Residual Stress Field Effect on Fatigue Crack Growth Direction
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The authors present a series of experimental results for crack growth in modified CT specimens and corresponding numerical crack growth simulations. The main modification of the CT specimen is that a hole is inserted, which is expanded plastically with a mandrel in order to generate residual compressive stress on the edge of the hole. The influence of residual stress on the crack path and the crack growth rate is investigated when a fatigue crack propagates from the starter notch of the CT specimen in the direction of the hole.
A method for numerical crack growth simulation is presented. This method is based on damage mechanics. The method tends to determine the crack paths correctly as long as the crack essentially grows in a straight line. However, unrealistic crack paths are predicted for large crack extensions, high stress intensities at the crack tip and larger crack deflections. In some cases, the cracks grow backwards or almost in a circle, which is not to be expected with the specimens used despite the residual stress. This fact should be taken into account when discussing the results.
Please see the comments in the attached file.
Comments for author File: 
Comments.pdf
Author Response
Thank you for your insight and comments on our research. Yes, you are right. This is a complex subject to deal with, especially with a novel approach like ours. We are trying to use the results of fatigue life testing in order to predict the onset and growth of a crack subjected to a non-homogeneous field of relaxing residual stress. Yes, the subject is as complex as the previous sentence. This study is the first comprehensive attempt, and therefore great care has been taken to realistically represent the benefits of such a method and, more importantly, the pitfalls, which we must address in the future. The current state of the algorithm predicts non-conservative results, which we clearly show, and therefore, we realize that this is by no means an accepted solution. But given the fact that the algorithm, functioning under all these limitations, produces results that are roughly the ones we measured, it is a promising indication.
Your review has been answered in the attached file. Red colored text are changes, blue is new text.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors
The manuscript explores the effect of residual stress fields on fatigue crack growth direction through experiments and numerical simulations. There are a few areas where further improvements could be made:
- The Introduction aims to explore how residual stress fields influence fatigue crack behaviour; however, it is framed more as an informal thought experiment than as a concise, critical review of existing knowledge. Crucially, it never makes clear whether the work focuses on (1) the initiation of cracks in the presence of residual stresses or (2) the propagation and direction of cracks once they have already formed. Although the Abstract explicitly highlights “crack growth direction,” the Introduction repeatedly conflates this objective with the possibility of initiation, leaving the reader uncertain about the study’s primary research question. Moreover, the discussion lacks a concise synthesis of the current literature. Recent studies (Chen et al., 10.1016/j.oceaneng.2025.121400; Zhang et al., 10.1016/j.ress.2025.111406) have assessed fatigue crack propagation and lifetime considering welding residual stresses relaxation. These studies have demonstrated that such WRS relaxation can profoundly affect fatigue propagation behaviour and lifetime predictions. In view of these findings, the Introduction should be revised to incorporate a focused discussion on residual stress relaxation mechanisms and their implications for modelling fatigue crack growth.
- Friction coefficient μ = 0.1 is taken from graphene lubrication data [18], but the authors state that graphene was used only for mandrels. Verify that μ = 0.1 is appropriate for the specimen–mandrel interface.
- S235JR is a structural steel, specify actual chemical composition and tensile properties. The use of a mild steel with low yield strength may exaggerate residual stress relaxation effects—discuss this limitation.
- The symbol “S22” is introduced in Figure 6 and reused later, but its definition is only given in the caption. Include a dedicated Nomenclature table or define it in the text the first time it appears.
- The overlay of experimental vs. predicted paths is helpful, but the stress legends in Figures 14is difficult to read. Provide zoomed insets for crack length at given cycles.
- Providing units in all figures will improve clarity and reproducibility.
- Captions for Figures 14, 20, 23, 26, 29, 32 are nearly identical. Condense repetitive wording and highlight only the distinguishing feature.
- Fig.25 & 31: Red circles for cold-expanded holes are inconsistently sized and sometimes obscure crack paths. Use arrows or labels instead.
- The manuscript could include a section on future work, outlining potential areas for further research.
