Hello there.

In fact, CT specimens are used to evaluate the behavior of materials for Fracture Mechanics tests, not fot fatigue SN curves. These are not the right specimens for SN curves. The mechanical parameters obtained from these specimens are standardized and typically, the Stress Intensity Factor and the integral J are used.

Think inversely: What if you want to study the behavior of a crack under controlled conditions (advance, opening) with typical tension specimens. You would have to induce and surveille the crack with your “own recipe”. That´s why there standards for fracture mechanics tests use CT specimens.

The stress state in CTs is not homogeneus and tend to growth to infinity (mathematical ideal model) as we approach to the crack tip. For SN curves yo need and even, homogeneous stress behaving in a tipically sinus spectrum over time.

To conclude, my advice is to avoid the use of CT specimens to build SN curves of your material.

Many thanks for your comment.

I can understand that the fracture phenomenon (and the stress state) related to CT testing is quite different in respect to the tensile one. But, theoretically, I would not see any inapplicability of the S-N approach to CT testing, especially, because this is expression of the fatigue fracture behaviour of notched and pre-cracked (standard) samples.

However, since there are no significant experimental studies on that issue, and, according to your interesting comments, it is not hard for me to believe that, in practice, S-N curves related to CT tests are not as useful as the typical ones, evaluated by tensile samples.

Hello Danilo,

As you said we use C-T specimens to characterise the fracture properties of a material. We could also use them to determine a Paris law type curve to predict the crack growth rate vs. cycles. In this regard, instead of using a life curve we would have another a more advanced design philosophy. In the composite field, I haven't seen fatigue experiments with C-T samples because of the complexity of the test. However, if you want to study the notched behaviour you can use open-hole or DENT specimens. This is my experience with composites.

Kitagawa diagrams (stress range vs crack length) are typically used to relate fatigue crack propagation data and smooth sample SN fatigue behavior. The original reference is: H. Kitagawa and S. Takahashi, Second International Conference on Mechanical Behavior of Materials, edited by N. Promisel and V. Weiss (Am. Society for Metals, Metals Park, OH, 1976), pp. 627-631. However, you can search the web for it, and find lots of examples and papers.

Danilo:

To add to the useful comments made by the previous responses, let me add the following.

S/N (or Wohler) curves have been used since the mid 1800s to assess the role of initial stress (and sometimes strain) on the total fatigue life, i.e., the number of cycles both to initiate and propagate a crack. For this reason, S/N tests invariably involve experiments on smooth-bar samples with geometries that confer a simple stress-state (this is important because S represents the initial stress (or strain) and you do not want any complex stress-state to provide a large geometry-effect on life). This is particularly relevant for the compact-tension of C(T) sample as depending upon the notch/crack size, the stress-state is either tension plus bending (when a/W is small) leading to a almost pure bending state (when a/W exceeds ~0.6). So for the C(T) sample, what stress will you use for the initial stress S in your S/N characterization, given the stress intensification at the notch/crack tip? Will you adjust this stress for the stress concentration there? If so which stress-concentration factor will you use? The theoretical (elastic) stress concentration factor? The effective stress concentration factor for fatigue (which you won't know a priori)? Or perhaps the strain-concentration factor (which is possibly even more relevant to fatigue)? Will you use an average stress over a volume ahead of the notch/crack tip (possibly a better choice for fatigue failures)? But if so what volume will you use (this is the critical distance issue)? All these issues are imponderables and confounding variables to your analysis. Why make life so difficult for yourself?

Additionally, if you use a C(T) sample, you will have put in a notch and accordingly you will have truncated the crack-initiation life, meaning you will be measuring the crack-propagation life. This being the case, why not use the C(T) specimen for what it was intended in the first place and measure the crack-propagation life properly by using fracture mechanics and monitoring the rate of growth of the crack, da/dN, as a function of the stress-intensity range, delta-K, or an equivalent fracture-mechanics field parameter?

My advice to you would be to stick to simple geometries for S/N-type assessments of the fatigue properties of materials, and leave complicated geometries like the C(T) sample for what they were designed for, determining the damage-tolerant (crack-propagation) life using fracture-mechanics methodologies.

