rb1957]

i thought the point to your thread was not using a stress concentration factor for static analysis ?

 

[StressMan2506]

Hi rb1957:

I stated from the outset that the convention in the office in which I work is not to use a stress concentration factor with static stress, whereas Roark has a section headed "Static Stress & Strain Concentration Factors" and I can follow the rationale presented therein and tend to favour it myself. A colleague of mine tells me that in a previous workplace the practice was to calculate static stresses with stress concentration factors.

The link below will take you to a copy of pages from Roark.

https://download.xdrive.com/s/298238582Poh8CSCxBUo52MFSCO1?partner=plus

Louis

 

[rb1957]

hi loius,

i've read the doc; i haven't seen that approach before.

from a static perspective, the key question is how much load can be applied before the strcuture fails. typically this is too difficult to determine precisely, so we make approximations. the approach used in your office (of calculating a net stress neglecting the stress concentration) is a typical approximation; one i'd say is reasonably commonly used. cerainly you can analyze with this approach and i'd be willing to be that you get lower RFs (assuming you compare the "maximum" stress under load with Ftu).

alternatively you could increase the load applied on your section untill the "maximum" stress is equal to ftu ... presumably a fair bit more work. you could do a non-linear FEA ... similarly a lot of work. even after all this, your structure will probably not fail as predicted as the internal loadpaths will change and load will be redistributed away from your yielding element.

 

[StressMan2506]

Hi rb1957:

Yes, you get lower RFs by the Neuber method for a given load. Assuming you start with a moderate overall load you will have a healthy RF by the conventional gross-to-net method and maybe a low one at the stress raiser. If you then increase the load by a factor 'X', the peak will go up less than 'X' as Neuber takes you along the non-linear part of the curve; i.e. the min. RF will fall by less than 1/X.

I believe the Neuber method should ideally be used with non-linear field stresses; i.e. apply a plastic correction to gross stress if the linear elastic value is beyond yield, before going to Neuber. With Mathcad, it is not too difficult to do it using Ramberg-Osgood.

Louis

 

[jetmaker]

Hi all,

The effect being refered to here by StressMan has a commonly used name, which presently escapes me at the moment. However, the effect is that for certain materials, the presence of stress concentrations causes a reduction in the overall axial load capability of the part below what would be obtained thru standard P/Anet.

I have only had a cursory look at the possible theory behind this effect, and my thoughts are that for a single SCF detail with sufficient bulk material around it, there would be little effect as previously pointed out by the local yielding and stress redistribution. However, when SCF are interacting between neighbouring details, there is no place for the local redistribution of stress. This lack of redistribution into the bulk area results in higher net section stresses than predicted simply by the P/Anet.

Just my thoughts on this topic. Comments are always welcomed.

jetmaker

 

[StressMan2506]

Hi People:

The link below will take you to a copy of a couple of pages from "Peterson's Stress Concentration Factors" 2nd edition which describes the effect replicated by the Neuber method using the Ramberg-Osgood equation.

http://download.xdrive.com/s/361982075TrW5MN2g0U1cPahzoU5&partner=plus

Louis

 

[rb1957]

jetmaker,

if the material was brittle it would probably have problems with stress concentrations (ultra high strength steels, like 300M, for example)

 

[jetmaker]

rb1957,

You are absolutely correct. It is important to remember that stress concentration effects are very significant in materials like 300M or composites. These brittle materials exhibit low ductility and hence do not allow significant load redistribution.

 

[JacobL]

unless you have a very good margin of safety, which can ignore the possible stress concentrations, I think you need to consider the holes and chamfers/fillets for stress.
Also, assuming linear static analysis is not the only one you'll use, but also do buckling analysis using non-linear static calculation, the result will greatly depend on the geometric properties of the element, including any holes in it.

 

[StressMan2506]

Hi JacobL:

I think you're the first to wholeheartedly agree that SCFs should be taken into account when considering static stresses; thanks.

Louis

 

[corus]

In general, a stress at a hole is classed as a stress concentration and would be assessed against fatigue criteria. If you refer to structural design codes such as DIN or Eurocode standards then for a static load (non-fatigue) you would only consider the nominal stress component at the hole, ie. the stress across the gross section and ignore the peak stress component due to the stress concentration.

corus

 

[StressMan2506]

Hi Corus:

As I understand it, the quantities commonly referred to as stress concentration factors are in fact linear-elastic static stress concentration factors. Neuber's method enables the determination of static stresses in the non-linear region arising from stress-raisers, giving rise to an effective stress static concentration factor; see Peterson's Stress Concentration Factors, 2nd edn, pp. 36-40. Peterson presents a quantity q, notch sensitivity which links effective and linear-elastic static stress concentration factors. By definition, q lies between 0 & 1. Fatigue is then introduced into the picture. A stress concentration factor for fatigue (Ktf) is defined. The expression is:-
Ktf=q(Kt -1)+1
where Kt is the linear-elastic static stress concentration factor. Ktf is never greater than Kt.

In my opinion, we should use Kt with Neuber for static analysis and Kt for fatigue.

Louis