A Mathematical Solution for Calculating the Springback of Laminated Beech Stacks Molded within the Elastic Range

Round 1

Reviewer 1 Report

Great job. 

I just have a few comments:

L2-19: It does look like to me the authors did not read forests guidelines.

L26: ... is important in multiple applications. --- None was given.

L31: Currently, trial and error, and developing of finite elements analysis are the two main approaches...

L35: Promising studies...

L36: What do you mean by "there"?

L41-42: I recommend including some references in here.

L42: "just" in the beginning of a sentence is not adequate.

L50: Therefore

L67: The goal was to derive

L68: FEM. Not everybody knows about this.

L72: The use of phrasal verbs is not recommended. (make up)

L78: Reference. "Also this wood has good mechanical properties. Reword this sentence to make it stronger.

L84: I recommend: Deutsches Institut für Normung - DIN, then its respective number, then (DIN, year)

L85: A universal testing machine (TIRAtest 28025) (City, Country).

L86-87: "The needed supporting... I understand that the equation is in the standard, however, its access is not available
for everyone. I recommend describing the equation.

L87: What kind of minor changes?

L89: MoE. If this is the first time citing it, you should use Modulus of Elasticity (MOE) and be consistent with throughout.

L91-92: Try to merge this paragraph with other one.

L93: Did you prepare the resin? did you obtain it from the market? was it donated? ph? Viscosity? Moisture?

L100: does CAD mean computed-aided design? Also, AutoCAD is a trademark you should be careful.

L104: The adjustment coefficient. Ok, What is that? where does it come from? If this is defined in Jones, please provide
minimal understanding.

L108: Did you attempt to do the the notation here? It look I R to me, which may be misleading.

L117: to my understanding R is a language and environment for statistical computing and graphics, not a program. You must
reference R creators here. Tell its version and so on.

L121: this paragraph is confusing. Rewrite it.

L143: This figure needs adjustments. Your y is yhat. The p value is missing. Did you check any outliers? I ask this
because I see a huge gap from 1700 to 3000 N/mm2

Figure 3. Too big. Also, what does as guide to the eye mean? This is totally non-scientific.

Figure 4. Too big. Adjust axis with capital letters.

A graph with the errors is missing.

I really liked the discussion.

Conclusions

I miss a paragraph of the importance of the results obtained and future perspectives.

Author Response

First of all, we would like to thank you for your constructive and helpful comments! Because there was a misconception of one reviewer to the test setup, we have tried to clarify at various points of the document with supplementary explanations (from the title over the abstract to the very end). All the additional references shall lead the reader to the unique approach of our setup. We have only bent the lamination within the linear elastic region and without prior plasticization while all the other paper concentrated on exactly that. However, we toned done the claim to be first J. The statistical analysis is now shown in more details.

L2-19: It does look like to me the authors did not read forests guidelines.

I changed the title and abstract format. I hope that was the problem. If not, please notice that minor changes will be done by the editors.

L26: ... is important in multiple applications. --- None was given.

We swapped application with disciplines, e.g. metal forming and molded composites. The next sentences are dealing with quite a few of them in details.

L31: Currently, trial and error, and developing of finite elements analysis are the two main approaches...

changed to: Currently, trial and error, and Finite Elements Analysis (FEA) are the two main approaches to achieve the desired results.

L35: Promising studies...

Changed to: The latest findings on springback in form laminated plywood, showed a relationship of temperature and moisture content [9] and contributed to an empirical equation [10]. In both studies the 3-ply laminates were pre-softened in water prior to assembly, before being cured at high temperatures whilst set in the die. Similar pre-softening processes were performed with simultaneous form fixation with single wood veneer by Herold and Pfriem [11].

L36: What do you mean by "there"?

This sentence belongs to the previous one. We changed “there” to “here”.

L41-42: I recommend including some references in here.

We would love to, but for that particularly problem it seem there is no scientific study but to cabinetmaker “papers”. In the paragraph before we included more wood related references e.g. Chanda (2020, 2018). We understood that we had to lead towards our approach of bending within the elastic range without plasticization.

