Oblique Crashworthiness Analysis of Steel Circular Tubes: Parametric Study on Wall Thickness Effect and Critical Loading Angle Identification

Round 1

Reviewer 1 Report

The manuscript was reviewed. The idea of compression of the empty steel tubes under axial and oblique loading seems to be interesting. The authors must address the following comments:

1. The mesh sensitivity analysis for the numerical studies must be highlighted clearly in the manuscript.

2. All tubes were mounted on the rigid based for both axial and oblique compression tests. What happens if some portion of the tubes' cross section mounted on the base plate during oblique loading?

3.It is interesting to provide some information if the empty tubes get filled with some foam material fillers.

4. All Force-displacement curves need to be combined in a single curve to make a clear comparison.

5. The influence of deformation velocity on energy absorption and deformation mechanism of the steel tubes under oblique loading needs to be addressed.

6. The Introduction section has missed the deformation of the empty tubes and foam filed tubes. To this end, the authors are suggested to include the related research studies in the literature review.

Author Response

The Authors would like to thank the reviewer for the time devoted to this study.

Authors have rephrased various parts of introduction in order to improve that section of this work and provide a better and more extensive summary of relevant previous works and to underline better the aim and the tools of this study aiming to highlight its contribution to the respective research field.

1) Authors clarify that mesh sizing has been adjusting properly to tube wall thickness in every case as according to previous studies referred to the second paragraph of subsection 2.4 Finite Element Modeling (“In addition, FE mesh is generated properly considering the wall thickness in order to provide reliable results regarding the folds formulation [24].”) that mesh density ensures sufficient accuracy regarding the number and the type of formulated folds during plastic deformation. For this reason, authors have not implemented further a mesh sensitivity analysis given that the computational cost is not high enough for the examined simulations.

2) Authors have rephrased the last part of first paragraph of subsection 2.1 Experiments in order to provide a more clear and better understanding (“The bottom tube end is embedded into a 20 mm height external–internal ringed configuration which is positioned to the bottom base and restricts the bottom tube end from deforming externally or internally clamping that way a bottom zone of tube end and reducing the specimen effective initial length by that height. In more specific, the bottom support configuration contains a steel ringed cylindrical device fixedly connected to bottom base and properly dimensioned to tubular specimen external and internal diameter in order to provide an interference fit for clamping bottom tube end.”). In that part, authors explain that clamping bottom tube end reacts to its effective length decrease and provides a more stationary support as in case of oblique loading there is the danger of contact loss between base and tube when the loading angle increases enough. Given that the effect of tube end support types is not included to the aims of current study, authors desire was to avoid any sliding or rotation between tube and base which would lead to contact loss, and in consequence miscalculations about force-displacement fluctuation and the respective crashworthiness metrics.

3) The main target of current work has been focused on investigating the effect of loading angle and wall thickness regarding oblique impact of circular empty tubes in order to identify a critical angle which reflects the transition from progressive to unstable collapse. Authors aim to further expand their analysis on crashworthiness behavior of different geometries for empty and foam-filled tubes subjected to oblique impact, which is under investigation and authors’ goal is to be published as a future work in order to highlight more the foam-filling effect on collapse stability and critical loading angle.

4) Authors have already tried to plot all F-x curves in a single figure according to reviewer’s comment. However, given that for each examined angle (5 in total) two curves (test and simulation) have been produced, the respective figure of 10 in total curves seems confusing and difficult to be read. Further, in case of combining F-x curves separately for experiments and simulations, the validating point of view would be lost according to authors’ thinking. In contrast, regarding wall thickness parametric study where only simulations were carried out, authors have indeed plotted all F-x curves (the ones of each different thickness) in one single figure regarding each angle, as in every case it is a more indicative way for presenting results when figure reading does not suffer from confusion.

