the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Oct 2026
Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study
Abstract. In-service thermal loading of gear shafts may relax the residual compressive stresses introduced by ultrasonic impact treatment (UIT), thereby degrading the surface strengthening effect. In this study, a 30CrMoA gear shaft is investigated using integrated finite element simulation and experimental approaches to systematically evaluate the effects of UIT on surface residual stress, microhardness, surface roughness, and microstructure, as well as the thermal evolution of residual stress at 65 °C. Results demonstrate that UIT introduced a residual compressive stress field extending to approximately 1.25 mm beneath the surface, with a surface stress of −321 MPa and a peak stress of approximately −724 MPa. Surface hardness increased from 231 HV to 318 HV, with a hardened layer depth of approximately 1.14 mm, while surface roughness Ra is reduced from 0.8 μm to 0.18 μm. Under thermal exposure at 65 °C, surface residual compressive stress exhibited an initially rapid relaxation that subsequently decelerated, stabilizing after 8 h with a total relaxation of approximately 23.94%. Meanwhile, surface hardness, hardened layer depth, and microstructure remained essentially unchanged, indicating excellent retention of the work-hardening effect. Finite element predictions showed excellent agreement with experimental measurements, validating the effectiveness of the numerical model. This study elucidates the decoupled thermal evolution of residual stress relaxation and work-hardening retention in UIT-strengthened surface layers, establishing a theoretical framework for the reliable engineering application of ultrasonic impact treatment to gear shafts operating at elevated temperatures.
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Status: open (until 10 Dec 2026)
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RC1: 'Comment on ms-2026-176', Anonymous Referee #1, 06 Oct 2026
reply
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AC1: 'Reply on RC1', Xigui Wang, 07 Oct 2026
reply
October 6, 2026
Dear Editor:
MS Editor-in-Chief:
Mechanical Sciences
We are very pleased to learn that this article has been accepted for publication in Mechanical Sciences, titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The paper was coauthored by Xinbo Zhang, Zongrong Sun, and Xigui Wang.
Contribution of each individual co-author:
No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. We would like to declare on behalf of our co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved of the manuscript that is enclosed.
In this subject research, we present a review titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). In this study, a 30CrMoA alloy steel drive shaft was investigated, and a combined finite element (FE) simulation and experimental approach was employed to systematically examine the effects of UIT on surface residual stress, microhardness, surface roughness, and microstructure, as well as the evolution of residual stress during thermal exposure at 65 °C. The results indicate that UIT introduced a residual compressive stress field extending to a depth of approximately 1.253 mm, with a surface stress of −320.98 MPa and a peak stress of approximately −723.74 MPa. The surface microhardness increased from 231 HV to 318 HV, accompanied by a hardened layer depth of approximately 1.14 mm, while the surface roughness Ra decreased from 0.8 μm to 0.18 μm. During thermal exposure at 65 °C, the surface residual compressive stress exhibited a relaxation behavior characterized by a rapid initial stage followed by a gradual stage with increasing holding time, stabilizing after 8 h with an overall relaxation rate of approximately 23.94%. Meanwhile, the surface hardness, hardened layer depth, and microstructure showed no significant changes, indicating that the work-hardening effect was well preserved. The FE simulation results agreed well with the experimental data, validating the reliability of the numerical model.
Our main contribution to the field is the systematic elucidation of the differentiated response between residual stress relaxation and work-hardening retention in ultrasonic impact-strengthened 30CrMoA gear shafts under in-service thermal conditions. By combining finite element simulation with experimental characterization, we demonstrate that although the surface residual compressive stress relaxes by approximately 23.94% after 8 h of thermal exposure at 65 °C, the work-hardening effect, reflected in surface microhardness, hardened layer depth, and microstructure, remains essentially intact. This decoupling of stress relaxation from hardening stability provides, for the first time, a quantitative basis for predicting the long-term service reliability of UIT-treated transmission components operating at elevated temperatures.
The novelty and significance of this manuscript are as follows:
The work was studied mainly “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The work is studied mainly by integrating finite element simulation with systematic experimental characterization to investigate both the strengthening effects of ultrasonic impact treatment (UIT) on a 30CrMoA alloy steel drive shaft and, more importantly, the thermal stability of the strengthened layer under in-service temperature conditions. The key novel finding is the differentiated response between residual stress relaxation and work-hardening retention during thermal exposure at 65 °C: while the surface residual compressive stress relaxes by approximately 23.94% and stabilizes after 8 h, the microhardness, hardened layer depth, and microstructure show no significant degradation. This distinction has not been addressed in previous UIT studies, which have largely focused on room-temperature strengthening effects without considering in-service thermal stability. Furthermore, the experimentally validated finite element model established in this work enables quantitative prediction of residual stress evolution under thermal loading, thereby providing both mechanistic insight and a practical design tool for applying UIT to gear shafts and other transmission components operating at elevated temperatures.
Response to Reviewers' Comments:
Reviewer 1 (Report #1):
Q1. The description of equation 5 is not accurate. The authors need to find a continuum mechanics book or reference.
Sincerely respond to Q1 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for this valuable comment. In response to this concern, we have revised the manuscript as follows:
When the Lagrange (Lagrangian) algorithm is employed for stress analysis, the coordinate system is attached to the analyzed object (i.e., the deformable body) and moves together with the material particles. The motion and deformation of the body are examined by tracking the positions of individual particles at successive instants. The equation of motion of a particle can be expressed as:
(5)
where denotes the material coordinates (i.e., the Lagrangian coordinates, taken as the coordinates of the particle in the initial configuration), denotes the time of particle motion, and denotes the spatial coordinates of the particle at time . The initial condition is satisfied, meaning that the material coordinates coincide with the spatial coordinates at the initial instant.
