Finite Element Modeling of Orthogonal Machining of Brittle Materials Using an Embedded Cohesive Element Mesh
Round 1
Reviewer 1 Report
The authors presented a study on finite element simulation of orthogonal machining of brittle materials using a cohesive zone concept. The treatment of cohesive elements in this paper is different from existing work. The validity of this modeling approach appears promising, but more validation seems to be necessary. Below are some questions/comments for the authors to address.
1. How does the element tilt angle affect cutting results? Different tilt angles should be tested for this purpose, as it is shown clearly in Fig. 6c this angle could have significant effect on crack formation during cutting.
2. The comparison of the chip formation between simulation and experiments in Fig. 5 show that the chips from experiments are much larger (based on different scale bars). So the brittle material removal nature is in good agreement but not the size distribution. The conclusion of good agreement should be further justified.
Author Response
The authors presented a study on finite element simulation of orthogonal machining of brittle materials using a cohesive zone concept. The treatment of cohesive elements in this paper is different from existing work. The validity of this modeling approach appears promising, but more validation seems to be necessary. Below are some questions/comments for the authors to address.
1. How does the element tilt angle affect cutting results? Different tilt angles should be tested for this purpose, as it is shown clearly in Fig. 6c this angle could have significant effect on crack formation during cutting.
Response: The reviewer made a great point. Indeed, the result can be sensitive to the mesh configuration. The 45-degree angle was determined by the theoretical shear angle based on a frictionless condition (no chip-tool contact), which has been explained in Line 96. This means that the shear-induced crack is preferred at this angle. However, different angles may work as well. Therefore, to address this comment, we added Section 2.5 Sensitivity Study in the revised manuscript to discuss about the effects of different tilt angles and recommended approaches to handle the difference. It should be noted that cracks are randomized in reality and cannot really be compared point-by-point to the simulation.
2. The comparison of the chip formation between simulation and experiments in Fig. 5 show that the chips from experiments are much larger (based on different scale bars). So the brittle material removal nature is in good agreement but not the size distribution. The conclusion of good agreement should be further justified.
Response: The reviewer is correct. Different scales are used in those figures due to the resolution of the high-speed camera. However, the chips are not necessarily much larger because the images are at a closed-up view. The difference is in the order of 0.1 mm.
Besides, it is also difficult to precisely model chip size distribution as that depends on the material initial condition and internal defects, etc. What we are looking is the chip behavior as described in Figure 4 (Section 2.4) rather than the details like cracks, chip size, and surface finish at this point. To address this comment, we have clarified in Line 270: “The results of 30 pcf with the selected scaling factor show qualitative agreement between the model and experiment in terms of chip behavior. Chip sizes of simulation and experiment do not match exactly due to the limited observation window and material uncertainty, but the difference is in the order of sub-mm.”
Reviewer 2 Report
The manuscript presents a discrete-continuum finite element methodology to simulate machining of high-density polyurethane (PU) foams. Thereby, the discrete cohesive elements are scaled to control material ductility and chip behavior.
The paper is well written with clear description of the FE model. The key contribution of the manuscript is the introduction of a scaling parameter that allows for simulating the machining process realistically. In general, the procedure is fine, but the reviewer has numerous questions with regards to this scaling factor:
- It is stated in line 151 that the corrected separation f\delta is shown in Figure 2. The reviewer cannot see any of this correction. Please add this to the figure.
- In line 147 it is stated that ‘the deflection [of a CZ element] can become larger than the element size when a fine mesh is used’. What is meant by element size? Zero-thickness CZ elements are used here. The reviewer does not see any problem with the separation becoming large in CZ elements. This motivation of using a scaling factor needs to be better explained and illustrated. In the best case, the authors come up with a simple FE model where this problem is shown.
- In line 151, the authors state that ‘when the deflection is scaled, the fracture energy and the cutting force will be scaled accordingly’. This needs more explanation. As a material property, the fracture energy should remain constant. Therefore, the maximum traction tc should be scaled such that the fracture energy is constant. This is a common technique in using cohesive elements.
- Furthermore, it is not clear why the cutting forces need to be scaled. By maintaining a constant fracture energy, there is no need of scaling the cutting forces.
