Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws
Round 1
Reviewer 1 Report
In the reviewer opinion, the paper can be recommended for publication in Applied science journal after addressing the following comments:
- References analyzed in the introductory section should be updated new 2020-2023 references should be added in this section such as:
https://doi.org/10.1007/s42464-020-00040-0
https://doi.org/10.1007/s13369-021-05919
- The abstract and introductory paragraph (from line 129 to line 156) are very long and should perhaps be shortened.
- The sample dimensions shown in figure 1.b must be standardized. The reference of the standard used to select the type and shape of the sample must be specified.
- A reference for figure 1.e should be added and the quality of this figure improved.
- Table 2. Temperature, bending speed and sheet thickness are not mechanical properties of the material tested, but these parameters constitute the test conditions.
- The parameters of Poisson's ratio and Young's modulus are logically obtained from the experimental test carried out after this table.
- Why is the voce law used to determine hardening parameters, and why not other laws such as the Hill 48 law?
- Figure 3. To carry out the experimental test of the V-bending process using a circular profile punching tool, it is logically preferable to use a die of the same shape and not a U-shaped die.
- After Table 4. It is recommended to plot springback curves as a function of punch radius.
- Looking at figure 4.a, we can see that the mesh elements are very large, which can affect the accuracy of the numerical results. It is therefore preferable to reduce the size of the mesh elements and test the efficiency of the mesh using experimental results.
- It is necessary to underline the novelty of current research in the concluding section.
Author Response
Dear Editors and Reviewers
Thank you for your email regarding our manuscript titled " Predictive Modeling of Spring-Back Behavior in V-Bending of SS400 Steel Sheets under Elevated Temperatures Using Combined Hardening Laws" submitted to The Applied Sciences. We appreciate the feedback received from the reviewers, and we are pleased to hear that our manuscript has the potential for publication pending revisions. In response to the reviewers' comments, we would like to address each point as follows:
Reviewer 1
Comments and Suggestions for Authors
In the reviewer's opinion, the paper can be recommended for publication in the Applied Science journal after addressing the following comments:
Comment 1: References analyzed in the introductory section should be updated, and new references from 2020-2023 should be added, such as:
https://doi.org/10.1007/s42464-020-00040-0
https://doi.org/10.1007/s13369-021-05919
Answer 1: We have included the following references:
Ben Said, L. et al. [24] conducted numerical and experimental studies comparing conventional bending methods with rubber-pad cushion bending for AA1050-H14 Aluminum thin sheets, using finite-element simulations with specific material models and hardness variations. Then, a comprehensive study involving numerical and experimental investigations assessed the use of an NC lathe machine in the SPIF process for producing dome parts from AA1060-H14 aluminum alloy sheets. The study revealed that the NC turning machine could efficiently manufacture axisymmetric components with improved accuracy compared to traditional 3-axis NC milling machines [25].
Comment 2: The abstract and introductory paragraph (from line 129 to line 156) are very long and should perhaps be shortened.
Answer 2: We have revised the abstract and introductory paragraph to make them more concise:
Abstract:
This research presents an innovative methodology for accurately predicting spring-back tendencies in V-bending of SS400 steel sheets under elevated temperatures. The study leverages extensive tensile test data to determine parameters for pure isotropic and kinematic hardening laws at varying temperatures, crucial inputs for Finite Element Method (FEM) simulations. While using pure isotropic or kinematic hardening laws alone has limitations, especially at elevated temperatures, a hybrid approach is recommended for robust predictive models in ABAQUS software. To address this challenge, a novel method is introduced, utilizing flow stress curve ratios between elevated and room temperatures as a function of equivalent strain to derive combined hardening law parameters. Rigorous comparison of simulation and experimental results confirms the model's effectiveness in predicting spring-back in V-bending of SS400 steel sheets, particularly under elevated temperatures. This innovative approach enhances understanding of material behavior at high temperatures and improves predictive capabilities for designing and optimizing complex V-bending processes.