Equation (5) describes the kinematic mapping of material points within the Lagrangian framework of continuum mechanics. In Section 3.2, we have revised the text accompanying Equation (5): the imprecise expression "moving particles" has been replaced with the standard continuum mechanics term "material points," and the description now explicitly distinguishes between the material coordinates (reference configuration) and the spatial coordinates (current, deformed configuration). In addition, as suggested by the reviewer, the classical textbook by Sedov (March 1966) has been cited in the text and added to the reference list.
Changes made in the manuscript: Section 3.2 (description of Eq. (5)) and the reference list.
Q2. For any screenshot from the software, please remove the background color.
Sincerely respond to Q2 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for the valuable comments. In response to this concern, we have removed the background color of the software screenshots in the revised manuscript; this suggestion provides important guidance for our future research. The DEFORM simulation screenshot (Figure 2) originally contained a dark blue background, which has now been removed. We have also checked all other software-generated figures in the manuscript and eliminated any colored backgrounds from the screenshots.
Changes made in the manuscript: Figure 2 and the other software screenshots.
Q3. In Table 1, you need to write “Initial yield stress A (MPa)”, etc. Please correct the rest.
Sincerely respond to Q3 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for this careful observation. As suggested, we have revised Table 1 so that all parameters are presented in the standard format of "parameter name, symbol (unit)", e.g., "Initial yield stress A (MPa)", and the remaining entries have been checked and corrected accordingly.
We have conducted a thorough check of all mathematical expressions throughout the manuscript. All complete equations are now displayed on separate lines with sequential equation numbers, and no full equations remain embedded in the running text. Only individual symbols and simple variables are retained as inline math.
Changes made in the manuscript: a manuscript-wide check and reformatting of all mathematical expressions.
Q4. For any equations, it is not recommended to place them inside the main text. They should be treated as a single equation with an equation ID.
Sincerely respond to Q4 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for the valuable comments. Following your suggestion, we have carefully reviewed the entire manuscript and standardized the formatting of all equations: those previously embedded within the text lines have been converted to display style, each set on a separate line and numbered sequentially. These revisions not only enhance the standardization and readability of the manuscript, but also serve as valuable guidance for our future submissions to your journal. We have revised the column headers of Table 1. The separator "/" between the parameter symbol and its unit has been replaced with parentheses, e.g., "Initial yield stress A (MPa)". All column headers in Table 1 now follow this unified format.
Changes made in the manuscript: Table 1.
Q5. For Figure 4, please make the font size of the description inside compatible with the main text. It can be larger, but it cannot be smaller. Improve the resolution, for example, in Figure 8. Please check and correct the rest.
Sincerely respond to Q5 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for the valuable comments. In response to this concern, we have carefully examined and revised all figures throughout the revised manuscript: the font size of the text within the figures has been uniformly adjusted to be no smaller than that of the main text, and the resolution of the figures has been improved accordingly. These revisions apply to Figs. 3, 4, and 8, among others.
(1) For Figure 4: We have adjusted the font size of the in-figure text so that it matches the main text and is no smaller than the main text size. (2) Regarding image resolution: Figure 8 has been re-exported from the original Origin project at a resolution of 300 dpi. We have also systematically checked all figures throughout the manuscript, and all low-resolution figures have been replaced with high-resolution versions.
Changes made in the manuscript: Figure 4 (font size); Figure 8 and all other figures (resolution improvement).
Thank you and best regards.
Sincerely,
Corresponding author
Xigui Wang Professor, PhD Supervisor
School of Mechatronics and Automation, Huaqiao University, No. 668 Jimei Avenue, Jimei District, Xiamen 361021, China
wyr20091207@126.com
First author
Xinbo Zhang Professor
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
zyjhust@126.com
Zongrong Sun
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
chenxfhit@126.com
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RC2: 'Reply on RC1', Anonymous Referee #2, 10 Nov 2026
reply
Major comments
- Inconsistent and possibly mixed-up data. Surface stress (−321, ~310, 320.98 MPa), peak stress (−724, 720.24, −723.74 MPa), layer depth (1.20, 1.25, 1.253, 1.273 mm) and plastic layer thickness (44.61, ~45, ~50 µm) differ between abstract, text, figures and conclusions. The stated 23.94 % relaxation corresponds to 244.15 MPa, which Section 5.1.2 gives as the 4 h value but Section 5.1.4 calls the measured 8 h value (239.68 MPa would give 25.3 %). Please provide one table of measured and simulated values for every state (U, UHT-1 to UHT-4) with uncertainties.
- Selective validation. In Fig. 9 the measured surface stress (about −580 MPa) differs from the simulated one (about −320 MPa) by roughly 45 %, so the claim that all deviations are within 5 % is incorrect. This discrepancy must be discussed, and full profiles compared quantitatively.
- Thermal relaxation simulation is not described. The Johnson–Cook model is time-independent and cannot by itself produce stress decay during a constant 65 °C hold. The relaxation/creep model, DEFORM module, thermal boundary conditions and missing parameters (m, Tm, Tr) must be given; otherwise the thermal validation cannot be assessed.
- Hardness retention is not measured. The conclusion of unchanged hardness relies on simulated PEEQ (Fig. 15), which cannot change during a stress-free hold by construction. Measured hardness profiles after each exposure are required. In addition, an HV1 indent on ~300 HV steel is about 78 µm wide, so the stated 10 µm spacing is physically impossible (ISO 6507-1 requires ≥ 2.5d).
- Incomplete and partly copied model description. Section 3.5 refers to a "TC11 titanium alloy workpiece" and "ultrasonic rolling" from another study. A 0.7 mm element size cannot resolve a 375 µm stress peak or a 45 µm layer; a mesh study is needed. The applied load type (5 µm amplitude, 600 N, or 0.01 mm interference), number of simulated impacts and material data must be stated. Eqs. (1)–(4) are never used and should be applied or removed.