In addition, please see below further comments/remark to improve the quality of the paper:
- In the introduction, a recently published paper on orthogonal cutting of composite materials should be added: X. Yan, J. Reiner, M. Bacca, Y. Altintas and R.Vaziri, ‘A study of energy dissipating mechanisms in orthogonal cutting of UD-CFRP composites’, Composite Structures, Volume 220, 15 July 2019, Pages 460-472.
- In line 82, it is stated that ‘CZ elements are embedded all around the main elements’. Considering Fig.1, does this mean that you include CZ elements vertically and horizontally? Fig.1 could be updated to account for the implementation used here.
- Has a mesh sensitivity been performed? What is the motivation of using 0.01mm elements?
- With respect to the damage criterion and evolution of the ‘main element’ in Section 2.2:
o Is the built-in Johnson-Cook model used in Abaqus here?
o The energy Gf needs be scaled with the element size to guarantee physically meaningful energy dissipiation. Was this done here?
o Equation 2 mentions equivalent plastic displacements. Is a coupled plasticity-damage law used? This needs more explanation!
- Line 183 needs a better reference to Figure 3. What elongation corresponds to the used scaling factor f?
- Section 4.1 states that ‘a qualitative comparison of chip formation behavior against the experiment is conducted’. How is this comparison evaluated? What measure was used to compare simulation and experiment?
- As mentioned earlier, the scaling of the simulated forces mentioned in line 280 seems not to be reasonable.
- Why does Fig. 7 not show the simulated forces before 0.005 s?
Overall, the paper is well written and deserves publication after clarification of the previously mentioned points. Fig 5 and 6 show a nice comparison of the cutting response between simulation and experiments. It is worth mentioning that the ECZ-FEM framework used here is NOT new as mentioned in the abstract. Many researchers have uses fully discrete FE models consisting of CZ elements.
Author Response
The manuscript presents a discrete-continuum finite element methodology to simulate machining of high-density polyurethane (PU) foams. Thereby, the discrete cohesive elements are scaled to control material ductility and chip behavior.
The paper is well written with clear description of the FE model. The key contribution of the manuscript is the introduction of a scaling parameter that allows for simulating the machining process realistically. In general, the procedure is fine, but the reviewer has numerous questions with regards to this scaling factor:
1. It is stated in line 151 that the corrected separation f\delta is shown in Figure 2. The reviewer cannot see any of this correction. Please add this to the figure.
Response: We agree that the original figure was unclear. A new Figure 2 has been added to show the scaled displacement. Since the maximum displacement of the CZ element is scaled, the fracture energy is also scaled because the traction tc cannot exceed the material’s strength.
2. In line 147 it is stated that ‘the deflection [of a CZ element] can become larger than the element size when a fine mesh is used’. What is meant by element size? Zero-thickness CZ elements are used here. The reviewer does not see any problem with the separation becoming large in CZ elements. This motivation of using a scaling factor needs to be better explained and illustrated. In the best case, the authors come up with a simple FE model where this problem is shown.
Response: To clarify the statement, we have added a new figure (Figure 3) in the revised manuscript to show a simple scenario. Since the CZ elements are embedded in the regular elements, they can deform (up to delta c) under extreme cases. Therefore, it does not make sense if delta c is in the same order of magnitude as the surrounding element size (d) because that increases the material ductility. For this reason, delta c must be scaled to control the material brittleness as explained in Line 150 to Line 157 in the revised manuscript.
3. In line 151, the authors state that ‘when the deflection is scaled, the fracture energy and the cutting force will be scaled accordingly’. This needs more explanation. As a material property, the fracture energy should remain constant. Therefore, the maximum traction tc should be scaled such that the fracture energy is constant. This is a common technique in using cohesive elements.
Response: The reviewer is correct. Fracture energy is supposed to be a material property that contributes to the cutting force. However, since the maximum deflection of CZ element must be controlled, the fracture energy is inevitably scaled as shown in Fig. 2.
Be noted the maximum traction tc should not be scaled as that can significantly affect the whole material behavior because a small tc allows early failure of the CZ element and more deformation (more ductile). Only scaling the CZ deflection can control the material brittleness. To correct this scaling on the material property, the force needs to be linearly scaled, which has been explained in Line 160 to Line 169.
4. Furthermore, it is not clear why the cutting forces need to be scaled. By maintaining a constant fracture energy, there is no need of scaling the cutting forces.