L42: "just" in the beginning of a sentence is not adequate.

done

L50: Therefore

Done. The “e” was added.

L67: The goal was to derive

Done. The “to” was added.

L68: FEM. Not everybody knows about this.

Changed it to FEA (previously mentioned on the article)

L72: The use of phrasal verbs is not recommended. (make up)

Changed to: …number of laminations represented in the sample.

L78: Reference. "Also this wood has good mechanical properties. Reword this sentence to make it stronger.

Changed to and has now a reference: Currently also used in steam bending this wood has very good mechanical bending properties

L84: I recommend: Deutsches Institut für Normung - DIN, then its respective number, then (DIN, year)

Like this? : Deutsches Institut für Normung - DIN 52186: 1978-06 - …

L85: A universal testing machine (TIRAtest 28025) (City, Country).

Done

L86-87: "The needed supporting... I understand that the equation is in the standard, however, its access is not available for everyone. I recommend describing the equation.

The equation was added as a description in the sentence: The required supporting span was calculated using the equation supplied by the standard, where the span is at least 15 times the thickness of the material.

L87: What kind of minor changes?

We added a sentence and modified the one of interest to: Minor changes to the specifications of the standard were made to the bearing support span if the elasticity of the stack was too low to get proper reading or the maximum length of the support was reached. In those cases the span was shorter than desired.

L89: MoE. If this is the first time citing it, you should use Modulus of Elasticity (MOE) and be consistent with throughout.

done

L91-92: Try to merge this paragraph with other one.

done

L93: Did you prepare the resin?

No, it is ready to use in a bottle.

did you obtain it from the market?

It was a standard PUR by Kleiberit as stated.

was it donated?

Yes, it was donated glue by Kleiberit. We acknowledged it at the end.

ph? Viscosity? Moisture?

This was not tested. Ph and Viscosity change when the resin is cured. In the end it wouldn´t matter for the springback value.

Moisture: the PUR needs water to cure as a second compound. The moisture content of the PUR is therefore 0%. The water is in the humidity and wood which was conditioned at 20 °C and 65% Humidity. The wood moisture content reached at this climate about 10-12%. The PUR used this and that’s why the moisture content afterwards does not matter in the sample.

L100: does CAD mean computed-aided design? Also, AutoCAD is a trademark you should be careful.

Changed CAD to technical drawing program and added the ® to AutoCAD.

L104: The adjustment coefficient. Ok, What is that? where does it come from? If this is defined in Jones, please provide minimal understanding.

It´s now changed to proportionality constant (this should be the mathematically correct translation) and the equation is furthermore explained in the introduction. (L65)

L108: Did you attempt to do the notation here? It look I R to me, which may be misleading.

Changed to real numbers for better comprehension.

L117: to my understanding R is a language and environment for statistical computing and graphics, not a program. You must reference R creators here. Tell its version and so on.

done

L121: this paragraph is confusing. Rewrite it.

This introduction-sentence may help the reader: The wood tested shows no discrepancies when compared to known data. The samples of beech had. The random samples of the beech had a density…

L143: This figure needs adjustments. Your y is y_hat. The p value is missing. Did you check any outliers? I ask this because I see a huge gap from 1700 to 3000 N/mm2

At 3.3. elasticity value, there is now an additional paragraph at line 187:

According to calculation in R the p value of the slope is very small at 7.487725e-43, which means that the slope value to determine y_hat is significant. The gap between 1600 N/mm² and 3000 N/mm² is a natural phenomenon due to the fact that the sheets were not glued yet. There is an exponential correlation between the number of laminations and the elasticity value which explains the increasingly smaller distances between clusters, e.g. the number of laminations for the elasticity value from approximately 300 N/mm² is two, while stacks with three laminations can be found to have a value of elasticity between 1200 N/mm² and 1700 N/mm². The higher the number of laminations, the lower the elasticity value. However an overlap of elasticity values can be seen in samples with more laminations.

Figure 3. Too big.

The editing of the figures is with the journal. Eventually they will suggest a size or even change it.