Author Response
C1: The Introduction aims to explore how residual stress fields influence fatigue crack behaviour; however, it is framed more as an informal thought experiment than as a concise, critical review of existing knowledge. Crucially, it never makes clear whether the work focuses on (1) the initiation of cracks in the presence of residual stresses or (2) the propagation and direction of cracks once they have already formed. Although the Abstract explicitly highlights “crack growth direction,” the Introduction repeatedly conflates this objective with the possibility of initiation, leaving the reader uncertain about the study’s primary research question. Moreover, the discussion lacks a concise synthesis of the current literature. Recent studies (Chen et al., 10.1016/j.oceaneng.2025.121400; Zhang et al., 10.1016/j.ress.2025.111406) have assessed fatigue crack propagation and lifetime considering welding residual stresses relaxation. These studies have demonstrated that such WRS relaxation can profoundly affect fatigue propagation behaviour and lifetime predictions. In view of these findings, the Introduction should be revised to incorporate a focused discussion on residual stress relaxation mechanisms and their implications for modelling fatigue crack growth.
R1: You are right, the abstract only focused on the crack propagation and not explicitly saying that also fatigue cycles to crack nucleation are inherently present. The study focuses on both approaches.
We have reviewed your suggested studies. The first one was deemed appropriate therefore an entire paragraph was added to the introduction. Please see lines 27-34.
C2: Friction coefficient μ = 0.1 is taken from graphene lubrication data [18], but the authors state that graphene was used only for mandrels. Verify that μ = 0.1 is appropriate for the specimen–mandrel interface.
R2: Upon reviseting the publication [18] the resulting friction factor is taken from Fig 6 right. Also in the past, studies have shown good correlation by using this friction coefitient value. In this case, the lubrication is used to lube the mandrel as it pushes through the hole and which would result in a complex interplay because the lubrication is squezzed out. The cold expansion was simulated only in the begining of our study, showing the nature of the entry and exit surfaces. Later in this study the residual stress was introduced by mowing the surface of the hole in the radial direction, therefore not simulating the pulling effect.
C3: S235JR is a structural steel, specify actual chemical composition and tensile properties. The use of a mild steel with low yield strength may exaggerate residual stress relaxation effects—discuss this limitation.
R3: this issue has been addresed. Please see lines 93-105 in the attached file, also Figure 1 showing the stress-strain relationship has been added.
C4: The symbol “S22” is introduced in Figure 6 and reused later, but its definition is only given in the caption. Include a dedicated Nomenclature table or define it in the text the first time it appears.
R4: it has been defined in the nomenclature/abbrevations section. Please see line 485 in the attached file.
C5: The overlay of experimental vs. predicted paths is helpful, but the stress legends in Figures 14is difficult to read. Provide zoomed insets for crack length at given cycles.
R5: Figure 14, in the revised document Figure 16, has been redone in order to improve the clarity of displayed results. Please see the attached file lines 311 and 312.
C6: Providing units in all figures will improve clarity and reproducibility.
C7: Captions for Figures 14, 20, 23, 26, 29, 32 are nearly identical. Condense repetitive wording and highlight only the distinguishing feature.
C8: Fig.25 & 31: Red circles for cold-expanded holes are inconsistently sized and sometimes obscure crack paths. Use arrows or labels instead.
R6 & R7 & R8: As you will find in the attached document, some images have been improved in order to promote clarity and reproductibility. Yes the captions are nearly identical, because these images show the same results for different specimens. Because these are screen-shots no direct editing are possible. That is why we decided to clearly state in captions of each figure what is visible on then.
C9:The manuscript could include a section on future work, outlining potential areas for further research.
R9: Not a seperate chapter for future work was added, but a couple of lines addressing the main issues to be solved in the future. Please see lines 462-465 in the attached document.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
My comments on the first version have essentially been taken into account. There are still a few questions that need to be answered.
Please see the comments in the attached file.
Comments for author File: Comments.pdf
Author Response
Thank you again for your insight. Below you can find Ci your comments and Ri our response. We have also attached the revised version of the manuscript.
C1: I still believe that this method does not overcome the mesh size dependency. (line 221)
R1: Please see the revised text in lines 220-224.
C2: I still wonder if these cracks on the notch surface have been observed during the experiments.
R2: Please see the revies text in lines 270-282
C3: Where does this high tensile stress in the starter notch come from if a crack has already grown? The notch is relieved by the crack and the tensile stress should be close to zero at the starter notch.
R3: We have made a mistake when exporting the image. The high tensile stress you observed was due to the fact that the image was taken when the tensile load was at maximum. This image was replaced so that all of the reference specimens show their state at the end of the analysis step, where force = 0 N. Please see Fig. 16 for the revised version.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors
The comments have been properly addressed and this paper can be accepted.
Author Response
We appreciate your review and the time you took to provide feedback.
