# Probability Study on the Thermal Stress Distribution in Thick HK40 Stainless Steel Pipe Using Finite Element Method

*Reviewer 1:*Anonymous

*Reviewer 2:*Anonymous

*Reviewer 3:*Anonymous

**Round 1**

*Reviewer 1 Report*

**Comments and Suggestions for Authors**

** Line: 1**: Suggest changing the article type from “

*Brief Report*” to “

*Article*”.

* *

** Line: 6-9**: The professional title of the author should not be shown here. The email address of all authors should be placed after their affiliation. Please carefully follow the manuscript preparation guideline of the journal.

** **

** Line: 10**: The name and the contact information of the corresponding author are missing.

** **

**1. Introduction**

** Line: 37**: “

*So, the probability theory and mathematical statics have been applied which allows us...*”

Please change the word “*So*” to “*Therefore*”.

* *

** Line: 39**: “

*The stress distribution in the NPP piping system remains a main concern...*”

Please add the full term “*nuclear power plant*” before the abbreviation “*NPP*”.

** Line: 50**: “

*...*

*material properties in terms of their means, standard deviations or COV’s and...*”

Please add the full term “*coefficient of variation*” before the abbreviation “*COV*”.

** Line: 61**: “

*Chanylew Taye and Alem Bazezew [2] studied the creep analysis of boiler tubes by FEM,...*”

Please add the full term “*finite element method*” before the abbreviation “*FEM*”.

** Line: 75-99**: There are too many symbols in the paragraph. I suggest adding a nomenclature as well as a list of acronym at the end of the article.

**2. Analytical Solution**

** Line: 78**: Please correct the headline position of section 2.

** Line: 80**: “

*2.1. The stresses for thick walled cylinder pipe under internal pressure (P) and thermal gradient (Δ*

*?*

*)*”

Section 2.2 is missing.

** Line: 98**: “

*,the Thermal gradient of outer wall and inner wall temperature is...*”

Please change the capital “*T*” to lowercase “*t*”.

* *

** Line: 105**: “

*It is stressed to a pressure of =40*

*?Pa*

*.*”

Please delete the symbol “*=*” or rephrase to “*pressure of P=40**?Pa** .*”

** Line: 138-148**:

There is no description for Figure 5-8 and Table 2.

** Line:151**: “

*3.1 Comparison of Analytical and FEA using Abaqus:*”

Please move the section headline to a proper position.

** Line:153-160**:

There is no description for Figure 9-11and Table 3.

** Line:158**: “

*Comparison of Analytical, FEA using Abaqus and FEM using Mat lab Results*”

Please move the section headline to a proper position.

**4. Probabilistic study**

** Line:200-224**:

There is no description for Figure 12-14.

** **

**6. Derivation of stiffness matrix**

** Line: 268**: “6

*.1. Material Specifications*”

Section 6.2 is missing.

**7. Probabilistic study: output distribution**

** Line:283-294**:

There is no description for Figure 16-19. In addition, the labels of both x and y axis are too small, please enlarge them.

**8. Probability of failure of Von-Mises stress with respect to Yield strength**

** Line:307**:

There is no description for Figure 20. In addition, the labels of both x and y axis are too small, please enlarge them.

**9. Stress Contours**

** Line:316**: “

*9.1. Mean stress contours for HK40 material*”

Section 9.2 is missing.

* *

** Line:318-328**:

There is no description for Figure 21-23. In addition, the labels of both x and y axis are too small, please enlarge them.

**Other**

The authors should carefully check and modify the format of the article in order to meet the requirement for publication in the journal of *Designs*. The “*Author Contributions*”, “*Acknowledgment*” and “*Conflicts of Interest*” should be added at the end of the article. In addition, the English of this article should be thoroughly checked and polished by a native English speaker.

*Author Response*

** Line: 1**: Suggest changing the article type from “

*Brief Report*” to “

*Article*”-

**Done**

* *

** Line: 6-9**: The professional title of the author should not be shown here. The email address of all authors should be placed after their affiliation. Please carefully follow the manuscript preparation guideline of the journal-

**Changed as per guide lines**

** **

** Line: 10**: The name and the contact information of the corresponding author are missing-

**Changed**

** **

**1. Introduction**

** Line: 37**: “

*So, the probability theory and mathematical statics have been applied which allows us...*”

Please change the word “*So*” to “*Therefore*”.-**Done**

* *

** Line: 39**: “

*The stress distribution in the NPP piping system remains a main concern...*”

Please add the full term “*nuclear power plant*” before the abbreviation “*NPP*”.-**Done**

** Line: 50**: “

*...*

*material properties in terms of their means, standard deviations or COV’s and...*”

Please add the full term “*coefficient of variation*” before the abbreviation “*COV*”.-**Done**

** Line: 61**: “

*Chanylew Taye and Alem Bazezew [2] studied the creep analysis of boiler tubes by FEM,...*”

