**Figure 7.** MLAs on the small workpiece. (**a**) The machining system; (**b**) partial enlarged view.

#### **4. Results and Discussion**

#### *4.1. Form Error of Micro Lens*

As illustrated in Figure 8a, the three-dimensional topography of the machined micro lenses was measured using a white light interferometer (Zygo Newview 8200 from Zygo Corp., Middlefield, CT, USA). Wavy distortions can be clearly observed at the cut-in part along the cutting direction. The form error between the machined micro lens surface and an ideal spherical surface (*R* = 2.995 mm) was derived using a post-process software (Metropro, from Zygo Corp., Middlefield, CT, USA) and revealed in Figure 8b, appearing to obvious chatter mark in the same part. Owing to the location of both the distortion and the chatter mark which are a one-to-one correspondence, it is expected that the distortions of micro lens surface are caused by the chatter mark. It is a general problem with the fabrication of MLAs using trajectory method or forming method based on STS diamond turning.

To investigate the generation of the chatter mark, the real-time motion information of the cutting axis (X-axis) was collected synchronously via the UMAC during processing, including actual acceleration, follow error, actual position, and command position, as revealed in Figure 9. In addition, the green lines as highlighted in Figure 9b represent the surface of the workpiece, i.e., the initial position of the cutting process for every micro lens. As observed in Figure 9a, there are a few overlarge

acceleration oscillations occurring for the X-axis in the MLAs processing. Further, the fluctuations of the follow error are accordingly caused by the acceleration oscillations. It can be seen that the maximum amplitude of follow error is up to several micrometers, but the oscillation amplitude will decrease over time. Even so, once the large fluctuations of follow error occur in the cutting area, i.e., the upper part of the green line in Figure 9b, both the actual position and the command position of the cutting axis (X-axis) are obviously misaligned, as highlighted with a black dotted circle in Figure 9b. This phenomenon will result in the distortion of the profile for machined micro lenses. Thus, it can be determined that excessive follow error is reflected to the surface of micro lens in the form of a chatter mark. Further, the chatter mark can be attributed to an overlarge instantaneous acceleration and deceleration of the cutting axis (X-axis) of the machine tool during processing.

**Figure 8.** Zygo photographs of micro lens. (**a**) 3-D topography of machined micro lens; (**b**) The form error of machined micro lens surface from a designed sphere (*n* = 100, *t* = 1 ms).

**Figure 9.** The collected real-time kinematic information of the cutting axis. (**a**) Actual acceleration and follow error; (**b**) Follow error, actual, and command position.

#### *4.2. Effect of the Number of Discrete Points*

In this section, the effects of the number of discrete points for the form error of micro lens will be investigated in detail. The corresponding experiments were carried out on the aluminum alloy (6061) roller mold using the STS approach based on the self-developed ultra-precision horizontal drum roll lathe. The number of discrete points is 100, 200, 400, 600, and 800 for a single micro lens, and the cutting time of every discrete point is 1 ms. The size of machined micro lenses is shown in Table 2. The plot of form error of machined micro lenses at a various number of discrete points is shown in Figure 10. In this study, Root-Mean-Square (RMS) is used for characterizing the form error of machined micro lenses. In addition, the measured data were processed using a Gaussian low-pass filter provided by Metropro before the calculation of RMS. The mathematical definition and the digital implementation of RMS can be formulated as:

$$Z\_{RMS} = \sqrt{\frac{1}{N} \sum\_{n=1}^{N} |z\_n|^2} \tag{1}$$

where *N* is the number of the measurement point of every micro lens and *zn* the form error of the profile at point number *n*.

