Predictive assessment of the ultrasonic shearing quality of AZ31B magnesium alloy sheet based on coupled vibration-thermal model

Poor-quality sheet sections and excessive burrs may be resolved by incorporating ultrasonic vibration into the shearing process of hard-to-deform magnesium alloy sheets. It is challenging to simulate the complicated mechanical process of ultrasonic shearing process because it involves material deterioration and fracture, elastic–plastic deformation of the material, and the impacts of ultrasonic indirect sexual contact. Relying on ABAQUS/Explicit finite element simulation software, this paper for the first time proposes a boundary constraint method of constructing a converter to connect displacement reference points and vibration reference points in order to perform numerical simulation of the ultrasonic shearing process of AZ31B magnesium alloy. The team’s ultrasonic vibration system serves as the basis for the simulation’s shearing model. This model utilizes three variables, namely sheet temperature, shear edge clearance, and ultrasonic amplitude, to analyze the weight coefficients and the influence law on the equivalent stress using the orthogonal test in order to further characterize the processing characteristics of ultrasonic shearing. This research demonstrates that numerical simulation is an effective method for examining the influence of process parameters on stress distribution. The results showed that in the ultrasonic shearing of AZ31B magnesium alloy sheet, the process parameter with the greatest influence on the weight coefficient was the sheet temperature, which was 49.8667, followed by the shear edge clearance, which was 31.2667, and the ultrasonic amplitude, which was 17.5333. When the sheet temperature is 150 ℃, the optimization effect is maximal, and the equivalent stress is reduced by 63.9 MPa. Under identical conditions, ultrasonic shearing substantially reduces the equivalent stress on the sheet compared to conventional shearing. During the ultrasonic shearing procedure, the equivalent stress of the sheet appears to be stress superposition and stress fluctuation, resulting in a significant improvement in sheet section quality. As a result, the paper can serve as a quantitative guide for predicting the ultrasonic shearing quality of the AZ31B magnesium alloy sheet.


