A method of friction heating incremental sheet forming (FHISF) is presented with friction heating of rotating tools and sheet metal, which does not necessitate the use of external heating and saves costs. Utilizing orthogonal experimental design, CATIA reverse engineering methods and finite element model (FEM) analysis, the deformation characteristics of AZ31B magnesium alloy FHISF are investigations, which include formability, geometrical accuracy, thickness distribution, Mises stress and plastic strain at various forming stages. The findings reveal that: In FHISF, increasing the spindle speed is the most significant method to improve the formability, and the maximum forming angle is similar to that of other heating-assisted incremental sheet forming can reach 71°. The bending phenomenon appears early in the forming process, causing the upper corner area to have the poorest precision, and the lower corner area to have visible flaws. The actual part sidewall stabilization region is 11% thinner than the theoretically stable thickness. By the establishment of the FEM, observed and predicted the thickness and stress-strain changing trend of the complete FHISF process satisfactorily.
Research Article
Investigations on Deformation Characteristics of AZ31B Magnesium Alloys during Friction Heating Incremental Sheet Forming
https://doi.org/10.21203/rs.3.rs-1643905/v1
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AZ31B
Friction heating
Deformation characteristics
Incremental sheet forming
Under the background of energy-saving and emission reduction, lightweight has attracted much attention. Magnesium alloys have emerged as among the most promising lightweight structural materials in aerospace, transportation and biomedicine due to their advantages of low density, high specific strength, high specific stiffness and abundant resources [1, 2]. Nevertheless, magnesium alloys present low plasticity at room temperature because of their hexagonal close-packed crystal structure [3]. To overcome these challenges, some scholars have proposed that forming at high temperatures is an effective solution [4]. As a result, it is critical to identify an alternative advanced manufacturing method that can increase the formability and forming accuracy of magnesium alloy sheets by raising the forming temperature at a low cost and with high efficiency.
Incremental sheet forming is a kind of flexible deformation process, which can be used to improve forming limit of metal sheets by using local forming instead of traditional integral forming [5–7]. Scholars often improve the formability of magnesium alloys by raising the forming temperature through auxiliary heating, and then a large number of warm incremental sheet forming technologies emerge [8, 9]. Duflou et al. [10, 11] proposed a laser-assisted single point incremental sheet forming method, and the results of experiments show that this process can reduce forming force and greatly improve forming ability and precision of metal sheets. Zhang et al. [12] heated magnesium alloy sheets globally through an oil bath and tried to use the maximum forming angle as a method to evaluate and optimize the formability. Hino et al. [13] embedded the heater into the tool to form the aluminum-magnesium alloy A5083 and magnesium alloy AZ31. Fan et al. [14–16] proposed an electric heating-assisted incremental sheet forming approach, which uses current to realize local heating to form AZ31B magnesium alloy. Göttmann et al. [17, 18] used a laser beam combined with resistance heating to heat titanium alloy sheet metal and proved that warm incremental forming can greatly improve the formability of sheet metal. Palumbo et al. [19] successfully realized the incremental forming of titanium alloy sheet metal utilizing electric heating combined with tool rotation.
Thermal fluid convection and electric-assisted heating are prone to the problems of excessive energy consumption, uneven heating and unsuitable sheet metal temperature control, while laser-assisted heating equipment is more complex and expensive [20–22]. In contrast, FHISF directly uses friction between tool and sheet metal to generate heat without any additional equipment [23]. Although this method has a very simple device structure and is rather inexpensive, on which experimental research is rarely worldwide.
In this work, a novel and simple experimental device for forming magnesium alloy sheets were explored. To evaluate and optimize the process capability of FHISF, orthogonal experimental design and analysis of variance (ANOVA) were carried out on the factors affecting the forming of the AZ31B sheet. Formability was analyzed with processing parameters including forming temperature, spindle speeds, step depths, and tool diameters. In addition, the dimension accuracy and thickness distribution of parts during different forming periods were digitalized by CATIA reverse engineering and compared with the simulation to verify each other.
Materials and methods
Hot-rolled sheets of AZ31B magnesium alloy with a thickness of 1.6 mm and a square size of 250×250 mm² were employed in this experiment. Table 1 lists its chemical components. The experiment adopted negative forming without dying support and mainly consists of a tool, clamping plate, supporting plate, blank sheet and other parts, as illustrated in Fig. 1. The flowchart of the whole experiment is given in Fig. 2. The truncated cone shown in Fig. 3 was formed on a three-axis CNC milling machine by FHISF. The G code of computer-aided manufacturing was used to regulate the tool path, as depicted in Fig. 4. The 45° wall angle was selected to study the changes of parts in the process of FHISF and the processing parameters are shown in Table 2. The experiment was designed to analyze the influences of forming factors (spindle speed, step depth and tool diameter) on sheet metal formability. The range of each processing parameter was selected based on common knowledge and experiences are given in Table 3.
