Rate-Dependent Cohesive Models for Dynamic Mode I Interfacial Propagation and Failure of Unidirectional Composite Laminates

Round 1

Reviewer 1 Report

Congratulations. The work is good, however, there are some concerns about your work, which can be addressed, improving the paper and its understanding. Please see attachment. 

Comments for author File: Comments.pdf

Author Response

Point 1: In the introduction, in line 39, the authors can add one or two references.

 

Response 1: Thanks for your kind suggestion. We have added two references in line 39.

 

Point 2: "et al." must be in italics. Fix it in your work.

 

Response 2: Thank you for the correction. We have corrected this typing error in revised manuscript.

 

Point 3: Place the registered trademark symbol ® whenever the authors mention a trademark, in line49, you have "Abaqus" and should be "Abaqus® ". Check throughout the document.

 

Response 3: Thanks for your kind suggestion. We have checked the trademark symbol throughout the document.

 

Point 4: It would be interesting for the authors to have more information about the High-speed camera used in this work, for example, its capacity.

 

Response 4: Thanks for your kind suggestion. Additional information of the camera has been added in the revised manuscript.

 

Point 5: Line 227, How were the two strain gauges used to guarantee the symmetry of the loading connected? Were they connected on individual circuits or were they connected on the same circuit to detect balance, for example on the same Wheatstone bridge?

 

Response 5: Thanks for the comment. Actually, the two strain gauges were placed symmetrically on the two beams of the DCB specimen and connected on individual circuits. And the strain signal of the two strain gauges were recorded by one oscilloscope. When the signals of the two strain gauges are remarkably close, the loading is supposed to be symmetrical. More details of the experimental technique can be found in ref. [32].

 

Point 6: When the authors present the sample dimensions on lines 234/238, it would be interesting for the image to have the dimensions. Its interpretation would be much more noticeable and faster.

 

Response 6: Thanks for the suggestion. We have added dimensions in figure 3 for better interpretation.

 

Point 7: Line 244, did the authors try to fine-tune the mesh to see if the results improved? What was the criterion for choosing the mesh size?

 

Response 7: Thanks for the comment. Mesh sensitivity analysis were conducted to guarantee the accuracy of the results. We used 0.1 mm, 0.2 mm and 0.5 mm as the mesh size in longitudinal direction. The result of 0.1 mm and 0.2 mm are almost the same, while the result of 0.2 mm and 0.5 mm have some differences. Thus, the mesh size of 0.2 mm in longitudinal direction is chosen as the mesh size.

 

Point 8: Table 1, check the spaces between variables, the equal sign, numbers and units. You should check throughout the text, for example, line 258, you have "ν=0.32 and ρ= 2700 kg/m3".

 

Response 8: Thank you for the suggestion. We have checked typing error throughout the text in revised manuscript.

 

Point 9: The first person of the plural is used on the work. Please avoid this situation, because in scientific documents the first person does not be used. See line 311.

 

Response 9: Thank you for your kind reminder. We have corrected this typing error in revised manuscript.

 

Point 10: Table 3:The experimental speed can have the units on top like the others shown in the table. I did not understand the values of the errors presented in this table, for example, the value of 3.44%. If you are calculating the error between 111 m/s and 108 m/s, with 108 being the reference, then you should calculate as follows: |108-111|/108 = 0,0278 = 2,78%

The reference value must be in the fraction denominator, in this case, the 108.

Another example, in the exponential model, has an error of 21.70%. If you are comparing the value of 106 m/s with the experimental speed of 108 m/s, then the value of that error does not make sense. Check if the error calculation is correct ...

 

Response 10: We are sorry for this mistake. Some errors are calculated by the previous number with decimal point, for example, the value of 3.44% is calculated as |108-111.72|/108 = 3.44%. And we forgot to update the values. We have checked carefully and corrected these mistakes in revised manuscript.

 

Point 11: The conclusions would be richer if the authors quantified, with values presented throughout the work, the differences between the models studied and the experimental. Whenever possible, they should be compared with other works mentioned in the introduction.

 

Response 11: Thank you for your suggestion. The conclusion was improved based on the reviewers’ suggestions. Quantitative values between modelling results and experimental results are mentioned in the conclusion. This paper aims at examining the modelling capability of three cohesive models based on the DCB test. Thus, it is not feasible to compare with results of other works. However, some of the observation were consistent with existing work, which were mentioned in the conclusion section as well.

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript is very interesting and focuses on rate-dependent cohesive models for dynamic Mode I interfacial propagation and failure of unidirectional composite laminates. I have the following comments:

 

• The introduction has to be improved. The introduction is expected to have an extensive literature review followed by an in-depth and critical analysis of state of the art. authors should avoid reference overkill/run-on, i.e., do not use more than three references per sentence. I suggest adding information to describe better what other researchers have done in this area. Each one of the cited references within the body of the paper should be discussed individually and explicitly to demonstrate their significance to the study. (Authors cite 8 references as one, without description)
• Carefully check the article again for typos. (line 266, no space between number and unit “5×105N/mm3“)
• the article (especially the implementation section) lacks detailed information about the hardware and software used. (models, software and SDK versions, etc.)
• the article lacks information and photos about the testing bench.
• the authors should spend more attention on indicating the novelty of the developed solution.
• The authors should pay more attention to the conclusion section