Please add the full term “*finite element method*” before the abbreviation “*FEM*”.-**Done**

** Line: 75-99**: There are too many symbols in the paragraph. I suggest adding a nomenclature as well as a list of acronym at the end of the article.-

**Done**

**2. Analytical Solution**

** Line: 78**: Please correct the headline position of section 2.-

**Done**

** Line: 80**: “

*2.1. The stresses for thick walled cylinder pipe under internal pressure (P) and thermal gradient (Δ*

*?*

*)*”

Section 2.2 is missing.-**Done**

** Line: 98**: “

*,the Thermal gradient of outer wall and inner wall temperature is...*”

Please change the capital “*T*” to lowercase “*t*”.-**Done**

* *

** Line: 105**: “

*It is stressed to a pressure of =40*

*?Pa*

*.*”

Please delete the symbol “*=*” or rephrase to “*pressure of P=40**?Pa** .*”-**Done**

** Line: 138-148**:

There is no description for Figure 5-8 and Table 2.-**Done**

** Line:151**: “

*3.1 Comparison of Analytical and FEA using Abaqus:*”

Please move the section headline to a proper position.-**Done**

** Line:153-160**:

There is no description for Figure 9-11and Table 3.-Done

** Line:158**: “

*Comparison of Analytical, FEA using Abaqus and FEM using Mat lab Results*”

Please move the section headline to a proper position.-**Done**

**4. Probabilistic study**

** Line:200-224**:

There is no description for Figure 12-14.-Done

** **

**6. Derivation of stiffness matrix**

** Line: 268**: “6

*.1. Material Specifications*”

Section 6.2 is missing.-**Done**

**7. Probabilistic study: output distribution**

** Line:283-294**:

There is no description for Figure 16-19. In addition, the labels of both x and y axis are too small, please enlarge them.-**Done**

**8. Probability of failure of Von-Mises stress with respect to Yield strength**

** Line:307**:

There is no description for Figure 20. In addition, the labels of both x and y axis are too small, please enlarge them.-**Done,Since they were the screen shot taken from FEM technique used in the article**

**9. Stress Contours**

** Line:316**: “

*9.1. Mean stress contours for HK40 material*”

Section 9.2 is missing.-**Done**

* *

** Line:318-328**:

There is no description for Figure 21-23. In addition, the labels of both x and y axis are too small, please enlarge them.-**Done**

Author Response File: Author Response.docx

*Reviewer 2 Report*

I suggest to improve the description of FE modelling assumptions. I also suggest to show the validation of the model against some physical experimental data.

Please also improve the state of the art as well as the quality of figures

*Author Response*

I suggest to improve the description of FE modelling assumptions. I also suggest to show the validation of the model against some physical experimental data- T**he data is more, since it is an article the description of FE modelling is minimized. Physical experimental data is under review**

Please also improve the state of the art as well as the quality of figures-T**he figure are taken from the analysis but have done to the maximum extent **

Author Response File: Author Response.docx

*Reviewer 3 Report*

The authors study the stress distribution in a thick tube due to the thermal gradient and statistical variation of parameters (material's elastic modulus, temperature gradient, pressure load).

Below is a list of comments the authors need to address before considering this manuscript for publication:

- there are a lot of misprints: "statics" (instead of statistics); Fig.3 caption: "verses"; pag.5 row123 the reference to fig.6 must be checked; table 3 caption, "Mat lab" should be written "Matlab"; pag.9 row 126, "meal"; pag.10 row 214 "Mpa"... Please check carefully all the paper (and captions).

pag.1 row39: before to use an acronym (NPP) it must be defined.

pag.2, rows 45-46: The Elastic modulus is not a "strength variable" is it a material properties related with stiffness not with strength. Please modify the sentence

pag. 2 row 50: define the acronym COV before to use it.

pag. 2 row 60: HK40 or HK-40,please in the paper use just one definition.

pag.2 row 72: The sentence "The node correction in a control volume mesh is not possible because the mesh needs to be regular." is not clear: why are we interested in the correction of the nodal volume? Please, explain better the sentence.

pag.2 row 75: add a proper reference for the analytical equations.

pag.3 row 78, the parameters used in equations 1 and 2 should be described (or at least you should say that the parameters description will provided in section ...).