As it can be seen from Figure 10, when the number of discrete points is 100, RMS is more than 1 μm. The shape of every micro lens distorts at the cut-in part due to the generation of the overlarge chatter mark, as shown in Figure 8b. With the increasing of the number of discrete points, RMS decreased obviously. Furthermore, MLAs have a fine surface quality with 0.724 μm RMS when the discrete point is 400, i.e., RMS is decreased by about 28.10%, as shown in Figure 11. No chatter mark appears at the cut-in part along the cutting direction. But the surface quality of MLAs could not be improved significantly when the discrete point is 800, i.e., RMS is reduced by about 31.88% (RMS = 0.686 μm).

**Figure 10.** Form error of micro lenses machined at various discrete points.

**Figure 11.** Zygo photographs of micro lens. (**a**) 3-D topography of machined micro lens; (**b**) The form error of machined micro lens surface from a designed sphere (*n* = 400, *t* = 1 ms).

According to the above experimental results, the surface quality can be improved effectively by increasing the number of discrete points of every micro lens. This is because as the number of discrete points increases, the cutting depth at each discrete point decreases accordingly. So, when the cutting time of every discrete point is a constant value, acceleration and deceleration of the cutting axis (X-axis) also reduce during processing. Then above overlarge acceleration oscillations of the cutting axis can be eliminated, and so do fluctuations of its follow error, when the number of discrete points is sufficient. Consequently, the micro lens with no surface chatter mark can be fabricated. It is noted that too many discrete points do not always reduce form error significantly. After the chatter mark

disappears on the surface of micro lens, the number of discrete points is no longer the main factor affecting surface quality.

#### *4.3. Effect of Cutting Time of Every Discrete Point*

The cutting time of every discrete point is another major cutting parameter for MLAs machining. Cutting time of every discrete point and the number of discrete points together determine the machining speed of the micro lens. To analyze the influences of the cutting time of every discrete point on form error of micro lens, some cutting experiments were conducted at various cutting times when the number of discrete points was a constant value. The form error is not significantly improved when the number of discrete point is greater than 400. Taking the machining efficiency into account, the number of discrete points is 400 for a single micro lens. The cutting time of every discrete point is 0.5, 1, 1.5, 2, and 2.5 ms. The plot of form error of machined micro lens with different cutting times of every discrete point is shown in Figure 12. It can be seen that increasing the cutting time has a certain impact on improving form error of micro lens. When the cutting time of every discrete point is 0.5 ms, RMS is 0.746 μm. As the cutting time of every discrete point increases, RMS decreases slightly. Furthermore, when the cutting time of every discrete point is 1.5, 2, and 2.5 ms, RMS are 0.632, 0.651, and 0.626 μm, respectively.

This is because increasing the cutting time of every discrete point can further reduce acceleration and deceleration of the cutting axis when the cutting depth is the same value. In addition, fluctuations of follow error of the cutting axis also further decrease correspondingly. Thus, the surface quality of micro lens can be improved further. Similarly, too much cutting time of every discrete point do not decrease form error significantly.

**Figure 12.** Form error of micro lenses machined at different cutting time of every discrete point.

#### *4.4. Effect of Cutting Depth*

The amplitude of the form error is greater at the cut-in part and cut-off part in comparison to other cutting areas along the cutting direction. It is an obvious feature in the 2D sectional profile of the form error of machined micro lens surface, as shown in Figures 8b and 11b. This is because cutting depth of every discrete point is different when the equal-angle method is used during processing, as shown in Figure 13. The maximum value of cutting depth occurs at the first and last discrete point; the minimum value of cutting depth appears at the bottom of every micro lens. With the increasing cutting depth, the cutting force is also bigger. Certainly, the cutting force will determine the elastic recovery of materials and relieving amount, i.e., bigger cutting force generates greater elastic recovery and relieving amount after cutting [29]. The form accuracy of micro lens will degrade due to the existence of elastic recovery and relieving amount. Therefore, the form error at the cut-in part and cut-off part is larger under the influence of bigger elastic recovery and relieving amount.

