Analysis of Deformation Characteristics of AZ31B Friction Heating Incremental Forming

A friction heating incremental forming (FHIF) is proposed, which does not require external heating. By means of orthogonal experimental, nite element analysis and CATIA reverse engineering methods, the forming characteristics of magnesium alloy AZ31B FHIF are studied, such as forming limit angle, dimensional accuracy, thickness distribution, equivalent stress and equivalent strain at different forming stages. The results show that: For the FHIF, the forming limit angle can be up to 76°, and the most obvious way to increase the forming limit angle is to increase the spindle speed. In the FHIF, due to the limitations of the experimental conditions, it will be different from the ideal model. The bending phenomenon rst occurs in the early stage of forming, which makes the upper corner part the worst accuracy, and the lower corner part obvious defects. Compared with the theoretically stable thickness, the actual part sidewall is thinned by 11%. The simulation successfully predicts and observes the thickness change and stress-strain change trend of the entire FHIF.


Introduction
Magnesium alloys are di cult to process at room temperature and generally require heating [1,2]. To overcome these challenges, a few forming processes have been conducted to address those issues. An effective solution is to employ a forming process at high temperatures [3,4].The friction heating incremental forming (FHIF) is used to improve the plasticity of the magnesium alloy and save the cost of heating equipment. In the past ten years, scholars have continuously explored the research on the incremental forming process, but there are still many problems in the processing e ciency, surface quality, and geometric accuracy of parts. The incremental forming process has a long history and has great advantages over traditional processes [5,6].
Most scholars are studying the incremental forming process of Al alloys. Shrivastava P et al. to observe the effect of strain levels, three different types of SPIF parts were formed that were subjected to early, intermediate and nal forming stages. Further, microstructural and textural changes in the formed parts were identi ed for plane strain and biaxial strain deformation modes [7]. Kim T J et al. research ndings that the uniformity of thickness throughout the deformed region is one of the key factors to improve the formability, and the double-pass forming method is found to be very effective [8]. Some scholars studied the in uence of forming parameters on forming performance, the research work allowed identifying a critical threshold for the ratio between the thickness of the sheet and the radius of the tool that distinguishes between fracture with and without previous necking, for large tool radius, the stabilizing effect of dynamic bending under tension seems to improve forming ability, and the less the tool radius, the more severe the plate damage and the lower the formability, the size of the surface roughness can be changed by vertical step size and the forming angle [9][10][11]. Some scholars use the cruciform biaxial tension test and a speci c simulation analysis model to predict the fracture strain, and observed that bending is the main deformation mechanism that affects the behavior of materials in SPIF [12][13][14].
Over the past decades, warm incremental sheet forming has received attention for Mg alloy sheet forming [15,16]. The forming process of AZ31B magnesium alloy was used the method of hot air heating [17], electropulse-assisted [18], heating furnace [19], electromagnetic [20] and oil bath heating [21]. Different heat-assisted methods have their strengths and weaknesses. The common weakness of the above method is that it requires expensive heating equipment. And the HFIF does not have this shortcoming, which does not require external heating, and according to current experimental results, the unique characterization of ISF process is its increased forming limit compared with conventional sheet forming processes [22][23][24].
To the best of our knowledge, the proposed approach has an extremely simple apparatus structure and is quite economical, yet experimental investigations on the approach are particularly rare all over the world.
Therefore, one of the main objectives of the present paper is to explore an innovative and simple experimental setup to form Mg alloy sheets or other hard-to-form metallic materials. But there is not much research on the HFIF, in this work, by means of orthogonal experimental to study the forming limit angle of AZ31B FHIF, and by means of CATIA reverse engineering to study the dimensional accuracy and thickness distribution of parts in different forming stages, then compared with the simulation results to con rm the correctness of the simulation. The FHIF improve and supplement the incremental forming process of magnesium alloy, it is of great signi cance to the incremental forming technology of magnesium alloy.

