The Investigation of the Sensitivity of the Compliance to the Shape of the Spot in Welded Thermoplastic Single-Lap Shear (SLS) Joints

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors   In the Introduction, it would be worth mentioning the influence of welding process parameters and element cleanliness on weld quality. What material models and finite element types have been used for FEM analysis? Has a study of the mesh size on solution convergence been completed? Figure 2 - Distance reference sections would be useful. Figure 3 - Unclear for laypeople - the notations used in the figure caption need to be explained. Figure 4 - Incomplete baoundary conditions - indicate the sense and direction of displacement in the X-axis direction. Figures 5, 6, and 7 - Using different colors for markers is recommended, otherwise the graphs will be unreadable. Figure 8 - Better resolution is required. In graphs, the legend should be placed outside the graph area (for example, on the front page) and not within the graph area. The obtained results were poorly compared to other results published in the available literature. The aim is given in the abstract and introduction, not in the conclusions, where only information on whether it was achieved or not is provided. The bibliography needs to be updated a bit. There's a lot happening in this area right now. Comments on the Quality of English Language

English checking is recommended.

Author Response

Thank you for taking the time to review the manuscript, the responses to the comments are included here and all the changes are marked in the revised PDF version of the manuscript.

 

Comment 1:    In the Introduction, it would be worth mentioning the influence of welding process parameters and element cleanliness on weld quality. 
Response 1: We have added this to the 4th paragraph of the introduction.

Comment 2:    What material models and finite element types have been used for FEM analysis?
Response 2: For the adherends, the SC8R (8-noded continuum shell) elements have been used and the interface was modelled using cohesive zone elements.

Comment 3:    Has a study of the mesh size on solution convergence been completed?
Response 3: Yes, the results are included in the 4TU.ResearchData repository along with the data for the graphs in this paper.

Comment 4:    Figure 2 - Distance reference sections would be useful.
Response 4: The widths of the welds has been added

Comment 5:    Figure 3 - Unclear for laypeople - the notations used in the figure caption need to be explained. 
Response 5: The clarification of the symbols is added to the caption of figure 3.

Comment 6:    Figure 4 - Incomplete baoundary conditions - indicate the sense and direction of displacement in the X-axis direction.
Response 6: The loading direction is added to the figure

Comment 7:    Figures 5, 6, and 7 - Using different colors for markers is recommended, otherwise the graphs will be unreadable. 
Response 7: The colors have been changed.

Comment 8:    Figure 8 - Better resolution is required.
Response 8: The image is replaced by a higher resolution version. 

Comment 9:    In graphs, the legend should be placed outside the graph area (for example, on the front page) and not within the graph area. 
Response 9: The editor has not specified whether the legend should be placed within the graph area or not. In this manuscript, placing the legend outside of the graph area would decrease the figure size when the 2-column layout is used. Therefore, the choice was made to place the legends within the graph area to maintain the desired level of detail.

Comment 10:    The obtained results were poorly compared to other results published in the available literature.
Response 10: The results are compared to experimental results, we have noticed that the manuscript gives the impression that the experimental campaign was a part of the current work, which it is not. A section was added that describes the experimental validation data to make this more explicit. To the authors' knowledge, this is the only available similar experimental data.

Comment 11:    The aim is given in the abstract and introduction, not in the conclusions, where only information on whether it was achieved or not is provided.
Response 11: The aim is repeated in the first sentence of the conclusions.

Comment 12:    The bibliography needs to be updated a bit. There's a lot happening in this area right now.
Response 12: The bibliography has been updated to include additional references.

Reviewer 2 Report

Comments and Suggestions for Authors

1) The manuscript does not clearly justify the selection of the specific joint geometries investigated. A rationale grounded in industrial relevance or previous literature should be provided.

2) The definition of “shear compliance” used in the manuscript is not sufficiently rigorous. The authors should provide a clear mathematical formulation and explain how it relates to displacement measurements during testing.

3) The description of the spot welding process parameters is incomplete. Critical variables such as welding temperature, pressure, dwell time, and cooling conditions should be reported to ensure reproducibility.

4) The paper lacks a detailed characterization of the thermoplastic material properties used in the joints. Mechanical properties (elastic modulus, yield stress, viscoelastic behavior) should be presented, preferably with references or experimental measurements.

5) The authors should clarify whether the material behavior in the analysis was assumed to be linear elastic, elastic-plastic, or viscoelastic, as thermoplastics often exhibit time-dependent behavior affecting compliance.

6) The manuscript does not provide sufficient detail regarding the manufacturing tolerances of the spot weld geometry. Variations in weld diameter and nugget shape could significantly affect compliance results.