Introductory paragraph (from line 129 to line 156):
In this study, we explore spring-back tendencies in V-bending parts made from SS400 steel sheets under elevated temperatures. We conducted tensile tests at various temperature thresholds (room temperature, 300°C, and 600°C). To model stress-strain behaviors under isotropic hardening laws, we utilized the Voce hardening model with parameters determined via the least-squares method in Excel 2013's Solver tool. We further conducted computational analyses of V-bending processes in ABAQUS software, considering both room temperature and elevated scenarios, incorporating pure isotropic and kinematic hardening laws. Comparisons between simulations and experimental results revealed disparities, with isotropic hardening overestimating spring-back tendencies, while kinematic hardening underestimated them. In response, we developed a novel methodology to derive parameters for combined hardening laws, improving the prediction of spring-back behaviors, especially under elevated temperatures. Our research also introduces an innovative technique for determining hardening parameters in V-bending SS400 steel sheets at elevated temperatures, based on a back stress formulation that correlates flow stress ratios between elevated and room temperatures. The strong alignment between simulation outcomes and empirical data underscores the reliability and potential utility of our proposed method.
Comment 3: The sample dimensions shown in figure 1.b must be standardized. The reference of the standard used to select the type and shape of the sample must be specified.
Answer 3: The shapes and dimensions of the specimens were prepared in accordance with TCVN 197-85 (197-2000). The tensile test specimens were cut from a 6 mm thick steel sheet using wire cutting in the rolling direction and conformed to the national standard TCVN 197-85 (197-2000) [38].
Comment 4: A reference for figure 1.e should be added, and the quality of this figure improved.
Answer 4: The data for figure 1.e was conducted by our research. We have improved the quality of this figure.
Comment 5: Table 2. Temperature, bending speed, and sheet thickness are not mechanical properties of the material tested, but these parameters constitute the test conditions.
Answer 5: We have revised the title of Table 2 to clarify its content. The new title is: "Table 2: Test Conditions and Mechanical Properties of the Material."
Comment 6: The parameters of Poisson's ratio and Young's modulus are logically obtained from the experimental test carried out after this table.
Answer 6: We have revised the explanation to clarify the source of the parameters: "The outcomes of the tensile tests conducted under various temperature conditions are depicted in Figure 1(e). The values for Poisson's ratio and Young's modulus are deduced from the experimental tests conducted following the material test conditions outlined in Table 2. The material parameters essential for the Finite Element Method (FEM) analysis are also listed in Table 2."
Comment 7: Why is the Voce's law used to determine hardening parameters, and why not other laws such as the Hill 48 law?
Answer 7: We employed Voce's law for fitting stress-strain curves. The Hill 48 law is primarily used to characterize material anisotropy. Research concerning material anisotropy, such as the Hill 48, Yld2000-2d, and BBC2005 models, is slated for investigation in future studies.
Comment 8: Figure 3. To carry out the experimental test of the V-bending process using a circular profile punching tool, it is logically preferable to use a die of the same shape and not a U-shaped die.
Answer 8: In this study, the utilization of 3-point V-bending is chosen to enhance the spring-back characteristics of the sheet material. This configuration involves point contact, allowing for the exploration of different punch and die radius parameters. Given the nature of point contact, there is no strict requirement for the punch and die shapes to be identical. The 'V' shape is created by adjusting the height of the punch stroke during the pressing process. As a result, the spring-back effect becomes more pronounced.
Comment 9: After Table 4. It is recommended to plot springback curves as a function of punch radius.
Answer 9: This particular study did not investigate the influence of the punch radius. As indicated in Table 4, the research primarily focused on altering the bending angle by varying the height of the punch stroke. Consequently, the degree of deformation and the resulting spring-back behavior were experimentally examined.
Comment 10: Looking at figure 4.a, we can see that the mesh elements are very large, which can affect the accuracy of the numerical results. It is therefore preferable to reduce the size of the mesh elements and test the efficiency of the mesh using experimental results.