Introduction
Magnesium alloys have the advantages of high specific strength and stiffness, sound damping, and electromagnetic shielding [1].They are the lightest metal substance used in industrial applications and are a crucial new material in the biomedical, aerospace, electronic communications, and modern vehicle industries [2].In the automotive industry, since magnesium alloy sheet has the advantages of both lightweight and high strength, many companies are eager to select magnesium alloy material for the car's components in order to reduce the CO2 emissions of fuel cars or increase the mileage endurance of new energy vehicles [3].Despite this, the applicability of magnesium sheets is limited in several ways due to the high cost and low quality of the conventionally produced product.Rolling is one of the primary methods for producing magnesium alloy sheets, which can be produced in a variety of widths and thicknesses and is also the most cost-effective method [4].Magnesium ingots and magnesium billets with massive cross-sections are reduced in cross-section and lengthened during the sheet rolling production process.Various magnesium alloy products must undergo shearing during manufacturing to satisfy subsequent processes' requirements and product dimension specifications [5].The section quality of the magnesium alloy sheet sheared on the finishing line directly affects subsequent processing, such as the adhesion of the coating [6].Nevertheless, sawing is currently the most popular method for cutting magnesium alloy sheets to length.Even though the sawing process can produce comparatively highquality sections, compared to the shearing method, it is less productive and wastes more material.Additionally, there are significant safety risks because the sawing process produces combustible and explosive detritus [7].Consequently, developing the shearing procedure for magnesium alloy sheets is a problem that must be resolved.
In recent years, domestic and international academicians have investigated the shearing of magnesium alloy sheets.Scintilla et al. [8] conducted experiments on thin AZ31B sheet fiber laser cutting and determined relevant process parameters.Piemaan Fazily et al. [9] performed microscopic characterization experiments on AZ31B magnesium alloy sheet sections following warm shear investigations and determined that 150 ℃ was the optimal shear temperature for warm shear.Liu Kai et al. [10] proposed an experiment of electrically assisted blanking of AZ31B magnesium alloy sheet using pulsed current and demonstrated that the process could reduce the blanking force and improve the part section quality; however, the magnesium chips generated in the blanking were flammable in the pulsed current field and thus required processing in a protective gas atmosphere.Shokri Saleh M Khalifa et al. [11] studied the cutting resistance of rolled AM60 and AZ61 alloys and analyzed the influence of various punch varieties on the punching force.Although substantial advancements have been made in studying the shearing process of magnesium alloy sheets, more research needs to be conducted on the shearing equipment used in the finishing line of magnesium alloy sheets.Consequently, this paper investigates the shearing process of magnesium alloy sheets and its apparatus advancements to acquire an advanced process capable of producing a satisfactory section.
Ultrasonic machining technology was developed in the 1950s and comprises three primary varieties.The first vibration processing method involves applying ultrasonic frequency vibrations to the tool or workpiece in a particular direction.The second technique is using ultrasonic vibration tools in liquid media with abrasives or dry abrasives to generate abrasive impact, abrasive bombardment, hydraulic impact, and the resultant cavitation for material removal.The third form consists of combining workpieces using ultrasonic vibration [12].Ultrasonic machining technology has the advantage of enhancing both processing quality and efficiency, according to studies [13], and is therefore frequently used on materials that are challenging to process with conventional machining.Ultrasonic machining technology has generated a lot of attention recently in several areas.Tong Wen et al. [14] investigated the effect of ultrasonic vibration on the plastic deformation of AZ31 during the tensile process, and the results indicated that the degree of ultrasonic energy significantly altered the plastic properties of magnesium alloy and its deformation mechanism.Weiching Yeh et al. [15] used DEFORM-2D finite element software to study the effect of ultrasonic vibration on thin plate punching.They analyzed different vibration directions and ultrasonic amplitudes by adopting a segmental superposition ultrasonic vibration approach; the results demonstrated that the edge profile quality of thin plates could be improved by increasing the vibration amplitude.Yanxiong Liu et al. [16] did a two-dimensional simulation of the ultrasonic vibration fine blanking process by putting the vibration on the punch and the blanking motion on the workpiece; the results showed that ultrasonic vibration could reduce the rollover size in fine blanking.Feng Luo et al. [17] performed ultrasound-assisted micro-shear punching simulation and experiments on amorphous alloys using ultrasonic vibration and molten plastic viscous medium and successfully fabricated shapes and products from micro-length to macro-length in 50ms.Xingshuai Xu et al. [18] investigated the influence of machining parameters on surface roughness, surface topography, and chip shape in ultrasonic vibration-assisted turning of Inconel 718 alloy and determined the optimal machining window.Xuesen Zhao et al. [19] demonstrated that highprecision surface micro-structures could be fabricated on 316L stainless steel by using the ultrasonic impact peening (UIP) method using YG6 cemented carbide tool and constructed a non-linear isotropic/kinematic hardening model to complete the simulation and experimental validation of the UIP method.Guangjun Chen et al. [20] investigated the effect of ultrasonic amplitude on the machined quality of 3D needle-punched Cf/SiC composites at different fiber cutting angles in ultrasonic vibration-assisted milling (UVAW), showing that UVAW significantly suppressed some typical defect problems and remarkably improved the machining quality.Juan Liao et al. [21] used ultrasound-assisted warm single-point incremental forming to form AZ31B magnesium alloy sheets, and they found that the surface quality was greatly improved and that ultrasonic vibration significantly affected the dynamic recrystallization and grain regeneration of magnesium alloy.V.K. Patel et al. [22] analyzed the behavior of AZ31B magnesium alloy's microstructure, texture, and lap shear strength during ultrasonic spot welding and investigated the processing parameters and mechanism of deformation.Ultrasonic processing technology has been consistently researched and developed in various disciplines.However, there are few studies on using ultrasonic processing technology to enhance the section quality of magnesium alloy sheets.Most current research focuses on applying ultrasonic vibration technology for precise removal procedures, such as milling and piercing, of materials such as titanium and aluminum alloys [23].Meanwhile, most ultrasonic vibration-assisted machining simulation experiments in related simulation studies involve vibrating the workpiece or altering the material's constitutive model [24].
Therefore, this paper combines ultrasonic machining technology with the shearing process, utilizing the display dynamic analysis module of ABAQUS/Explicit simulation software, by establishing a converter to connect the displacement reference points and vibration reference points for the first time to achieve the ultrasonic vibration loaded on the shear direction of the shear blade, that is, the shear direction has two motion states simultaneously, to achieve the purpose of this paper.The paper selects AZ31B magnesium alloy sheet at medium temperature (greater than room temperature and less than recrystallization temperature) and shear edge clearance of 8-12% for numerical simulation of the ultrasonic shearing process by temperature-displacement coupling based on the results of a previous study [25].The influence weight coefficients of ultrasonic shearing process parameters were determined using the orthogonal test method to analyze the results.The influence laws of sheet temperature, shear edge clearance, and ultrasonic amplitude on the equivalent stress of the ultrasonic shearing process were investigated to provide quantitative guidelines for predicting and evaluating the ultrasonic shearing quality of AZ31B magnesium alloy shearing.

Ultrasonic shearing testing devices
This paper designs an ultrasonic shearing device for magnesium alloy sheets, which includes an ultrasonic generator and an ultrasonic vibration system.The ultrasonic vibration system mainly includes a transducer, a horn, a fixed flange, and an upper shear blade.The working principle of the device is to use an ultrasonic generator to convert 50Hz alternating current into an ultrasonic frequency electrical signal and send the signal to the transducer, which generates ultrasonic frequency mechanical vibration through the PZT-8 piezoelectric ceramic piece in the transducer, and then amplifies the mechanical vibration through the horn.The schematic diagram of the device is shown in Fig. 1.

