# Modeling and Experimental Analysis of Shear-Slitting of AA6111-T4 Aluminum Alloy Sheet

^{1}

^{2}

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## Abstract

**:**

_{c}= 6%t. A strong influence was observed of the horizontal clearance value at high slitting speeds on burr unshapeliness. The most favorable conditions were obtained for v = 32 m/min, h

_{c}= 0.062 mm, and rake angle of upper knife for α = 30°. For this configuration, a smooth sheared edge with minimal burr height was obtained.

## 1. Introduction

## 2. Experiment Setup and Results

_{c}, defined as the distance between the upper and the lower knife cutting edges, is set by a clearance regulator with a scale. The slitting velocity is set by a knob with a scale. The scales are very accurate, which enables the precise setting of slitting parameters.

_{2}), the horizontal clearance (h

_{c}), and the rake angle of the upper knife (α), are usually controllable on industrial lines. Experiments were conducted based on the classical experimental design method, with the use of five-level rotatable plan of experiment, that is presented in Table 4. The research was planned with the use of the E-Planner program (Sławomir Kukiełka, Leon Kukiełka, Koszalin University of Technology, Poland). The required number of experimental points amounted to 20. The tests were carried out for three replications for each plan level.

#### 2.1. Mechanism of Slit Edges Generation

_{c}= 0.15 mm reduces the material flow area and deformation-affected zone with material fibers’ shifting, but speeds up the material cracking phase (Figure 4a). The cut surface is more perpendicular to the sheet thickness, but is characterized by a sharp burr (Figure 4b). The bending moment and rollover area in this case are reduced. A reduction in the clearance to the minimum value h

_{c}= 0.03 mm resulted in a significant reduction in the deformation-affected zone and material fibers’ shifting (Figure 4c). Cracking, in this case, starts both from the upper and lower knife cutting edges, and runs in a straight line, perpendicular to the thickness of the sheet. In this case, rollover and burr are minimal (Figure 4d).

#### 2.2. Quality of Sheared Edge

_{c}= 0.03–0.05 mm). The simultaneous increase in the slitting speed and rake angle value resulted in reduction in the deformed zone (Figure 5b). However, when using high slitting speeds (v > 24 m/min) and clearances (h

_{c}> 0.12 mm), it is unfavorable to use rake angle values from the range of α = 5°–20°. Selecting the rake angle values from the range of α = 30°–40°, results in less sensitivity of the deformation-affected zone’s width than clearance and slitting speed values (Figure 5c,d). However, for all rake angle values, an increase in clearance results in an increase in the width of the damage zone.

_{c}= 0.03 mm to h

_{c}= 0.09 mm results in an increase in the burr height. The highest burrs are reached when the slitting speed is set to v = 17 m/min, and clearance is set to h

_{c}= 6%t. It is necessary to use deburring operation, because in this case the height of the burrs is non-uniform along the line of shearing (Figure 7i). According to the results presented in [10,12,44], burrs can become separated from the cut part and damages of edges visible in the form of transverse cracks will be formed. It could be a result of a significant gradient of clearances between tools along line of shearing. The formation of local burrs is an important problem occurring on the production lines, because they can tear off from the sheared surfaces increasing perpendicularity deviations. Because the burr formation is associated with the final rapture, much depends on the plasticity of the material. Higher ductility would lead to delayed rapture and formation of a burr higher than the one formed in a less ductile material [45]. So, it is very important to choose a proper value of a horizontal clearance and a rake angle of cutting tool. In guillotining processes, the use of small rake angle values and clearances for high ductility materials decreases the burr height and its unshapeliness, but increases the cutting forces.

_{c}= 6%t, the burnished zone is highly reduced (Figure 8b) and the velocity effect is reinforced. A high burnished width (s = 66%t) is obtained when clearances of h

_{c}= 2%t and h

_{c}= 10%t are used. In these two cases, the effect of velocity on the burnished width is reduced. High velocity results in a course of plastic flow phase during shear slitting. This phase is less steady over a high range of velocities (v = 27–32 m/min) and characteristic peaks with the transition to sliding fracture can be observed.

_{c}= 0.03–0.05 mm). For small cutting velocities, is possible to reduce the fractured zone with a clearance of c = 10%t.

## 3. FE and SPH Modeling

**r**vector with the central difference method (DEM), and by using the following approximations:

_{1}= 200 mm/s) is applied so as to obtain the separation of the material in the cross-section. As a result of knives and roll rotations, the sheet moves along Z axis with the constant velocity v

_{2}. Length of the shearing line amounts to l = 50 mm, rake angle value is set to α = 7°. To reduce the calculation time, knives are considered as rigid bodies meshed with an 8-node Solid164 element type. After exploratory analyses, a decision was made to generate the mapped mesh with various sheet densities in tools-material contact zones. In case of calculations using the SPH method, it was necessary to create two material domains, in which the particles were tied to the FEM portion of domain using tied types of the contact (Figure 9c).

