Basic Fatigue and Fracture Questions

[James Wong]

Dear Forum,

Pardon me for asking such simple questions but I would humbly like some clarifications to my questions.

Assuming a plate plate, fixed at the left end, pulled on the right end.
From the stress distribution, I can obtain the maximum stress and also the stress range (max stress during loading minus the stress during unloading).
I can then obtain the fatigue life of this plate by looking up the stress range against the S-N curve and find the number of cycles.

My question is:

1. How do I find the number of cycles to failure if there is a line crack on the plate surface? The maximum stress is now at the cracked line and the stress range is now much higher, I cant compare the stress range against the S-N curve because the stress range in a S-N curve is derived from an uncracked material. So how do I determine the number of cycles my cracked plate can undertake before the crack starts growing?

2. I was told that to restrain this crack from growing, holes, half the plate depth, are drilled at the crack ends. I was told to use BS7910 to determine if the crack will propagate. I have a MathCAD spreadsheet with the BS7910 code in it. Can I assume an initial crack flaw size of a=3 mm deep and 2c=10mm as a start?

3. From my understanding, the number of cycles in BS7910 is an input for it to calculate final crack size?

Thank you in advance for your time and advice.

Regards,
James Wong,
UWA.

 

[rb1957]

1) this sounds like an edge crack growing through the thickness; is "a line crack on the plate surface" a notch (crack) extending across the width of the plate ? Damage Tolerance analysis should be applicable. Using net area (sounds like what you mean when you say "The maximum stress is now at the cracked line and the stress range is now much higher") can be very conservative or unconservative !? "So how do I determine the number of cycles my cracked plate can undertake before the crack starts growing?" ... damage tolerance, not fatigue, analysis.

2) what you're describing is "stop drilling", although I've never heard of drilling to 1/2 the depth ?? Stop drilling is better described as "pause drilling" as the crack will nearly always restart. A successful stop drill would be a hole that completely removes the "yield zone" ahead of the crack, which is probably a bigger hole than you'd think you'd need ...

3) no comment !?


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

 

[EdStainless]

I remember flying in Beech Metroliners, The engine covers would crack and there would be a row of holes drilled trying to arrest it. No one wanted to drill a hole that was large enough and far enough ahead.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[James Wong]

Thank you for your advice.

Yes, I do find that using the net area for stress calculations leads to very high stress, hence I knew I couldn't just compare it to the S-N curve. Yes, I should be looking into fatigue damage. I got a book on Fatigue Damage by Christian Lalanne.

Thanks for the advice on the stop drilling. I wasn't aware of the criteria for the drill hole. Thanks for letting me know. At least now I have some basis to proceed.

I cant drill the hole through the surface as the grains would leak out. So it will have to, at max, at 80% of thickness. I will have to do a stress analysis to find out the life of the remaining ligament (the balance thickness) so that a crack doesn't start from the end of the hole and rips apart through the 20% thickness.

Thank you both for your advice.

 

[dhengr]

James Wong:
You better really study that book you just got, because I think there is some real confusion flitting around here, in both your OP and your last post. You have to do a much better job of describing the structure you are dealing with, dimensions, sizes, thicknesses, etc, its loading and cyclic loading conditions, the crack and its location in the structure, etc. etc. What are all the stress conditions in the structure around that location, original design, without the crack? It sounds like you are dealing with a grain silo/bin if ‘the grains would leak out.’ How do you know how deep the crack is and its full extent? How do we know that this is really a fatigue crack, and not just a crack at a flaw in the material or workmanship, or at best low cycle fatigue? The idea behind the stop drilling or “pause drilling” as Rb1957 calls it, is that at the tip of the crack the stresses are very high and cause it to continue to propagate. This drilling method usually pertains to the crack tip in a through plate crack, not a surface crack. The stresses are a function of the radius of the crack tip which is very small. In fact they are inversely proportional to the radius, so the small crack tip radius quickly makes the tip stress essentially infinite. Thus, drilling the hole at the crack tip makes that radius much larger and the local stress much lower, maybe even manageable. You should drill all the way through the plate or you haven’t stopped the underside tip/edge of the crack from propagating further and under your drilling. Why can’ t you drill all the way through the plate and just put a temporary patch over the hole on the inside to retain the grain? Why can’t you unload this structure, or this area, and repair weld the crack? I would like to understand better what really caused this crack, and if it really is a high cycle fatigue crack. I would like to study how to fix it and reinforce the structure rather than cogitate about S-N curves and life cycles.

 

[rb1957]

if you have to stop drill, drill through the thickness and cover with duct tape. if you drill only part way through, then the crack will rapidly grow across this reduced thickness (increased stress) and continue out the other side. Do Not drill part thru thickness.

how cyclical is your loading ? Is this a fatigue/crack growth problem, or a residual strength problem ?



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

 

[boo1]

Fatigue crack growth analysis is used to determine the consequences of such a crack to the overall structural integrity of the structure. Often it is found that one of these small defects is the failure origin. The stress at the root of a flaw or crack is more intense than the nominal applied stress. This stress intensity is called K, the stress intensity factor. The basic relationship between stress intensity factors, nominal stress, and flaw size proposed by G. R. Irwin is

K=δ(√Πa) Stress Intensity

At some value of stress or at some length of crack, the crack will become unstable and propagate quickly until the structure fractures or the remaining cross section is reduced to the point that rupture occurs. That critical stress intensity is called the fracture toughness. It is of special note that fracture toughness is a material property just like Young’s modulus or density. For crack normal to direction of stress in an infinite plate and where it is one-half the crack length. The Roman numeral subscript ‘I’ designates mode I fracture, which is the crack opening mode. Mode I fracture is the most prevalent mode of fracture and is the primary mode of concern in this discussion.

K_ic=δ_d(Πa_c)^1/2 Critical Stress Intensity

When making fatigue crack growth calculations under random loading, load sequence effects are very important because the amount of crack growth at each loading cycle is dependent on the total crack length. Therefore, if analysis was made with all of the highest loads occurring first, the effect of lesser loads would be intensified. For random loading, similar to the linear cumulative fatigue initiations described above, the most crack growth occurs at intermediate values of loadings where there are many load cycles with stress ranges high enough to cause significant crack growth. To calculate the allowable surface crack length, empirical correlations must be applied to the basic equation to account for the specific situation. Since the assumption has been made that the crack is semicircular, a and c are equal. Using φ = 90° (max stress), fracture Toughness equation reduces to:


K_ic=1.1(2/Π)δ_d(Πa_c)^1/2)
Where K_IC is the critical stress intensity or fracture toughness,
(material property),
1.1 is the free surface correction
2 is the reduced elliptical integral for semicircular cracks
Π is ~ 3.14
σ_d is the allowable design stress
a_c is the critical flaw depth
K_IC= material property in ksi √in²

Ref G.R, Irwin. Analysis of stress and strains need the end of a crack transversing a plate. Trans A.S.M.E., Applied Mechanics, 361-364, 1957