Fatigue Lifetime Analysis of a Bicycle Frame Made by Additive Manufacturing Technology from AlSi10Mg

Round 1

Reviewer 1 Report

The experimental design of this article is rigorous and the content is appealing. The method of improving the fatigue life of SS316 by intermittent recovery heat treatment (RHT) in argon environment at different temperatures is with clear application prospects. The work is exhaustive and well supported by theory. It is suggested that the research can be received after minor revise. The following are some suggestions for the authors.

(1) In the abstract, experimental data are suggested to show the influence of intermittent RHT method on fatigue life.

(2) In paragraph 2.1, a graph of finite element simulation analysis can be provided to enhance the persuasiveness of the article.

(3) In Figure 4, the different stages referred to in the article need to be labeled.

(4) Some equations are missing, such as the relationship between material damping and dislocation density and PSB density.

(5) It is suggested to add a table of experimental summary (similar to the style of Table 3) at the end of the experimental part of 3.4 to make the experimental results more intuitive.

Author Response

Thank you for your time and comments!

The experimental design of this article is rigorous and the content is appealing. The method of improving the fatigue life of SS316 by intermittent recovery heat treatment (RHT) in argon environment at different temperatures is with clear application prospects. The work is exhaustive and well supported by theory. It is suggested that the research can be received after minor revise. The following are some suggestions for the authors.

(1) In the abstract, experimental data are suggested to show the influence of intermittent RHT method on fatigue life.

In this paper, the material produced by conventional technology and additive technology in as-built condition was compared. The effect of heat treatment on the increase of cyclic properties was not investigated in this paper -due to the extensiveness of further cyclic tests needed, this may be a suggestion for further research and further cyclic testing of materials demonstrating the effect of heat treatment, as mentioned in the conclusions.

(2) In paragraph 2.1, a graph of finite element simulation analysis can be provided to enhance the persuasiveness of the article.

Fig. 1 and Fig. 6 shows the images obtained by FEM analysis in the most stressed part of the frame for all three stress directions - more detailed images are not shown in order to maintain the clarity of the paper and to highlight the methodology of the fatigue life assessment procedure.

(3) In Figure 4, the different stages referred to in the article need to be labeled.

The labels for each loading situation are above each graph.

(4) Some equations are missing, such as the relationship between material damping and dislocation density and PSB density.

These relationships have not been investigated or used in the fatigue life assessment methodology described.

(5) It is suggested to add a table of experimental summary (similar to the style of Table 3) at the end of the experimental part of 3.4 to make the experimental results more intuitive.

Section 3.4 is not included in the paper. The graphical interpretation of the results in Figures 11 and 12 is, in our opinion, more telling. What is appropriate to compare in numbers is in Table 6

Reviewer 2 Report

This is not a full-length paper. The results are too short to support the conclusions. Also, there is no discussion and the introduction is insufficient. Many recently published papers are not well descripted. Furthermore, the contents reported in this paper is not novel. The conclusions are already known, and the model is too old.

Author Response

This is not a full-length paper. The results are too short to support the conclusions. Also, there is no discussion and the introduction is insufficient. Many recently published papers are not well descripted. Furthermore, the contents reported in this paper is not novel. The conclusions are already known, and the model is too old.

Thank you for your time, opinion and comments!

The introduction has been extended and the conclusion has been completed. The main intention of the authors of the paper was to assemble a suitable methodology for the application of existing procedures for this complex structural case. Approaches to fatigue life assessment of additively manufactured components are still a subject of scientific research and debate. The approaches used in this paper (load multipliers for determining stresses for the local stress-strain approach at the root of the notch, selection of an appropriate criterion to account for multiaxiality, proper cycle counting for disproportionality of normal and shear stresses, identification of the critical plane with maximum fatigue damage) show the applicability of the safe life methodology for fatigue life assessment also for structures manufactured by additive technologies.

Reviewer 3 Report

The authors compare three different aluminum alloys - additively manufactured, cast and wrought - with respect to their estimated fatigue lifetime when used for a bicycle frame.

To this purpose, for characterizing the loading, the accelerations are measured for four different load cases (stairs up, stairs down, jump, ditch); the stresses are computed from the accelerations via influence matrices obtained from finite element simulations (and verified by strain gauge measurements); a synthetical load history for a virtual track is composed therefrom. 

For characterizing the resistance, fatigue testing is performed for the three alloys, and Basquin curves are derived, including their 95% prediction bands.

