Dynamic vs Quasi-static Crack propagation problem 1

[neusun001]

I'm trying to formulate the crack propagation problem for metal components of rotating machinery. Being an Electrical engineer, I started off learning fem and then fracture mechanics recently. Hence, forgive me for my ignorance.
I'm trying to find a guideline, or some sort of reasoning, as to when to use a quasi-static (iterative methods) for crack propagation vs a full-blown dynamic problem for crack propagation.

Many thanks in advance for your responses.

 

[rb1957]

you migt want to research Kr curves. these allow for stable crack growth. i imagine you're interested in fracture.

for stable crack growth (LEFM), it's enough to know the material toughness and to approach it in small enough increments (iterative ?). but i wouldn't "fuss" the very small crack life available as the crack appraoches critical (heck, fatigue ignores the stable crack growth all together !).

any help ?

Quando Omni Flunkus Moritati

 

[neusun001]

Thanks rb1957.. I'm not interested in fracture but only crack growth. I'd want the machine to be taken out of operation before the fracture happens, to save a lot of money .
I read that quasi-static is accurate enough unless the crack growth is 'brutal'. Is that so? Does the natural modes of the component in any way effect the actual growth?

Thanks once again.

 

[rb1957]

IMHO crack growth is easy enough to calc, using standard crack geometry factors (plus fudge factors !) i think this is what you mean by "quasi-static" (determine the crack geometry factor at different crack geometries, then using some cycle counting to get from A to B). i think "brutal" means really short (which you probably aren't going to solve with analysis, but with changing something physical).

"natural modes" ... means vibration induced stresses ?

Quando Omni Flunkus Moritati

 

[neusun001]

Thanks for your response!
By quasi-static I mean a XFEM problem to be solved with time update via level set methods. So that, I take time updates, without doing the dynamic problem (only using [K]{u}={R}). Yes, by "natural modes" I mean vibration induced stresses. I'm not going to depend on "factors" because I want this model to be time sensitive for factors like changes in loads, speed, lubrication, temperature etc.
Thanks.

 

[spongebob007]

I may be a bit off base here but from your second post I get the impression you are going down the wrong path assuming that I am correctly guessing that you are trying to predict when a part on a machine will fail so you can replace it before hand. What you are trying to do falls under the subject of machinery condition monitoring. In a nutshell, the "signature" of a machine is monitored while running and any changes indicate a potential problem. At my last job I did an R&D project on something known as Acoustic Emsissions. Basically when a crack forms and grows, the strain field in the vacinity of the crack will change. This redistribution of strains emits sound waves that can be used to predict when a crack as formed and even how rapidly it is growing. By using multiple sensors one can even triangulate exactly where the crack is occuring. It's pretty neat technology because it allows you to detect a crack before it can cause failure. It's pretty repeatable. I designed a bunch of test samples that were designed to fail within a short number of cycles and monitored them during cycling. In every case there was advanced warning of failure. However I found that as the samples were cycled at higher frequencies and the stress levels were increased the time from when the equipment first detected a crack starting to the time the sample broke was only a few seconds.

I also think that something known as cepstrum analysis has something to do with condition monitoring. Personally from what little you have written here I think this is really what you are looking for.

 

[spongebob007]

Also, I think you are confused on the meaning of quasi-static. In my mind quasi-static is using static analysis techniques for dynamic problems. Let's say you know your structure is subject to a steady state sinusoidal load of 10g peak accelearation at a given frequency. You want to know the stresses this load will cause on your structure. There are three ways you can do this with FEA: First, you can do a transient analysis where the program solves for the response at every time step. This is the most computationally intensive way to go and probably is overkill since as an engineer you are really only interested in peak stresses. What happens at intermediate times is of little interest. Transient is probably only useful if there are nonlinearities in your structure. The second method is to use harmonic response or some other modal combination technique. First you solve for the natural frequencies and then use the eigenvaues and eigenvectors to calculate the peak response. The math behind these techniques rely on constant stiffness matrices (orthogonal eigenvectors). Harmonic response gets you what you want with less time and computing power than transient. Third, if the natural frequency of your structure is at least two times the forcing frequency, minimal error would be introduced by applying the 10gs as a static body load to your FEA model.

 

[spongebob007]

Using static body loads for dynamic problems is what I have always seen referred to as quasi-static.