Towards a Methodology for Component Design of Metallic AM Parts Subjected to Cyclic Loading
Round 1
Reviewer 1 Report
RE: metals-1168830
The authors proposed a method for estimating fatigue endurance limit of metallic AM materials based on fracture mechanics concepts. The basic idea seems to originate from the Kitagawa-Takahashi diagram, assuming that below an intrinsic threshold, corresponding to a0, micro-cracks can all be arrested such that the stress level at a0 is effectively the “fatigue endurance limit”.
In practice, at least in the past, the fatigue threshold DKth is assessed using the load-shedding technique that ends up at a low K with much longer crack size than that in the transition region of KT diagram. One may argue by K-similitude that is fine (equivalent to small crack size under large load), but those experimentally measure long-crack threshold data are associated with crack closure that is crack-size dependent. Unfortunately, the crack closure interference also breaks the K-similitude, as the closure behavior below Kop is uncertain, which means the mechanical energy being consumed by crack closure is not uniquely defined if the closure compliance is not measured. That means non-uniqueness of K, as K is defined and experimentally verified by Irwin and Kies in terms of compliance changes. This has long been discussed by Wu (1995) in Wu, XJ, An energy approach to crack closure, Int. J. Fracture 73 (1995) 263-262; Wu XJ, Wallace W, Koul AK, A new approach to fatigue threshold, Fatigue Fracture Eng. Struct. & Mater. 18 (1995) 833-845. The authors should discuss these aspects, as their entire methodology is built on the premise of fatigue threshold.
The authors also presented a cyclic R curve approach, but the reviewer is not sure whether it is measured (using what kind of specimen?) or just calculated? The authors should specify more clearly in the finally proposed procedures.
All in all, what is needed is an actual example of predicting the fatigue endurance limit from the fracture mechanics/fatigue crack growth data for validation.
The authors should revise their manuscript to address the above points for publication.
Author Response
The authors want to thank the reviewer for his work. In the following only the critical points are addressed.
Reviewer: The authors proposed a method for estimating fatigue endurance limit of metallic AM materials based on fracture mechanics concepts. The basic idea seems to originate from the Kitagawa-Takahashi diagram, assuming that below an intrinsic threshold, corresponding to a0, micro-cracks can all be arrested such that the stress level at a0 is effectively the “fatigue endurance limit”.
Response: This is common view today and the authors also cite own results where they theoretically demonstrated the effect for steels of different strength (lines 106 to 110 referring to [7]).
Reviewer: In practice, at least in the past, the fatigue threshold DKth is assessed using the load-shedding technique that ends up at a low K with much longer crack size than that in the transition region of KT diagram. One may argue by K-similitude that is fine (equivalent to small crack size under large load), but those experimentally measure long-crack threshold data are associated with crack closure that is crack-size dependent. Unfortunately, the crack closure interference also breaks the K-similitude, as the closure behavior below Kop is uncertain, which means the mechanical energy being consumed by crack closure is not uniquely defined if the closure compliance is not measured. That means non-uniqueness of K, as K is defined and experimentally verified by Irwin and Kies in terms of compliance changes. This has long been discussed by Wu (1995) in Wu, XJ, An energy approach to crack closure, Int. J. Fracture 73 (1995) 263-262; Wu XJ, Wallace W, Koul AK, A new approach to fatigue threshold, Fatigue Fracture Eng. Struct. & Mater. 18 (1995) 833-845. The authors should discuss these aspects, as their entire methodology is built on the premise of fatigue threshold.
Response: The authors are aware of the similitude problem in fatigue crack propagation which predominantly manifests at the threshold and in the threshold regime of the cack propagation curve. It is, e.g., the reason behind their statement in lines 320-322 (“For materials prone to corrosion, the value of can depend on the method of experimental determination at low ratios”). However, as this not simply a mechanical problem they do not expect to solve this by an energy approach. From their point of view, it is primarily an environmental problem, i.e. corrosion. A detailed discussion would exceed the scope of this paper. However, the topic is the subject of ongoing research by the authors and citations are provided where the reader can inform.
Reviewer: The authors also presented a cyclic R curve approach, but the reviewer is not sure whether it is measured (using what kind of specimen?) or just calculated? The authors should specify more clearly in the finally proposed procedures.
Response: This is one of the key points of the approach the authors propose. The cyclic R curve characterizes the dependency of the fatigue crack propagation threshold on the crack depth in the physically short crack propagation regime. The authors use a method for its experimental determination. To make this clear they will add a sentence at line 354: “A discussion of the experimental determination of this curve is provided in [54].” The source will be given as: Maierhofer, J., Kolitsch, S., Pippan, R., Gänser, H.-P., Madia, M. and Zerbst, U. The cyclic R-curve – determination, problems, limitations and application. Engng. Fracture Mech. 2018, 198, 45-64. A detailed discussion would overload the present paper.