Table 1 Chemical composition (% in weight) of AZ31B
|
Al |
Si |
Cu |
Mn |
Zn |
Mg |
|
2.38 |
0.05 |
0.01 |
0.22 |
0.19 |
Bal. |
Table 2 Friction heating incremental sheet forming (FHISF) parameters
|
Spindle speed (rpm) |
Step depth (mm) |
Tool diameter (mm) |
Feed rate (mm/min) |
Lubricating oil |
|
2000 |
1.0 |
12 |
1000 |
Lithium grease |
Table 3 Processing parameters with 6 levels
|
Symbol |
Parameters |
Levels 1 |
Levels 2 |
Levels 3 |
Levels 4 |
Levels 5 |
Levels 6 |
|
A |
Spindle speed (rpm) |
500 |
1000 |
1500 |
2000 |
2500 |
3000 |
|
B |
Step depth (mm) |
1.0 |
1.5 |
2.0 |
|
|
|
|
C |
Tool diameter (mm) |
8 |
12 |
16 |
|
|
|
To observe the changes in sheet material throughout the whole forming process, the deformation characteristics at various stages need to be evaluated. Therefore, the FHISF stage is qualitatively divided into early forming stage, intermediate forming stage and final forming stage, and its forming depth is 15mm, 30mm and 60mm, respectively. According to the CATIA reverse engineering, the cross-sectional digital model of the part was recorded at each stage, which can accurately represent the various HFISF stages. Then the part was compared with each CAD model center and the deviation between the part and the CAD model was analyzed. Ideal CAD models and parts at each stage, as shown in Fig. 5.
The FEM of FHISF process
The incremental sheet forming is a complicated elastic-plastic large deformation process, which includes geometric, material and boundary condition nonlinearity [24]. The FEM was established by ABAQUS software, the thinning of sheet metal wall thickness and stress during the forming process were analyzed, and the area most prone to fracture was obtained.
To simulate this process, the uniaxial tensile tests of the samples were carried out by using the universal material testing machine in Fig. 6(a), in which the mechanical parameters of the material at different rolling directions and temperatures were measured. The geometric shape and sizes of the sample and the samples cut along the rolling direction of 0°, 45° and 90° are shown in Fig. 6(b) and Fig. 6(c) respectively. The measured parameters of the samples at 120℃ are given in Table 4, and the true stress-strain curve is shown in Fig. 7. A four-node shell element was used for sheet metal meshing. The tool is regarded as the rigid body and the tool path is allocated to the master node of the tool. The FEM is illustrated in Fig. 8.
Table 4 Mechanical properties of AZ31B at 120℃
|
Direction |
0 |
45 |
90 |
|
Young modulus (Gpa) |
27.3 |
27.2 |
33.5 |
|
Yield stress (Mpa) |
136.23 |
133.41 |
139.07 |
|
Ultimate tensile strength (Mpa) |
210.71 |
241.88 |
268.52 |
|
Elongation(%) |
44.2 |
44.3 |
48.6 |
|
Poisson ratio |
0.378 |
0.369 |
0.382 |
Formability analysis
The forming angle is depicted in Fig. 9 as the angle α between the forming surface and the vertical direction in the process of NC incremental sheet forming. During the deformation process, shearing and stretching of the sheet material can produce thinning and fracture, the thickness change of the deformation region conforms to cosine law [25], as given in Eq. (1). When the forming angle α increases to a certain value that makes the deformation region rupture, then the limit value is called the forming limit angle (αmax), which can be used as an important index to measure the formability of sheet metal [26]. As the αmax increases, the deformation will be larger and the formability will be improved. In this experiment, the αmax was used as the standard of material formability.