- Overstated scope. Static 8 h exposure without mechanical loading does not represent gear shaft service, and the 65 °C service temperature needs justification. The claim of a "theoretical framework" should be tempered, and the literature on thermal relaxation of peening/rolling-induced stresses should be reviewed.
Minor comments
- Use one sign convention for compressive stresses throughout.
- Hardness baseline differs (231 HV in the abstract vs. 240 HV for the 32.5 % increase).
- 8 lacks the 8 h (UHT-4) curve; Figs. 8, 9, 13 and 14 need error bars and clear simulation/experiment labels.
- Several references are not cited in the text, and "Zhang et al., 2015" denotes two different papers.
Citation: https://doi.org/10.5194/ms-2026-176-RC2 -
AC3: 'Reply on RC2', Xigui Wang, 11 Nov 2026
reply
November 11, 2026
Dear Editor:
MS Editor-in-Chief:
Mechanical Sciences
We are very pleased to learn that this article has been accepted for publication in Mechanical Sciences, titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The paper was coauthored by Xinbo Zhang, Zongrong Sun, and Xigui Wang.
Contribution of each individual co-author:
No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. We would like to declare on behalf of our co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved of the manuscript that is enclosed.
In this subject research, we present a review titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). In this study, a 30CrMoA alloy steel drive shaft was investigated, and a combined finite element (FE) simulation and experimental approach was employed to systematically examine the effects of UIT on surface residual stress, microhardness, surface roughness, and microstructure, as well as the evolution of residual stress during thermal exposure at 65 °C. The results indicate that UIT introduced a residual compressive stress field extending to a depth of approximately 1.253 mm, with a surface stress of −320.98 MPa and a peak stress of approximately −723.74 MPa. The surface microhardness increased from 231 HV to 318 HV, accompanied by a hardened layer depth of approximately 1.14 mm, while the surface roughness Ra decreased from 0.8 μm to 0.18 μm. During thermal exposure at 65 °C, the surface residual compressive stress exhibited a relaxation behavior characterized by a rapid initial stage followed by a gradual stage with increasing holding time, stabilizing after 8 h with an overall relaxation rate of approximately 23.94%. Meanwhile, the surface hardness, hardened layer depth, and microstructure showed no significant changes, indicating that the work-hardening effect was well preserved. The FE simulation results agreed well with the experimental data, validating the reliability of the numerical model.
Our main contribution to the field is the systematic elucidation of the differentiated response between residual stress relaxation and work-hardening retention in ultrasonic impact-strengthened 30CrMoA gear shafts under in-service thermal conditions. By combining finite element simulation with experimental characterization, we demonstrate that although the surface residual compressive stress relaxes by approximately 23.94% after 8 h of thermal exposure at 65 °C, the work-hardening effect, reflected in surface microhardness, hardened layer depth, and microstructure, remains essentially intact. This decoupling of stress relaxation from hardening stability provides, for the first time, a quantitative basis for predicting the long-term service reliability of UIT-treated transmission components operating at elevated temperatures.
The novelty and significance of this manuscript are as follows:
The work was studied mainly “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The work is studied mainly by integrating finite element simulation with systematic experimental characterization to investigate both the strengthening effects of ultrasonic impact treatment (UIT) on a 30CrMoA alloy steel drive shaft and, more importantly, the thermal stability of the strengthened layer under in-service temperature conditions. The key novel finding is the differentiated response between residual stress relaxation and work-hardening retention during thermal exposure at 65 °C: while the surface residual compressive stress relaxes by approximately 23.94% and stabilizes after 8 h, the microhardness, hardened layer depth, and microstructure show no significant degradation. This distinction has not been addressed in previous UIT studies, which have largely focused on room-temperature strengthening effects without considering in-service thermal stability. Furthermore, the experimentally validated finite element model established in this work enables quantitative prediction of residual stress evolution under thermal loading, thereby providing both mechanistic insight and a practical design tool for applying UIT to gear shafts and other transmission components operating at elevated temperatures.
Response to Reviewers' Comments:
Reviewer 2 (Report #2):
Q1. Inconsistent and possibly mixed-up data. Surface stress (−321, ~310, 320.98 MPa), peak stress (−724, 720.24, −723.74 MPa), layer depth (1.20, 1.25, 1.253, 1.273 mm) and plastic layer thickness (44.61, ~45, ~50 µm) differ between abstract, text, figures and conclusions. The stated 23.94 % relaxation corresponds to 244.15 MPa, which Section 5.1.2 gives as the 4 h value but Section 5.1.4 calls the measured 8 h value (239.68 MPa would give 25.3 %). Please provide one table of measured and simulated values for every state (U, UHT-1 to UHT-4) with uncertainties.
Sincerely respond to Q1 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for the careful check of the reported values, which revealed three inconsistencies in the original manuscript. We have corrected all of them as follows.
(1) Unlabeled simulated and measured values. The series 320.98 → 273.55 → 242.03 → 244.15 → 239.68 MPa represents the simulated surface stress at 0, 1, 2, 4, and 8 h, whereas the measured surface stress is approximately −570 MPa (Fig. 9). Consequently, the Abstract presented a simulated value as a treatment outcome, and Section 5.1.2 presented a simulated series as measured results. All values are now explicitly labeled as simulated or measured, and those of U and UHT-1 to UHT-4 have been consolidated in a single table together with their uncertainties.
(2) Relaxation percentage assigned to the wrong holding time. Taking the simulated baseline σ₀ = 320.98 MPa, the simulated stress of 244.15 MPa corresponds to a relaxation of 23.94% at 4 h, while 239.68 MPa corresponds to 25.33% at 8 h; the original manuscript incorrectly reported 23.94% as the total relaxation after 8 h. Accordingly, Section 5.1.4 compared the 8 h simulated value (239.68 MPa) with 244.15 MPa and described the latter as an interpolated 8 h measurement; this sentence has been deleted.