7) The sensitivity analysis methodology is insufficiently explained. It is unclear whether the study uses a parametric sweep, statistical sensitivity analysis, or derivative-based methods.

8) Boundary conditions used in the lap shear simulations or experiments require clearer explanation. The current description does not ensure that the loading conditions accurately replicate standard lap shear testing protocols.

9) The influence of bending effects inherent in single lap joints is not discussed in depth. Since eccentric loading introduces peel stresses, the authors should explain how this was considered in the compliance evaluation.

10) The authors should justify why only a limited set of weld shapes was considered. Other plausible geometries might significantly influence the mechanical response.

11) The finite element model description is incomplete. Information about mesh density, element types, convergence criteria, and contact modeling should be provided.

12) The manuscript does not report any mesh convergence study, which is essential when evaluating compliance sensitivity to geometric variations.

13) The interface behavior between welded thermoplastic layers is not discussed. It is unclear whether perfect bonding was assumed or whether an interfacial model was implemented.

14) The effect of residual stresses generated during the welding process has not been addressed, although these stresses may influence the mechanical response.

15) The experimental setup lacks sufficient detail regarding displacement measurement methods. It is not clear whether extensometers, digital image correlation, or crosshead displacement was used.

16) The authors should clarify the sample size used for each configuration. Statistical reliability cannot be assessed without knowing the number of tested specimens.

17) No statistical analysis of experimental variability is presented. Confidence intervals or standard deviations should accompany compliance measurements.

18) The results section primarily reports trends but does not provide a mechanistic explanation for the observed sensitivity of compliance to weld shape.

19) The authors should compare their results with previously published studies on thermoplastic spot welded joints to establish consistency or highlight differences.

20) The role of the heat-affected zone around the weld is not discussed, although it may significantly influence joint stiffness.

21) The manuscript would benefit from microstructural or morphological observations of the weld region (e.g., microscopy) to confirm the assumed weld shape and bonding quality.

22) The study does not address possible failure modes associated with different weld geometries, even though these modes may influence compliance measurements.

23) The load-displacement curves for the tested joints are not presented in sufficient detail. Representative curves should be included.

24) The discussion does not sufficiently differentiate between geometric effects and material effects on joint compliance.

25) The authors should explain whether environmental conditions (temperature, humidity) during testing were controlled, as thermoplastics are sensitive to such conditions.

26) The sensitivity results are presented without normalization, making it difficult to compare the relative influence of different geometric parameters.

27) The conclusions appear to generalize the findings beyond the specific material system studied. The applicability to other thermoplastic systems should be clarified.

28) The manuscript would benefit from a dimensional analysis to better understand the governing parameters affecting compliance.

29) The influence of lap length and adherend thickness is not discussed, although these parameters strongly interact with weld geometry.

30) The authors should discuss the potential implications of their findings for industrial design guidelines for thermoplastic spot welded joints.

31) Finally, the manuscript would benefit from a clearer structure separating experimental methodology, numerical modeling, and sensitivity analysis to improve readability and technical clarity.

Author Response

First of all, we would like to thank you for taking the time for reviewing the manuscript. The thorough feedback is appreciated. Below are all the comments with our reply and all the changes are marked in the revised PDF.

Comment 1:    The manuscript does not clearly justify the selection of the specific joint geometries investigated. A rationale grounded in industrial relevance or previous literature should be provided.
Response 1: A reference to the relevant ASTM testing standard has been added.

Comment 2:    The definition of “shear compliance” used in the manuscript is not sufficiently rigorous. The authors should provide a clear mathematical formulation and explain how it relates to displacement measurements during testing.
Response 2: The term is not used as such, but as a part of "single lap shear compliance" meaning, the compliance of a SLS specimen. The title has been rephrased to make this difference more clear. At the start of the methodology section a sentence has been added to elaborate on the definition of compliance that ws used.

Comment 3:    The description of the spot welding process parameters is incomplete. Critical variables such as welding temperature, pressure, dwell time, and cooling conditions should be reported to ensure reproducibility.
Response 3: The current manuscript describes a numerical study. Previously published experimental data is used to validate the conclusion. A sentence has been added to specifically mention that the process parameters can be found in the previous  publication. From the feedback from both reviewers, we have understood that the distinction between the current numerical study and the validation with the published data is not clear. A sentence has been added to the introduction and a  section in the discussion now explicitly discusses the validation to clarify this.
Comment 4:    The paper lacks a detailed characterization of the thermoplastic material properties used in the joints. Mechanical properties (elastic modulus, yield stress, viscoelastic behavior) should be presented, preferably with references or experimental measurements.
Response 4: Table 1 shows the mechanical properties of the material. The title of section 2.1 has been adapted to better reflect this and the yield stresses have been added. The properties are obtained from the datasheet provided by the manufacturer of the material, no further characterization has been performed. 