Also, what does as guide to the eye mean? This is totally non-scientific.

Because the equation is only valid in the domain of N, the line of the regression curve is not the real graph and just a guide to the eye to the calculated values which are very close to the mean value but not exactly. We changed the expression to “trend curve”.

Figure 4. Too big. Adjust axis with capital letters.

The editing of the figures is with the journal. Eventually they will suggest a size or even change it.

A graph with the errors is missing.

We added an error graph:

The deviations of the estimated data from the experimental data, the errors (e)

are shown in figure 5.2. The errors are relatively evenly distributed above and below zero.

Figure 5.2. Error plot of all 57 springback values (circle) obtained by measurement and calculation with the formula (15).

I really liked the discussion.

Thank you!

Conclusions

I miss a paragraph of the importance of the results obtained and future perspectives.

I didn´t like to repeat the part from the discussion, but changed the last part to:

Further studies could show the influence of more wood properties when different wood species are used.

In the first part there is now a sentence which highlights again the differences to the usual papers.

Reviewer 2 Report

Manuscript ID: forests-820444

Title: A mathematical Solution for calculating the Springback of molded laminated Beech Stacks

Authors: Moritz Sanne, Gudrun Ahn-Ercan, Alexander Pfriem

Journal: Forests

Outcome: Rejected

General Comments:

The paper addresses the springback effect in molded wood laminations and claims that it has not been mathematically described yet. Test pieces of Beech laminations of 1mm, 2mm and 4mm thicknesses and stack sizes of between 2 and 16 laminations were used. The elasticity value of the stack was obtained using laminations (both glued and not glued) in a three-point bending test within the elastic region. The laminations were mounted in a radius form die. The stress induced by the die onto the stack was within the elastic region of the material. After curing, the actual radius was calculated by using CAD and a circular equation measuring three points on the stack. The radius of the die was claimed to have a negligible effect on the springback of the stack. The exponential correlation between springback and the number of laminations was used to calculate the springback effect on molded laminated stacks. The current facts and statements are hugely contradictory and needs to be significantly changed. The work is alright and provides Another equation for calculating the spring-back of laminated wood/plywood/veneer. However, the work lacks proper research and has very contradicting statements, which have been dealt with in the specific comments section.

Specific Comments:

1. The statement in line 41 “there is no scientific study available to calculate the springback effect” shows that the research is very limited, and the authors have not explored even a little. There are quite a few works based on the spring back calculation. Primarily, the laminates and their work has often been related to sheet-metals and there are numerous models for that. However, the major difference between them is the structure and the requirement of temperature and moisture control while forming. So, for wood laminates/plywood/veneers, there has again been various approached in finding the spring-back analytically. One of those ways was first pioneered in 1989 by Zahlan and O’Neil, which has then been modified significantly over the years by Inoue et al. (2007), Walcott and Shuttler (2007), Srinivas et al. (2007-2008) and Chanda et al. (2018,2020). These are just a few examples and the authors need to do a significant amount of research to study and observe the results before coming up with a new equation, based on different aspects.
2. Many studies have said that forming wood needs thermo-forming processes, else the wood doesn’t form because of the visco-elastic nature and often experience nearly 100% spring-back. There has been no mention of the forming temperature, and if ignored during forming/molding, then it is important to explain the reason with proper logic as to why they have been ignored.

1. The conditioning chamber parameters are strange, and the authors need to define why those parameters are given the said values and based on which work/standard/practice. Usually, wood is soaked to get or reach a certain moisture value before forming. However, it is important to understand how long the samples were conditioned and what is the moisture content of the wood after conditioning.

4. Line 87 states that some minor changes were made from the standard in order to accommodate the test variations. It is important to state the changes and why do the authors think that it might not affect the final results.

1. The test rig and the testing is not graphically represented properly, neither are the variations of the experimental SB and calculated SB. A more detailed table with the values is desirable and a better representation of the actual test rig and samples are needed.

