Review Reports - Finite Element Modeling of Ceramic Green Part Warping Induced by Shrinkage During the Stereolithography Printing Process

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

Thank you very much for your interesting and well-reasoned scientific research.

The following comments can be made regarding the article:

The paper presents micrometer-sized alumina particles particle measurements but does not provide data (photographs or size distributions) to support this conclusion. The standard error of measurement of this value is also not presented.
What number of specimens were used in the tensile testing? The figure and text suggest one specimen per test. If this is true, the conclusion about the properties in the article is incorrect. It is necessary to study the values on at least three specimens, indicating the standard measurement error.
When determining the yield strength, the curves shown in Figures 8 and 13 are different. Which curves are correct for measuring the yield strength?

Author Response

Comment 1 : The paper presents micrometer-sized alumina particles particle measurements but does not provide data (photographs or size distributions) to support this conclusion. The standard error of measurement of this value is also not presented.

Response 1. : The alumina paste was supplied by 3D-Ceram Sinto. The particle size in the paste was provided to us, but for confidentiality reasons, no further information was shared. This paste has already been used in one of our previous studies. The particle size data were therefore already reported in the paper cited as reference [9]. This reference has therefore been added at line 130-page 4.

We agree with this comment 1 but we cannot provide a response due to confidentiality reasons.

Comment 2 : What number of specimens were used in the tensile testing? The figure and text suggest one specimen per test. If this is true, the conclusion about the properties in the article is incorrect. It is necessary to study the values on at least three specimens, indicating the standard measurement error.

Response 2 : The main goal is to identify a trend and feed the model qualitatively rather than quantitatively. The primary purpose of these tensile tests was to extract representative constitutive laws (elastoplastic behavior with time-dependent evolution) to feed the Finite Element Model. Furthermore, the specimens were manufactured in a single, strictly controlled stereolithography batch using the same ceramic slurry. In their green state, these parts behave like highly filled polymer matrix composites rather than brittle sintered ceramics. Consequently, they are much less sensitive to the statistical scattering of flaw-induced failures during tensile testing, which can lead to a reproducible macroscopic elastoplastic response.

we are agree with this comment 2. No changes were made to the revised manuscript regarding this point.

Comment 3 : When determining the yield strength, the curves shown in Figures 8 and 13 are different. Which curves are correct for measuring the yield strength?

Response 3 : The curves are indeed identical. The day-zero curve (as stated in the text in line number 353) is the one used to characterize the elasto-plastic behavior. The stress-strain curve represented in Figure 13 is the corresponding curve to the zero-day of the Figure 8. The sentence on line 363-page 12 has been modified.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper develops a finite element model that integrates time-dependent degree of conversion, elastoplastic behavior, and cohesive contact to address the warping issue during the SLA process of ceramic green parts, which has clear engineering application value. However, the following issues need to be resolved:
1. The paper makes several assumptions to simplify the model. The rationality of these assumptions and their impact on the results need to be rigorously assessed one by one; otherwise, the prediction accuracy and generalizability of the model cannot be guaranteed. For example, the model assumes that the degree of conversion within each printed layer is uniform, ignoring the conversion gradients that may arise from the laser scanning path, along the curing depth direction, and in adjacent exposed areas. To address this, a simplified case could be designed to compare the stress results between considering the in-layer conversion gradient (the stress field could be initialized based on a photocuring model) and the uniform assumption.
2. The paper points out that the simulated and experimental warping profiles have the "same shape" (Fig. 17), but there is a significant difference in the displacement amplitudes. It is recommended to supplement a quantitative error analysis of the simulated and experimental warping curves and discuss the possible sources of the discrepancy (e.g., the limitations of the assumptions mentioned in the previous point).
3. It is suggested to add a parameter sensitivity analysis section to show the influence of key parameters (such as shrinkage ratio, contact stiffness, yield stress, etc.) on the final warping prediction results when they fluctuate within a reasonable range. This will clarify the model's dependence on different parameters and enhance the robustness of the study.
4. If possible, consider supplementing independent experimental cases (e.g., green parts with different geometries or different printing parameters) for model prediction validation, rather than using only the same set of data employed for model construction. This will make the model validation more convincing.
5. The suggestions for improving dimensional accuracy proposed at the end of the paper are relatively generic. It is recommended to propose more specific solutions, such as support structure design and first-layer curing parameter settings, which can directly guide engineering applications.
6. The conclusion section is somewhat plain and mainly restates the work done. It is recommended to summarize and condense the most critical mechanisms revealed by this study and the most effective improvement approaches.

Author Response

Comment 1 : The paper makes several assumptions to simplify the model. The rationality of these assumptions and their impact on the results need to be rigorously assessed one by one; otherwise, the prediction accuracy and generalizability of the model cannot be guaranteed. For example, the model assumes that the degree of conversion within each printed layer is uniform, ignoring the conversion gradients that may arise from the laser scanning path, along the curing depth direction, and in adjacent exposed areas. To address this, a simplified case could be designed to compare the stress results between considering the in-layer conversion gradient (the stress field could be initialized based on a photocuring model) and the uniform assumption.

Response 1 : The heterogeneity of exposure within a polymerized part, as well as the associated conversion field, were investigated and characterized in a previous publication [11]. Based on the relatively homogeneous nature of both exposure and conversion for the printing parameters used, we chose to consider a single degree of conversion per layer. However, this assumption could be further supported by additional simulations comparing the case of a homogeneous conversion with that of a conversion gradient along the z-direction. Comparing the evolution of the S11 and S22 stresses as a function of depth within a multilayer part would then make it possible to quantify the influence of this assumption. Accordingly, the paragraph from lines 328 to 333 has been replaced by the paragraph from lines 334 to 340 (page 11). We are agree with this comment.