Based on the discussion above, the optimal cutting parameters were adopted for generating typical MLAs (20.52-μm height and 700-μm aperture), which took into account form accuracy, as well as machining efficiency. The number of discrete points was 400, and the cutting time of every discrete point was 1.5 ms. The measurement result is shown in Figure 14 with 0.632 μm RMS and no chatter mark was observed. Compared with the previous research, both aperture and height of the machined micro lens vary from different researchers. So, RMS cannot be directly compared to evaluate the form error of micro lens. In terms of chatter mark, the acquired surface quality is similar to or even better than the conventional trajectory method based on FTS/STS diamond turning of MLAs [21,28]. Therefore, the experimental result proves the effectiveness of the novel forming method based on STS diamond turning. The extendable fabrication of similar microstructure surfaces can be also performed in this way.

**Figure 13.** Schematic of the change trend of cutting depth for the equal-angle method.

**Figure 14.** Zygo photographs of micro lens. (**a**) 3-D topography of machined micro lens; (**b**) The form error of machined micro lens surface from a designed sphere (*n* = 400, *t* = 1.5 ms).

#### **5. Conclusions**

A novel forming method based on STS diamond turning is presented to generate MLAs on the roller mold, which addresses the inherent drawback of relatively low production efficiency associated with traditional trajectory method. The MLAs (20.52-μm height and 700-μm aperture) is successfully machined without a chatter mark using the optimal cutting parameters. The proposed method can be extensively applied to other microstructures. According to the above experimental results, the conclusions can be presented as follows:

#### **6. Future Work**

In the current study, although the forming method can be used for generating the MLAs with no chatter mark efficiently. As for the form accuracy of the machined micro lens, the effect of elastic recovery and relieving amount for the form accuracy cannot be neglected. If both factors can be studied and compensated, the form accuracy is likely to be improved further. In the future research, compensation strategy of form accuracy will become the focus based on the forming method.

**Author Contributions:** Investigation, Y.L., D.L., Z.Q. and D.Q.; Methodology, Y.W. and J.X.; Validation, B.W.; Writing for original draft, Y.L.; Writing for review & editing, Y.L. and D.L.

**Funding:** This work was supported by National Science and Technology Major Project of High-end CNC Machine Tools and Basic Manufacturing Equipment of China (grant number 2011ZX04004–021).

**Acknowledgments:** The authors would like to thank the fund from National Science and Technology Major Project of High-end CNC Machine Tools and Basic Manufacturing Equipment of China (grant number 2011ZX04004-021).

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Investigation on Microsheet Metal Deformation Behaviors in Ultrasonic-Vibration-Assisted Uniaxial Tension with Aluminum Alloy 5052**

**Chunju Wang 1,2,\*, Weiwei Zhang 3, Lidong Cheng 1, Changqiong Zhu 2, Xinwei Wang 4,\*, Haibo Han 5, Haidong He 1 and Risheng Hua 1**

Received: 22 December 2019; Accepted: 29 January 2020; Published: 31 January 2020

**Abstract:** Ultrasonic vibration (UV) is widely used in the forming, joining, machining process, etc. for the acoustic softening effect. For parts with small dimensions, UV with limited output energy is very suitable for the microforming process and has been gaininf more and more attention. In this investigation, UV-assisted uniaxial tensile experiments were carried out utilizing GB 5052 thin sheets of different thicknesses and grain sizes, respectively. The coupling effects of UV and the specimen dimension on the properties of the material were analyzed from the viewpoint of acoustic energy in activating dislocations. A reduction of flow stress was found for the existing acoustic softening effects of UV. Additionally, the residual effects of UV were demonstrated when UV was turned off. The uniform deformation ability of thin sheet could be improved by increasing the hardening exponent with UV. The experimental results indicate that UV is very helpful in improving the forming limit in microsheet forming, e.g., microbulging and deep drawing processes.