Experimental
The material used in the experiment is AZ31B magnesium alloy sheet. The initial thickness of sheet is 1.6 mm. Square blanks of 250×250 mm2 were cut from the sheets. The chemical composition is given in Table 1. The experiment adopts negative forming and does not require mold support. It is mainly composed of forming tool, sheet, clamping plate, blank holder, as shown in Fig. 1. And Fig. 2 is shown the CAD model of the cone box to be formed on the three-axis CNC milling machine (HNC-21/22M) by FHIF. The forming tool was controlled by G code generated by Computer Aided Manufacturing, and the tool path is shown in Fig. 3.
In order to study the parts in FHIF, the wall angle of 45° was selected, and the process parameters values are given in Table 2.

Simulation Modeling
The progressive forming process is a complex elastoplastic large deformation process such as geometric nonlinearity, material nonlinearity and boundary condition nonlinearity. AQABUS software is used to establish the nite element model of AZ31B magnesium alloy FHIF, and the thinning and stress of the sheet metal wall during the forming process is analyzed.
In order to simulate this process, the material model parameters were evaluated through uniaxial tensile test of the dog bone samples. The universal material testing machine of Fig. 5a was used to measure the mechanical parameters of the material under different rolling directions. Fig. 5b and Fig. 5c show the dog bone samples size and the sample cut along the rolling direction of the sheet 0°, 45°, 90°. The model parameters with the temperature of 100°C are shown in Table 3, and the true stress-strain curves are shown in Fig. 6. Finite element analysis of FHIF process has been performed using AQABUS software. Mid surfaces of both the geometries were extracted and meshed in HyperMesh environment. For the meshing of the sheet, the four node shell element was adopted, and the thickness of the shell element was considered same as the initial thickness of the sheet (1.6mm). In FHIF, because the sheet remains xed during operation the nodes present on the outer periphery of sheet were constrained in both translational and rotational motion in "X", "Y", and "Z" directions. The tool was constrained with rotation in the "X" and "Y" directions, and the rotation was allowed in the Z direction. Input the magnesium alloy material parameters measured above into the sheet node, the tool is considered as the rigid body and the tool path is assigned to the master node of the tool. The contact modeling of forming tool and sheet is shown in Fig. 7.
3 Results And Analysis 3.1 Forming limit analysis "Orthogonal experiment design" is a scienti c method of analyzing multi-factor experiments, which can greatly reduce the number of experiments and will not reduce the feasibility of experiments. The orthogonal experiment design was used to study the in uence of forming parameters on the forming ability of the sheet metal. The three factors are the rotational speed, vertical step size, tool diameter, the level of the orthogonal experiment factors as shown in Table 4, and the angle and temperature when the sheet material was broken were recorded. The table of orthogonal experiment results was got, then the experimental data was analyzed, the impact of each process parameter on the forming performance was observed, and the relatively good set of process parameters for later test analysis was got. Tool diameter mm C 8 12 16 In the HFIF, the angle α between the forming sheet and the vertical direction was the forming angle, as shown in Fig. 8. The thickness of the deformation zone conforms to the law of cosine t=t 0 × cosα. From this rule, it can be seen that the larger the forming angle, the smaller the thickness t of the deformation zone, the higher the thinning rate, and the easier it is to break. When α reaches a certain value, the deformation zone was cracked. At this time, the angle α can be used as a judgment value of whether the sheet metal was broken. The larger the forming limit angle, the greater the amount of deformation that the sheet can produce, and the higher the forming performance. In the experiment, the forming limit angle was used as the standard for the forming performance of the material [25][26][27].