For the reviewer: The key point of the method is to generate a fatigue pre-crack free of crack closure. To this purpose the authors use compression pre-cracking on a common fracture mechanics specimen with an extremely sharp notch (e.g. by using a razor blade). The crack closure effects (plasticity, roughness, oxide etc. induced) will then gradually build up during subsequent loading. This probably will not completely remove the similitude effects but will reduce them significantly. The experiment also provides a long crack threshold, which at low R rations is usually significantly smaller than the one obtained by load shedding. No detailed discussion on this can be included in the present paper for reasons of space and in order not to interfere with the explanation of the basic methodology that the authors would like to bring to the reader's understanding. He can, however, inform himself on the basis of the extensive list of citations.
Reviewer: All in all, what is needed is an actual example of predicting the fatigue endurance limit from the fracture mechanics/fatigue crack growth data for validation.
Response: Much of the content described here is part of the ongoing work of the authors. Nevertheless, an S-N curve is provided for L-PBF steel 316L in Figure 11 up to a strength level equivalent to an endurance limit (which does not really exist in an austenitic steel) along with experimental data. This shows at least that the approach is promising for additive manufacturing applications.
Reviewer: The authors should revise their manuscript to address the above points for publication.
Response: Done as mentioned above.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript presents an interesting review of concepts and methodologies for predicting the fatigue life of metallic components manufactured by powder bed fusion.
The overall organization of the manuscript is very good with quality figures and a vast literature research.
This is not a research article, but a well written state of the art or book chapter. There are no original findings described in the manuscript.
The major good points of the manuscript are its clarity and good organization which I consider of interest for many readers.
However, the statements are not supported by direct experimental validation, which makes the proposed methods a mere speculation. Also, the discussion is quite generic and not very detailed especially for AM parts.
Author Response
The authors want to thank the reviewer for his work. In the following only the critical points are addressed.
Reviewer: This is not a research article, but a well written state of the art or book chapter. There are no original findings described in the manuscript.
Response: This is true. However, the authors refer to results which they recently have obtained. Based on the extensive list of citations the reader can follow this. The very aim here was to present a basic methodology for the fatigue assessment of components formed by additive manufacturing with conscious avoidance of a detailed discussion of all aspects that the paper would have overloaded. But, again, all information is provided in the citations such that the reader can get an extensive picture.
Reviewer: However, the statements are not supported by direct experimental validation, which makes the proposed methods a mere speculation. Also, the discussion is quite generic and not very detailed especially for AM parts.
Response: That methods such as the Kitagawa diagram or the cyclic R curve approach are not developed specifically for additive manufacturing is clear, but they potentially will play a big role just for these applications. The authors discuss at the beginning why the classical fatigue methods have a limited applicability with respect to AM. What is specific of the proposed approaches is the use of short crack fracture mechanics which has a high potential in this field. However, the discussion also highlights the problems. This is anything but state-of-the-art knowledge. That their proposed approach is not pure speculation shows Figure 11 where it is applied to the S-N curve of AM fabricated 316L steel along with experimental results. The cited paper also provides a satisfying Kitagawa plot of the results, which was not included here for reasons of space.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have answered the reviewer’s question partly in their response, but not made much change to the manuscript to reflect the question and answer, except added some new references, which the reviewer has gone through. The problem the reviewer still has difficulty understanding is that, as the cyclic R curve still evaluates the threshold Kth for long cracks, albeit with much less crack closure, being called intrinsic effective threshold, ΔKth, eff (K is calculated considering the initial notch length), so the K-similitude hypothesis is still being used dealing with microstructurally and physically short cracks as in AM materials. There are amble discussions in the literature shedding doubts on using LEFM to deal with microstructurally and physically short cracks, and the authors are aware of the problem. The fact is that in measuring the fatigue crack growth properties from conventional specimens containing long and through-the-thickness notches/cracks, the crack front contains numerous grains so the measurement is an average. Those unfavorably oriented grains certainly have an effect to impede crack advance overall. Whereas AM microstructural defects situate in a single or a few grains, and they propagate along a nature-selected favorably oriented grain path, so either the “threshold” or the crack growth rate of such cracks are different than artificially prepared long cracks. Despite the authors replace the physical crack length in the KT diagram with Δa measured from the cyclic R tests, the physical nature of problems are still different. The reviewer does understand how a S-N curve may be obtained by integration of the crack growth law, still the assumptions are presumably based on measurement from long cracks (BTW, the crack growth properties in predicting the S-N curve are not given for the AM material in this paper), not necessarily the true behavior of microstructurally and physically short cracks. The reviewer does not mean to totally deny such an approach, but it would be beneficial to the readers and the community in large to state the assumptions and limitations clearly up front. The authors should revise their manuscript reflecting the above questions and arguments.