**Keywords:** ultrasonic vibration; acoustic softening; residual effect; microthin sheet; forming limit

#### **1. Introduction**

As demands on miniature/micrometal products increase significantly, for example, metallic parts with microchannels fabricated through ultra-thin sheets are widely used in mass and heat transfer areas, e.g., heat exchangers and proton exchange membrane fuel cells (PEMFCs). Due to its advantageous characteristics for mass production, microforming has become an attractive option in the manufacture of these products [1]. However, the geometrical size of the workpiece, the microstructural length scale of deforming materials, and their interaction significantly affect the deformation response of microscale objects, e.g., flow stress, springback, forming limit. [2–4]. Several kinds of microsheet forming processes, e.g., rigid stamping, hydroforming, and rubber pad forming, have been carried out to manufacture microchannels in recent years [5,6]. Microrigid stamping was a commonly used technology for microchannels due to its advantages of low cost and high productivity. A significant thinning easily occurred at the corner regions of the formed microchannel in rigid stamping, which

was associated with the tensile force applied at the corner and the friction, resulting in the occurrence of localized strain [7,8]. Then, forming limit diagrams were used to determine the safe limit of the metallic bipolar plates [9]. Since hydroforming has obvious merits, e.g., flexibility, higher drawing ratio, good surface quality, less springback, and the low cost of mold, it has attracted more attention [10,11]. However, the channel height of a hydroformed workpiece was a function of the pressure, and high pressure and the seal became a big problem [5,12]. For rubber pad forming, only half of a single rigid tool is needed, and the punch-cavity misalignment problem can be avoided. A metallic bipolar plate was successfully fabricated using stainless steel SS304 [13] and titanium with a TiN layer [14]. To improve the filling percentage, thinning percentage, and dimensional accuracy, semi-stamp rubber forming was carried out instead of convectional rubber forming [15]. However, the main drawback of the rubber pad forming process is that the life of the rubber pad is not so long and should be replaced after the production of only about 100 plates. Previous investigations have indicated that the existing process cannot be used for the manufacture of microchannels due to the obvious drawbacks mentioned above.

To improve the formability of thin sheet, industrial applications of dynamic load/ultrasonic vibration (UV) were utilized in many metallic sheet forming processes. The application of 20 and 28 kHz oscillation increased the limit drawing ratio (LDR) from 2.68 to 3.01 for cold rolled steel for deep drawing. Greater accuracy and deeper cups can be formed by stopping the oscillation after the maximum punch load rather than applying the oscillation throughout the deep drawing process [16]. In the rigid bulging of microchannels, a kind of dynamic load with a frequency of 0.5Hz could improve the forming depth of 7% and decrease material thinning from 10.7% of static loading to 7.8% [17,18]. In UV-assisted microdeep drawing, the punch force decreased as the oscillation amplitude increased, and LDR increased from 1.67 to 1.83, from 1.75 to 1.92, and from 1.83 to 2 for a thickness of 50, 75, and 100 μm, respectively [19]. Further, wrinkling and cracking could be avoided through ultrasonic vibration to decrease the coefficient of friction between the sheet material and the die [20]. Using UV to form molten plastic as a flexible punch, a trapezoidal cross-section microchannel of 697.2 μm width and 248.4 μm depth was successfully replicated up to 98% on a thin T2 copper sheet of an initial thickness of 50 μm [21,22]. The UV-assisted microforming processes have shown that it was helpful in improving the quality of microparts. However, the mechanism of deformation behavior should be investigated in detail, especially for the thin sheet when UV is applied.