Comment 5:    The authors should clarify whether the material behavior in the analysis was assumed to be linear elastic, elastic-plastic, or viscoelastic, as thermoplastics often exhibit time-dependent behavior affecting compliance.
Response 5: The material behaviour was assumed to be linear-elastic.

Comment 6:    The manuscript does not provide sufficient detail regarding the manufacturing tolerances of the spot weld geometry. Variations in weld diameter and nugget shape could significantly affect compliance results.
Response 6: Since this paper discusses the numerical work, merely using the experimental data as validation, the choice was made to omit the details regarding the manufacturing process. The reader can refer to the previous publication for this information

Comment 7:    The sensitivity analysis methodology is insufficiently explained. It is unclear whether the study uses a parametric sweep, statistical sensitivity analysis, or derivative-based methods.
Response 7: A sensitivity analysis was performed for the numerical parameters to ensure that these variables to not influence the conclusions. Since this is not a part of the main focus of the paper, these results have been added to the online data repository, together with the data for the graphs. This is now mentioned in section 2.4

Comment 8:    Boundary conditions used in the lap shear simulations or experiments require clearer explanation. The current description does not ensure that the loading conditions accurately replicate standard lap shear testing protocols.
Response 8: An arrow was added to Figure 4 to show the loading direction and the section regarding the boundary conditions has been updated.

Comment 9:    The influence of bending effects inherent in single lap joints is not discussed in depth. Since eccentric loading introduces peel stresses, the authors should explain how this was considered in the compliance evaluation.
Response 9: The compliance was evaluated using the ratio of the applied displacement and the reaction force, this definition was chosen due to the simplicity of measurement during mechanical testing. The manuscript investigates the sensitivity of the compliance to the shape of the weld, but does not consider any mechanical explanation. A discussion section has been added to explain this.

Comment 10:    The authors should justify why only a limited set of weld shapes was considered. Other plausible geometries might significantly influence the mechanical response.
Response 10: The manuscript considers spot welds that are based on the experimental study from a previous publication where the spot welds were manufactured with a circular sonotrode. Therefore, the geometry of the weld is not expected to deviate significantly from the shapes considered here.  Since the aim is to investigate the expansion of observations made in previous work, including a wider range of shapes is considered outside of the scope of the current work, this is mentioned at the end of the discussion

Comment 11:    The finite element model description is incomplete. Information about mesh density, element types, convergence criteria, and contact modeling should be provided.
Response 11: The detailed description of the FE model including the mesh specifications, interface model and boundary conditions is in section 2.4. The beginning of this section has been changed to indicate this better.

Comment 12:    The manuscript does not report any mesh convergence study, which is essential when evaluating compliance sensitivity to geometric variations.
Response 12: The mesh convergence results have been added to the online data repository with the sensitivity in order to maintain the focus of the manuscript.

Comment 13:    The interface behavior between welded thermoplastic layers is not discussed. It is unclear whether perfect bonding was assumed or whether an interfacial model was implemented.
Response 13: The interface is modelled using cohesive zone modelling, the parameters for the cohesive zone can be found in subsection 2.4.2. The beginning of section 2.4 is changed to indicate this.

Comment 14:    The effect of residual stresses generated during the welding process has not been addressed, although these stresses may influence the mechanical response.
Response 14: The publication focusses on how the shape of the spot weld influences the compliance. This study does not investigate possible causes of this insensitivity, or other factors affecting the mechanical response. This has been added to the discussion.

Comment 15:    The experimental setup lacks sufficient detail regarding displacement measurement methods. It is not clear whether extensometers, digital image correlation, or crosshead displacement was used.
Response 15: A short description has been added to the discussion, where the validation with the previously published data is presented. For a more detailed explanation, the reader is referred to the previous publication

Comment 16:    The authors should clarify the sample size used for each configuration. Statistical reliability cannot be assessed without knowing the number of tested specimens.
Response 16: The FE analyses are purely deterministic; no statistical or stochastic effects were investigated. The information regarding the experimental procedures and sample sizes can be found in the previous publication

Comment 17:    No statistical analysis of experimental variability is presented. Confidence intervals or standard deviations should accompany compliance measurements.
Response 17: The compliance measurements that are used as validation data are single measurements from single specimens, therefore there are no standard deviations calculated.

Comment 18:    The results section primarily reports trends but does not provide a mechanistic explanation for the observed sensitivity of compliance to weld shape.
Response 18: The aim of the paper was to explore this trend and the validity of the observations that were made during previous experimental campaigns. The mechanicstic explanation is considered out of the current scope. A discussion section has been added regarding the recommendations for future studies

Comment 19:    The authors should compare their results with previously published studies on thermoplastic spot welded joints to establish consistency or highlight differences.
Response 19: The results are compared to a previously published study, the introduction and methodology were adapted to make this more clear.