6. The abbreviations used are not clearly specified and it is hard for the readers to understand the various abbreviations used. A more detailed explanation of the manual calculation and the abbreviations are required for readers to understand the working.
7. The glue used is Kleiberit PUR. However, the reason behind using the glue and the characteristics are not mentioned. The composition of the glue plays a critical role in the SB value and the molding aspect, again detailed in the literature. Nothing is mentioned or detailed in this aspect as well.
8. The claims made in the work are not correct for all laminates or plywood as there have been works were increase in layers has resulted in more SB and even decrease in the layer has resulted in the same, inferring that there is a certain number of laminates that gives best results, with samples more or less resulting in greater Sb and various other effects. The authors need to justify the claim based on the current work and have to limit them to the current work and wood type only.
9. Line-162 states the first SB equation. However, as highlighted earlier there are numerous others and the authors need to observe and analyse accordingly.
10. Line 178-179 states that the “variance coefficient increases with more laminations”. However, proper results and accurate data is missing giving a vague result. The authors need to make sure that the exact results are represented, and the variations are reported to observe the limit of the equation and to observe the errors for higher laminates.
11. There are many experimental data available in the literature against which the equation can be validated and the authors can achieve similar results in the larger scale. However, it is important to report those in the work. More importantly, the authors should understand that this is not the first equation for calculating SB and the work needs to be changed and reporting needs to be modified drastically. There are many complex equations already reported and they give good results. This equation is a very basic one and can be used in a very general way. However, the claims need to be changed and further research needs to be conducted on the literature review.
12. Finally, the radius of the bending rig does effect molding/forming, but definitely not when the radius is so large as in the present case. Studies have shown that the radius of molding/forming must be greater than 2t (t=thickness). Again, proper research on the literature is missing.

Grammar, language and formatting issues:

The English is good with a few errors as listed:

1. Line 16-17, “The radius of the die has a negligible when predicting the springback of the stack” makes no sense and needs to be modified.
2. The paper struggles to maintain the tense with a very common error of past and present tense being mixed together reporting the same parts of the paper. Make sure the tense is checked properly.

Recommendation: As such, the paper reports an equation based on quite a few experiments, which can be used in a very general form. The claims in the work are baseless and need to be carefully studied and a more detailed literature review is required to be conducted. The only good thing about the work is the equation, which can roughly predict the SB values for certain conditions. The authors need to make sure that is clear in the paper and remove the false claims.

Author Response

Generally we would like to thank you for your constructive comments! Because there was a misconception to the test setup, we have tried to clarify at various points of the document with supplementary explanations (from the title over the abstract to the very end). All the additional references shall lead the reader to the unique approach of our setup. We have only bent the lamination within the linear elastic region and without prior plasticization while all the other paper concentrated on exactly that. However, we toned done the claim to be first J. The statistical analysis is now shown in more details.

Specific Comments:

1.The statement in line 41 “there is no scientific study available to calculate the springback effect” shows that the research is very limited, and the authors have not explored even a little. There are quite a few works based on the spring back calculation. Primarily, the laminates and their work has often been related to sheet-metals and there are numerous models for that. However, the major difference between them is the structure and the requirement of temperature and moisture control while forming. So, for wood laminates/plywood/veneers, there has again been various approached in finding the spring-back analytically. One of those ways was first pioneered in 1989 by Zahlan and O’Neil, which has then been modified significantly over the years by Inoue et al. (2007), Walcott and Shuttler (2007), Srinivas et al. (2007-2008) and Chanda et al. (2018,2020). These are just a few examples and the authors need to do a significant amount of research to study and observe the results before coming up with a new equation, based on different aspects.

To make sure that the reader understand the difference between the publications available and our findings we had change several part of the paper. We are not plasticizing (neither chemically nor physically) the wood prior to the bending. Also we don´t exceed the linear elastic region to have the maximum strength in the molded part. That’s why the springback calculations of the mentioned papers are not usable in our case.

We included the paper to give more background and show the differences. Unfortunately we could not find Inoue et al and Srinivas et al. but as long as they haven´t done anything vastly differently than the other, we would like to keep the introduction as simple as possible.

Thank you for the Paper investigating actually wood. Chanda´s latest publication was a great one to transition to our approach.