Establishment of ultrasonic vibration simulation model
ABAQUS/Explicit is used to build a three-dimensional geometric model to conduct the coupled ultrasonic vibration-thermal simulation tests.As the upper and lower shear blades, the pressing plate, and the concave die are deformed to a small extent during the shearing process, and the purpose of this simulation is to observe the stress changes in the sheet during shearing, the shear blades and the matching die are set as rigid bodies, and the sheet is set as an elastoplastic deformation body.The sheet temperature is 100 ℃, and 150 ℃, and 200 ℃, and 250 ℃, respectively, and the shear edge clearance is set initially at 8%, 10%, and 12% of the sheet thickness (0.8mm, 1mm, and 1.2mm).
In the meshing settings, the mesh type for both the shear blade and the sheet is set to C3D8RT mode, which is a hexahedral cell with eight nodes, each with threeway linear displacement and three-way linear temperature degrees of freedom, with a coupling mode of the thermaldisplacement couple.In addition, the simulation selects a first-order reduction integral to generate uniform strain, an enhanced hourglass control mode to simulate thermomechanical processes, a cell deletion mode, and a twist control mode to prevent too much damage to the mesh during processing, while the rest is the default.In the mesh size setting, to ensure calculation accuracy while saving calculation time, double precision control is used to divide the sheet into the dense mesh in the shear zone and the sparse mesh in the non-shear area.Set the mesh size of the mold part to an approximate global size of 10, set the maximum size of the shear part of the sheet to 1, and the minimum size to 0.2.A total of 3190 units are divided on the scale, as shown in Fig. 3.
In the ultrasonic vibration setup, how to load ultrasonic vibration in the upper shear blade in the shear direction is one of the critical points of this simulation.The simulation uses the method of setting reference points and constructing converters to achieve this purpose, as follows: ① Create two reference points, RP1 and RP2, in the upper shear blade, with RP2 located at the upper portion of RP1, whose position relationships are shown in Fig. 3, where RP1 controls the vibration displacement and RP2 controls the shear displacement.② Create a line feature on the reference point RP2, connecting RP1 and RP2.③ Create a converter to constrain the freedom of RP2 in directions other than the shear direction.
In the boundary condition constraints, the displacement and rotation of the upper shear blade in the x and y direction are first constrained.Setting the shear direction as the ultrasonic vibration direction means that the linear and vibrational displacements of the downward movement of the upper shear blade are set simultaneously in the z direction.Three boundary conditions are therefore required in this simulation, namely complete fixation of 6° of freedom on the sheet, lower shear blade and pressing plate, shearing motion in the z direction at reference point RP2, and ultrasonic vibration in the z direction at reference point RP1 (the setting for the counterpressure plate is the same as for the upper shear blade).
Creating the amplitude Amp-1 and selecting the period mode, defining the velocity amplitude "a" of the reference point RP2 in the y direction as the Fourier series: where A 0 is the constant term in the Fourier series, indicat- ing the initial amplitude; A n is the cosine term coefficient; B n is the sine term coefficient; n is a user-defined constant, n = 1, 2, 3...N; 0 is the period frequency; t 0 is the starting time.Equation ( 1) can be simplified as follows: The displacement amplitude curve S in the y direction at the reference point RP2 is as follows: That is, the maximum amplitude of the displacement of the reference point RP2 in the y direction is as follows: According to Eq. ( 4), the ultrasonic amplitude of the upper shear blade is set to 0, 6, and 10μm, respectively, from which the parameters related to the ultrasonic vibration amplitude can be obtained.

Setting sheet and mold material parameters
The material used for the shear sheet in the simulations is the rolled AZ31B magnesium alloy.Some of the specific values of the thermal, physical, and mechanical properties of AZ31B magnesium alloy that change with temperature are shown in Table 1.The cutting tool material used is the Cr12MoV, a high wear resistance and toughness tool steel, the basic physical, and thermal properties of which are shown in Fig. 2.
In shearing process, the yield stress of the sheet is influenced by the strain rate, strain, and temperature softening.The Johnson-Cook isotropic strengthening model, which can better reflect the interrelationship between various stress-strain parameters of the material, is selected as the intrinsic model of the material for this simulation, with the following expressions [9].where A is the initial yield stress related to temperature and strain rate; B is the strain hardening coefficient; C is the strain rate coefficient; n is the hardening strain index; m is the material thermal softening index; is the equivalent plastic strain; ε is the equivalent strain rate; ε * is the dimension- less strain rate, ε * = ε∕ ε0 ; ε0 is the reference strain rate, that is, the strain rate under quasi-static conditions, ε0 = 1 × 10 −3 ; T * = T − T r ∕ T m − T r is the corresponding temperature; T is the current temperature;T r is the transition temperature; and T m is the melting temperature.This paper determined the parameters after repeated validation [10], as shown in Table 2.