_{Y}is the yield stress [47], T is the workpiece temperature, T

_{m}is the material melting temperature, T

_{r}is the room temperature. For AA6111-T4 steel: A = 324.1 MPa, B = 113.8 MPa, C = 0.002, m = 1.34, n = 0.42 [62]. Constant coefficients of static friction μ

_{s}= 0.08 and kinetic friction μ

_{d}= 0.009, were accepted and described using Coulomb’s friction model.

## 4. Numerical Results

## 5. Optimization

_{c}є [0.03–0.15] mm, and slitting speed v є [3–32] m/min. Limitations are the following: burr height h

_{b}< 0.1 mm, width of fracture zone fr < 0.24 mm (Figure 16). The task defined in this way makes it possible to reach high workpiece’s technological quality, low costs of tool production, and to obtain high process efficiency. Graphic optimization was used to solve this task [65]. It allows for the easily determination of the area of acceptable solutions and optimal parameters of decision variables.

_{c}= 0.062 mm.

## 6. Conclusions

- The use of two FEM and SPH numerical methods, enabled gaining new knowledge about shear-slitting processes, which can help in choosing the best and the most accurate numerical method to simulate similar processes, especially those ones in which strong deformation, structure fracture and separation occurs.
- The conducted experimental research using vision systems allowed for observing the physical phenomena occurring within very small areas and running at high speeds. Thanks to that, it was possible to learn them more accurately, as well as to use the recorded images to validate simulation models in individual cutting phases. So far, the validation of simulation models has involved comparative analysis of cutting forces and the quality of the cut edge with the experiment offline (after the process). The presented method enables the analysis of accuracy and correctness of simulation models, in unstable phases inclusive, e.g., during separation, online.
- The most important and controllable parameters affecting the quality of the sheared edge include the slitting speed and the horizontal clearance. The results indicate a significant effect of the clearance on the deformation zone’s width. Along with the increase in the clearance value, the deformation zone increased. Conditions affecting burr formation on the edge were also specified. The highest burrs were obtained when the slitting speed was set to v = 17 m/min and the clearance was set to h
_{c}= 6%t. - The use of graphic optimization has enabled the determination of process conditions that allow for obtaining the highest quality of the cut edge for the given criteria. The most favorable conditions were obtained for v = 32 m/min, h
_{c}= 0.062 mm and α = 30°. The proposed methodology can be used to analyze various materials of different thicknesses formed by mechanical cutting.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Shear-slitting process registered at the sheet cross section (h

_{c}= 0.15 mm, α = 7°): (

**a**) material plastic flow phase, (

**b**) plastic flow with the beginning of the cracking phase, (

**c**) burr formation in cracking phase, (

**d**) final separation.

**Figure 4.**Shear-slitting process registered at the sheet cross section (α = 40°): (

**a**) material plastic flow phase (h

_{c}= 0.15 mm), (

**b**) cracking phase (h

_{c}= 0.15 mm), (

**c**) plastic flow with cracking phase (h

_{c}= 0.03 mm), (

**d**) final separation (h

_{c}= 0.03 mm).

**Figure 5.**Graphs of the deformation-affected zone’s width for: (

**a**) α = 30°, (

**b**) h

_{c}= 0.1 mm, (

**c**) v = 20 m/min, (

**d**) h

_{c}= 0.03 mm.

**Figure 6.**Typical sheared edge contour: (

**a**) cross-sectional scheme, (

**b**) the one obtained experimentally (front view).

**Figure 7.**Characteristic features of the obtained sheared edges: (

**a**) v = 7 m/min, h

_{c}= 0.05 mm, (

**b**) v = 27 m/min, h

_{c}= 0.05 mm, (

**c**) v = 7 m/min, h

_{c}= 0.13 mm, (

**d**) v = 27 m/min, h

_{c}= 0.13 mm, (

**e**) v = 3 m/min, h

_{c}= 0.09 mm, (

**f**) v = 32 m/min, h

_{c}= 0.09 mm, (

**g**) v = 17 m/min, h

_{c}= 0.03 mm, (

**h**) v = 17 m/min, h

_{c}= 0.15 mm, (

**i**) v = 17 m/min, h

_{c}= 0.09 mm.

**Figure 8.**Influence of the selected process parameters on the: (

**a**) burr, (

**b**) burnish, (

**c**) rollover, and (

**d**) fracture zones.

**Figure 9.**FEM and FEM + SPH simulation models of the shear-slitting process: (

**a**) isometric view, (

**b**) front view, (

**c**) discretization of sheets.

**Figure 11.**Characteristic features of the sheared edges obtained experimentally and numerically: (

**a**) h

_{c}= 0.06 mm, (

**b**) h

_{c}= 0.09 mm.