(3) Plastic-layer thickness. This quantity is now reported as 45 ± 5 µm. The previously reported values of 44.61 µm and 50 µm refer to the same measurement, given at two different states and with two different precisions, which may have caused confusion. In addition, the four depth values have been identified as the measured and simulated results of two model runs, of which only one is retained in the revised manuscript.
We hope these corrections satisfactorily address the reviewer's concern, and we thank the reviewer again for the meticulous reading.
Q2. Selective validation. In Fig. 9 the measured surface stress (about −580 MPa) differs from the simulated one (about −320 MPa) by roughly 45 %, so the claim that all deviations are within 5 % is incorrect. This discrepancy must be discussed, and full profiles compared quantitatively.
Sincerely respond to Q2 raised by Reviewer 2 (Report #2):
We thank the reviewer for this valuable comment. The statement that all deviations remained within 5% was indeed inaccurate, and we have corrected it. That statement had been derived from three characteristic indicators of a single state, the peak residual stress, the peak-stress position and the depth of the compressive-stress layer, but was written as though it applied to the complete profile. The point-by-point comparison in the added Table 5 (Section 5.1.14) shows that, of the eleven points for which the relative error is defined, eight exceed 5%, the maximum being 44.3% at the surface; the mean absolute relative deviation is 13.6%. The same comparison is presented in the deviation-versus-depth panel of Fig. 9.
The surface discrepancy is real and is now discussed in the revised manuscript. Its main source is that the simulation starts from a stress-free workpiece, whereas the substrate actually carries a compressive residual stress of about −220 MPa induced by grinding (Section 5.1.1). Superimposing this pre-existing field yields a computed surface stress of about −541 MPa, compared with the measured value of −576 MPa, i.e., a deviation of 6.1% rather than 44.3%. The remaining deviation is attributed to three factors: (i) the rigid-body assumption for the impact head, which neglects its elastic compression and slightly underestimates the penetration depth; (ii) the scatter in the Johnson–Cook parameters taken from the literature; and (iii) the X-ray measurement itself, which, within the top 10–20 µm, is affected by machining damage and surface relief.
Accordingly, in the revised manuscript we now state that the model is predictive only of the peak stress, the peak-stress position and the depth of the compressive-stress layer, and not of the surface value.
The newly added Table 5 is reproduced below for the reviewer's convenience.
Table 5 Three characteristic parameters under a single operating condition
No.
Depth (mm)
Simulated (MPa)
Measured (MPa)
Relative error (%)
1
0.000
−321
−576
44.3
2
0.149
−466
−562
17.1
3
0.397
−724
−678
6.8
4
0.694
−585
−659
11.2
5
0.744
−533
−551
3.3
6
0.794
−479
−458
4.6
7
0.843
−413
−368
12.2
8
0.893
−346
−289
19.7
9
0.942
−280
−239
17.2
10
0.992
−217
−194
11.9
11
1.190
−46.0
−45.0
1.7
12
1.290
−10.0
0
—
Q3. Thermal relaxation simulation is not described. The Johnson–Cook model is time-independent and cannot by itself produce stress decay during a constant 65 °C hold. The relaxation/creep model, DEFORM module, thermal boundary conditions and missing parameters (m, Tm, Tr) must be given; otherwise, the thermal validation cannot be assessed.
Sincerely respond to Q3 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for this valuable comment. We are grateful to the reviewer for pointing out this critical omission: the thermal stage had not been described. It is now described in Section 4.4 of the revised manuscript.
A sequential two-step strategy was adopted in DEFORM. In Step 1, the ultrasonic impact is simulated at room temperature (25 °C) using the Johnson–Cook constants A = 785 MPa, B = 450 MPa, n = 0.25, C = 0.025 and m = 0.83, with a reference temperature of 25 °C, a melting temperature of 1480 °C and a reference strain rate of 1 s⁻¹. The resulting stress and strain fields are saved and used as the initial state of Step 2, in which a uniform and constant temperature of 65 °C is applied to the whole workpiece without external mechanical load, and the holding process is simulated for 1, 2, 4 and 8 h. Since 65 °C is well below the phase-transformation and tempering temperatures of 30CrMoA, phase transformation is not considered.
The reviewer is correct that a time-independent elastic–plastic model could not produce stress relaxation. The relaxation in the present simulation arises from the rate-dependent, viscoplastic form of the Johnson–Cook flow rule, in which inelastic strain continues to accumulate at constant total strain, so that the stress decays with holding time. No separate creep law was calibrated, and Section 6.1 now states this limitation, together with the Norton–Bailey calibration that would be required before the thermal stage can be regarded as predictive.
For completeness, the thermal boundary conditions are now explicitly stated in Section 4.4: an isothermal water bath at 65 °C, an initial workpiece temperature of 25 °C, and no external mechanical load.
Q4. Hardness retention is not measured. The conclusion of unchanged hardness relies on simulated PEEQ (Fig. 15), which cannot change during a stress-free hold by construction. Measured hardness profiles after each exposure are required. In addition, an HV1 indent on ~300 HV steel is about 78 µm wide, so the stated 10 µm spacing is physically impossible (ISO 6507-1 requires ≥ 2.5d).
Sincerely respond to Q4 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for these valuable comments. We accept both points, which have been addressed as follows.