Response: Since the deflection of CZ element must be scaled to control the brittleness, the fracture energy is scaled, and consequently the corresponding cutting force. For a linear relationship between fracture energy and cutting force under the assumptions listed in Lines 160-169, the cutting force is scaled.
5. In the introduction, a recently published paper on orthogonal cutting of composite materials should be added: X. Yan, J. Reiner, M. Bacca, Y. Altintas and R.Vaziri, ‘A study of energy dissipating mechanisms in orthogonal cutting of UD-CFRP composites’, Composite Structures, Volume 220, 15 July 2019, Pages 460-472.
Response: This citation has been added in [6] in the revised version. It should be mentioned that fiber-matrix interface is a different application as there is no issue of volume expansion as noted in our embedded method.
6. In line 82, it is stated that ‘CZ elements are embedded all around the main elements’. Considering Fig.1, does this mean that you include CZ elements vertically and horizontally? Fig.1 could be updated to account for the implementation used here.
Response: Yes, Figure 1 has been revised accordingly.
7. Has a mesh sensitivity been performed? What is the motivation of using 0.01mm elements?
Response: A new Section 2.5 has been added to address this comment. The 0.01 mm was selected to compromise the computational load and data convergence. A smaller mesh size of 0.005 mm was tested and found a similar output but the computation could hardly continue due to the large amounts of elements and surfaces.
8. With respect to the damage criterion and evolution of the ‘main element’ in Section 2.2:
8.1. Is the built-in Johnson-Cook model used in Abaqus here?
Response: No. J-C model is not used because brittle materials do not undergo plasticity.
8.2. The energy Gf needs be scaled with the element size to guarantee physically meaningful energy dissipiation. Was this done here?
Response: No. The damage of main element is to prevent excessive element distortion. The primary failure is intended to be through the CZ mesh. Energy dissipation between the element and CZ does not physically exist because there is no actual interface.
Also, our understanding is that Gf is a material constant and should not be size dependent. The reviewer may clarify this point for us, thanks.
8.3. Equation 2 mentions equivalent plastic displacements. Is a coupled plasticity-damage law used? This needs more explanation!
Response: We apologize for the confusion. There is no plasticity involved in the computation for brittle materials. However, Equations (1)-(3) must be determined to allow element failure, which correspond to the post-failure region (“Damage Evolution”) of the material defined by energy. To address the confusion, Section 2.2 has been revised to remove the word “plasticity” to avoid confusion:
“where u is the equivalent element displacement after the damage initiation; uf represents the equivalent displacement at failure.”
9. Line 183 needs a better reference to Figure 3. What elongation corresponds to the used scaling factor f?
Response: This has been defined in Line 150 and Figure 3 in the revised version. Also, Line 189 (former Line 183) has been added with an explanation.
10. Section 4.1 states that ‘a qualitative comparison of chip formation behavior against the experiment is conducted’. How is this comparison evaluated? What measure was used to compare simulation and experiment?
Response: As noted in the manuscript in Figure 4, chip behavior changes when the scaling factor reduces to half. The comparison is rather qualitative (not quantitative) based on the chip formation behavior (e.g., continuous chip, equal-sized debris, mix-sized debris, etc.) as mentioned in Section 2.4 and Conclusion. Currently, there is no any quantitative measure proposed because chip distribution and cracks are randomized in reality and are difficult to capture with the current experiment setup.
11. As mentioned earlier, the scaling of the simulated forces mentioned in line 280 seems not to be reasonable.
Response: This has been clarified in the previous comments for the purpose of scaling factor. We hope this concern can be resolved automatically. A factor of 50 seems a lot but this is a result of controlling the chip and material behavior to be physically reasonable. The force is simply scaled linearly so should not be a problem.
12. Why does Fig. 7 not show the simulated forces before 0.005 s?
Response: The force plots have been aligned in the revised Figure 9 (formerly Figure 7).
Overall, the paper is well written and deserves publication after clarification of the previously mentioned points. Fig 5 and 6 show a nice comparison of the cutting response between simulation and experiments. It is worth mentioning that the ECZ-FEM framework used here is NOT new as mentioned in the abstract. Many researchers have uses fully discrete FE models consisting of CZ elements.
Response: We appreciate this comment. We have also revised the abstract to indicate the need for such a model instead of claiming the uniqueness.
Round 2
Reviewer 1 Report
The review questions have been addressed reasonably well by the authors.
