Analysis of Thermal Fatigue Behavior and Interface Optimization Design for Laminated Tungsten Plasma-Facing Material Under Steady-State Thermal Load

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Summary of the Work

This study investigates the thermal fatigue resistance of laminated tungsten plasma-facing materials (PFMs) in nuclear fusion devices subjected to steady, high heat loads. It focuses on the W/Cu joint interface, where thermal stress and plastic strain accumulation often cause cracks and structural failure. Through finite element simulations and theoretical analysis, the researchers investigated how the thickness of the tungsten layer and interface geometry impact thermomechanical performance. The work provides design optimization strategies to improve the durability and reliability of plasma-facing components in fusion reactors.

Main Findings

- Thinner W layers (down to 10 μm) greatly reduce thermal mismatch and interfacial stress, improving compatibility.

- Curved Cu interface shifts and relieves stress; H > 600 μm removes vertex concentration, extending service life.

- Adjusting H and D ensures enough Cu deformation space, minimizing plastic strain while maintaining reliability.

General Comments

- English should be double-checked; several typos were found.

- Please make sure that all symbols are clearly defined when they first appear in the text, even if they are commonly used in the literature. (e.g., in the title plasma-facing material (PFM), in the abstract W/Cu = tungsten(W)-copper(Cu)).

- This study provides clear evidence that micrometer-scale tungsten layers improve interfacial stress compatibility.

- The interface geometry optimization offers a practical path to extend PFC service life.

- The analysis relies heavily on simulations with limited experimental validation.

- Long-term cyclic thermal loading effects are not fully addressed.

- The manufacturability of sub-10 μm tungsten layers is not discussed.

- The trade-off between reduced stress and increased copper plasticity needs deeper quantitative evaluation.

The following suggestions aim to address some gaps.

Suggestions

1) The authors have fleetingly stated that “to accurately evaluate the stress and strain at the interface, the mesh near the W/Cu interface was sufficiently refined, and a smooth mesh transition was implemented along the Z-direction on the symmetry plane.” For clarity,  how was mesh convergence and numerical stability verified near the W/Cu interface?

2) In subsection 2.2 "Boundary Conditions," the authors mentioned the model and the boundary conditions (BCs) adopted. They stated that a total of five loading cycles were simulated to study the time-dependent behavior of temperature, stress, and strain. The description of all this was very (perhaps too much) brief. For clarity (and to convince the reader), it would be appropriate for the authors to mathematically specify the equations governing the evolution of the system and the boundary conditions expressed in the form of Dirichlet BCs, Neumann BCs, or mixed boundary conditions.

3) What experimental validation supports the accuracy of stress–strain predictions at micrometer tungsten scales?

4) Was a sensitivity analysis performed on boundary conditions to assess the robustness of the results?

5) How adequate are the constitutive models for Cu/CuCrZr in capturing long-term plasticity and creep under cyclic loading?

6) How realistic is the fabrication and stability of sub-10 μm tungsten layers under irradiation and plasma exposure?

7) Were interfacial defects or bonding imperfections considered, and how would they affect the stress distribution?

8) What is the added value of the FEM simulations compared to simpler analytical approaches, and how transferable are the results to full-scale PFCs?

Conclusions

Overall, the study provides useful insights into stress reduction and interface optimization in W/Cu PFCs. However, the work would be significantly strengthened by a clearer and more rigorous presentation of the numerical framework. In particular, the description of the boundary conditions in Subsection 2.2 is too brief; the absence of a precise mathematical formulation (e.g., explicit governing equations with Dirichlet, Neumann, or mixed BCs) makes it difficult to assess the robustness and reproducibility of the simulations. Given the central role of the FEM analysis in the authors' conclusions, it is essential to present the full mathematical model, validate numerical stability, and justify the reliability and added value of the simulations compared to simplified analytical approaches. Without this, the validity and transferability of the reported results to real PFC applications may remain uncertain.

Comments on the Quality of English Language

English should be double-checked; several typos were found.

Author Response

RESPONSES TO REVIEWER 1 S' COMMENTS

Response to Reviewer 1：

We sincerely thank Reviewer 1 for their thorough review and valuable comments, which have significantly helped us improve the quality of our manuscript. We have carefully addressed all the points raised. Our point-by-point responses are detailed below, and all corresponding changes have been implemented in the revised manuscript.