One of reasons dynamic load/ultrasonic can improve formability is the acoustic softening effect, as shown in many research studies. High frequency vibration was found to significantly reduce the apparent static shear stress necessary for the plastic deformation of metals [23]. Further, the amount of reduction was directly proportional to the acoustic energy input to the specimen; this yielding of metals due to ultrasonic irradiation has the possibility to be more efficient than other methods, e.g., heating [24]. To realize the mechanism of the softening effect of ultrasonic vibration, a significant reduction in subgrain formation was found and analyzed from the viewpoint of acoustic energy, which can be attributed to its ability to enhance dislocation dipole annihilation to cause dislocations to travel longer distances [25]. A modeling framework for acoustic plasticity was proposed to model the acoustic softening considering the acoustic energy intensity based on the crystal plasticity theory [26]. An opposite result by a dislocation dynamics simulation indicated that the acoustic effect was associated with extensive enhancement of subgrain formation [27]. However, the effects of UV on the properties of materials have not been investigated considering dimensions of microparts in UV-assisted microforming processes. The mechanism of stress reduction was investigated, and the evolution of the microstructure was observed through experiments and simulation. However, research was seldom carried out on the small specimens. From the viewpoint of acoustic energy, the density is changed during the miniaturization of specimens. Additionally, the density of microdefects in metallic specimens, e.g., dislocations and grain boundaries, becomes smaller in small specimens, which is considered to absorb the acoustic energy. Investigations should be done to analyze the effect of grain size and specimen size on deformation behavior in UV-assisted deformation.

In the investigation, UV-assisted uniaxial tensile tests were carried out utilizing GB 5052 thin sheets with different thicknesses from 50 to 100 μm. Further, the effects of UV parameters, e.g., vibration amplitude and duration, were also studied. Properties of materials, e.g., yield stress, tensile strength, elongation, and hardening exponent, were obtained from the UV-assisted experiments. The coupling effects of UV and specimen dimension were analyzed from the viewpoint of acoustic energy in activating dislocations.

#### **2. Materials and Methods**

#### *2.1. Experimental Set-Up*

In this investigation, a kind of ultrasonic-vibration-assisted uniaxial tension device was utilized as shown in Figure 1 [28], which was developed by our group based on a testing machine (UTM6104, Shenzhen Suns Technology Stock Co., Ltd., Shenzhen, China) with a 10 kN load cell. A vibrator was designed, including an ultrasonic transducer and an ultrasonic horn. A piezoelectric ceramic transducer (PZT-8) with a sandwich structure was selected as the ultrasonic transducer, and it could effectively transform the electric energy to mechanical longitudinal vibration. To clamp the thin sheet specimen, a groove structure was designed at the top end of the ultrasonic horn. The width and depth of the groove were selected as 0.2 and 10 mm, respectively, based on finite element analysis using the ABAQUS commercial software (v6.12, Dassault Systems SIMULIA, France). One side of the thin sheet specimen is clamped by the vibrator using the groove structure at the top end of the ultrasonic horn, which is fixed at the bottom parts of the testing machine. Another side of the specimen is clamped by a tool installed on a moving beam of the testing machine. In the uniaxial tension device, the moving beam can move upward, then a force is applied on the specimen to fix the bottom part of the specimen. During the tensile test, the vibrator can be turned on, and UV is applied on the specimen by the ultrasonic horn.

**Figure 1.** Ultrasonic-vibration-assisted uniaxial tension device.

Measured by the laser vibrometer Polytec OFV-5000, the longitudinal vibration frequency of the manufactured vibrator was 21.1 kHz, and its vibration amplitude could be changed from 0.48 to 15 μm depending on the input current, which could meet the requirement of uniaxial tension in these experiments.