Determination of damage evolution and fracture failure model
Failure of the material during shearing of magnesium alloy sheets divides into two parts: damage evolution and fracture failure, which occurs when the stiffness of the unit integration point degrades entirely.

Damage evolution
When a material cracks, the mesh size is sensitive to the local strain, and the material's behavior cannot predict accurately with simple − ( for stress, for strain) curves.At the same time, the energy dissipated is reduced due to the refinement of the local mesh.Therefore, after establishing the damage model, it is necessary to reduce the correlation of the model to the mesh [11].In this simulation, by setting the type of damage evolution to energy mode, the softening to exponential form, and the degradation to maximum [12], and defining the fracture energy G f as a constant value, the expressions are as follows: where u pl is the equivalent plastic displacement of the material during failure; u pl f is the equivalent plastic displacement of the material at complete failure; and L 0 is the characteris- tic length of the unit in the simulation model.
According to the literature [13], the calculation formula follows: (5) where is the Poisson's ratio; E is Young's modulus; and K IC is the fracture toughness of the plane strain, taken as 15.33 MPa √ m to 16.07 MPa √ m [14].Therefore, set the fracture energy G f to 6 mJ/mm 2 in the simulation.

Fracture failure
In ultrasonic shearing, the punching pressure fractures and deforms the sheet.Consequently, the Johnson-Cook damage failure model, primarily used in the field of impact in ABAQUS simulation software, is selected for this simulation.The expressions are as follows: where f is the fracture strain; * is the triaxial stress degree,  * = σ∕ e ; σ is the hydrostatic pressure; e is the Mises equivalent force; D 1 , D 2 , D 3 , D 4 , and D 5 are material con- stants;T * is the gauge temperature parameters, and ; T r is the reference temperature, must be lower than or equal to the lowest temperature in the test temperature range, generally does not involve low-temperature test is selected room temperature; and T m is the melting tempera- ture of the material.This paper determines its parameters after repeated verification [10], as shown in Table 3.

Orthogonal test of the process parameters
for equivalent stress

Comparison of ultrasonic shear and conventional shear stress clouds
In a previous study, our team performed conventional shearing tests on magnesium alloy sheets with 8%, 10%, and 12% shear edge clearance from 100 to 250 ℃, respectively.By observing the height of the bright band in the section and the percentage of the bright band area, the process parameters which can achieve the optimum section quality were derived, and the experimental results are shown in Fig. 4. The results show that the optimum section quality was achieved at a sheet temperature of 150 ℃ when the shear edge clearance is constant and at a shear edge clearance of 10% when the sheet temperature is constant.In this paper, in addition to sheet temperature and shear edge clearance, the ultrasonic amplitude is added to the process parameters as an influencing factor in the ultrasonic shearing simulation test.
Figure 5 shows the equivalent stress maps for the critical stages of the entire process of conventional and ultrasonic shearing (amplitude 10 μm) of magnesium alloy sheets, and Fig. 6 shows a graph of the comparative data, with a sheet temperature of 100 ℃ and a shear edge clearance of 10%.The diagram shows that during the shearing process in both methods, the sheet successively proceeds through the elastic deformation phase, the plastic deformation phase, and the fracture phase.The maximum stress point is located at the sheet near the upper and lower shear blades, resulting in a stress concentration.When the stress reaches the shear strength of materials, a crack develops, followed by a further extension of the crack on the side of the upper and lower shear blades near the cutting towards the center of the sheet, where the two cracks meet and cause the sheet to fracture.In addition, as a result of changing the section's shape and the thickness's thinning, it is observed that the equivalent stress in both conventional and ultrasonic shearing increase and then decrease.The plastic deformation stage and fracture stage of ultrasonic shearing is delayed compared with conventional shearing, so the plasticity of the magnesium alloy sheets is relatively enhanced during ultrasonic shearing.By using finite element simulation, it can be found that the equivalent stress of the sheet changes with the selection of different process parameters.This section selects the three process parameters of sheet temperature, shear edge clearance, and ultrasonic amplitude for the orthogonal simulation tests of ultrasonic shearing.As mentioned above, the weight coefficients of the three parameters are initially determined by extracting the maximum stress and average stress of magnesium alloy sheets in the shearing simulation experiments.Subsequently, the impact of each process parameter on the shearing stress is further examined.