Answer 10: The mesh elements for all components in the simulation were designed to have dimensions of approximately 2 × 2 × 8 mm (Thickness × width × length). We conducted extensive simulations with varying mesh sizes, aiming to enhance accuracy. However, reducing the mesh element size and validating its efficiency using experimental data proved to be a time-consuming process without substantial improvements in accuracy. As a result, we opted for a mesh element size of approximately 2 × 2 × 8 mm (Thickness × width × length), which provided a reasonable compromise between computational efficiency and accuracy.
Comment 11: It is necessary to underline the novelty of current research in the concluding section.
Answer 11: We have revised the conclusions to emphasize the novelty of the research:
"This study conducted an extensive experimental investigation, encompassing both tensile and V-bending tests, with the inclusion of thermal assistance. The results from the tensile tests, conducted at three distinct temperature levels (32°C, 300°C, and 600°C), revealed a noteworthy trend: as the temperature increased, the mechanical properties of the material exhibited a discernible decline, while the formability of the sheet metal notably improved. A pioneering framework was introduced for determining parameters related to the combined hardening law within the context of V-bending, both under standard room conditions and at elevated temperatures. The validity of this approach was substantiated through a rigorous comparative analysis, which involved finite element analysis using ABAQUS software and experimental results obtained from V-bending trials. Impressively, the predictions for V-bending at room temperature closely matched the corresponding experimental findings. Furthermore, a novel model rooted in the back stress function, derived from the relationship between flow stress at elevated temperatures and room temperature, consistently demonstrated its predictive capabilities by aligning with the associated experimental dataset. Consequently, the proposed methodology stands as a powerful tool for simulating springback predictions across diverse bending processes involving SS400 steel sheets at elevated temperatures. The ingenious amalgamation of experimental exploration, computational analysis, and the conceptualization of novel methodologies in this research makes a significant contribution to the understanding of material behavior under thermal-assisted bending conditions. Moreover, the outcomes hold substantial promise for optimizing bending procedures in practical industrial applications, where accurate springback predictions can significantly influence process efficiency and product quality, marking a distinct and innovative contribution to the field."
Author Response File: 
Author Response.docx
Reviewer 2 Report
This manuscript reports on a combined experimental-numerical
study to determine the strain hardening parameters of a
stainless steel (SS) 400 at room and elevated temperatures.
The experiments include static tension and V bending with
spring-back measurements across a temperature range.
First, separate isotropic and kinematic hardening models
are studied. The parameters are used in FE modeling of the
V-bending experiments. These results show some deviation
from the test data, so a combined isotropic-kinematic hardening
law is then proposed. This combined law produces closer
agreement between FE simulations and bending experiments.
The procedures are then extended to the elevated temperature
regime, whereby the model and parameters are adjusted to
fit the data.
The paper topic is of general interest to the engineering
mechanics industry and plasticity research community.
The introduction and references are substantial and
more than adequate. The experimental and numerical
results seem to make physical sense. However, some
issues should be considered in revision:
1) It was unclear to this reader if the results are
truly predictive for the V-bending simulations, or
if the parameters are calibrated to best-fit the
bending springback phenomenon. This should be
clarified in the paper. If the parameters are
adjusted to fit all the data, then the model cannot
be stated to be truly predictive. A truly predictive
model would require agreement with independent
test data against which the modeling constants
have not been tuned.
Please explain this in the manuscript revision.
2) This reader did not understand how the
isotropic and kinematic hardening variables, for example
eqs. 1 and 2, affect the total flow stress and
the yield surface. Please add the equations for
the total flow potential and show how the different
hardening terms enter the net flow resistance.
3) The model does a poor job of fitting the softening
portions of the elevated temperature curves in Fig. 1e,
Fig. 2b, Fig. 2c. This deficiency should be explained
in the paper. Is there necking/localization in
the tests that is not captured by the parameter fitting?
4) Equations 5 and 6 should be combined into a
single equation 5.
5) Decimal points rather than commas should be
used for numerical values. For example,
Table 1, C should be 0.19-0.21
6) Formatting of the Tables is poor. Table 3
should not be separated across pages. The
use of bold versus regular fonts in the
Tables is inconsistent. Please correct.