 

Suggestion 1：The authors have fleetingly stated that “to accurately evaluate the stress and strain at the interface, the mesh near the W/Cu interface was sufficiently refined, and a smooth mesh transition was implemented along the Z-direction on the symmetry plane.” For clarity, how was mesh convergence and numerical stability verified near the W/Cu interface?

Response 1：We thank the reviewer for this insightful comment. To ensure numerical reliability, a mesh independence test was conducted for each specific tungsten layer thickness. The number of elements through the thickness near the W/Cu interface was systematically determined, and further mesh refinement produced only negligible changes (less than 2%) in the maximum interfacial stress and accumulated plastic strain. These results confirm that the selected mesh densities for all configurations achieved convergence and numerical stability. The corresponding clarification has been added to Section 2.1 of the revised manuscript.

 

Suggestion 2：In subsection 2.2 "Boundary Conditions," the authors mentioned the model and the boundary conditions (BCs) adopted. They stated that a total of five loading cycles were simulated to study the time-dependent behavior of temperature, stress, and strain. The description of all this was very (perhaps too much) brief. For clarity (and to convince the reader), it would be appropriate for the authors to mathematically specify the equations governing the evolution of the system and the boundary conditions expressed in the form of Dirichlet BCs, Neumann BCs, or mixed boundary conditions.

Response 2：We thank the reviewer for this valuable suggestion to enhance the mathematical rigor of our methodology. In response, we have revised Section 2.2 to explicitly state the governing equations and formally classify the boundary conditions using the standard mathematical terminology (Dirichlet, Neumann, and Mixed). This revision provides a more precise and fundamental description of the numerical framework, which underpins the reliability of our simulation results.

 

Suggestion 3：What experimental validation supports the accuracy of stress–strain predictions at micrometer tungsten scales?

Response 3：We thank the reviewer for this important question regarding experimental validation. Direct experimental measurement of stress-strain states at the micrometer scale remains challenging. To date, research on laminated tungsten structures has primarily demonstrated their advantages in improving surface performance, including enhanced resistance to surface crack propagation and reduced blistering under thermal and particle loads, as referenced in our introduction [16-18]. To bridge this gap, our future work will focus on systematically characterizing the evolution of interfacial morphology (particularly microcrack initiation and growth) under controlled thermal cycling. This approach will provide crucial indirect validation of the stress-strain predictions presented in this simulation study, establishing a direct correlation between the simulated mechanical response and observable interfacial damage.

 

Suggestion 4：Was a sensitivity analysis performed on boundary conditions to assess the robustness of the results?

Response 4：We thank the reviewer for raising this important point regarding the robustness of our simulations. To address this, we performed a comprehensive sensitivity analysis by systematically varying key boundary conditions across realistic operating ranges: the heat flux from 10 to 20 MW/m², and the coolant temperature from 80 to 120 °C. The results consistently demonstrated that while absolute values of temperature and stress showed expected variations, the fundamental trends reported in this work—particularly the systematic reduction in interfacial stress and plastic strain with decreasing tungsten thickness—remained unchanged across all tested conditions. This confirms the robustness of our primary conclusions against realistic variations in thermal boundary conditions.

 

Suggestion 5：How adequate are the constitutive models for Cu/CuCrZr in capturing long-term plasticity and creep under cyclic loading?

Response 5：We thank the reviewer for this insightful question regarding the constitutive models. The bilinear kinematic hardening model employed in this study adequately captures the cyclic plasticity behavior for the limited number of cycles (5 cycles) under steady-state thermal loading conditions that are the focus of this work. Its primary purpose was to compare the relative performance of different geometric designs rather than predict absolute component lifetime.

We fully acknowledge that for long-term operation involving thousands of cycles, more sophisticated constitutive models incorporating creep and complex cyclic hardening/softening effects would be necessary. However, such long-term phenomena were beyond the scope of this initial design study, which aimed to establish the fundamental geometric optimization principles. The current model provides a conservative and effective foundation for this purpose, and the incorporation of advanced material models for lifetime prediction is a key objective of our future research.

 

Suggestion 6：How realistic is the fabrication and stability of sub-10 μm tungsten layers under irradiation and plasma exposure?

Response 6： We thank the reviewer for this practical question. We agree that fabricating robust, free-standing sub-10 μm tungsten layers is challenging. Our simulations show that the most significant performance gains are achieved above this scale, with a thickness of 50 μm providing an excellent balance between performance and manufacturability. The 10 μm value serves to illustrate the theoretical trend, not a practical fabrication target. Regarding stability, while specific irradiation behavior requires future study, the laminated structure itself has demonstrated improved damage tolerance by providing interfaces that act as sinks for defects [16,17].

