Cracking growth prediction for a structure with creep and plasticity deformation

Thanks a lot, Zhigang,

You are right - the problem we are discussing has huge practical significance. Image the buckets in a heavy-duty gas turbine. The loading for a bucket is similar to what I have described for the beam, high temperature like 2000 plus F, high loading caused by pressure and centrifugal force, among others. It is subject to cyclic loading. Right now, gas turbine industry regularly does a NDE such as bore scope inspection to see if there is a crack, if yes, typically people either take risk to continue using it until the next big outage that gives a chance to replace the cracked bucket with a new, or reconditioned one, or take the cracked bucket out immediately if the “experience” or “engineering judgment” tells that a catastrophic event is imminent if leaving the cracked bucket in. Unfortunately gas turbine outage implies huge economic compromise. So, the ideal case will be to minimize the gas turbine outage. This is why it has huge financial implication to predict the bucket crack growth rate and direction so people can know the residual life of this expensive bucket - the cost of one bucket, for part only, is almost two times of that of a BMW car!

Now, looking back your points above. Obviously, a typical bucket will be subject to both plastic and creep deformation, with plastic deformation developed almost immediately after service – design people are struggling to avoid this, but found it was just difficult. The creep deformation is a function of time and can be big, say, a creep strain of 2% after only 5,000 hours. Typically the first scheduled inspection or replacement time is about after running the gas turbine for 24,000 hours. But many times, by much earlier time, say, 5,000 hours, the cracks should usually have already initiated.

With all this being said, you can see our problem unfortunately falls in the one which you said has not been fully resolved, it is about crack prediction for a structure with plastic and creep deformation. The crack tip inelastic region is big; the rest of the structure is of inelastic deformation as well. It is a large-scale yield problem.

I will read carefully the paper you have given above. Before that, I have a couple of points I want to further clarify with you:

 (1). If a structure is under large-scale yielding condition, the K value is meaningful. People cannot rely on K value and Paris law to predict the crack growth rate, is this correct?

(2). Some other methods such as you referred in point 6 and 7 have to be used to predict the crack growth rate. What is your understanding about their industrial application? As you know, the K value and Paris law have been used by many industries to predict the crack growth rate.

(3). We understand some other method you pointed could be difficult, and/or, immature at this time. So, how about the following method? Let say we run a creep analysis for an uncracked structure. Therefore, at any time point, we will get the total strain composed of elastic, plastic and creep strain component in this structure. Let's assume that the crack was initiated at the time point T. We then map the plastic and creep strain from the uncracked model to a cracked model (we can insert a crack to the uncracked model, and there are a number of computer programs capable of doing this), and then we run a typical linear analysis to get K value. After that, we can use Paris law to predict the crack growth rate.

I understand the K value calculated by above method is based on the assumption, at least, that the inelastic deformation for the cracked model is the same as that for the uncracked model. But if we focus on the small crack domain, I may think that this assumption could hold. Also, I think the K value here will be still different, but not sure by how much, from what is calculated by considering the large-scale inelastic deformation. Do you have any sense how much this difference will be?

I am an engineer, and also unfortunately, my background is not in the fracture mechanics although I love this field. So, I typically try to simplify the problem based on engineering judgment, and a number of "dirty" assumptions. The goal is to make some assumptions and get a quick answer reasonably right within a reasonable timing frame.

Thanks again and regards,

Wangming LU