After orthogonal experiment, the forming limit angle α max (°) and temperature T(°C) were obtained (Table   5).  17  3000  1  2  16  3  2  65  125   18  3000  2  3  12  1  3  52  135   Table 5 was imported into SPSS software for orthogonal test variance analysis. The results are shown in Table 6. According to the data analysis table of the orthogonal test results, the effects of the three main factors and their interaction on the forming limit angle are A>B×C>B>C>A×B>A×C. the rotational speed has the most signi cant effect on the forming angle, and other factors have less effect. It can be seen from Fig. 9 that the forming limit angle is gradually increased sharply from 500prm to 2000prm with the spindle speed is increased, but after 2000prm, the forming limit angle is basically unchanged, the forming ability of magnesium alloy has been greatly improved compared with 500prm. Generally speaking, the forming ability is increased with the rotational speed is increased. After rotational speed is reached a certain speed, the forming ability is basically unchanged. The forming limit angle gradually is decreased with the vertical step size is increased, but the change range is small. The forming limit angle is also increased only slightly with the tool diameter is increased, with a change of about 5°, the forming ability is basically unchanged. According to the optimal parameters, rotational speed is 2000prm, vertical step size is 1mm, and the tool diameter is 16mm, the forming limit angle can be up to 76°.
It can be seen from the in uence of each process parameter on the temperature at the forming limit angle that the rotational speed, vertical step size, and the tool diameter is increased will increase its temperature. The most important factor is the rotational speed. As the speed is increased, the temperature is doubled, and the trend of temperature increase is roughly the same as the trend of forming ability. The vertical step size and tool diameter have little effect on the temperature, and the change is about 10°C.
The in uence of various process parameters on the forming ability and temperature is analyzed, and the conclusion is that the forming ability and temperature change trend is basically the same as the temperature is increased, but the vertical step size is different, as the vertical step size is increased, the forming capacity gradually decreases, but the temperature is increased. The main reason is that the vertical step size is increased within this range, the pressure of the sheet is increased, causing the sheet is broken, and the forming ability is reduced. At this time, the in uence of pressure on the plate is greater than the in uence of temperature increase on the sheet forming capacity.
The rotational speed is the biggest factor affecting the forming limit angle. When the speed is increased above 2000prm, the forming ability is not changed basically. When the speed is increased, the temperature will increase, reducing the service time of the forming tool. In the experiment, it was also found that when the temperature is increased, the outer surface of the parts will have "ripple marks", which makes the surface quality poor, as shown in Fig. 10. 2000prm is the best choice for other deformation characteristics experiments.
Vertical step size is an important factor that affects forming e ciency. As the vertical step size is increased, the processing time is reduced and the production e ciency is improved, but at the same time the surface roughness will be increased. The vertical step size is small, which is helpful to reduce the surface roughness of the parts, but the processing time will be increased.
The tool diameter has little effect on the forming ability. The tool diameter is increased will increase the contact area between the forming tool and the sheet, the temperature will be increased, and the forming ability will be increased. The lower tool diameter will cause more serious damage to the plate, thus forming capacity is reduced. On the other hand, the tool diameter is too large and the corners of the formed parts are not easy to form, therefore, the choice of forming tool diameter depends on the complexity of the forming part.