5) Current study investigated the crashworthiness response of obliquely loaded steel circular tubes by conducting both experiments and simulations. The experimental tests were carried out under quasi-static conditions due to cost equipment, while in contrast finite element simulations were conducted under dynamic loading rate representing more realistic impact conditions and reducing further the computational cost. Regarding the above, authors have added additional explanation in order to provide more clear understanding in last sentence of subsection 2.4 Finite Element Modeling (“Finally, the difference in impact velocity between tests and simulations is attributed to the fact that dynamic loading rate reduces computational cost of simulation and represents also more realistic crushing condition in contrast to quasi-static tests which are conducted at lower loading rate in order to restrict cost equipment.”). In addition, according to validation results between tests and simulations, the difference in crushing velocity did not seem to react to significant variation on the predicted deformation mechanism and the provided energy absorption regarding at least the examined impact velocities. Authors do recognize that an impact velocity parametric study would increase the level of research contribution and completion of current work, however that case was not included in the targets of this study.

6) Authors have reported to previous works whose analysis was emphasized on the foam-filling effect regarding energy absorption capability in the fourth paragraph of introduction. Considering that, as the energy absorption is strongly connected to occurred deformation mode because a progressive collapse reacts to greater energy absorption in contrast to an unstable one which leads to lower energy, the effect of foam-filling on absorbed energy and deformation can be considered similar. For this reason, authors did not choose to refer specifically to each observed deformation mode regarding empty and foam-filled tubes given that the respective part was included in introduction section and authors’ aim was to provide a summarizing and representative information about relevant works rather than details.

We hope the reviewer finds our changes to be satisfactory. Thank you very much.

Reviewer 2 Report

This paper studies the oblique crashworthiness of steel circular tubes. The structure is complete, including experiments and numerical investigation. The topic in interesting. Here are some advises for the author:

1. Although literature review are presented in the introduction, the knowledge gap should be given more clearly. The objective of current study shoud originated from the shortcoming from the exsting research.

 2. The introduction of the experiment seems too simple. Why not provides some table and figures. For example, the table of details of the specimens.

3. Please provides more details of the adopted constitutive relation, how about the model parameters?

4. There are some phase difference in Fig. 3, can author explain the reason?

Author Response

The Authors would like to thank the reviewer for the time devoted to this study and for his/her kind and encouraging comments.

1) The last paragraph of introduction section has been partially rephrased in order to highlight more sufficiently the knowledge gap which has been covered by current study compared to previous works.

2) In subsection 2.1 Experiments, a proper table (Table 1) has been added containing the experimental test data according to reviewer’s suggestion.

3) According to authors’ understanding, it is believed that the finite element modeling procedure in 2^nd and 3^rd paragraphs of subsection 2.4 Finite Element Modeling describes the considerations and treatments taken into account from authors for material mechanical behavior during its deformation. In that subsection, it is also provided the necessary model parameters adjusted during modeling such as material parameters, boundary conditions for specimen support, element size and number of integration points through thickness, hourglass coefficient and details of loading condition, while finally the utilized formulas regarding element formulation, hourglass, contact algorithms etc. have been presented too.  

4) Authors have added further explanation in subsection 3.2.1 Deformation Modes at first paragraph (“Thus, the phase difference between experimental and numerical F-x curves (Figure 3a) is attributed to the slight deviation between test and simulation regarding the number of formulated folds which are associated with force peaks and lows.”) and second paragraph (“Despite the accuracy in the number of predicted folds, experimental and numerical F-x curves also reveal a slight phase difference as captured in Figures 3b-3c, which however is now paid on slight deviations in energy dissipation rate which affects plastic deformation work required for folding formulation, as verified by the partially slight difference in EA slope between test and simulation as captured in Figures 4b-4c.”) trying to provide more clear understanding to reviewer’s comment.

We hope the reviewer finds our changes to be satisfactory. Thank you very much.

Reviewer 3 Report

 

The paper studies the crashworthiness of thin walled steel tubes. Experimental test on tubes subjected to quasi-static loading were performed, under variation of the impact angle. They were accompanied by FEA numerical investigations that showed the ability of the model to correctly represent the structural response. A parametric study was then performed to examine the influence of wall thickness to the important response parameters. The paper is well written but needs revision prior to publication.