Orthogonal test and analysis of results
The orthogonal test method is a mathematical and statistical method for analyzing and arranging multi-factor tests by designing orthogonal test tables.The advantage of this method is that it can reduce the number of tests while ensuring uniform dispersion of sampling, making the test results reliable and valid [15].In ultrasonic shearing experiments, the main influencing factors on the section of magnesium alloy sheet are sheet temperature, shear edge clearance, and ultrasonic amplitude.Accordingly, this paper adopts the orthogonal test analysis method to investigate the influence weight of each factor in the shearing process.Table 4 shows the relevant factors and levels of the orthogonal test.
Based on the number of factors and levels of the orthogonal tests in Table 4, the L 9 (3 3 ) orthogonal table is chosen to design a 9-group orthogonal test scheme.The maximum processing stresses (in MPa) are derived separately for each group of tests by simulating each of the nine tests in the table.The range for each factor is obtained by calculation and analysis.Table 5 shows the orthogonal table of L9(33) with its test and results, and Fig. 7 shows the stress map in the orthogonal test table.
The range analysis of the orthogonal test enables the results to present visually.The calculations reveal the primary and secondary factors, the optimal level, the optimal combination, and the optimal combination of factors in the test, which can be widely used in research and production practice to screen the optimal production conditions, the best  processes, and the best formulations.In Table 5, the R-value is the range value.The larger the range value is, the greater the influence of the factor on the test index, and vice versa, the smaller the influence.Thus by comparing the size of the range value R, the weighting of the factors on the maximum stress can be known.The range values for the factors in Table 5 are ranked in descending order, and the results are as follows: This result shows that the sheet temperature T in column 3 significantly influences the maximum processing stress, followed by the shear edge clearance c in column 2 and, finally, the ultrasonic amplitude A from column 1.It is clear from the comparison that adding ultrasonic vibration can effectively reduce equivalent stress and increase assistance for section quality improvement.However, the selection of ultrasonic amplitude needs to integrate the simultaneous effects of sheet temperature and shear edge clearance.In order to provide technical guidance for innovative breakthroughs in the shearing process of magnesium alloy plates and maximum optimization of sheet section quality, further research on the mapping relationship between process parameters and ultrasonic shearing equivalent stress has to follow.

Effect of ultrasonic amplitude on equivalent stress
Figure 8 shows the equivalent stress map for different amplitudes at a vibration frequency of 20kHz, with a sheet temperature of 150 ℃ and a shear edge clearance of 10%.The amplitude is 0μm, which is conventional shearing.Figure 9 shows the line graphs of maximum stress and average stress for different amplitudes.As can be seen in Figs. 8 and 9, the maximum equivalent stress in conventional shearing is 371.6MPa, and the average equivalent stress is 328.6MPa.In ultrasonic shearing, the maximum equivalent stress is 377.1MPa,366.4MPa, and 307.7MPa for ultrasonic amplitudes of 3μm, 6μm, and 10μm; the average equivalent stress is 320.5MPa,310.7MPa, and 284.96MPa, respectively.The analysis shows that applying ultrasonic vibration in the conventional shearing can effectively reduce the maximum equivalent stress and the average equivalent stress; moreover, with the increase of ultrasonic amplitude, the equivalent stress is minor.The burr on the shear section is generated by the tensile stress when the cracks overlap.Thus, reducing the equivalent stress can minimize the tensile stress in the shear section, the height of the burr zone in the ultrasonic shear section decreases, and the height of the bright zone increases.Analysis of the reasons: ultrasonic shearing is the traditional process with intermittent contact between the shear blade and the sheet.Between the shear blade and the sheet will generate a large pulse force, and the sheet is relatively more susceptible to fatigue damage under the action of this pulse force, so the addition of ultrasonic vibration assisted in reducing the processing stress.