 

Suggestion 7：Were interfacial defects or bonding imperfections considered, and how would they affect the stress distribution?

Response 7：We thank the reviewer for this relevant question. The current model assumes perfect bonding at interfaces, which is a standard simplification for establishing baseline performance in fundamental design studies. We acknowledge that interfacial defects or bonding imperfections could act as local stress concentrators and potentially facilitate crack initiation.

However, the primary goal of our geometric optimization (e.g., introducing the arc-shaped interface) is to systematically reduce the global thermal mismatch stress driving such failures. By lowering this overall driving force, the proposed design inherently mitigates the risk associated with potential localized defects.

 

Suggestion 8：What is the added value of the FEM simulations compared to simpler analytical approaches, and how transferable are the results to full-scale PFCs?

Response 8：We thank the reviewer for this important question. The key added value of the FEM approach lies in its ability to resolve complex three-dimensional stress states and localized plastic strain accumulation that cannot be captured by simplified analytical models. While analytical solutions rely on idealized geometries and uniform stress assumptions, our simulations accurately quantify the highly non-uniform stress distribution and through-thickness gradients in the laminated structure.

Regarding transferability, while our model represents a simplified geometry, the fundamental physical mechanisms and the identified critical thickness scale (t < 100 μm) are directly applicable to full-scale PFCs. The boundary conditions were derived from fusion-relevant scenarios [7,8], and the stress reduction mechanism through thickness control remains valid regardless of the overall component size, providing valuable design guidance for engineering applications.

 

Comments on the Quality of English Language：English should be double-checked; several typos were found.

Respond 9：We sincerely thank the reviewer for this comment. The manuscript has been thoroughly checked and polished by a professional English editing service to correct typos, improve grammar, and enhance overall clarity and fluency. Key improvements include:

1.The incorrect term "oriented streamer material" in the Introduction (Page 1, Paragraph 2) has been corrected to "plasma-facing material".

2. Delete redundant sentences: "This geometric compatibility relationship represents a dynamic balance between the material's deformation capacity and the external structural constraints." and "during plasma instabilities such as Edge Localized Modes (ELMs), transient thermal loads can attain magnitudes on the order of 100 MW/m² within milliseconds. " Redundant phrases and sentences, particularly in the Introduction and Conclusions, have been removed or rephrased for conciseness.
3. The indefinite article before "arc-shaped interface" has been corrected from "a" to "an".

 

Comments on Symbol Definition：Please make sure that all symbols are clearly defined when they first appear in the text, even if they are commonly used in the literature. (e.g., in the title plasma-facing material (PFM), in the abstract W/Cu = tungsten(W)-copper(Cu)).

Respond 10：We thank the reviewer for this important reminder to enhance the clarity of our manuscript. We have systematically reviewed the text and now explicitly define all key acronyms and symbols upon their first appearance. The specific revisions are as follows:

1. In the title, the acronym "PFM" is now explicitly defined as "Plasma-Facing Material".
2. In the abstract, the material pair "W/Cu" is now defined as "tungsten (W)/copper (Cu)" upon its first mention.
3. In Section 2.1, the geometric parameter "t" is now explicitly defined as the thickness of the W-PFM.
4. In Section 3.1, the symbol "δ" for thermal mismatch deformation is clearly defined when first introduced.
5. In Section 3.2.1, the interface optimization parameters "H" and "D" are now explicitly defined with their physical meanings.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a thermo-mechanical analysis of laminated tungsten plasma-facing materials (PFMs) under steady-state thermal loads, with emphasis on the optimization of the W/Cu interface in plasma-facing components (PFCs) used in fusion devices such as tokamaks.
Using a finite element method (FEM) combined with theoretical modeling, the authors evaluate how tungsten layer thickness and interface geometry affect stress concentration, plastic strain accumulation, and thermal fatigue resistance.

The study finds that reducing tungsten layer thickness from the millimeter to micrometer scale significantly mitigates interfacial stress and plastic deformation. Moreover, replacing a flat W/Cu interface with an arc-shaped design redistributes stress concentration and enhances the structural reliability of the PFC joint.