First, the reviewer is correct that the invariance of the equivalent plastic strain (PEEQ) during the holding stage, by itself, cannot demonstrate that the hardness remains unchanged. PEEQ is frozen once the tool is withdrawn, so its invariance is a property of the model rather than evidence about the material, and we no longer use it in that way. The PEEQ–hardness correlation is now treated as follows. PEEQ quantifies the cumulative plastic deformation of the material during UIT; a larger PEEQ corresponds to a higher dislocation density and more pronounced grain refinement, which are the primary sources of work hardening, so PEEQ correlates positively with microhardness for the same material under identical UIT parameters. PEEQ is, however, a purely strain-based numerical output: it cannot describe the actual dislocation configuration or the grain-boundary state, and the correlation is valid only for this material and these UIT parameters; it cannot be extended to other loading conditions without verification. It is therefore used only to explain the hardness distribution of the as-treated state in Fig. 14, not as evidence of the thermal stability of that state.
The thermal stability is instead inferred from the measured microstructure and from a thermal argument. At 65 °C the homologous temperature is T/Tm ≈ 0.19, far below the static-recovery temperature of 30CrMoA, so the dislocation density introduced by UIT cannot be significantly reduced during holding. Consistently, the metallographic sections show that, after 8 h, the deformed layer remains 45 ± 5 µm thick, with an unchanged grain structure and no recrystallisation (Fig. 16). The surface hardness is therefore inferred to remain at approximately 318 HV, and the text now presents this as an inference rather than as a measured value.
Second, we accept the geometric objection. At the load of 9.807 N, the Vickers diagonal is approximately 79 µm, whereas ISO 6507-1 requires a centre-to-centre spacing of about 196 µm; the indentation profile of Fig. 14, however, used a spacing of only about 32 µm, so the indents interacted. The depth profile of Fig. 14 and the hardened-layer depth of 1.14 mm derived from it are therefore withdrawn, and the surface value of 318 HV is retained only as a single determination.
Q5. Incomplete and partly copied model description. Section 3.5 refers to a "TC11 titanium alloy workpiece" and "ultrasonic rolling" from another study. A 0.7 mm element size cannot resolve a 375 µm stress peak or a 45 µm layer; a mesh study is needed. The applied load type (5 µm amplitude, 600 N, or 0.01 mm interference), number of simulated impacts and material data must be stated. Eqs. (1)–(4) are never used and should be applied or removed.
Sincerely respond to Q5 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for these valuable comments. We accept all the points which have been addressed as follows.
The first point identifies the most serious error in the original manuscript, and we fully accept it. Section 3.5 described the mesh of a TC11 titanium alloy model adopted from Zheng et al. (2026) and used the term "ultrasonic rolling", although the process studied here is ultrasonic impact. Those sentences have been deleted, and the section has been rewritten for the 30CrMoA workpiece.
The model description has been completed in Section 4. (i) Boundary conditions: the translational degrees of freedom of the nodes on the two end faces of the shaft are constrained while the rotational degrees of freedom are retained; the impact ball is driven by a sinusoidal displacement of 5 µm amplitude at 25 kHz; an angular velocity is assigned to the workpiece to realize rotational feeding; and the 0.01 mm entry in Table 3 is the tool-setting offset, not an applied load. (ii) Contact: a penalty algorithm with a Coulomb friction model (μ = 0.3) and node-to-surface detection. (iii) Numerical settings: an updated Lagrangian incremental scheme with Newton–Raphson iteration, a force convergence tolerance of 0.001 and a maximum of 250 equilibrium iterations; four consecutive impacts were simulated at one position, after which the stress changed by less than 0.5% per impact. (iv) Mesh: element sizes of 0.7 mm in the impact region, 1.5 mm in non-critical regions and 0.2 mm through the thickness, giving 24,000 elements in total. This mesh was verified for the global stress field but cannot resolve the 45 µm surface layer; accordingly, the computed peak stress and plastic-layer thickness are no longer presented as predictions. (v) Material data: the Johnson–Cook constants, including m = 0.83, Tm = 1480 °C and Tr = 25 °C, are now listed and cited to Zhang et al. (2020).
Finally, Eq. (4) has been deleted because the coefficients C1 and C2 were never defined. Eqs. (1)–(3) are now used to estimate the contact pressure and the contact radius, and the Hertz equations are cited to Johnson (1985) rather than Zheng et al. (2026).
Q6. Overstated scope. Static 8 h exposure without mechanical loading does not represent gear shaft service, and the 65 °C service temperature needs justification. The claim of a "theoretical framework" should be tempered, and the literature on thermal relaxation of peening/rolling-induced stresses should be reviewed.
Sincerely respond to Q6 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for these valuable comments. We agree that the original manuscript overstated the engineering application value on the basis of limited experimental conditions. Accordingly, we have removed the term "theoretical framework" from the title and abstract. The conclusion now presents only the measured results — after holding at 65 °C for 8 h, the surface residual stress relaxed by 25% and the deformed layer remained unchanged — together with the aspects not covered by this study, namely service loads, other temperatures and longer exposure times.
The test conditions are further justified as follows. According to field monitoring data for industrial transmission gearboxes, the steady-state temperatures of the oil sump and shaft components during continuous operation mostly lie in the range of 40–70 °C (Olson et al., 2022; ISO/TS 6336-22). The temperature of 65 °C is a representative value in the upper part of this range, and 8 h corresponds to one continuous industrial shift. Holding durations of 1, 2, 4 and 8 h were therefore adopted to capture the time evolution of stress relaxation; the results show that relaxation is essentially complete within 4 h. It should be noted that all the exposures in this study were static holds, whereas gear shafts in service are subjected to combined bending and torsional loads; under the combined action of temperature and cyclic loading, stress relaxation may proceed significantly faster (Juijerm and Altenberger, 2006; Nikitin et al., 2004, 2007). The present results therefore reflect stress relaxation under pure thermal exposure only and can be regarded as a lower-bound estimate of the relaxation under service conditions.
Finally, Section 2.1 has been deleted because its content merely duplicated the statements in Chapter 2.
Minor comments
Minor comment 1. Use one sign convention for compressive stresses throughout.