Effect of sheet temperature on equivalent stress
According to the experimental results in Section III of this paper, the influencing factor of sheet temperature is the largest in the ultrasonic shearing process of magnesium alloy.Therefore, this section performs ultrasonic shear simulation for magnesium alloy sheets at different temperatures with other parameters unchanged.The ultrasonic amplitude is 10μm, and the shear edge clearance is 10%.
Figure 10 shows maps of the maximum equivalent stress for ultrasonic and conventional shearing at different temperatures.The maximum stress at 100 ℃, 150 ℃, 200 ℃, and 250 ℃ for ultrasonic shearing are 352.1MPa,307.7MPa, 299.9MPa, and 267MPa, respectively.Compared to ultrasonic shearing, the maximum stresses in conventional shearing increased by 60.4MPa, 63.9MPa, 29.4MPa, and 24.6MPa for the same process parameters, respectively.
The stresses for ultrasonic shearing and conventional shearing at different temperatures are extracted and processed, plotting the line graphs of maximum and average stresses for ultrasonic shearing and conventional shearing at different temperatures, as shown in Fig. 11.From the figure, it is clear that the average stresses at 100 ℃, 150 ℃, 200 ℃, and 250 ℃ are 362.3MPa,328.6MPa, 296.8MPa, and 264.2MPa, respectively, for conventional shearing, and 309.3MPa, 284.9MPa, 265.1MPa, and 247.3MPa for ultrasonic shearing at 100 ℃, 150 ℃, 200 ℃, and 250 ℃.Compared to ultrasonic shearing, the average stresses for conventional shearing with the same process parameters increased by 52.9MPa, 43.6MPa, 31.7MPa, and 16.8MPa, respectively.In addition, the analysis in Fig. 11 still shows that the optimization of ultrasonic processing is better at 100 to 150 ℃.In contrast, the optimization of ultrasonic vibration gradually decreases as the temperature continues to rise.
Figure 12 shows the trend of equivalent stresses in conventional shearing at different temperatures, and Fig. 13 shows the trend of equivalent stresses in ultrasonic shearing at different temperatures.From the analysis in Fig. 12 and Fig. 13, it can be seen that the stresses in both conventional shearing and ultrasonic shearing gradually decrease as the temperature increases.In Fig. 12, the conventional shear equivalent stress rises to the peak and then decreases, and the curve is smooth and smooth, with the same trend of equivalent stress at different temperatures and different times to peak stress.There are fluctuations in the trend of ultrasonic shearing equivalent stress changes at different temperatures in Fig. 13, which did not keep decreasing after reaching the peak, but instead appeared to fluctuate.At the same time, ultrasonic vibration will make the sheet metal internal particles also produce a corresponding vibration, resulting in the interior metal activity being excited to make the plate temperature rise, which is why a reduction in the dynamic deformation resistance and an oscillating in the flow stress of the magnesium alloy sheet, and finally appearing the phenomenon of stress superposition and stress fluctuations.
The plastic properties of magnesium alloy at room temperature are poor because few slip systems can open at room temperature, and twinning is the primary plastic deformation mechanism.Under warm and hot conditions, the conical slip systems of magnesium alloys are successively activated, and the plasticity of magnesium alloys is greatly improved.Therefore, the plastic deformation mechanism of magnesium alloys after temperature increase is no longer dominated by twinning, but rather the internal particle diffusion is enhanced, generating climbing and dynamic recrystallization [18].At the same time, when ultrasonic vibration shearing is performed on heated magnesium alloy sheets, in addition to the effect of temperature on the metal, the ultrasonic vibration also has a softening effect on the sheet, achieving a common coupling effect of vibration and temperature on the forming of the material.
Figure 14 shows the trend of stress changes in ultrasonic shearing and conventional shearing processing at the same temperature.Rather than a continuous increase in equivalent stress in shearing, a gradual decrease can be observed.This phenomenon indicates that the magnesium alloy shows a corresponding softening characteristic after dynamic recrystallization.The data in the graph shows that at 100 ℃, the peak time for ultrasonic shearing is 0.13 and for conventional shearing is 0.075.At 150 ℃, the peak time for ultrasonic shearing is 0.09 and for conventional shearing is 0.06.At 200 ℃, the peak time for ultrasonic shearing is 0.13 and for conventional shearing is 0.06.At 250 ℃, the peak time for  ultrasonic shearing is 0.13 and for conventional shearing is 0.045.The longer the time required to reach the peak stress, the longer the plastic deformation phase during shear, by extending the plastic deformation phase can be achieved relatively higher material shaping purposes, and in shear processing, sheet sections of good plasticity bright band height can be higher.Analysis shows that due to the influence of ultrasonic energy in ultrasonic shearing, the fluidity of metal shear deformation is enhanced, the plastic deformation phase is prolonged compared with conventional shearing, and the height of the bright band in the sheet section is increased.Ultrasonic shearing with a thermal-vibration coupling effect on the magnesium alloy simultaneously produces a softening and intermittent contact effect, improving the magnesium alloy's shear strength.In the meantime, due to the crosswise change of direction of friction in the shearing deformation, the shear force is reduced, and the stress state near the uneven deformation zone of the metal is improved, effectively improving the forming limit of the material processed by shearing and the surface quality of the section.