Author Response

Point 1: The introduction has to be improved. The introduction is expected to have an extensive literature review followed by an in-depth and critical analysis of state of the art. authors should avoid reference overkill/run-on, i.e., do not use more than three references per sentence. I suggest adding information to describe better what other researchers have done in this area. Each one of the cited references within the body of the paper should be discussed individually and explicitly to demonstrate their significance to the study. (Authors cite 8 references as one, without description)

 

Response 1: Thank you for the suggestion. There are several locations where we cite several references, for example “The other type of method is to develop phenomenological expressions in which the fracture toughness and cohesive strength are expressed as functions of the opening rate at the crack tip [15-23].”. However, this is a leading sentence, and all the cited references are discussed individually in the following paragraphs. We have checked the introduction and make sure most of the references have been explicitly discussed.

 

Point 2: Carefully check the article again for typos. (line 266, no space between number and unit “5×105N/mm3“)

 

Response 2: We are sorry for this typing error. We have checked this article carefully and corrected the typing error in revised manuscript.

 

Point 3: The article (especially the implementation section) lacks detailed information about the hardware and software used. (models, software and SDK versions, etc.)

 

Response 3: Thank you for your kind advice. We have added the information about the computational time, CPUs and software in Section 4.1.

 

Point 4: The article lacks information and photos about the testing bench.

 

Response 4: Thank you for your suggestion. We have added a photo of the testing bench in Fig. 1(b).

 

Point 5: The authors should spend more attention on indicating the novelty of the developed solution.

 

Response 5: Thanks for your suggestion. The Abstract and Conclusion sections are further improved to show the novelty and useful insights of this work.

 

Point 6: The authors should pay more attention to the conclusion section

 

Response 6: Thanks for your suggestion. Conclusion section has been improved.

Author Response File: Author Response.docx

Reviewer 3 Report

The aims of the paper were to assess and evaluate the applicability of three-types of rate-dependent cohesive models (logarithmic, exponential and power) in numerical delamination simulation, through comparison with  dynamic test results of double cantilever beam (DCB) specimens made from T700/MTM28-1 composite laminate. Authors should make some changes and additions in the text:

Keywords

• Authors should consider to use the “crack propagation” keyword.

Introduction

• The state of the art correctly has been presented.

Theories and Models

• Such Section should be removed after Material and Tests Section (e.g. connected with the Finite element model Section).

Materials and Tests

• Authors should give the basic properties of the epoxy resin.
• Information about conditioning parameters in the laboratory (temperature, relative humidity and time) should be given.
• Number of repetitions of tests is necessary for further analysis (for example in Section Results and discussion).

Conclusions

• Authors wrote “… This paper studies and examines the applicability of different rate-dependent cohesive models in the simulating of model I delamination of unidirectional composite. The dynamic DCB tests were conducted using an advanced electromagnetic Hopkinson bar apparatus. Logarithmic, exponential and power type rate-dependent cohesive models are selected from literature [18,20,23] for evaluations and programed as VUMAT subroutines. Finite element models based on the dynamic DCB test and rate-dependent cohesive models are established in Abaqus…“. Such sentences are not conclusions and should be removed!

Paper can be published after minor changes and additions.

Author Response

Point 1: Keywords

• Authors should consider to use the “crack propagation” keyword.

 

Response 1: Thank you for your kind advice. We have added “crack propagation” as keywords.

 

Point 2: Theories and Models

• Such Section should be removed after Material and Tests Section (e.g. connected with the Finite element model Section).

 

Response 2: Thanks for your kind advice. We have moved this Section after Material and Tests Section.

 

Point 3: Materials and Tests

• Authors should give the basic properties of the epoxy resin.

 

Response 3: We have added the basic properties of the epoxy resin in the Materials and Tests section.

 

Point 4: Materials and Tests

• Information about conditioning parameters in the laboratory (temperature, relative humidity and time) should be given.

 

Response 4: Thank you for your suggestion. We have added the information of temperature and relative humidity in the laboratory in this section. The test was going on all day, so the time is not meaningful.

 

Point 5: Materials and Tests

• Number of repetitions of tests is necessary for further analysis (for example in Section Results and discussion).

 

Response 5: Thank you. We have done multiple tests for the same specimen, however, the repeatability of dynamic fracture tests is difficult to guarantee. Even all the test conditions are set to be the same, the loading speed, the mechanical responses and cracking process may still have some differences between different tests. In this work, three typical test conditions were selected for model validation. And the focus of this work is to investigate the feasibility of different rate-dependent cohesive models.

 

Point 6: Conclusions

• Authors wrote “… This paper studies and examines the applicability of different rate-dependent cohesive models in the simulating of model I delamination of unidirectional composite. The dynamic DCB tests were conducted using an advanced electromagnetic Hopkinson bar apparatus. Logarithmic, exponential and power type rate-dependent cohesive models are selected from literature [18,20,23] for evaluations and programed as VUMAT subroutines. Finite element models based on the dynamic DCB test and rate-dependent cohesive models are established in Abaqus…“. Such sentences are not conclusions and should be removed!

 

Response 6: Thanks for your suggestion. Conclusion section has been improved.

Author Response File: Author Response.docx