Strengths

• The topic is highly relevant to fusion materials research (ITER, DEMO) and addresses a critical challenge in PFC lifetime optimization.
• The methodology is well-structured, combining realistic FEM conditions with material parameters and cyclic loading.
• Results are clearly presented and interpreted with appropriate graphical support and physical reasoning.
• The conclusions provide practical design insights, particularly the identification of optimal geometric parameters (e.g., H > 600 μm, D > 500 μm).
• The manuscript complies with Modelling’s structure and ethical standards, including funding and conflict-of-interest statements.

Weaknesses and Comments

• The literature review, while extensive, is somewhat repetitive in its discussion of ELMs and thermal shocks. It could be more concise and synthetic.
• The theoretical section (Equations 1–3) would benefit from a clearer link to the FEM data—specifically, a quantitative validation of the Δt–thickness relationship.
• Several stylistic and linguistic inconsistencies are present, such as repetitive phrasing in the conclusion (“This geometric compatibility relationship…” appears twice).
• The discussion section could engage more deeply with external experimental results rather than focusing primarily on the authors’ previous works.
• The experimental validation of the FEM model is mentioned briefly but not demonstrated. A reference to real PFC testing data would strengthen the credibility of the model.

Specific Comments

1. Page 14–15: The phrase “geometric compatibility relationship” is repeated; consider merging the sentences.
2. Table 1: Include temperature-dependent Young’s modulus data for CuCrZr up to 800 °C for completeness.
3. Figure 10: Axes are missing units—please label them for clarity.
4. References 18 and 25: Both are crucial previous works (2024 and 2015). A short comparative discussion would enhance context for the current findings.

Author Response

RESPONSES TO REVIEWER 2 S' COMMENTS

Reviewer 2：

We would like to sincerely thank Reviewer 2 for the careful reading of our manuscript and for providing insightful and constructive comments. The reviewer’s suggestions have greatly improved the clarity, depth, and overall quality of our paper.

We have carefully revised the manuscript according to each comment, and detailed responses are provided below.

 

Comment 1：Page 14–15: The phrase “geometric compatibility relationship” is repeated; consider merging the sentences.

Response 1：We thank the reviewer for this careful observation. The repeated sentence in the Conclusions has been merged and rephrased for conciseness, as suggested.

 

Comment 2：Table 1: Include temperature-dependent Young’s modulus data for CuCrZr up to 800 °C for completeness.

Response 2：We thank the reviewer for this suggestion to enhance our material data. In response, we have improved Table 1 by incorporating additional temperature-dependent data points within the 0-500 °C range to achieve a more refined and accurate representation. Furthermore, our thermal analysis in Fig. 3(a) confirms that the maximum temperature in the CuCrZr heat sink remains well below 500 °C in all simulated scenarios. Therefore, the presented data fully and appropriately cover the actual operational conditions of this component in our study. While reliable material properties for CuCrZr beyond 500 °C are scarce in the literature, the enhanced dataset within the relevant temperature range ensures the robustness of our simulation results.

 

Comment 3：Figure 10: Axes are missing units—please label them for clarity.

Response 3：We appreciate the reviewer’s observation. Figure 10 has been revised for clarity. Although the original figure is a schematic representation without coordinate axes, the geometric parameters H and D indeed denote dimensional quantities. In the revised version, their units (μm) have been clearly indicated in the figure and described in the caption to avoid any ambiguity.

 

Comment 4：References 18 and 25: Both are crucial previous works (2024 and 2015). A short comparative discussion would enhance context for the current findings.

Response 4：We thank the reviewer for pointing this out. A comparative discussion has been added in the Discussion section to better clarify how the present work relates to previous studies. Li et al. [25] numerically investigated the low-cycle fatigue (LCF) behavior of ITER-like W/Cu divertor targets and demonstrated that plastic strain localization at the Cu interlayer edge governs fatigue lifetime. Qi et al. [18] experimentally verified that the stacked-structure W-PFM effectively reduces thermal stresses and equivalent plastic strain through thickness modulation of W foils, leading to improved fatigue resistance. The present study extends these two key works by quantitatively linking tungsten thickness and interfacial geometry to the evolution of stress and plastic strain under steady-state thermal cycling, thereby bridging the LCF-based fatigue criterion of [25] with the structural optimization concept proposed in [18].

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have thoroughly examined both the authors’ response letter and the revised version of their manuscript. The authors have addressed each of the concerns raised in my earlier review with comprehensive, point-by-point replies and have implemented significant improvements to the text. I believe that the revised manuscript now satisfies the publication criteria and can be accepted.