Effect of shear edge clearance on equivalent stress
Shearing is a complex process that concentrating on small areas with large deformations.The deformation process involves several academic areas, such as elastic-plastic deformation, fracture damage, and finite element calculations, as well as being susceptible to various factors, among which the choice of shear edge clearance directly affects the morphological quality of the sheet section.If the shear edge clearance is too small, the upper and lower shear blade on the plate form a reduced bending moment, and the machine is easy to overload and produce secondary shear, resulting in a severe hardening process section.If the shear edge clearance is too large, the bending moment formed by the sheet's upper and lower shear blades increases so that cracks cannot overlap.The central part of the sheet is forcibly pulled off, in  In order to obtain the best quality sheets in the section, it is crucial to study the influence of the shear edge clearance on the ultrasonic shearing.The choice of shear edge clearance in shear processing of magnesium alloy sheets differs from that of conventional steel sheets.The shear edge clearance is generally selected from 6 to 8% for most steel sheets.However, the suitable shear edge clearance for magnesium alloy sheets is slightly increased compared to steel sheets, which is still related to the particular structure and properties of magnesium alloy.Magnesium is a dense hexagonal structure, much less plastic than steel plates at the same temperature.Therefore, magnesium alloy requires a slightly larger shear edge clearance to obtain the same high-quality sheet section.In the previous phase, the team completed a warm shearing experiment with different shear edge clearances for the conventional shearing of magnesium alloy sheets.Three types of shear edge clearance were set, 8%, 10%, and 12%, and the results showed that 10% shear edge clearance was the best for the sheet section profile in conventional shearing.At 150 ℃, the sheet section profile is best at 12% shear edge clearance.Based on the study's results, ultrasonic shearing simulations are carried out for 8%, 10%, and 12% shear edge clearance at a sheet temperature of 150 ℃.
Figure 15 shows the stress maps for conventional and ultrasonic shearing with different shear edge clearances.Figure 16 shows the maximum and average stresses in ultrasonic shearing and conventional shearing with different shear edge clearances.As can be seen from the graph, when the sheet edge clearance is 8%, 10%, and 12%, respectively, the maximum stresses for conventional shearing are 364.3MPa,371.6MPa, and 375.1MPa.In contrast, the maximum stresses for ultrasonic shearing are 306.2MPa,307.7MPa, and 369.9MPa, respectively.Compared to conventional shearing, the maximum stresses are reduced by 58.1MPa, 63.9MPa, and 5.2MPa, respectively.The average stresses for conventional shearing are 329.1MPa,328.6MPa, and 328.2MPa, respectively.In contrast, the average stresses for ultrasonic shearing processing are 293.9MPa,284.97MPa, and 299.5MPa, respectively, reducing 35.1MPa, 43.6MPa, and 28.6MPa, respectively, compared to conventional shearing.Data analysis shows that ultrasonic shearing effectively reduces the maximum and average equivalent stresses in the shearing process, but the degree of optimization varies due to different shear edge clearances.The optimization is best when the shear edge clearance is 10%.
As can be seen in Fig. 17 and Fig. 18, which is the stress trend in conventional shearing and ultrasonic shearing at different shear edge clearances, the variation in shear edge clearance in ultrasonic shearing affects the stress in the sheet.When the shear edge clearance is 8%, the internal stress of the sheet increases sharply in the initial stage of shear, and the stress changes more smoothly after entering the shear stage.When the shear edge clearance is 10%, the stress in the sheet is greater than the stress at 8% in the elastoplastic phase and less at 8% shear edge clearance in the shear phase and tends to smooth out.When the shear edge clearance is 12%, compared to the previous two, the sheet stress rises slightly more slowly in the elastoplastic phase and jumps sharply in the shear phase and then decreases steadily and finally decreases to a stress close to that at 10% shear edge clearance.The comparison shows that when the shear edge clearance is 8%, the bending moment in the shear area of the magnesium alloy sheet is too small.The sheet is mainly subject to compressive stress, hindering the crack expansion near the upper and lower shear edges.Hence, the cracks are not easy to overlap and easy to produce secondary shear.Shear edge clearance of 12%, the bending moment in the shear area of the magnesium alloy sheet is too large, the sheet is mainly subject to tensile stress, and the tensile stress will assist the crack expansion near the upper and lower shear edge, so the crack expansion is accelerated and easy to produce burrs.
Figure 19 shows the trend in ultrasonic shearing and conventional shearing stresses at the same shear edge clearance.It is clear from the figure that for both conventional and ultrasonic shearing, the larger the shear edge clearance, the longer it takes for the sheet to reach maximum stress, which is the longer it takes to go through the elastic-plastic phase.For the same process parameters, the time to reach maximum stress in ultrasonic shear is longer than in conventional shear.From the analysis of force perspective, ultrasonic shearing effectively prolongs the time of the elastic-plastic phase of plate shearing, that is, the time of crack expansion increases, the rate of crack expansion decreases, and the shear strength of magnesium alloy thus increases, so the bright band of the sheet section after ultrasonic shearing processing increases and the rollover depth and width decrease.