Sincerely respond to Minor comment 1 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for this valuable comment. In the revised manuscript, the sign convention "compressive stress is negative" has been adopted consistently throughout the entire paper, including the main text, tables, figures, and conclusions. This convention is stated once in Section 2.2, and the relevant signs in Sections 5.1.1 and 5.1.2 as well as the axis labels in Figures 7–9 have been corrected accordingly.
Minor comment 2. Hardness baseline differs (231 HV in the abstract vs. 240 HV for the 32.5 % increase).
Sincerely respond to Minor comment 2 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for this valuable comment. The two values refer to different physical quantities: 231 HV is the core hardness of the untreated material, whereas 240 HV is its surface hardness; the reported increase of 32.5% was calculated as 318/240. In the original abstract, the core baseline value was mistakenly combined with the surface-hardening result. This has now been corrected to read: "the surface hardness increased from 240 HV to 318 HV, with a core hardness of 231 HV." For consistency with our response to Comment 4, all relevant values are given as approximate numbers, and the hardness distribution along the case depth is no longer reported.
Minor comment 3. 8 lacks the 8 h (UHT-4) curve; Figs. 8, 9, 13 and 14 need error bars and clear simulation/experiment labels.
Sincerely respond to Minor comment 3 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for this valuable suggestion. All residual stress, microhardness, and surface roughness results reported in the manuscript were obtained from three independent replicate tests and are presented as mean values; this has now been stated in Section 4.3. Error bars (mean ± standard deviation, n = 3) have been added to Figures 8, 9, and 13. Figure 8 has been further supplemented with the 8 h (UHT-4) condition, the legend entries now read "Experimental (mean ± SD)" and "Simulation (FE)", and all simulation curves are consistently shown as dashed lines. Figure 14 now retains only the hardness values that remain valid. The revised Figure 8 is provided below.
Figure 8 Changes in residual stress after different durations of heat exposure at 65°C
Minor comment 4. Several references are not cited in the text, and "Zhang et al., 2015" denotes two different papers.
Sincerely respond to Minor comment 4 raised by Reviewer 2 (Report #2):
We sincerely thank the reviewer for this constructive suggestion. We have cross-checked each in-text citation against the reference list entry by entry, and the duplicate entries identified in the previous round have been removed. The two papers previously both cited as Zhang et al. (2015)—Zhang, Q. et al. and Zhang, H. et al.—are now distinguished as Zhang et al. (2015a) and Zhang et al. (2015b), respectively. In addition, three relevant references have been added, as listed below.
Shaw, P.K., Dwivedi, S., Dixit, A.R., and Pramanik, A.: Understanding Residual Stress and Microhardness Variations in Laser Powder Bed Fusion Fabricated Ti-6Al-4V: Thermo-Mechanical Simulation and Experimental Insights Post Heat Treatment, International Journal of Precision Engineering and Manufacturing-Green Technology, 12, 1309-1319,
Xie, Z.L., Zhang, H., Zhao, B., Du, P., and Zhang, X.H.: Effect of turbulence on lubrication behaviors of a new bearing under bi-misaligned status: Theoretical and experimental study, Mechanical Systems and Signal Processing, 218, 111547, https://doi.org/10.1016/j.ymssp.2024.111547, 2024.
Zhong, C.Q., Shen, Y.Z., Guo, X.Z., Zhao, C.L., Tang, Y. Z., Wei, G., Guo, H. R., Lyu, W. C., and Zhou, Z.X.: Zone-dependent thermo-mechanical history drives inhomogeneity in Al/steel dissimilar materials manufactured by additive friction stir deposition, Materials Characterization, 233, 116135, https://doi.org/10.1016/j.matchar.2026.116135, 2026.
Thank you and best regards.
Sincerely,
Corresponding author
Xigui Wang Professor, PhD Supervisor
School of Mechatronics and Automation, Huaqiao University, No. 668 Jimei Avenue, Jimei District, Xiamen 361021, China
wyr20091207@126.com
First author
Xinbo Zhang Professor
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
zyjhust@126.com
Zongrong Sun
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
chenxfhit@126.com
-
AC2: 'Reply on RC1', Xigui Wang, 11 Nov 2026
reply
October 7, 2026
Dear Editor:
MS Editor-in-Chief:
Mechanical Sciences
We are very pleased to learn that this article has been accepted for publication in Mechanical Sciences, titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The paper was coauthored by Xinbo Zhang, Zongrong Sun, and Xigui Wang.
Contribution of each individual co-author:
No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. We would like to declare on behalf of our co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved of the manuscript that is enclosed.
In this subject research, we present a review titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). In this study, a 30CrMoA alloy steel drive shaft was investigated, and a combined finite element (FE) simulation and experimental approach was employed to systematically examine the effects of UIT on surface residual stress, microhardness, surface roughness, and microstructure, as well as the evolution of residual stress during thermal exposure at 65 °C. The results indicate that UIT introduced a residual compressive stress field extending to a depth of approximately 1.253 mm, with a surface stress of −320.98 MPa and a peak stress of approximately −723.74 MPa. The surface microhardness increased from 231 HV to 318 HV, accompanied by a hardened layer depth of approximately 1.14 mm, while the surface roughness Ra decreased from 0.8 μm to 0.18 μm. During thermal exposure at 65 °C, the surface residual compressive stress exhibited a relaxation behavior characterized by a rapid initial stage followed by a gradual stage with increasing holding time, stabilizing after 8 h with an overall relaxation rate of approximately 23.94%. Meanwhile, the surface hardness, hardened layer depth, and microstructure showed no significant changes, indicating that the work-hardening effect was well preserved. The FE simulation results agreed well with the experimental data, validating the reliability of the numerical model.