The data table 5 recorded by the orthogonal experiment, A (spindle speed), B (step depth), C (tool diameter), αmax and T (forming temperature) were imported into SPSS data analysis software for the ANOVA, which the results are as shown in Table 6. The analyses were carried out with a 95% level of confidence. As a result, the value of P represents the confidence factor. If the value of P is less than 0.05, it is an important factor. The relevance is represented by the value of F. So the larger the value of F, the greater the influence of this factor on the αmax. According to the results, A (spindle speed), B (step depth), C (tool diameter) and their interaction have effects cataloging on the is A > B×C > B > C > A×B > A×C, the most significant factor is spindle speed A, then the step depth and tool diameter interaction B×C, other factors have little influence. It can be seen from the results that the increase of αmax with the enhancement of spindle speed. The formability of magnesium alloy increases sharply at 500rpm~2000rpm but does not change after 2000rpm. Compared with 500rpm, the formability has been greatly improved. Generally speaking, the formability increases with the increase of spindle speed, but the formability is basically unchanged when it reaches a certain speed. However, as the rotational speed increases, the temperature will continue to rise, resulting in ripple marks on the parts' exterior surfaces, making the surface quality very poor, as shown in Fig. 10. In addition, the αmax gradually decreases with the increase of step depth, but the change range is small. With the increase in tool diameter, the αmax only slightly increases, and the forming ability is slightly improved.
By analyzing the effect of processing parameters on forming ability and temperature, it can be concluded that the changing trend of forming ability is almost the same as that of temperature. With the increase of temperature, forming ability will be improved. However, the change of step depth on forming ability and temperature is the opposite. The main reason is that when the step depth increases in this range, the pressure of the sheet metal by the tool head will increase, which will increase the thinning rate, causing the sheet metal to crack, thus reducing the formability. At this point, the influence of pressure on the sheet metal is greater than that of temperature increase. The tool diameter has little influence on the formability. With the increase of tool diameter, the contact area between tool head and sheet the formability. With the increase of tool diameter, the contact area between tool head and sheet metal will be increased, resulting in an increase in temperature, thus improving the forming ability. Moreover, the smaller the diameter of the tool is, the more serious the sheet metal damage will be, and the poorer the formability will be.
Table 5 Experimental plan and results
|
Test no. |
A (mm) |
B (mm) |
A×B |
C (mm) |
A×C |
B×C |
αmax (°) |
T (℃) |
|
1 |
500 |
1.0 |
3 |
12 |
3 |
1 |
29 |
52 |
|
2 |
500 |
2.0 |
1 |
8 |
1 |
2 |
23 |
61 |
|
3 |
500 |
1.5 |
2 |
16 |
2 |
3 |
27 |
60 |
|
4 |
1000 |
1.0 |
1 |
12 |
1 |
1 |
36 |
87 |
|
5 |
1000 |
2.0 |
2 |
8 |
2 |
2 |
41 |
90 |
|
6 |
1000 |
1.5 |
3 |
16 |
3 |
3 |
33 |
110 |
|
7 |
1500 |
1.5 |
2 |
12 |
1 |
1 |
59 |
80 |
|
8 |
1500 |
1.0 |
3 |
8 |
2 |
2 |
47 |
100 |
|
9 |
1500 |
2.0 |
1 |
16 |
3 |
3 |
56 |
112 |
|
10 |
2000 |
2.0 |
2 |
16 |
3 |
1 |
71 |
140 |
|
11 |
2000 |
1.5 |
3 |
12 |
1 |
2 |
62 |
110 |
|
12 |
2000 |
1.0 |
1 |
8 |
2 |
3 |
49 |
95 |
|
13 |
2500 |
2.0 |
3 |
12 |
2 |
1 |
59 |
120 |
|
14 |
2500 |
1.5 |
1 |
8 |
3 |
2 |
51 |
100 |
|
15 |
2500 |
1.0 |
2 |
16 |
1 |
3 |
55 |
120 |
|
16 |
3000 |
1.5 |
1 |
8 |
2 |
1 |
64 |
130 |
|
17 |
3000 |
1.0 |
2 |
16 |
3 |
2 |
65 |
125 |
|
18 |
3000 |
2.0 |
3 |
12 |
1 |
3 |
52 |
135 |
Table 6 ANOVA results of αmax
|
Factor |
Mean average error |
Degree of freedom |
F value |
Sig value |
Significance |
|
A |
560.633 |
5 |
21.425 |
0.045 |
Significant |
|
B |
33.500 |
2 |
1.280 |
0.439 |
|
|
C |
32.000 |
2 |
1.223 |
0.450 |
|
|
A×B |
4.081 |
2 |
0.156 |
0.865 |
|
|
B×C |
80.082 |
2 |
3.061 |
0.246 |
|
|
A×C |
0.333 |
2 |
0.013 |
0.987 |
|
Dimensional accuracy analysis
To intuitively comprehend the deformation characteristics and thickness distribution at each FHISF stage, contour maps of the cross-sectional CAD model and the digital model of the part were extracted from CATIA for comparison, as shown in Fig. 11. Due to the symmetry of the parts, only the half-part outline was discussed, which is "+" when the parts are above the CAD model and "-" at the bottom. The edge areas of the part bent to varying degrees in each period, which was caused by the clamping plate. Due to the lack of backing support, the load applied during the initial forming step caused bending in the sheet. This is mostly determined by the distance between the clamping edge and the tool's contact location. There is no obvious upper and lower corner in the initial forming stage of the sidewall region, where the main occurrence is bending deformation. It was found that there are obvious convex marks in the lower corner at various forming stages, which are left by the tool during the last lap. The tool squeezes the metal, causing it to flow to the side edge and accumulate at the undeformed area, increasing the thickness of this section. The part's bottom is uneven all around, with the center position being higher than the edge position. Because the bottom edge location is subjected to more downward pressure from the tool during the process of local plastic deformation, the bottom center position is always higher than the tool processing position throughout the machining process.