Finally, the estimated lifetime is computed using the Basquin curves, Miner's linear damage accumulation rule and Findley's multiaxial fatigue criterion for the synthetic load history.

The topic is of high relevance; introduction and methodological approach are written in a concise, clear manner. However, there are a couple of questions regarding results and conclusions, which the authors are urged to address:

Fig. 3: legend for red and blue curves is missing. 

Filtering: please document sampling frequency, type and cutoff frequency of filter. 

Figs 8, 9: classical confidence, prediction and tolerance intervals from linear regression are narrowest near the mean value of the data; the delimiting curves are not straight lines. This is not the case here. Why? How have the Basquin parameters for the straight-line PI been calculated? Please describe the procedure in sufficient detail (Ref. [14] could not be found on the Internet, DOI for Ref. [15] did not work).

Results: Please document in detail which statistical distributions (and distribution parameters) have been assumed for the resistance parameters; cumulative distribution functions for the lifetime cannot be obtained from the parameters in Tables 4-5 alone. The load has been assumed deterministic?

Conclusions: Owing to the early stage of development, the conclusions (must) remain rather vague; therefore, it is recommended to shorten them instead of getting into speculations about heat treatment and welding.

As a final minor remark, while the English langue is grammatically correct, clear and easy to understand throughout the manuscript, the authors are nevertheless asked to check that the appropriate standard expressions are used (e.g. influence matrix instead of influential matrix, filtering instead of filtration, design instead of construction).

Author Response

Thank you for your time, and highly competent comments!

The authors compare three different aluminum alloys - additively manufactured, cast and wrought - with respect to their estimated fatigue lifetime when used for a bicycle frame.

To this purpose, for characterizing the loading, the accelerations are measured for four different load cases (stairs up, stairs down, jump, ditch); the stresses are computed from the accelerations via influence matrices obtained from finite element simulations (and verified by strain gauge measurements); a synthetical load history for a virtual track is composed therefrom. 

For characterizing the resistance, fatigue testing is performed for the three alloys, and Basquin curves are derived, including their 95% prediction bands.

Finally, the estimated lifetime is computed using the Basquin curves, Miner's linear damage accumulation rule and Findley's multiaxial fatigue criterion for the synthetic load history.

The topic is of high relevance; introduction and methodological approach are written in a concise, clear manner. However, there are a couple of questions regarding results and conclusions, which the authors are urged to address:

Fig. 3: legend for red and blue curves is missing. 

Have been added.

Filtering: please document sampling frequency, type and cutoff frequency of filter. 

Sampling frequency directly follows from the data on r. 71, filter data has been added.

Figs 8, 9: classical confidence, prediction and tolerance intervals from linear regression are narrowest near the mean value of the data; the delimiting curves are not straight lines. This is not the case here. Why? How have the Basquin parameters for the straight-line PI been calculated? Please describe the procedure in sufficient detail (Ref. [14] could not be found on the Internet, DOI for Ref. [15] did not work).

DOI for Ref. [15] have been corrected (syntax error).

Results: Please document in detail which statistical distributions (and distribution parameters) have been assumed for the resistance parameters; cumulative distribution functions for the lifetime cannot be obtained from the parameters in Tables 4-5 alone. The load has been assumed deterministic?

The first sentence of the conclusion states that the results in probabilistic form (which is represented by the distribution function) include the variance of the material properties. The variance of the loading process was not considered. The confidence intervals use quantiles of the Student distribution for a range of probabilities from 2.5 to 97.5%. The entire methodology is explained in detail in references 14 and 15 and explaining it in detail would detract from the clarity and main objective of the paper.

Conclusions: Owing to the early stage of development, the conclusions (must) remain rather vague; therefore, it is recommended to shorten them instead of getting into speculations about heat treatment and welding.

Conclusions have been added for a better understanding of the contribution of the paper (taking into account the comments of other reviewers as well).

As a final minor remark, while the English langue is grammatically correct, clear and easy to understand throughout the manuscript, the authors are nevertheless asked to check that the appropriate standard expressions are used (e.g. influence matrix instead of influential matrix, filtering instead of filtration, design instead of construction).

Thank you, your recommendations have been taken into account and the expressions used have been modified 

Round 2

Reviewer 2 Report

I would like to recommend its publication.

Author Response

The article has been checked by a native speaker in our languages department - please see the attachement...

Author Response File: Author Response.pdf