2.Many studies have said that forming wood needs thermo-forming processes, else the wood doesn’t form because of the visco-elastic nature and often experience nearly 100% spring-back. There has been no mention of the forming temperature, and if ignored during forming/molding, then it is important to explain the reason with proper logic as to why they have been ignored.

As a cabinetmaker myself, we have bent and form fixed laminations always in ambient conditions. Also construction parts in buildings are done under room temperature although they are controlled to achieve always high qualities. Though temperature and other plasticization methods makes it easy to bend wooden part, it is not always possible or at great expense.

Have a look at this bike https://www.youtube.com/watch?v=3xCVLxABcgU&t=18s  and hopefully that explains the necessity of our work.

3.The conditioning chamber parameters are strange, and the authors need to define why those parameters are given the said values and based on which work/standard/practice. Usually, wood is soaked to get or reach a certain moisture value before forming. However, it is important to understand how long the samples were conditioned and what is the moisture content of the wood after conditioning.

The moisture content is not important. The conditioning was done until weight equilibrium and that is the standard for wood. The average moisture content of wood in general after the conditioning with 20°C and 65% humidity is approximately between 10% and 14%. This shall simulate the standard application equilibrium of moisture.

4.Line 87 states that some minor changes were made from the standard in order to accommodate the test variations. It is important to state the changes and why do the authors think that it might not affect the final results.

The changes are explained afterwards. The span was always changed to a smaller value because of a to elastic behavior when lots of laminations were used or the maximum availed support span was reached. Both scenarios only occurred at the outer edge of the test setup and had no observable influence of the result. A too narrow span would have changed the situation but since we were using a standard for solid wood and our laminations had strongly lower values (due to the non-glued situation) the effect is not visible in the data.

5.The test rig and the testing is not graphically represented properly, neither are the variations of the experimental SB and calculated SB. A more detailed table with the values is desirable and a better representation of the actual test rig and samples are needed.

We added figure 2 for more understanding of the test setup and table 2 as well as Figure 5.2 for more statistical knowledge.

6.The abbreviations used are not clearly specified and it is hard for the readers to understand the various abbreviations used. A more detailed explanation of the manual calculation and the abbreviations are required for readers to understand the working.

Where exactly are the comprehensive problems? We would very much like to explain and provide more details.

7.The glue used is Kleiberit PUR. However, the reason behind using the glue and the characteristics are not mentioned. The composition of the glue plays a critical role in the SB value and the molding aspect, again detailed in the literature. Nothing is mentioned or detailed in this aspect as well.

Additional infos were given in the paragraph belonging to the PUR in the method: “The sample stacks were glued with Kleiberit PUR 501.8, a single compound polyurethane resin (PUR) which is common in wood lamination processes and results in rapid and strong bonds.”

8.The claims made in the work are not correct for all laminates or plywood as there have been works were increase in layers has resulted in more SB and even decrease in the layer has resulted in the same, inferring that there is a certain number of laminates that gives best results, with samples more or less resulting in greater Sb and various other effects. The authors need to justify the claim based on the current work and have to limit them to the current work and wood type only.

Done and previously explained.

9.Line-162 states the first SB equation. However, as highlighted earlier there are numerous others and the authors need to observe and analyse accordingly.

Toned down, but we are still the first scientific work.

10.Line 178-179 states that the “variance coefficient increases with more laminations”. However, proper results and accurate data is missing giving a vague result. The authors need to make sure that the exact results are represented, and the variations are reported to observe the limit of the equation and to observe the errors for higher laminates.

We did so in the added error figure and the table 2 with statistical data.

11.There are many experimental data available in the literature against which the equation can be validated and the authors can achieve similar results in the larger scale. However, it is important to report those in the work. More importantly, the authors should understand that this is not the first equation for calculating SB and the work needs to be changed and reporting needs to be modified drastically. There are many complex equations already reported and they give good results. This equation is a very basic one and can be used in a very general way. However, the claims need to be changed and further research needs to be conducted on the literature review.