Deformation and geometrical accuracy in FHIF
In order to better understand the deformation characteristics and geometrical accuracy of the early, intermediate and nal forming stages, the ideal model and the contour drawing of the actual part cross section were extracted from CATIA for comparison, as shown in Fig. 11. Due to the symmetry of the part, only the half-part contour is analyzed. When the part is above the CAD model, it is "+", otherwise it is " ".
It can be seen from the comparison of the cross-sectional views of the CAD model and the part that the edge area of the part will be bended to varying degrees in each period, which is caused by the blank holder. This mainly depends on the distance between the clamping edge and the contact position of the forming tool. The bend is particularly obvious in the early stage, and the 45° sidewall area is not obvious, there are no obvious upper and lower corners, this is the shortcoming of no lower mold. Through analysis, it is found that there are defect in the lower corners in each period, which is left during the last round of the forming tool. The forming tool squeezes the metal and ows to the side edge, so that the metal is not deformed piled up, so the thickness of this part will be thicker. And the bottom of the part is not at, and the center position is higher than the edge position, this is because during the local plastic deformation process, the bottom edge position is subjected to more downward pressure on the tool head, so that the center of the bottom is always higher than the position where the forming tool is being processed during the entire process.

Thickness distribution in FHIF
Comparing the simulated thickness results with the actual results, it can be seen from Fig. 12 that the thickness of the sidewall area is not uniform in the early stage of forming, and the uniform thickness is 0.99mm in the intermediate and nal stages of forming, which is 11% thinner than the theoretical thickness of 1.13mm. Friction heating requires rotating contact friction between the tool head and the plate, material loss occurs, and it is impossible to use 100%, from the overall error analysis above, it can be seen that the thickness of the side wall region is partially thinned because part of the side wall material is squeezed into the bottom region. The experiment found that the thinning rate is basically the xed value is 11%, so 89% of the theoretical sidewall thickness is the thickness of the actual FHIF sidewall uniform area.
It is found that the designed simulation model can accurately predict the thinning trend, but because the metal ow in the entire process cannot be accurately simulated, the trend can only be predicted, and the thickness and the true value are somewhat different. In the simulated parts, the thickness of the corners found during the experimental research was rapidly reduced. Due to the symmetry of the parts, the thickness pro le (Fig. 13) only studies half-sections. In the unformed area, the sheet thickness is about 1.6 mm, and the sheet thickness was decreased rapidly in the upper llet area, in the side wall area, as the forming depth was increased, the thickness of the plate gradually was stabilized. The stable thickness is about 1.13mm, which is not much different from the theoretical thickness, which is in accordance with the cosine law of the plate.
The measured thickness distribution along the forming depth in the nal forming is as shown in Fig.14, it can be seen that the side wall area of the part does not reach a stable thickness at the beginning, but the thickness reaches a minimum after a certain forming depth. Through experiments, it is found that the forming thickness reaches a stable thickness when the forming depth is about 15mm, and the temperature also reaches a stable value, so in the forming process, special attention should be paid to forming depth 0-15mm, which is the easiest to break.

Strain and stress distribution in FHIF
Due to the nature and complexity of the process, it is impossible to obtain the stress state in the FHIF process. Therefore, the equivalent stress was evaluated by the nite element method. The stress evolution at each forming stage of the forming process is shown in Fig. 15. It can be observed that the maximum stress value was increased as the forming stage was increased. For the early forming stage, the value is 165.1MPa, 171.1MPa in the intermediate stage, and 174.2MPa in the nal forming stage. The maximum strain of the part in the early forming stage is 0.437, while the plastic strain of the part in the intermediate forming stage and the nal forming stage has increased but has not changed much, both are around 0.471. The strain measured in the side wall area is basically xed by grid experiment.
The plastic strain value increases from the early stage to the middle stage of forming, but the plastic deformation does not change much from the middle stage to the nal stage of forming, because the sidewall region at this stage is the maximum equivalent strain value, and the thickness of the sidewall region basically does not occur variety. The amount of strain changes from the beginning to the early stage is large, and then basically unchanged. Corresponding to the existence of a depth in the above experiment, after this depth the sheet will be basically not break.

Conclusions
(1) For the FHIF of frictional heat, the forming limit angle can be up to 76°. The most obvious way to increase the forming limit angle is to increase the rotational speed, but after increasing to 2000prm, the forming capacity does not increase much and serious defects will occur. The amount is an important factor that affects the forming e ciency. The tool diameter determines the size of the corner of the formed part.
(2) In the FHIF process, due to the limitations of the experimental conditions, it will be different from the ideal model. The bending phenomenon rst occurs in the early stage of forming, which makes the upper corner part have the worst accuracy, and the lower corner part has obvious convex marks.
(3) The side wall stabilization area of the actual part is 11% thinner than the theoretical stable thickness.
The side wall area of the part does not reach the stable thickness at the beginning, but the thickness is minimized at the forming depth of about 15mm, so the forming process should pay special attention to when the forming depth is 0-15mm, which is the most prone to cracking.       In uence of forming parameters      Simulated stress and plastic strain distribution in FHIF