Comment 2 :The paper points out that the simulated and experimental warping profiles have the "same shape" (Fig. 17), but there is a significant difference in the displacement amplitudes. It is recommended to supplement a quantitative error analysis of the simulated and experimental warping curves and discuss the possible sources of the discrepancy (e.g., the limitations of the assumptions mentioned in the previous point).

Response 2 : Regarding the analysis of the curves in Figure 17, we are fully aware that the relative error in the displacement values derived from the modeling is very large. As accurately noted, although the qualitative shape is captured, the model assumes a much stiffer mechanical response than reality. Four main unmodeled factors, three of which were described in the initial manuscript, can explain this overestimation.

Viscoelastic relaxation: The current model does not account for viscous relaxation, which plays a major role in reducing long-term residual stresses and subsequent warping.

Process-induced damage: Localized material damage resulting from mechanical fatigue may develop during the layer-by-layer printing process, contributing to stress relief and a lower overall curling magnitude.
Transient material properties: The continuous evolution of mechanical properties upon polymerization is simplified in the model, whereas capturing this transition might induce lower final stresses in the actual part.

Light exposure of upper layers: The current model does not account for the additional irradiation occurring during the exposure of the upper layers. This light penetration strongly influences the conversion kinetics of the previously printed layers and the resulting stress fields.

However, it is highly challenging to estimate the contribution of each of these factors to the observed discrepancies between the experimental and numerical displacement values.

Accordingly, the paragraph from lines 452 to 459 (page 15) has been replaced by the paragraph from lines 460 to 473 (pages 15 and 16). We are agree with comment.

Comment 3 : It is suggested to add a parameter sensitivity analysis section to show the influence of key parameters (such as shrinkage ratio, contact stiffness, yield stress, etc.) on the final warping prediction results when they fluctuate within a reasonable range. This will clarify the model's dependence on different parameters and enhance the robustness of the study.

Response 3 : Regarding the contact parameters (such as stiffness and maximum stress), it should be emphasized that the comparison between the 'tied' and 'cohesive' contact conditions already constitutes an extreme sensitivity analysis. Indeed, the tied contact condition is mechanically equivalent to infinite stiffness and infinite maximum stresses. By comparing this theoretical upper bound to the cohesive zone model, the study highlights the strong dependence of the final warping predictions on the contact interaction parameters.

Regarding the intrinsic material parameters (such as yield stress or shrinkage ratio), we fully agree that a sensitivity analysis would be relevant. However, conducting a meaningful parametric study, along with the experimental campaign necessary to acquire this data, followed by the corresponding numerical study, would be extremely time-consuming and falls beyond the scope of this work. No changes regarding this comment have been made in the revised manuscript.

Comment 4 : If possible, consider supplementing independent experimental cases (e.g., green parts with different geometries or different printing parameters) for model prediction validation, rather than using only the same set of data employed for model construction. This will make the model validation more convincing.

Response 4 : We agree that the validation of the numerical framework using independent experimental cases (involving different geometries and manufacturing parameters) would further demonstrate the predictive capabilities of the model.

However, carrying out a new experimental campaign with different designs, along with the associated mechanical testing, represents a substantial amount of work that unfortunately cannot be accomplished within the scope of this revision. No changes regarding this comment have been made in the revised manuscript.

Comment 5 : The suggestions for improving dimensional accuracy proposed at the end of the paper are relatively generic. It is recommended to propose more specific solutions, such as support structure design and first-layer curing parameter settings, which can directly guide engineering applications.

Response 5 : We thank the reviewer for this highly constructive comment. We agree that providing specific, actionable guidelines adds significant value for engineering applications. Based on your suggestion, we have included recommendations regarding first-layer curing and support structure optimization:

First-layer curing parameters: The model confirms that applying strong irradiation (overcuring) to the first layer helps reduce the final deformation of the printed part. This increased exposure ensures stronger adhesion to the build platform, which is mechanically represented in our study by the "tied" contact case. As demonstrated by the Z-displacement fields and profiles in Figures 16 and 17, this strong adhesion significantly minimizes the final warping compared to a weaker adhesion scenario (represented by the cohesive case).
Support structure design: From a general mechanical standpoint, improving dimensional accuracy requires restricting the displacement degrees of freedom as much as possible to minimize the elastic component of the polymerization shrinkage. Blocking these degrees of freedom through the strategic addition of support structures forces the material to undergo higher plastic deformations during the printing process. As highlighted by the equivalent plastic strain fields in Figure 21, increased constraints (such as the tied condition) lead to higher localized plastic strains, which effectively limits the residual elastic deformations responsible for post-print springback and warping.

These considerations have been added to the conclusion and perspectives section (we are agree with this comment)

From line 598 to line 601 (page 20) for First-layer curing parameters
From line 606 to line 611 (page 20) for Support structure design

Comment 6 : The conclusion section is somewhat plain and mainly restates the work done. It is recommended to summarize and condense the most critical mechanisms revealed by this study and the most effective improvement approaches.

Response 6 : The Conclusion and perspectives section has been revised (from line 582 to line 619) (pages 19 and 20). We are agree with this comment.