See answer to comment 1, 8 and 9.

12.Finally, the radius of the bending rig does effect molding/forming, but definitely not when the radius is so large as in the present case. Studies have shown that the radius of molding/forming must be greater than 2t (t=thickness). Again, proper research on the literature is missing.

We are operating within the elastic range and therefore the findings do not apply.

Grammar, language and formatting issues:

The English is good with a few errors as listed:

1.Line 16-17, “The radius of the die has a negligible when predicting the springback of the stack” makes no sense and needs to be modified.

The sentence was adjusted to: “The radius of the die within the limits of this study has a negligible effect when predicting the springback of the stack.”

2.The paper struggles to maintain the tense with a very common error of past and present tense being mixed together reporting the same parts of the paper. Make sure the tense is checked properly.

We did, but cannot promise to fulfill the expectations.

Recommendation: As such, the paper reports an equation based on quite a few experiments, which can be used in a very general form. The claims in the work are baseless and need to be carefully studied and a more detailed literature review is required to be conducted. The only good thing about the work is the equation, which can roughly predict the SB values for certain conditions. The authors need to make sure that is clear in the paper and remove the false claims.

We sincerely hope to achieve a better understanding to our approach and would like to suggest a re-read with respect of the linear-elastic range which is the major difference to all the paper mentioned.

Reviewer 3 Report

A mathematical Solution for calculating the Springback of molded laminated Beech Stacks

Authors: Moritz Sanne, Gudrun Ahn-Ercan  and Alexander Pfriem

The paper presents an original study on the springback of molded wood with a plan of experiment. It is probably the best way today to make a first analysis of this complex problem. Globally the writing of the paper is correct. The step in knowledge is in my opinion enough. The subject of the paper is within the scope of the journal and I didn’t found redundancy with other papers of the authors. However many points must be enhanced.

Comments and points requiring clarification are reported below.

• The bibliography is relatively poor even if I was not able to find a large number of paper on this subject which confirm the originality of the present At minima, do add the following paper and discuss it (you can add more) :

Hsu, W.E., Schwald, W., Schwald, J. et al. Chemical and physical changes required for producing dimensionally stable wood-based composites. Wood Sci.Technol. 22, 281–289 (1988). https://doi.org/10.1007/BF00386023

• I disagree with the statement of the authors on the research on springback restricted to the metallic area. There is a large number of research in the field of composite structures with very advanced modelling semi-empirical solution. It is necessary to make compensated mold especially for large aeronautic composite parts. The authors should add the following paper, discuss it and make the link with field  (you can add more) :

1. Mezeix et al. Spring-back simulation of unidirectional carbon/epoxy flat laminate composite manufactured through autoclave process Composite Structures Volume 124, June 2015, Pages 196-205

1. Erik Kappel, D. Stefaniak, G. Fernlund Predicting process-induced distortions in composite manufacturing – a pheno-numerical simulation strategy Compos Struct, 120 (2015), pp. 98-106

Johnston, A, Vaziri, R, Poursartip, A. A plane strain model for process-induced deformation of laminated composite structures. J Compos Mater 2001; 35: 1435–1469.

• I didn’t find the references [7] and [8], gives the doi links or the web address. Reference [9] is a personal paper with no references. The proposed laws should be discussed more deeply by the authors.

• The specimens are not described correctly. What are the overall dimensions for each radius and stacking? What is the angle of the specimens, 90°? Pictures would have been welcome.

• The way the measurement is done is not so clear. Explain with a graphic. Is the measurement done on one edge? Two? At the center of the specimen ? Why not using DIC or a 3D measurement machine?

• The springback percentage is never defined mathematically.

• P3, line 107: therefore

Author Response

Generally we would like to thank you for your constructive and helpful comments! Because there was a misconception to the test setup of one reviewer, we have tried to clarify at various points of the document with supplementary explanations (from the title over the abstract to the very end). All the additional references shall lead the reader to the unique approach of our setup. We have only bent the lamination within the linear elastic region and without prior plasticization while all the other paper concentrated on exactly that. However, we toned done the claim to be first J. The statistical analysis is now shown in more details.