Specific comments:

1.      The paper contains too many abbreviations. For better reading it is therefore recommended to add a list of abbreviations at the beginning of the paper.

2.      Line 26: The scope of the current research should be defined right from the beginning. It is therefore too general to declare in the first sentence “Current structures design….” without having defined what types of structures it refers to.

3.      Line 58: EA must be previously defined before an abbreviation used.

4.      Line 63: It is unclear what exactly the scaling factor 0.5 refers to.

5.      Line 72: The reference value to SEA must be defined here or reference to eq. (2) should be given.

6.      Line 43: PAM-CRASH must be included in the reference list.

7.      Line 99: LS-DYNA must be included in the reference list.

8.      Par. 2.1: It should be clarified whether the impact tests were performed in accordance with an international specification, or whether it followed the authors own design. If the latter is the case, the test configuration and execution should be compared to alternative ones proposed by other authors.

9.      The specification in accordance to which the impact tests was performed shall be given.     

1  Fig. 1: The test specimen, along with its dimensions (diameter, length) must be indicated in the Figure.

1.   Fig. 1: Construction details must be provided on the realization of the connection between the tube and its base.

1.   Angles are normally notated by Greek, not Latin, letters. Accordingly, the angle a should be written as α.

1.   Line 126: Although the tests simulate the crash response they were conducted under quasi-static loading. Difference between the two loading conditions should be reviewed and commented.

1.   Line 176: It is unclear what values presented in Table 1 are nominal values and which are derived from the coupon test.

1.   Line 210: It is unclear whether engineering or true material properties were introduced in the material model.

Author Response

The Authors would like to thank the reviewer for the time devoted to this study.

1) Authors have removed some abbreviation terms during revision and rephrasing especially in introduction subsection, and in the revised manuscript form there are about 8 abbreviations in total, from which the most ones refer to the crashworthiness metrics presented extensively in subsection 2.2 Crashworthiness Indicators. Finally, all abbreviations have been checked and reported the first time used in the text.

2) Introduction section has been rephrased in many areas by the authors trying to provide a more clear and better understanding. That significant sentence has been removed by authors according to reviewer’s comment, while further in last paragraph of introduction section, some more clear rephrasing has been implemented by the authors trying to highlight better the aim of this paper.

3) It has been corrected properly according to reviewer’s comment.

4) Authors have rephrased that specific part in order to provide a better understanding according to reviewer’s comment.

5) Authors have rephrased that specific part clarifying that the SEA increase refers to the comparison between foam-filled and empty tubes.

6) PAM-CRASH reference to the introduction has been removed from authors during their efforts for rephrasing most areas of introduction trying to provide more clear and compact information about relevant literature.

7)  It has been corrected properly according to reviewer’s comment.

8,9) The testing procedure conducted for experimental investigation has been carried out according to authors’ best experience and knowledge regarding impact tests and not according to specific standards. However, the test parameters have been chosen properly to be in sufficient agreement compared to relevant quasi-static impact tests conducted by previous studies, as for example the selected compressing velocity, specimen’s dimensions and the examined crushing angles.

10) Figure 1 has been updated to revised manuscript according to reviewer’s comment.

11) Authors have added further explanation on bottom ringed support configuration regarding its geometry and dimensions in the last sentence of first paragraph of subsection 2.1 Experiments (“In more specific, the bottom support configuration contains a steel ringed cylindrical device fixedly connected to bottom base and properly dimensioned to tubular specimen external and internal diameter in order to provide an interference fit for clamping bottom tube end.”) in order to provide a better and more clear understanding according to reviewer’s comment.

12) It has been corrected properly according to reviewer’s comment.