ROR

Dear Prof Robert O Ritchie,

Dear all,

many thanks for your clear and practical explanation.

My first aim was to simulate Fatigue Crack Growth of CT. I was also interested in (numerical) S-N curves (related to CT) in order to (a) generalise the numerical results (stress instead of peak load), (b) express the outcomes in terms of fatigue life and (c) check the wide accuracy of the modelling in regard to various load/geometrical conditions (peak load amplitude or sample thickness).

I can understand that the practical use of those curves is based on the simplicity and generality of the used samples (e.g., smooth samples under tensile loading) and, consequently, I can clearly see that an S-N curve evaluated by CT testing (numerical as well as experimental) represents a “stretch”. This fact is also confirmed by the absence of existing experimental campaigns performing this (particular) type of tests and aiming to produce those curves. At this point, I realised that my idea is essentially abstract and not easily applicable, especially in regard to the current practice/approaches.

I thank you again as well as the others for the insightful comments.

Best regards,

Danilo

I actually had to do something like this for a homework assignment as an undergraduate student. If I remember correctly (it was a very long time ago), we were given fatigue crack propagation curves for the same alloy in two different environments (one inert and the other aggressive). We then had to estimate fatigue service lives for the two environments from the data. To get full credit, you had to point out the assumption that the initiation time was zero (as Rob points out). For the inert environment, near ideal Paris behavior enabled integrating from an initial crack length to the final crack length and solving for time (or cycles). For the aggressive environment, a simple relationship could not be used to represent the entire range of the CP data, and you had to divide the curve into sections. The time (or cycles) required to traverse each section was then estimated and summed. Then, you were supposed to point out that by assuming an initiation time of zero, and keeping the estimates on the safe side of the real data, you could only err on the safe side.

Danilo:

As nicely explained by Prof. Ritchie, the purpose of C(T) specimen is to provide information about the crack propagation part (that ranges between 10 to 30%) of the total fatigue life. S-N curves are all about total fatigue life that has the crack initiation part as well as the propagation part for which we need to start with a flawless sample (having smooth surfaces). If you want to deal with C(T) samples, you will be getting only the crack propagation part of the total fatigue life, so generating S-N curves from it is meaningless in addition to the complications mentioned by Prof. Ritchie.

Dr. Ricker:

I'd liked your comment. I didn't do it as a homework, but I have done the same calculation myself. In principle, one should be able to reproduce stress-life data (at least the crack-propagation part) from the fracture mechanics da/dN vs. delta K plot by assuming some initial crack size and allowing it to grow according the resulting Paris law or equivalent. But you are right that there are so many uncertainties in this exercise (in addition to the ones that you mention), such as the shape of the crack and how this three-dimensional profile may change with its growth, the possible differing growth rate of the crack when its small (which may differ from the longer crack da/dN vs. delta K data), and so forth, that it is practically impossible to accurately predict real S/N data in this way. Ce la vie!

ROR

Rob, uncertainties are there only if we start with short cracks, but if we start with long ones, this is fine. Your friend can use Efatigue.com for example

Thanks Mike, but you mean long, through-thickness cracks - quite frankly, I can almost do those calculations on my iPhone. What I'm referring to here is that although da/dN vs. delta K data is derived from a vs. N data, in order to perform the counter calculation, i.e., to determine a vs. N data from da/dN vs. delta K results, and hence predict S/N data in a smallish smooth-bar specimen, demands a far more complex calculations involving phenomena which, as has been stated, involves imponderables like the number of cycles to initiate a crack, the size and shape of this 3-D (not though-thickness) crack, how this initiated crack will grow, i.e., how its shape may change depending on whether there is a difference in its more constrained depth-wise growth rate compared to its surface-wise extension, and of course the issue of the possible accelerated crack-growth rate if the crack is deemed small - all issues that long-crack da/dN data (measured in something like a C(T) specimen) can give you no insight about. I'm uncertain that software like Efatigue can ever handle this, not because it cannot relate da/dN vs. delta K to a vs. N results - that's the straightforward part - it's all the other imponderables that you simply don't know, or at best need to measured, or at worst need to guess.

ROR