Recent Developments on the Unified Fatigue Life Prediction Method Based on Fracture Mechanics and its Applications

Round 1

Reviewer 1 Report

Dear Authors,

Your study presented the further development of unified fatigue life prediction (UFLP) method to predict the fatigue life of marine structures. great Job!

The following point can maybe improve the quality of the work:

In the introduction part:

• Please address strengths or weaknesses of your model in comparison to other methods. (SWOT-analysis)

Thank you so much for your valuable research.

Author Response

Reply to the reviewers

1. Reviewer 1

 (1) Please address strengths or weaknesses of your model in comparison to other methods. (SWOT-analysis)

Authors’ reply: Thanks for your suggestion. We have explained it in section of Introduction, but in the revised manuscript, we restated it in the conclusion (The revised part is marked in red) as follows,

‘......However, due to the more embedded parameters, more tests are needed to determine the UFLP model parameters than the commonly used Paris law. In order to improve the convenience of application, the authors’ group also proposed some engineering determination methods of parameters through systematic research, which improves the availability of the model. At present, the fatigue calculation methods of ships and offshore structures in the classification society rules are mainly based on the cumulative damage method based on S-N curve. However, with the improvement of lightweight requirements of the structures, the use of high-strength steel, and the fact that there are inherent defects in welded structures, it is believed that this model can provide a theoretical basis for the formulation of new evaluation rules in the future. And in the continuous development, the UFLP method has become more applicable in the fatigue life prediction of marine structures. ‘

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is related to recent Developments on the unified fatigue life prediction method and its applications.

The paper is quite well understandable.

Correctly describes the state of the problem and associated issues.

The paper is a good contribution to the knowledge transfer between research institutions and society.

This is an interesting paper and worth of publishing after minor amendments. 

Title:

In my point of view, the title of the paper could be reformulated, because the article is related to fracture mechanics-based approaches.

1. Introduction

When the authors refer to safety of maritime structures, they need to cite a paper. This topic has no citation. The paper below can be mentioned:

1. Meng et al. Reliability-based optimisation for offshore structures using saddlepoint approximation, Maritime Engineering – ICE, 2020, in press.

2. The Unified Fatigue Life Prediction Method and Its Further Developments

Please, change the title.

May be: The Unified Residual Life Prediction Method and Its Further Developments

General Comments

A lot of scientific works were developed to study the extension or residual lifetime of offshore structures. This paper is a kind of review and progress state. Why not be more general?

The authors could to introduce topics such as:

• Fatigue crack growth laws;
• Fracture mechanics approaches;
• Stress Intensity Factor;
• Mk;
• DOB;
• Residual stresses
•  
• Present examples and compare with the design codes.

Author Response

Reply to the reviewers

1. Reviewer 2

• Correctly describes the state of the problem and associated issues.

Authors’ reply: Thanks for your suggestion. The sate of the problem and associated issues has been emphasized in the section of the Introduction of the revised manuscript (The revised part is marked in red) as follows,

‘......The disadvantage of damage cumulative method which is applied in current ship classification rules is that the initial defects of materials and the final failure state are not defined clearly. The inherent theoretical defects make the prediction results very dispersive. In order to reasonably take account of the influence of fatigue cracks on the ultimate strength of a marine structure......’

‘......There have been a lot of researches on crack growth rate models since the Paris law being put forward [9]. Although Paris law has been used widely in engineering because of its simple expression, it can only express the stable stage of crack growth, so it needs to simplify the analysis conditions in engineering application, and many later models have insufficient ability to explain various fatigue phenomena. ‘ 

• In my point of view, the title of the paper could be reformulated, because the article is related to fracture mechanics-based approaches.