7) The legends for the color contours and the
text at the bottom left in each figure of the
FE simulations are incredibly small. The reader
cannot read these numbers even for maximum
zooming in on the pdf file. This applies
to Figs. 4, 5, and 7.
The legends and fonts
should be increased in size so they
are all legible for all the figures.
English is acceptable. Main issue is to use decimal points rather than commas for fractional numeric values.
Author Response
Dear Editors and Reviewers
Thank you for your email regarding our manuscript titled " Predictive modeling of spring-back behavior in v-bending of 2 ss400 steel sheets under elevated temperatures using combined 3 hardening laws" submitted to The Applied Sciences. We appreciate the feedback received from the reviewers, and we are pleased to hear that our manuscript has the potential for publication pending revisions. In response to the reviewers' comments, we would like to address each point as follows:
Review 2
This manuscript reports on a combined experimental-numerical study to determine the strain hardening parameters of stainless steel (SS) 400 at room and elevated temperatures. The experiments include static tension and V bending with spring-back measurements across a temperature range. First, separate isotropic and kinematic hardening models are studied. The parameters are used in FE modeling of the V-bending experiments. These results show some deviation from the test data, so a combined isotropic-kinematic hardening law is then proposed. This combined law produces closer agreement between FE simulations and bending experiments. The procedures are then extended to the elevated temperature regime, whereby the model and parameters are adjusted to fit the data. The paper's topic is of general interest to the engineering mechanics industry and plasticity research community. The introduction and references are substantial and more than adequate. The experimental and numerical results seem to make physical sense. However, some issues should be considered in revision:
Comment 1: It was unclear to this reader if the results are truly predictive for the V-bending simulations, or if the parameters are calibrated to best-fit the bending spring-back phenomenon. This should be clarified in the paper. If the parameters are adjusted to fit all the data, then the model cannot be stated to be truly predictive. A truly predictive model would require agreement with independent test data against which the modeling constants have not been tuned. Please explain this in the manuscript revision.
Answer 1: We have revised the Abstract and Introduction to enhance clarity. In the context of predicting the bending springback phenomenon, relying solely on stress-strain curves and parameters from either pure isotropic or kinematic hardening laws has limitations, particularly at elevated temperatures. Therefore, our study advocates a hybrid approach to develop robust predictive models within the ABAQUS software. While initial parameters are adjusted based on fundamental experiments, it's important to note that these parameters are not solely tuned to fit the existing data. Instead, they are used as a foundation for making a large number of subsequent predictions. These predictions are rigorously verified against independent test data to ensure their accuracy. This approach has been explicitly detailed in our research article.
Comment 2: This reader did not understand how the isotropic and kinematic hardening variables, for example, eqs. 1 and 2, affect the total flow stress and the yield surface. Please add the equations for the total flow potential and show how the different hardening terms enter the net flow resistance.
Answer 2: We have added the equations for the total flow potential and shown how the different hardening terms enter the net flow resistance:
The Von-Mises yield surface, which represents the material's yielding behavior, translates and expands with plastic strain and is defined as follows (Equation 1):
(1)
Where:
is the uni-axial equivalent yield stress
is the second invariant of the deviatoric stress tensor.
The stress difference () is measured from the center of the yield surface and can be expressed as (Equation 2):
(2)
In Equation 3, the deviatoric part of the current stress is defined as:
(3)
Where:
is the current stress;
is the mean stress; and
is the identity matrix.
Now, let's discuss the implications of pure isotropic and kinematic hardening:
Pure Isotropic Hardening: In the case of pure isotropic hardening, the yield locus only evolves in size, and there is no translation (Equation 4):
(4)
Kinematic Hardening: For the kinematic hardening model, the size of the yield surface remains constant (), and the translation of the yield locus is determined by the back stress (α) (Equation 5):
(5)
The evolution of kinematic hardening is described by the increment in back stress (α) as a function of equivalent plastic strain, as shown in Equation 6:
(6)
Here: C and γ are material coefficients related to kinematic behavior.