The section title "Analytical solution" must be moved on a new line

pag.3 Equations 4-9 add a proper reference.

pag. 4 rows 107-108, The sentence should be modified "The dimensions of the thick pipe section are taken as..."

pag.4 row109, Which is the temperature effects on the elastic modulus value?

pag.4 table 1: two decimal (after the dot) digits are enough. Please modify the table accordingly.

pag.6 Fig 6: poor graphical quality: please increase the font size.

pag.7 table 3: for comparison purpose three decimal digits are enough.

pag.8 fig10-11: here we have a comparison between Abaqus and Matlab results. In the paper a Matlab model presentation is missing, please add some sentences to introduce the Matlab model, main assumptions, elements formulations...

pag.9 row 185: please improve the section title, for example "input parameters statistical distribution".

pag.9 eq.13: How is the statistical distribution selected? please explain or add a proper reference.

pag.9 row 197: the standard deviation value is missing.

pag. 10 fig.13: Is the statistical distribution not symmetric? If yes, why?

pag.10 row 222: add units to "80 and 4" values.

pag.10 fig.14: Is the statistical distribution is not symmetric? if yes, please justify.

pag.11 Fig15: please use the same scale for x and y axes.

pag.12 row 273: the symbol for displacement vector is missing.

pag. 14 rows 311-312: with "cut surface" do you mean "section surface"? A figure could be added to explain better where the section is made and to clarify which are the "Left and Right edges".

pag.14 row 313: do you have any experimental results to compare with the simulation's results?

pag.14 row 314: What do you mean with "the section is not symmetric"? Which should be the symmetry axis or plane?

pag.17 row 343: "correct stresses" do you mean that "the average stress is comparable/very similar with the result obtained using the analytical formula"? Please justify or re-arrange the sentence.

*Author Response*

The authors study the stress distribution in a thick tube due to the thermal gradient and statistical variation of parameters (material's elastic modulus, temperature gradient, pressure load).

Below is a list of comments the authors need to address before considering this manuscript for publication:

- there are a lot of misprints: "statics" (instead of statistics); Fig.3 caption: "verses"; pag.5 row123 the reference to fig.6 must be checked; table 3 caption, "Mat lab" should be written "Matlab"; pag.9 row 126, "meal"; pag.10 row 214 "Mpa"... Please check carefully all the paper (and captions)**-Done**

pag.1 row39: before to use an acronym (NPP) it must be defined.**-Done**

pag.2, rows 45-46: The Elastic modulus is not a "strength variable" is it a material properties related with stiffness not with strength. Please modify the sentence**-Done**

pag. 2 row 50: define the acronym COV before to use it.**-Done**

pag. 2 row 60: HK40 or HK-40,please in the paper use just one definition.**-Done**

pag.2 row 72: The sentence "The node correction in a control volume mesh is not possible because the mesh needs to be regular." is not clear: why are we interested in the correction of the nodal volume? Please, explain better the sentence.**-Done**

pag.2 row 75: add a proper reference for the analytical equations.**-Done**

pag.3 row 78, the parameters used in equations 1 and 2 should be described (or at least you should say that the parameters description will provided in section ...). **-Done**

The section title "Analytical solution" must be moved on a new line**-Done**

pag.3 Equations 4-9 add a proper reference.

**-Done**

pag. 4 rows 107-108, The sentence should be modified "The dimensions of the thick pipe section are taken as..."**-Done**

pag.4 row109, Which is the temperature effects on the elastic modulus value?

**-Done**

pag.4 table 1: two decimal (after the dot) digits are enough. Please modify the table accordingly.

pag.6 Fig 6: poor graphical quality: please increase the font size.**-Done**

pag.7 table 3: for comparison purpose three decimal digits are enough.**-Done**

pag.8 fig10-11: here we have a comparison between Abaqus and Matlab results. In the paper a Matlab model presentation is missing, please add some sentences to introduce the Matlab model, main assumptions, elements formulations...

**-Done**

pag.9 row 185: please improve the section title, for example "input parameters statistical distribution".

pag.9 eq.13: How is the statistical distribution selected? please explain or add a proper reference.

pag.9 row 197: the standard deviation value is missing.**-Done**

pag. 10 fig.13: Is the statistical distribution not symmetric? If yes, why?**-Done**

pag.10 row 222: add units to "80 and 4" values.**-Done**

pag.10 fig.14: Is the statistical distribution is not symmetric? if yes, please justify.**-Done**

pag.11 Fig15: please use the same scale for x and y axes.

**-Done**

pag.12 row 273: the symbol for displacement vector is missing- **Given in Nomenclature**

pag. 14 rows 311-312: with "cut surface" do you mean "section surface"? A figure could be added to explain better where the section is made and to clarify which are the "Left and Right edges".**-Done**

pag.14 row 313: do you have any experimental results to compare with the simulation's results? **-Done**

pag.14 row 314: What do you mean with "the section is not symmetric"? Which should be the symmetry axis or plane?**-Done**

pag.17 row 343: "correct stresses" do you mean that "the average stress is comparable/vevery similar with the result obtained using the analytical formula"? Please justify or re-arrange the sentence.

**-Done**

Author Response File: Author Response.docx

**Round 2**

*Reviewer 1 Report*

*Author Response*

Have done the corrections stated by the reviewer

Author Response File: Author Response.docx

*Reviewer 2 Report*

the authors revised properly the manuscript

*Author Response*

Have done the corrections and as attached in the manuscript

Author Response File: Author Response.docx