13) In general, the majority of previous relevant works choose quasi-static tests in order to examine experimentally the crashworthiness behavior due to lower cost equipment as this study also does. Authors have added more explanation regarding the difference between test and simulation in loading velocity in last sentence of subsection 2.4 Finite Element Modeling (“Finally, the difference in impact velocity between tests and simulations is attributed to the fact that dynamic loading rate reduces computational cost of simulation and represents also more realistic crushing condition in contrast to quasi-static tests which are conducted at lower loading rate in order to restrict cost equipment.”) aiming to comment loading rate difference according to reviewer’s suggestion.

14) Authors have rephrased that specific part in order to provide a better understanding according to reviewer’s comment.

15) Authors have rephrased that specific part clarifying that true stress-true plastic strain curve has been utilized for modeling material hardening behavior according to reviewer’s comment.

We hope the reviewer finds our changes to be satisfactory. Thank you very much.

Reviewer 4 Report

Documento anexado

Comments for author File: Comments.pdf

Author Response

The Authors would like to thank the reviewer for the time devoted to this study.

1) Authors have written the last paragraph of introduction focusing on the aim and the tools (experimental and modeling) of current study giving the analyses carried out in order to identify the loading angle and wall thickness effects on crashworthiness performance and the determination of a critical angle value to capture the transition to unstable collapse which brings significant decrease in energy absorption. The main purpose of that last paragraph is to summarize the aim and the tools of this work and to highlight its contribution to the already existed relevant works and the respective research field hoping to be treated of sufficient scientistic level and research contribution.

2) Authors rephrased that specific part in subsection 2 Crashworthiness Indicators according to reviewer’s comment.

3) According to best authors’ knowledge, authors have not obtained any difference between PCF and Fmax as both refer to the maximum crushing force. In addition, both abbreviations are widely used by other relevant works. The only reason authors chose PCF abbreviation is that mean crushing force also meets two possible abbreviations according to relevant literature which contain “F_avg or F_mean” and “MCF”. As authors selected to refer to mean crushing force with MCF abbreviation, they thought as more suitable abbreviation to peal force to be PCF rather than Fmax.

4) Authors have focused their work on capturing critical loading angle which decreases significantly energy absorption due to deformation instability. In specific, for that reason, the examined loading angle range was until 11° as according to various previous studies (included in references of current work) critical angle lies about 10° and so after that value, global bending mode occurs during collapse reacting to unstable deformation. In consequence, energy absorption reveals a significant drop, while for higher loading angles, energy absorption seems to be stabilized at low levels providing so a “sigmoid” variance with crushing angle. Therefore, as authors emphasized on capturing the transition from progressive collapse to unstable bending deformation mode, the examined loading angle range was selected until 11° allowing the identification of critical angle as verified by both experiments and simulations without needing to extent the investigation to higher angles.

5) Authors have rephrased various parts of conclusions section according to reviewer’s comment in order to provide a more useful and summarizing view of the founding of current study.

6) Authors have added the suggested figure (Figure 12 in the revised manuscript) according to reviewer’s suggestion, while further an additional paragraph has been added to the text explaining the observations and conclusions regarding the respective figure in the last paragraph of subsection 3 Wall Thickness Effect (“Figure 12 illustrates the effect of crushing angle and wall thickness on the variation of crashworthiness performance regarding SEA and PCF, where as the wall thickness increases the effect of loading angle seems to get stronger revealing sparser areas regarding the performance markers which refer to specific thickness. This tendency is attributed to the fact that low enough wall thickness reduces significantly the required buckling load facilitating thus a global bending collapse mode which results to lower SEA. Finally, considering an upper limit for PCF in order to benefit from triggering behavior which facilitates collapse initiation and further a lower SEA limit for ensuring sufficient energy capacity, the optimum tube dimensioning can be obtained with respect to the most beneficial loading angle.”).

We hope the reviewer finds our changes to be satisfactory. Thank you very much.

Round 2

Reviewer 3 Report

Authors did revise the manuscript in accordance with the comments made

Reviewer 4 Report

This reviewer thanks the efforts of the authors and considers that the review carried out brought a lot of quality to the article. In this sense, I recommend the publication in Machines