In Equation 7, the back stress (α) curve is obtained by offsetting tensile stress-strain curve data about the yield stress value (σY) and fitting it to the back-stress evolution law:
(8)
These equations illustrate how isotropic and kinematic hardening variables influence the total flow stress and the yield surface in the context of V-bending simulations.
Comment 3: The model does a poor job of fitting the softening portions of the elevated temperature curves in Fig. 1e, Fig. 2b, Fig. 2c. This deficiency should be explained in the paper. Is there necking/localization in the tests that is not captured by the parameter fitting?
Answer 3: Regarding the observed deficiency in fitting the softening portions of the elevated temperature curves (Fig. 1e, Fig. 2b, Fig. 2c), it's essential to clarify that the fitting of stress-strain curve data is primarily employed within very small equivalent strain regions. Consequently, the fitting data is applied prior to the occurrence of necking in the tests. As such, the softening portions of the curves are not utilized for simulation purposes.
In Figures 1 and 2, we intentionally maintain the softening portion of necking/localization in the tests. This decision is made to facilitate an honest and transparent comparison with the stress-strain curve fitting data. It's important to note that the objective of the simulation primarily focuses on the pre-necking phases to effectively capture and predict the spring-back phenomenon. This explanation has been included in our manuscript.
Comment 4: Equations 5 and 6 should be combined into a single equation 5.
Answer 4: We have combined Equations 5 and 6 into a single equation, enhancing the clarity and conciseness of our presentation.
Comment 5: Decimal points rather than commas should be used for numerical values. For example, Table 1, C should be 0.19-0.21.
Answer 5: We have revised the formatting to use decimal points instead of commas for numerical values to ensure consistency and clarity in our tables.
Comment 6: Formatting of the Tables is poor. Table 3 should not be separated across pages. The use of bold versus regular fonts in the Tables is inconsistent. Please correct.
Answer 6: We have improved the formatting of our tables to address the issues you raised. Table 3 has been adjusted to prevent separation across pages, and we have ensured consistency in the use of bold and regular fonts in our tables for better readability and presentation.
Comment 7: The legends for the color contours and the text at the bottom left in each figure of the FE simulations are incredibly small. The reader cannot read these numbers even when zooming in on the PDF file. This applies to Figs. 4, 5, and 7. The legends and fonts should be increased in size so they are all legible for all the figures.
Answer 7: In response to this valid feedback, we are committed to enhancing the quality of our figures to ensure optimal readability. We will increase the size of legends and fonts in these figures to make them legible even when the document is zoomed to its maximum extent. This improvement will significantly enhance the clarity and accessibility of the information presented in our figures. Your suggestion is greatly appreciated, and we addressed this issue in our revised manuscript.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
This version can be accepted for publication
Author Response
I appreciate the reviewer for accepting the revised article. Thank you.
Reviewer 2 Report
The authors made most of the suggested improvements. However, three issues remain to be fixed:
1) The commas were changed to decimals in Table 1, but not in the other tables. Please fix all the tables to use decimal points.
2) The authors added the requested equations on the yield behavior. However, there seems to be a typesetting malfunction with the equation editor software. There are question marks ?? throughout the pdf version of the manuscript where some mathematical symbols should be. This must be fixed.
3) The legends on the color figures from the simulations remain much too small. If the colors are not important, then the authors could simply paste a white box over these legends if the software doesn't allow them to be enlarged.
Author Response
Reply to Comment 1: We have made the necessary corrections and fixed all the tables to use decimal points. Thank you for pointing out this oversight.
Reply to Comment 2: We apologize for the typesetting malfunction with the equation editor software. We have now corrected the mathematical symbols throughout the PDF version of the manuscript.
Reply to Comment 3: We appreciate your suggestion regarding the legends on the color figures. Since the colors are not critical for the understanding of the figures, we have followed your advice and placed white boxes over these legends in the manuscript for improved readability. Thank you for your valuable feedback.