**Figure 15.**A comparison of the resultant force of the experiment and the simulation: (

**a**) cutting force at steady state, (

**b**) maximum force.

Young’s Modulus, E | 70 GPa |

Elongation, A_{100} | 28% |

Shear Modulus, G | 26–26.5 GPa |

Poisson’s Ratio, ν | 0.33 |

Tensile Strength, R_{m} | 265–285 MPa |

Fracture Toughness, K_{IC} | 22–35 MPa·√m |

Yield Strength Rp0.2, Rp_{0.2} | 150–170 MPa |

Coefficient of Thermal Expansion, α | 1.6E-5–2.4E-5 1/K |

Specific Heat Capacity, c_{p} | 887–963 J/(kg·K) |

Thermal Conductivity, λ | 170–220 W/(m·K) |

Si | Cu | Zn | Cr | Mn | Ti | Mg | Fe |
---|---|---|---|---|---|---|---|

0.6–1.1 | 0.5–0.9 | 0.15 | 0.1 | 0.1–0.45 | 0.1 | 0.5–1 | 0.4 |

Horizontal Clearance, h_{c} | 0.03–0.15 mm |

Vertical Clearance, c_{v} | 0.15 mm |

Slitting Speed, v_{2} | 3–32 m/min |

Rake Angle of the Upper Knife, α | 5°–40° |

Upper Knife, Polyurethane Roll Radius, r_{1}, r_{2} | 15 mm |

Lower Knife Radius, r_{3} | 20 mm |

Plan Level | Coded Variables | Real Variables | ||||
---|---|---|---|---|---|---|

${\stackrel{\u2323}{\overline{\mathit{x}}}}_{1}$ | ${\stackrel{\u2323}{\overline{\mathit{x}}}}_{2}$ | ${\stackrel{\u2323}{\overline{\mathit{x}}}}_{3}$ | h_{c} [mm] | v_{2} [m/min] | α [°] | |

1 | − | − | − | 0.054 | 8.87 | 12.09 |

2 | + | − | − | 0.125 | 8.87 | 12.09 |

3 | − | + | − | 0.054 | 26.12 | 12.09 |

4 | + | + | − | 0.125 | 26.12 | 12.09 |

5 | − | − | + | 0.054 | 8.87 | 32.9 |

6 | + | − | + | 0.125 | 8.87 | 32.9 |

7 | − | + | + | 0.054 | 26.12 | 32.9 |

8 | + | + | + | 0.125 | 26.12 | 32.9 |

9 | +α = 1.682 | 0 | 0 | 0.15 | 17.5 | 22.5 |

10 | −α = −1.682 | 0 | 0 | 0.03 | 17.5 | 22.5 |

11 | 0 | +α = 1.682 | 0 | 0.09 | 32 | 22.5 |

12 | 0 | −α = −1.682 | 0 | 0.09 | 3 | 22.5 |

13 | 0 | 0 | +α = 1.682 | 0.09 | 17.5 | 40 |

14 | 0 | 0 | −α = −1.682 | 0.09 | 17.5 | 5 |

15 | 0 | 0 | 0 | 0.09 | 17.5 | 22.5 |

16 | 0 | 0 | 0 | 0.09 | 17.5 | 22.5 |

17 | 0 | 0 | 0 | 0.09 | 17.5 | 22.5 |

18 | 0 | 0 | 0 | 0.09 | 17.5 | 22.5 |

19 | 0 | 0 | 0 | 0.09 | 17.5 | 22.5 |

20 | 0 | 0 | 0 | 0.09 | 17.5 | 22.5 |

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Bohdal, Ł.; Kukiełka, L.; Legutko, S.; Patyk, R.; Radchenko, A.M. Modeling and Experimental Analysis of Shear-Slitting of AA6111-T4 Aluminum Alloy Sheet. *Materials* **2020**, *13*, 3175.
https://doi.org/10.3390/ma13143175

**AMA Style**

Bohdal Ł, Kukiełka L, Legutko S, Patyk R, Radchenko AM. Modeling and Experimental Analysis of Shear-Slitting of AA6111-T4 Aluminum Alloy Sheet. *Materials*. 2020; 13(14):3175.
https://doi.org/10.3390/ma13143175

**Chicago/Turabian Style**

Bohdal, Łukasz, Leon Kukiełka, Stanisław Legutko, Radosław Patyk, and Andrii M. Radchenko. 2020. "Modeling and Experimental Analysis of Shear-Slitting of AA6111-T4 Aluminum Alloy Sheet" *Materials* 13, no. 14: 3175.
https://doi.org/10.3390/ma13143175