Authors’ reply: Thanks for your suggestion. The title of the manuscript has been changed to emphasize the fracture mechanics (The revised part is marked in red) as follows,

‘Recent Developments on the Unified Fatigue Life Prediction Method Based on Fracture Mechanics and its Applications’

• Introduction: When the authors refer to safety of maritime structures, they need to cite a paper. This topic has no citation. The paper below can be mentioned:

Meng et al. Reliability-based optimisation for offshore structures using saddlepoint approximation, Maritime Engineering – ICE, 2020, in press.

Authors’ reply: Thanks for your suggestion. The reference has been added in the revised manuscript as follows and the number of the references has been rearranged.

‘......Researchers attach importance to reliability-based optimisation for ships and offshore structures for safety [e.g. 2].’

• Please, change the title. May be: The Unified Residual Life Prediction Method and Its Further Developments

Authors’ reply: Thanks for your suggestion. We agree that the suggestion is very reasonable, however, this manuscript is actually an review and summary on our past research results. From the beginning of the research, the name of the model has been fixed to ‘Unified Fatigue Life Prediction Method’, so we use this title in the present manuscript. But in order for more easily understanding, we added ‘based on fracture mechanics’ into the revised manuscript.

• General Comments

A lot of scientific works were developed to study the extension or residual lifetime of offshore structures. This paper is a kind of review and progress state. Why not be more general?

The authors could to introduce topics such as:

• Fatigue crack growth laws;
• Fracture mechanics approaches;
• Stress Intensity Factor;
• Mk;
• DOB;
• Residual stresses
• Present examples and compare with the design codes.

Authors’ reply: Thanks for your suggestion. Fracture mechanics is the basis of this method, which has been pointed out in the title and the introduction of the revised manuscript. The purpose of this manuscript is to introduce the research progress of UFLPM. In fact, more basic concepts are introduced in our previous papers and books. Readers can trace back to previous papers listed in the references for more details. The have been not repeated presently, otherwise it will be very lengthy. However, as one of the most important achievements in the literature, Paris law is introduced with the concept of stress intensity factor. As for the comparison, the method based on fracture mechanics and the method based on cumulative damage theory have very different theoretical basis, so it is difficult to make an reasonable comparison as being lack of real measurement data for validation at present. However, as introduced in the revised manuscript, due to the inherent defects in theory, the cumulative damage theory-based method adopted in the current classification societies makes the results of fatigue life assessment very scattered by different users when considering the same structure in accordance with the classification society's specifications, which was concluded in the comparative study report of ISSC in 2003, so people have realized that the next generation of fatigue life assessment of ship and offshore structures must be updated to be the one based on a more clear basis. This can be referred to the application results in other industries such as aviation, bridge, etc. The authors are also tracking and promoting the improvement and application of the model based on fracture mechanics, hoping to promote the updating of classification society's specifications. The revised part with introduction of fracture mechanics\stress intensity factor range\Paris law\residual stress and the benchmark study is ISSC have been marked in red in the revised manuscript. And the following two papers have been added in the reference list.

Fricke, W., Cui, W.C., Kierkegaard, H., Kihl, D., Koval, M., Lee, H.L., et al. Comparative fatigue strength assessment of a structural detail in a containership using various approaches of classification societies. Mar Struct 2002,15(1),1–13.

Paris, P.C, & Erdogan, F. A critical analysis of crack propagation laws. J Basic Sci 1963, 85, 528–34.

Other revisions have been made as follows,

• A new reference is added besides those pointed out above as follows,

Wu, M., Wang, F., & Cui, W.C., Crack Evaluation of an Ultra-High-Pressure Chamber Used for Deep-Sea Environment Simulation, J Ship Mech (accepted), 2019.

• The following reference has been published now, so the publication information has been changed as follows,

Zhu, Y.M., Yao, X., Yang, L.F., Wang, F., Zhang, J. Effect of stress intensity factor on surface crack of deep-sea spherical shell, J Ship Mech 2020, 24,97(03), 371-379.

• The sources of the data in Tab.1 have been pointed out one by one as follows,

Table 1. Data of model parameters for common materials used in marine structures [14,43,44,56].