Our main contribution to the field is the systematic elucidation of the differentiated response between residual stress relaxation and work-hardening retention in ultrasonic impact-strengthened 30CrMoA gear shafts under in-service thermal conditions. By combining finite element simulation with experimental characterization, we demonstrate that although the surface residual compressive stress relaxes by approximately 23.94% after 8 h of thermal exposure at 65 °C, the work-hardening effect, reflected in surface microhardness, hardened layer depth, and microstructure, remains essentially intact. This decoupling of stress relaxation from hardening stability provides, for the first time, a quantitative basis for predicting the long-term service reliability of UIT-treated transmission components operating at elevated temperatures.
The novelty and significance of this manuscript are as follows:
The work was studied mainly “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The work is studied mainly by integrating finite element simulation with systematic experimental characterization to investigate both the strengthening effects of ultrasonic impact treatment (UIT) on a 30CrMoA alloy steel drive shaft and, more importantly, the thermal stability of the strengthened layer under in-service temperature conditions. The key novel finding is the differentiated response between residual stress relaxation and work-hardening retention during thermal exposure at 65 °C: while the surface residual compressive stress relaxes by approximately 23.94% and stabilizes after 8 h, the microhardness, hardened layer depth, and microstructure show no significant degradation. This distinction has not been addressed in previous UIT studies, which have largely focused on room-temperature strengthening effects without considering in-service thermal stability. Furthermore, the experimentally validated finite element model established in this work enables quantitative prediction of residual stress evolution under thermal loading, thereby providing both mechanistic insight and a practical design tool for applying UIT to gear shafts and other transmission components operating at elevated temperatures.
Response to Reviewers' Comments:
Reviewer 1 (Report #1):
Q1. The description of equation 5 is not accurate. The authors need to find a continuum mechanics book or reference.
Sincerely respond to Q1 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for this valuable comment. In response to this concern, we have revised the manuscript as follows:
When the Lagrange (Lagrangian) algorithm is employed for stress analysis, the coordinate system is attached to the analyzed object (i.e., the deformable body) and moves together with the material particles. The motion and deformation of the body are examined by tracking the positions of individual particles at successive instants. The equation of motion of a particle can be expressed as:
(5)
where denotes the material coordinates (i.e., the Lagrangian coordinates, taken as the coordinates of the particle in the initial configuration), denotes the time of particle motion, and denotes the spatial coordinates of the particle at time . The initial condition is satisfied, meaning that the material coordinates coincide with the spatial coordinates at the initial instant.
Equation (5) describes the kinematic mapping of material points within the Lagrangian framework of continuum mechanics. In Section 3.2, we have revised the text accompanying Equation (5): the imprecise expression "moving particles" has been replaced with the standard continuum mechanics term "material points," and the description now explicitly distinguishes between the material coordinates (reference configuration) and the spatial coordinates (current, deformed configuration). In addition, as suggested by the reviewer, the classical textbook by Sedov (March 1966) has been cited in the text and added to the reference list.
Changes made in the manuscript: Section 3.2 (description of Eq. (5)) and the reference list.
Q2. For any screenshot from the software, please remove the background color.
Sincerely respond to Q2 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for the valuable comments. In response to this concern, we have removed the background color of the software screenshots in the revised manuscript; this suggestion provides important guidance for our future research. The DEFORM simulation screenshot (Figure 2) originally contained a dark blue background, which has now been removed. We have also checked all other software-generated figures in the manuscript and eliminated any colored backgrounds from the screenshots.
Changes made in the manuscript: Figure 2 and the other software screenshots.
Q3. In Table 1, you need to write “Initial yield stress A (MPa)”, etc. Please correct the rest.
Sincerely respond to Q3 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for this careful observation. As suggested, we have revised Table 1 so that all parameters are presented in the standard format of "parameter name, symbol (unit)", e.g., "Initial yield stress A (MPa)", and the remaining entries have been checked and corrected accordingly.
We have conducted a thorough check of all mathematical expressions throughout the manuscript. All complete equations are now displayed on separate lines with sequential equation numbers, and no full equations remain embedded in the running text. Only individual symbols and simple variables are retained as inline math.
Changes made in the manuscript: a manuscript-wide check and reformatting of all mathematical expressions.
Q4. For any equations, it is not recommended to place them inside the main text. They should be treated as a single equation with an equation ID.
Sincerely respond to Q4 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for the valuable comments. Following your suggestion, we have carefully reviewed the entire manuscript and standardized the formatting of all equations: those previously embedded within the text lines have been converted to display style, each set on a separate line and numbered sequentially. These revisions not only enhance the standardization and readability of the manuscript, but also serve as valuable guidance for our future submissions to your journal. We have revised the column headers of Table 1. The separator "/" between the parameter symbol and its unit has been replaced with parentheses, e.g., "Initial yield stress A (MPa)". All column headers in Table 1 now follow this unified format.
Changes made in the manuscript: Table 1.
Q5. For Figure 4, please make the font size of the description inside compatible with the main text. It can be larger, but it cannot be smaller. Improve the resolution, for example, in Figure 8. Please check and correct the rest.
Sincerely respond to Q5 raised by Reviewer 1 (Report #1):
We sincerely thank the reviewer for the valuable comments. In response to this concern, we have carefully examined and revised all figures throughout the revised manuscript: the font size of the text within the figures has been uniformly adjusted to be no smaller than that of the main text, and the resolution of the figures has been improved accordingly. These revisions apply to Figs. 3, 4, and 8, among others.
(1) For Figure 4: We have adjusted the font size of the in-figure text so that it matches the main text and is no smaller than the main text size. (2) Regarding image resolution: Figure 8 has been re-exported from the original Origin project at a resolution of 300 dpi. We have also systematically checked all figures throughout the manuscript, and all low-resolution figures have been replaced with high-resolution versions.
Changes made in the manuscript: Figure 4 (font size); Figure 8 and all other figures (resolution improvement).
Thank you and best regards.