Author Response
Reviewer: The problem the reviewer still has difficulty understanding is that, as the cyclic R curve still evaluates the threshold Kth for long cracks, albeit with much less crack closure, being called intrinsic effective threshold, ΔKth, eff (K is calculated considering the initial notch length), so the K-similitude hypothesis is still being used dealing with microstructurally and physically short cracks as in AM materials.
Response: I think, I have got the point now. There seems to be a misunderstanding. The cyclic R curve does not primarily evaluate the long crack threshold. It describes the development of the threshold in the physically short crack regime. At the beginning there is no (not just much less) crack closure at all and the threshold is the intrinsic one (which only depends on the elastic properties and the lattice type). Then the crack closure mechanisms gradually build up until they reach a stable state when the crack becomes a long one. In the case of corrosion effects which contribute a lot to the similitude problem, the long crack threshold which is reached at the end of this process might be significantly smaller than the one obtained by a conventional load reduction regime. The point is that we start with a closure free state which is the case because we prepare the specimens in compression pre-cracking.
Reviewer: There are amble discussions in the literature shedding doubts on using LEFM to deal with microstructurally and physically short cracks, and the authors are aware of the problem.
Response: That is true. But we don’t deal with microstructurally short cracks. The complete method is limited to the physically short crack (characterized by the gradual build-up of crack closure) and the overlapping mechanically short crack for which K is not applicable. Indeed, our method determines the cyclic crack driving force as an elastic-plastic one which is then formally transferred to a K factor. We call it, therefore, Kp.
Reviewer: The fact is that in measuring the fatigue crack growth properties from conventional specimens containing long and through-the-thickness notches/cracks, the crack front contains numerous grains so the measurement is an average. Those unfavorably oriented grains certainly have an effect to impede crack advance overall. Whereas AM microstructural defects situate in a single or a few grains, and they propagate along a nature-selected favorably oriented grain path, so either the “threshold” or the crack growth rate of such cracks are different than artificially prepared long cracks.
Response: Again, our approach does not deal with the physically short crack stage which controls the plain or material fatigue strength. The component fatigue strengths refers to notches. There is another crack arrest mechanism than in the microstructurally short crack regime, namely the build-up of the closure mechanisms. In other words: Even if the crack size is beyond that of the microstructurally short one there might still be crack arrest – and this finally controls the fatigue strength of the component. This is the very basis of our approach.
Reviewer: Despite the authors replace the physical crack length in the KT diagram with Δa measured from the cyclic R tests, the physical nature of problems are still different. The reviewer does understand how a S-N curve may be obtained by integration of the crack growth law, still the assumptions are presumably based on measurement from long cracks (BTW, the crack growth properties in predicting the S-N curve are not given for the AM material in this paper), not necessarily the true behavior of microstructurally and physically short cracks. The reviewer does not mean to totally deny such an approach, but it would be beneficial to the readers and the community in large to state the assumptions and limitations clearly up front.
Response: We do not replace the physical crack length in the KT diagram with Δa measured from the cyclic R tests and we also do not integrate the crack growth law. Instead we perform a R curve analysis. Crack arrest (which defines the fatigue strength) is given when the plasticity-corrected cyclic crack driving force tangentially touches the cyclic R curve.
Reviewer: The authors should revise their manuscript reflecting the above questions and arguments.
Response: To explicitly include all this information in the present paper would totally overload it. Instead the reader is referred to an extended list of literature. E.g. the basic method (however, not in the context of additive manufacturing) is published as an own special issue of Engineering Fracture Mechanics in 2018 and in a Springer book of 2019. Also, the question of fatigue in AM is addressed in a comprehensive review paper which just appeared. To deal with the whole complex with a few sentences on the sidelines would generate confusion rather than being helpful. In addition, in my opinion, there are misunderstandings. I will, therefore, no add further discussion in the paper, not because I did not know that the paper doesn't contain complete information but because this is not reasonably possible in the context of the present paper.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
Now the question seems to boil down to whether fatigue of AM materials starts with microstructurally short cracks or just physically short cracks? The reviewer does not see much clear classification or discussion on this in the literature (even though he is inclined to the former). Therefore it is up to the authors to define.
