Numerical Evaluation of Fatigue Crack Growth of Structural Steels Using Energy Release Rate with VCCT
, Yupiter H. P. Manurung 1,*, Martin Leitner 3, Yusuf L. Shuaib-Babata 2, Muhd F. Mat 1, Hassan K. Ibrahim 4, David Simunek 5 and Mohd Shahar Sulaiman 1Round 1
Reviewer 1 Report
- how does the VCCT method compare to other crack propagation methods such as XFEM?
- How did the authors consider the fatigue life before the crack initiates?
- Can the authors provide a front view picture of fig. 2?
- The authors are suggested to include other recent papers on fatigue and damage modeling: (a) doi.org/10.1016/j.ijfatigue.2019.105302, (b) doi.org/10.2514/6.2019-0237, (c) doi.org/10.1016/j.cma.2019.112585
Author Response
Point 1: how does the VCCT method compare to other crack propagation methods such as XFEM?
Response 1: This research is focuses on using VCCT only, no comparison is made to XFEM. However, several numerical techniques to simulate crack propagation are available including surface and element based cohesive behaviour, virtual crack closure technique and XFEM. Apart from stresses strains and displacements, one quantity of interest when post processing XFEM results is the stress intensity factors. Both VCCT and XFEM in their calculation are based on the evaluation of an integral interaction over an area around the crack tip. The procedure is similar to the one for the FEM.
XFEM allows you to study crack growth along an arbitrary, solution-dependent path without needing to remesh your model. After a crack is nucleated in an enriched region, subsequent propagation of the crack is governed by LEFM criterion. We have used VCCT with FEM to implement mesh refinement usually necessary near the crack tips in order to represent the asymptotic fields associated with the crack tips with remeshing as the crack propagates. The aspect of computational time in 3D domains is well considered with sensitivity analysis.
Point 2: How did the authors consider the fatigue life before the crack initiates?
Response 2: Thank you for your observation, the fatigue crack initiation of metals and alloys is a very complex phenomenon. A pre-crack is assumed based on linear elastic fracture mechanics
Point 3: Can the authors provide a front view picture of fig. 2?
Response 3: Thank you for the excellent suggestion which is considered as important. However, the present Figure 2 was able to iluustates both measuring tool of crack. Unfortunately, your suggested figure inclusion it not available .
Point 4: The authors are suggested to include other recent papers on fatigue and damage modeling: (a) doi.org/10.1016/j.ijfatigue.2019.105302, (b) doi.org/10.2514/6.2019-0237, (c) doi.org/10.1016/j.cma.2019.112585
Response 4: We agree with this assessment. Accordingly, we have introduced the pervious and emerging study methods are presented clearly and cited in Line ( L71-L78) in the paper.
“The discretization of the FE approach makes it difficult for meshes to conform with the crack front geometry to capture the maximum point of SIF. Several numerical efforts like the feature-preserving discretization paired with a local refinement approach adopted to capture small geometric features and locally resolve regions of damage propagation have showed improvements in the efficiency and accuracy of singularities(Liu & Jeffers, 2019). Other interesting numerical tools for addressing similar challenges emerge in FE-based techniques, such as meshfree peridynamic methods that discretize areas into nodes, each with a defined volume in the reference configuration. In addition, hybrid meshfree discretization has recently been developed to improve the numerical performance of peridynamic models(Shojaei, Hermann, Cyron, Seleson, & Silling, 2022) (Nguyen, Oterkus, & Oterkus, 2021)”.