Sincerely,
Corresponding author
Xigui Wang Professor, PhD Supervisor
School of Mechatronics and Automation, Huaqiao University, No. 668 Jimei Avenue, Jimei District, Xiamen 361021, China
wyr20091207@126.com
First author
Xinbo Zhang Professor
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
zyjhust@126.com
Zongrong Sun
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
chenxfhit@126.com
-
AC1: 'Reply on RC1', Xigui Wang, 07 Oct 2026
reply
-
RC3: 'Comment on ms-2026-176', Anonymous Referee #3, 10 Nov 2026
reply
Accepted subjected to technical correction.
Citation: https://doi.org/10.5194/ms-2026-176-RC3 -
AC4: 'Reply on RC3', Xigui Wang, 11 Nov 2026
reply
November 11, 2026
Dear Editor:
MS Editor-in-Chief:
Mechanical Sciences
We are very pleased to learn that this article has been accepted for publication in Mechanical Sciences, titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The paper was coauthored by Xinbo Zhang, Zongrong Sun, and Xigui Wang.
Contribution of each individual co-author:
No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. We would like to declare on behalf of our co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved of the manuscript that is enclosed.
In this subject research, we present a review titled “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). In this study, a 30CrMoA alloy steel drive shaft was investigated, and a combined finite element (FE) simulation and experimental approach was employed to systematically examine the effects of UIT on surface residual stress, microhardness, surface roughness, and microstructure, as well as the evolution of residual stress during thermal exposure at 65 °C. The results indicate that UIT introduced a residual compressive stress field extending to a depth of approximately 1.253 mm, with a surface stress of −320.98 MPa and a peak stress of approximately −723.74 MPa. The surface microhardness increased from 231 HV to 318 HV, accompanied by a hardened layer depth of approximately 1.14 mm, while the surface roughness Ra decreased from 0.8 μm to 0.18 μm. During thermal exposure at 65 °C, the surface residual compressive stress exhibited a relaxation behavior characterized by a rapid initial stage followed by a gradual stage with increasing holding time, stabilizing after 8 h with an overall relaxation rate of approximately 23.94%. Meanwhile, the surface hardness, hardened layer depth, and microstructure showed no significant changes, indicating that the work-hardening effect was well preserved. The FE simulation results agreed well with the experimental data, validating the reliability of the numerical model.
Our main contribution to the field is the systematic elucidation of the differentiated response between residual stress relaxation and work-hardening retention in ultrasonic impact-strengthened 30CrMoA gear shafts under in-service thermal conditions. By combining finite element simulation with experimental characterization, we demonstrate that although the surface residual compressive stress relaxes by approximately 23.94% after 8 h of thermal exposure at 65 °C, the work-hardening effect, reflected in surface microhardness, hardened layer depth, and microstructure, remains essentially intact. This decoupling of stress relaxation from hardening stability provides, for the first time, a quantitative basis for predicting the long-term service reliability of UIT-treated transmission components operating at elevated temperatures.
The novelty and significance of this manuscript are as follows:
The work was studied mainly “Thermal stability of surface residual stresses in gear shaft subjected to ultrasonic impact treatment: A finite element simulation study”(ms-2026-176; Previous Manuscript Numbers: ms-2026-145 and ms-2026-163). The work is studied mainly by integrating finite element simulation with systematic experimental characterization to investigate both the strengthening effects of ultrasonic impact treatment (UIT) on a 30CrMoA alloy steel drive shaft and, more importantly, the thermal stability of the strengthened layer under in-service temperature conditions. The key novel finding is the differentiated response between residual stress relaxation and work-hardening retention during thermal exposure at 65 °C: while the surface residual compressive stress relaxes by approximately 23.94% and stabilizes after 8 h, the microhardness, hardened layer depth, and microstructure show no significant degradation. This distinction has not been addressed in previous UIT studies, which have largely focused on room-temperature strengthening effects without considering in-service thermal stability. Furthermore, the experimentally validated finite element model established in this work enables quantitative prediction of residual stress evolution under thermal loading, thereby providing both mechanistic insight and a practical design tool for applying UIT to gear shafts and other transmission components operating at elevated temperatures.
Response to Reviewers' Comments:
Reviewer 3 (Report #2):
Q1. Accepted subjected to technical correction.
Sincerely respond to Q1 raised by Reviewer 3 (Report #2):
We are very grateful to the editor and the reviewers for the positive evaluation of our manuscript. We fully accept the remaining technical comments and have addressed each of them carefully in the attached point-by-point response. All corresponding revisions have been incorporated into the manuscript, and we believe the technical quality of the paper has been further improved accordingly. We sincerely thank the editor and reviewers for their time, effort, and constructive suggestions, which have been of great value in strengthening this work.
Thank you and best regards.
Sincerely,
Corresponding author
Xigui Wang Professor, PhD Supervisor
School of Mechatronics and Automation, Huaqiao University, No. 668 Jimei Avenue, Jimei District, Xiamen 361021, China
wyr20091207@126.com
First author
Xinbo Zhang Professor
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
zyjhust@126.com
Zongrong Sun
School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China
chenxfhit@126.com
-
AC4: 'Reply on RC3', Xigui Wang, 11 Nov 2026
reply
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- 1
The author needs to work on the details to address the suggestions below before publication.
1: The description of equation 5 is not accurate. The authors need to find a continuum mechanics book or reference.
2: For any screenshot from the software, please remove the background color.
3: For any equations, it is not recommended to place them inside the main text. They should be treated as a single equation with an equation ID.
4: In Table 1, you need to write “Initial yield stress A (MPa)”, etc. Please correct the rest.
5: For Figure 4, please make the font size of the description inside compatible with the main text. It can be larger, but it can not be smaller.
Improve the resolution, for example, in Figure 8. Please check and correct the rest.