Conclusion
Based on the vibration-temperature coupling model, this study was the first three-dimensional finite element simulation of the ultrasonic vibration shear process in ABAQUS simulation software by establishing the converter which connected the displacement reference point and vibration reference point, verifying the excellence and feasibility of the ultrasonic shear process, and analyzing the variation law of equivalent stress of ultrasonic shear under different process parameters, which provides a foundation for the prediction and evaluation of the ultrasonic shear quality of AZ31B magnesium alloy sheet, and the main conclusions are as follows.
1. Ultrasonic shearing is another method used for the shearing process on AZ31B magnesium alloy sheets in addition to the existing shearing process.2. There is a big difference between ultrasonic shearing and conventional shearing.For the same process parameters, ultrasonic shearing's maximum and average equivalent stresses are lower than conventional shearing, which reduces the tensile stress at fracture.Because the burr on the shear section is a result of the tensile stress when the cracks intersect, the height of the burnish zone rises and the burr zone falls during ultrasonic sheet shearing.3. Due to the high-frequency vibration's effect, which also increases the crack expansion time and shear strength of magnesium alloy, the elastic-plastic deformation stage of ultrasonic shearing processing takes longer than that of conventional shearing processing.Consequently, during ultrasonic shearing processing, the elasticity of magnesium alloy sheets is noticeably increased, and the section quality of the sheet is also improved.4. The sheet temperature, the shear edge clearance, and the ultrasonic amplitude have a significant impact on the equivalent stress of ultrasonic shearing.The sheet temperature has the greatest weight coefficient on the effect of equivalent stress, and its effect law is that the maximum equivalent stress decreases as the temperature rises.The optimal effect of ultrasonic shear occurs at 150 ℃, where 63.9 MPa reduces the maximum equivalent stress.The shear edge clearance has the secondhighest weight coefficient on the effect of equivalent stress, and its effect law states that as the shear edge clearance increases, the equivalent stress first decreases and then increases; at 10% shear edge clearance, the equivalent stress of ultrasonic shearing is the lowest and most effective for optimization.The effect of ultrasonic amplitude on the equivalent stress is that the equivalent stress decreases as the ultrasonic amplitude increases, and 10 μm is chosen as the ultrasonic amplitude within the effective range of the ultrasonic vibration system. 5.The trend of equivalent stress change in the ultrasonic shearing process exhibits the phenomena of stress superposition and stress fluctuation, which is caused by the sheet generating alternating stress, which is affected by the intermittent contact effect of ultrasonic vibration, and which is superimposed on the constant stress pro- This paper establishes the simulation model by directly assigning the boundary conditions to the model itself.At the same time, most of the previous related studies implemented ultrasonic-assisted machining simulation experiments by changing material parameters and other indirect methods.Most ultrasonic-assisted machining processes are turning, milling, and other machining processes, which seldom apply to shear machining.The results of this simulation test mainly provide an evaluation reference for the prior quantitative prediction of the ultrasonic shearing process for magnesium alloy sheets.In the subsequent study, we will complete ultrasonic shear tests and fit the model with a correction based on the mechanical results obtained from the experiments.The modified model is further used to complete the simulation prediction and analysis of the experiments that cannot be conducted due to the constraints of the test conditions and to achieve the advanced planning and target setting of engineering design.

Figure 2 Fig. 1
Fig. 1 Schematic diagram of the ultrasonic shear processing device

Fig. 2
Fig. 2 Finite element simulation model and condition setting

Fig. 3
Fig. 3 Meshing and vibration constraint setting (a) Bright band height (b) Bright band area ratio

Fig. 4
Fig. 4 Analysis of bright band data (a) Bright band height, (b) Bright band area ratio

Fig. 6
Fig. 6 Comparison of conventional shearing and ultrasonic shearing equivalent stress map

Fig. 10
Fig. 10 Maps of the maximum equivalent stress for ultrasonic and conventional shearing at different temperatures.10-1 Maximum stress of conventional shearing at different temperatures, (a)100 ℃;

Fig. 11
Fig. 11 Maximum and average stress in conventional and ultrasonic shearing at different temperatures.a Maximum stress; b average stress

Fig. 17 Fig. 18
Fig. 17 Stress trend in conventional shearing at different shear edge clearance

Table 1
Thermal properties of AZ31B magnesium alloy (variation with temperature)

Table 2
Coefficient constants of the Johnson-Cook constitutive model for AZ31B magnesium alloy

Table 3
Damage model parameters for AZ31B magnesium alloy

Table 4
The relevant factors and levels of the orthogonal test

Table 5
The orthogonal table of L 9 (3 3 ) with its test and range results Fig. 7 Stress maps in the orthogonal test table.a No. 1; b No. 2; c No. 3; d No. 4; e No. 5; f No. 6; g No. 7; h No. 8; i No. 9