Thickness distribution in FHISF
Comparing simulated thickness results with actual results, as shown in Fig. 12, it could be found that the thickness of the sidewall region is not uniform in the early forming stage. At the intermediate and final forming stages, the thickness of the sidewall region is generally homogeneous at around 0.99mm, which is 11% thinner than the theoretical thickness. This is because friction heating necessitates rotational contact between the tool and the sheet, making it impossible to use 100% of the material, and a part of the materials in the deformation area is extruded to the bulge at the bottom. The massive thickness decrease identified during experimental investigation in the corner region was also found in simulated components. Fig. 13 exhibits the profile thickness distribution of the half part. In the unformed area, the sheet metal thickness did not change around 1.60mm, and the sheet metal thickness near the upper corner area decreased rapidly. In the sidewall area, the thickness of the sheet metal gradually reached a stable state as the tool descended, and was distributed around the theoretical thickness. It was found that the part's sidewall region did not attain a stable thickness at first, but reached the minimum thickness after a specific forming depth which was found during experimental investigation to be about 16mm (Fig. 14). The results show that the designed simulation model can accurately predict the thinning trend and can be used as a further reference for effective stress and strain.
Stress and strain distribution in FHISF
The stress and strain levels throughout the FHISF stages are extremely difficult to determine owing to the nature and complexity of the process. Therefore, Mises stresses and plastic strain were analyzed by the FEM. Fig. 15 illustrates the stress-strain evolution of HFISF stages. As the forming stage develops, the stress and strain values increase. The maximum stress value for the early forming stage is 165.1 MPa, 171.1 MPa for the intermediate stage, and up to 174.2 MPa at the final forming stage. The part's maximum strain is 0.437 in the early forming stage, whereas the plastic strain increases but does not vary significantly in the intermediate and final forming stages, both around 0.471. The plastic strain increased from the early to the intermediate stage, but it did not much change from the intermediate to the final stage. The plastic strain value reached its maximum value when forming the sidewall area, and the thickness of the sidewall area was almost unchanged. So the trend of stress and strain in the part is very similar during each forming stage.
In this study, deformation characteristics analysis of AZ31B magnesium alloy sheets has been performed. Several important findings can be stated:
-
In FHISF, the maximum forming angle can reach 71°. Increasing the spindle speed is the most significant method to improve the formability, but if it continues to increase after 2000rpm, the formability will not improve and massive ripples will appear.
-
Due to the limitation of experimental conditions, there will be a geometrical deviation between the precision of forming parts and the CAD model. The bending phenomenon occurs early in the forming stage, resulting in the lowest accuracy of the upper corner and there are obvious convex marks in the lower corner.
-
Compared with the theoretical stable thickness, the sidewall stability region is thinned by 11%. The part's sidewall region did not attain a stable thickness at first but reached the minimum thickness when the forming depth is about 16mm. As a result, the fracture is most likely to occur when the forming depth is between 10 and 20mm, which has guiding significance for follow-up research.
Acknowledgements
Not applicable.
Authors' contributions
LZ was in charge of the whole trial; PL and JW wrote the manuscript; XJ conducted FEM analysis; SY and QY assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Funding
Supported by National Natural Science Foundation of China (Grant No. 51465038).
Availability of Date and Materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Competing Interests
The authors declare that they have no conflict of interest.
Author Details
1 School of Advanced Manufacturing, Nanchang University, Nanchang 330031, China.
2 Key Laboratory of Lightweight and High Strength Structural Materials of Jiangxi Province, Nanchang 330031, China.
* Corresponding author: Liuru Zhou (e-mail address: zlrhust @163.com)
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