The answers to your Comments and points requiring clarification are below.

The bibliography is relatively poor even if I was not able to find a large number of paper on this subject which confirm the originality of the present At minima, do add the following paper and discuss it (you can add more) :

Hsu, W.E., Schwald, W., Schwald, J. et al. Chemical and physical changes required for producing dimensionally stable wood-based composites. Wood Sci.Technol. 22, 281–289 (1988). https://doi.org/10.1007/BF00386023

We don´t see the suggested paper to benefit the paper in the revised version. Steam treated particle reduce a lot of problems in a board but neither are we investigating particle boards nor are we using steam or other plasticization methods in our setup. We included a statement by a steam bending manufacturer (Heller 2020) to show other ways to bend solid wood parts.

I disagree with the statement of the authors on the research on springback restricted to the metallic area. There is a large number of research in the field of composite structures with very advanced modelling semi-empirical solution. It is necessary to make compensated mold especially for large aeronautic composite parts. The authors should add the following paper, discuss it and make the link with field (you can add more) :

1. Mezeix et al. Spring-back simulation of unidirectional carbon/epoxy flat laminate composite manufactured through autoclave process Composite Structures Volume 124, June 2015, Pages 196-205
2. Erik Kappel, D. Stefaniak, G. Fernlund Predicting process-induced distortions in composite manufacturing – a pheno-numerical simulation strategy Compos Struct, 120 (2015), pp. 98-106
3. Johnston, A, Vaziri, R, Poursartip, A. A plane strain model for process-induced deformation of laminated composite structures. J Compos Mater 2001; 35: 1435–1469.

The mentioned papers were included and referenced as part of the introduction. That should show the reader that springback is everywhere. So from metal to composites to solid, ply- and laminated wood there is now everything mentioned hopefully.

I didn’t find the references [7] and [8], gives the doi links or the web address. Reference [9] is a personal paper with no references. The proposed laws should be discussed more deeply by the authors.

After contacting the sources (not the publisher itself) we had to change the references to the following:

To better find the published materials we gave a directory to find the presentation of Roberts. The link to the presentation is mentioned in the newsletter. The presentation was not scientifically done but highlights the demand for proper investigations.

• Roberts, P., Wood bending using laminations , The Woodworking Association of Pretoria Newsletter “Tambotie” 2018, Volume 11, http://ptawoodworkers.com/tambotie/tambotie-2018/
•  

The second source can be found in a magazine for cabinetmakers. Unfortunately even after a couple of attempts to reach the editors or someone of the magazine by mail or phone, we were not able to get the year of the Volume. The Volume number should be sufficient if you have access to print versions. An online version does not exist.

• Clayden, B., Predicting the spring, Furniture & Cabinetmaking unknown, Volume 8, pp. 37-39

All three references show the necessity of our investigation and also that it is necessary to highlight the non-plasticization part of our setup, which we have hopefully achieved with our changes.

We described the mathematical findings and wrote their assumed intention in the Introduction.

The specimens are not described correctly. What are the overall dimensions for each radius and stacking? What is the angle of the specimens, 90°? Pictures would have been welcome.

Figure 2 should make visible what the material and method part is now in more details verbally describing.

The way the measurement is done is not so clear. Explain with a graphic. Is the measurement done on one edge? Two? At the center of the specimen ? Why not using DIC or a 3D measurement machine?

Figure 2 will help to understand the measurement of the arc. Furthermore we have changed the text a bit to clarify.

DIC or other 3D measurements would not work since there is a lot of movement when the clamps are released. The excessive glue would have to be removed from the part to make the real outer edge visible. This is time consuming and will not necessarily lead to better results. Although it would have been fun to use our DIC system, the radii were recorded with sufficient accuracy in our opinion.

The springback percentage is never defined mathematically.

Done, Formula 1

P3, line 107: therefore

Done, thank you.

Round 2

Reviewer 2 Report

The modifications are adequate and the present form can be considered.

Reviewer 3 Report

The authors have satisfactory answered to the comments of the reviewer.