Liu, N., & Jeffers, A. E. (2019). Feature-preserving rational Bézier triangles for isogeometric analysis of higher-order gradient damage models. Computer Methods in Applied Mechanics and Engineering, 357, 112585. https://doi.org/10.1016/j.cma.2019.112585
Nguyen, C. T., Oterkus, S., & Oterkus, E. (2021). An energy-based peridynamic model for fatigue cracking. Engineering Fracture Mechanics, 241, 107373. https://doi.org/10.1016/j.engfracmech.2020.107373
Shojaei, A., Hermann, A., Cyron, C. J., Seleson, P., & Silling, S. A. (2022). A hybrid meshfree discretization to improve the numerical performance of peridynamic models. Computer Methods in Applied Mechanics and Engineering, 391, 114544. https://doi.org/10.1016/j.cma.2021.114544
Author Response File: 
Author Response.docx
Reviewer 2 Report
Authors investigated the crack growth using the finite element simulation. Since the analysis is based on the simulation, much careful modeling is required to produce reliable predictions. The current manuscript has issues in English, format, and technical aspects. Please revise the manuscript between authors carefully again and submit the improved paper including enhanced technical analysis.
Author Response
Point 1: Authors investigated the crack growth using the finite element simulation. Since the analysis is based on the simulation, much careful modeling is required to produce reliable predictions. The current manuscript has issues in English, format, and technical aspects. Please revise the manuscript between authors carefully again and submit the improved paper including enhanced technical analysis.
Response 1: Thank you very much for valuable comments. We have revised the the manuscript and add new references. The technical analysis is also improved following other reviewer comments.
Author Response File: Author Response.docx
Reviewer 3 Report
This paper reports a comprehensive investigation into evaluation of fatigue crack growth of S355 and S960. Doing it so, a FE-based model is developed and the results are compared with those obtained from experimental data using optical and crack gauge measurements. Overall, the subject of the manuscript is interesting and within the aim and scope of the journal. However, the paper is poorly-written in English. There are many typos and grammatical mistakes in the text. Just as one example:
L 136: “his is example ….” ?
Even there is an extra paragraph (L 110 - 116) which was not removed from the template files of the journals. I would recommend the authors to extensively polish the whole text.
The authors have greatly endeavored in their project to circumvent some difficulties in the implementation of crack propagation in their FEM software. More recently, there are promising numerical tools to address such difficulties arise in FE-based approaches such as meshfree peridynamic methods. To this end, I would suggest the authors to mention such novel approaches in the introduction for the sake of completeness and to cite the following relative references [Computers & Structures Volume 83, Issues 17–18, June 2005, Pages 1526-1535], [Computer Methods in Applied Mechanics and Engineering Volume 391, 1 March 2022, 114544] and [Engineering Fracture Mechanics Volume 241, January 2021, 107373].
Author Response
Point 1: This paper reports a comprehensive investigation into evaluation of fatigue crack growth of S355 and S960. Doing it so, a FE-based model is developed and the results are compared with those obtained from experimental data using optical and crack gauge measurements. Overall, the subject of the manuscript is interesting and within the aim and scope of the journal. However, the paper is poorly-written in English. There are many typos and grammatical mistakes in the text. Just as one example:
L 136: “his is example ….” ?
Even there is an extra paragraph (L 110 - 116) which was not removed from the template files of the journals. I would recommend the authors to extensively polish the whole text.
Response 1: First of all, we would like to express our gratitude to the reviewer. This journal has undergone grammatical correction and improvement entirely by professional proofreader. Also, the the referenced sentence lines and Table 2were revised accordingly.
Point 2: The authors have greatly endeavored in their project to circumvent some difficulties in the implementation of crack propagation in their FEM software. More recently, there are promising numerical tools to address such difficulties arise in FE-based approaches such as meshfree peridynamic methods. To this end, I would suggest the authors to mention such novel approaches in the introduction for the sake of completeness and to cite the following relative references [Computers & Structures Volume 83, Issues 17–18, June 2005, Pages 1526-1535], [Computer Methods in Applied Mechanics and Engineering Volume 391, 1 March 2022, 114544] and [Engineering Fracture Mechanics Volume 241, January 2021, 107373].
Response 2: We agree with this assessment. Accordingly, we have introduced the pervious and emerging study methods are presented clearly and cited in Line ( L71- L78) in the paper.
Author Response File: Author Response.docx