Comment 20:    The role of the heat-affected zone around the weld is not discussed, although it may significantly influence joint stiffness.
Response 20: A paragraph has been added to the discussion to touch upon the heat-affected zone and other factors influencing the joint stiffness.

Comment 21:    The manuscript would benefit from microstructural or morphological observations of the weld region (e.g., microscopy) to confirm the assumed weld shape and bonding quality.
Response 21: A section has been added to explicitly discuss the experimental validation, the microscope images of the fracture surfaces have also been moved here.

Comment 22:    The study does not address possible failure modes associated with different weld geometries, even though these modes may influence compliance measurements.
Response 22: While it is expected that failure mode can influence the measurement of the compliance, the failure load, and the corresponding displacement, it is not expected that this will influence how the compliance is affected by the shape of the spot weld, therefore we have chosen not to include it in the manuscript

Comment 23:    The load-displacement curves for the tested joints are not presented in sufficient detail. Representative curves should be included.
Response 23: An example force-displacement curve has been added to the results section.

Comment 24:    The discussion does not sufficiently differentiate between geometric effects and material effects on joint compliance.
     Response 24: For the purpose of this paper, we consider the compliance as the ratio of the applied displacement and the global reaction force. Therefore, there is no differentiation between the effects on the joint compliance. The aim was to explore the role of the spot shape in the relationship between the welded area and the global compliance, the underlying mechanics were considered out of scope of the current work. A section has been added to the discussion to elaborate on this.

Comment 25:    The authors should explain whether environmental conditions (temperature, humidity) during testing were controlled, as thermoplastics are sensitive to such conditions.
Response 25: Since this paper reports the numerical work and the experimental data is from a previous publication to be used as validation, the experimental conditions are not included. A section was added with a summarized description of the validation data, for more information the reader is referred to the previous validation 

Comment 26:    The sensitivity results are presented without normalization, making it difficult to compare the relative influence of different geometric parameters.
Response 26: Since the focus was on exploring the influence of the shape on the compliance, not on setting up a prediction model or investigating a mechanical explanation, the  

Comment 27:    The conclusions appear to generalize the findings beyond the specific material system studied. The applicability to other thermoplastic systems should be clarified.
Response 27: With a different material, the mechanical response would indeed be different, meaning that the same weld area might lead to a different compliance. However, this would not affect how a change in shape, with a constant area, would influence the resulting compliance and would not affect the conclusions. This is now discussed in the discussion section.  

Comment 28:    The manuscript would benefit from a dimensional analysis to better understand the governing parameters affecting compliance.
Response 28: The focus of the paper is to determine whether the shape of the spot is affecting how the area and the compliance are related to each other. Therefore, there is no investigation regarding the influence of dimensions, material parameters or environmental conditions on the compliance. We agree that this is a necessary follow-up study, and we have mentioned it in the discussion section

Comment 29:    The influence of lap length and adherend thickness is not discussed, although these parameters strongly interact with weld geometry.
Response 29: These factors would indeed impact the weld geometry and the resulting compliance. However, the current paper focusses on how the shape of the welds changes the compliance for a given area with a constant specimen geometry. The aim is not to investigate how other factors change the compliance. Changing the specimen geometry will result in a different relationship between area and compliance, but it will not change the fact that this relationship is insensitive to the weld shape. 

Comment 30:    The authors should discuss the potential implications of their findings for industrial design guidelines for thermoplastic spot welded joints.
Response 30: The third paragraph of the conclusion discusses the implications of the findings regarding mechanical testing procedures. However, since the focus was on the influence of the shape on the measured quantities during testing, the current is not meant to have implications in the context of design guidelines.

Comment 31:    Finally, the manuscript would benefit from a clearer structure separating experimental methodology, numerical modelling, and sensitivity analysis to improve readability and technical clarity.
Response 31: We understand that the distinction between experimental and numerical work is confusing, a section concerning the experimental validation work has been added to clear this up.

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

After the implementation of major revisions, the manuscript has been considerably improved in terms of clarity, methodological rigor, and coherence of the presented analysis. The authors have adequately addressed the key reviewer concerns, resulting in a stronger and more comprehensive study. At this stage, only minor revisions are recommended—specifically, the inclusion of additional relevant citations to better position the work within existing literature, and a refinement of the conclusions section to more clearly highlight the key findings and their broader implications.

Author Response

Thank you for your quick response. We have added 9 citations to the bibliography, specifically numbers 17 to 25. If we are still missing any specific references, we would love to hear your suggestions. A paragraph has been added to the conclusions that discusses the broader implications in more detail.