#### *2.2. Experimental Material*

Commercial rolled aluminum alloy GB 5052 sheet was selected in this investigation for its excellent properties, e.g., higher strength alloys, excellent corrosion resistance, and high fatigue strength. The thicknesses *t* of selected rolled aluminum alloy sheets are 50, 60, 80, and 100 μm, and the dimensions of their specimens were designed according to the similar theory as shown in Figure 2. To study the effect of the grain size and reduce the effect of strain hardening induced by the rolling process, heat treatment experiments for a thickness of 50 μm were carried out using a tubular vacuum heat treatment furnace (T1200) at temperatures of 200, 300, 400, 500, and 600 ◦C for 1 h of the holding time with 10 ◦C/min of the heat rate, respectively. After heat treatment, specimens were electrochemically polished under a voltage of 5 V and current of 0.5 A for 8 s using a solution of 10 mL of HClO4 and 60 mL of C2H5OH. The obtained microstructures under different temperatures are shown in Figure 3, and the grain size as shown in Table 1 was manually measured using the intercept method according to ASTM E112 [29]. For other thicknesses of sheets, only the temperature of 400 ◦C was selected to eliminate the effect of strain hardening. The heat treatment process was only used to eliminate the hardening effect during the manufacturing of the thin sheet with the rolling process. The difference of grain size for different thicknesses was ignored for the same heat treatment process. Thus, grain sizes of thin sheets with different thicknesses were not measured in this investigation.

**Table 1.** Grain size of a GB 5052 thin sheet after annealing treatment (50 μm in thickness).

**Figure 2.** GB 5052 thin sheet specimens and their dimensions. (**a**) Dimensions of specimen (50 μm in thickness); (**b**) Dimensions of specimens with different thicknesses.

*Materials* **2020**, *13*, 637

(**e**)

**Figure 3.** Microstructure of a GB 5052 thin sheet after heat treatment at different temperatures (50 μm in thickness). (**a**) 200 ◦C; (**b**) 300 ◦C; (**c**) 400 ◦C; (**d**) 500 ◦C; (**e**) 600 ◦C.

#### **3. Results and Discussion**

#### *3.1. E*ff*ect of UV on Properties of Specimen with Di*ff*erent Thicknesses*

During the miniaturization, size effects have an obvious influence on the properties of the specimen. To realize this kind of effects, GB 5052 specimens with different thicknesses were utilized after heat treatment on the temperature of 400 ◦C for 1 h, and uniaxial tensile tests were carried out with a punch speed of 0.3 mm/min and vibration amplitude of 0.48 μm. The experimental results are shown in Figure 4, demonstrating that the flow stress decreases with the decrease of thickness both without and with UV. This means that the size effect on flow stress occurs, which has been studied in many papers [2].

**Figure 4.** Curves of stress–strain of specimens with different thicknesses. (**a**) Without UV; (**b**) With UV.

To study the effect of UV on the properties of materials in detail, the yield stress, tensile strength, elongation, and hardening exponent were achieved as shown in Figure 5 based on curves shown in Figure 4. It clearly shows that the thickness of the specimen has an obvious effect on the parameters of the thin sheet. The yield stress and tensile strength decrease with the decrease of thickness, and the elongation and hardening exponent increase with the decrease of thickness. Only the elongation for a thickness of 50 μm does not follow this rule, which becomes lower.

**Figure 5.** Effect of UV on properties of specimens with different thicknesses. (**a**) Effect of UV on yield stress; (**b**) Effect of UV on tensile strength; (**c**) Effect of UV on elongation; (**d**) Effect of UV on hardening exponent.

When UV was applied, the yield stress, tensile strength, and elongation decreased, and the hardening exponent increased, which was similar with the results shown above. For the acoustic softening effect, the flow stress can be reduced, since dislocations are activated by the energy and become easy to slip, even those on the 'hard' orientation. As a result, the yield stress and tensile strength become smaller in UV-assisted tests. When radial shrinkage occurs during tensile tests, UV can increase the extension of the crack since the acoustic energy density becomes bigger for the small cross-section area induced by the shrinkage. Then, the elongation is decreased by ultrasonic vibration. However, the proportion of uniform deformation is generally increased by UV, which is helpful in improving the critical limit. We plan to study these phenomena in future investigations.

An increase of the hardening exponent was observed in the tests by UV. The reason may be that UV activates more dislocations and promotes the interaction of dislocations. As a result, more subgrains are formed, which leads to the increase of the hardening exponent [27]

The effect of UV is almost the same for specimens with different thicknesses. This may be attributed to the fact that the acoustic energy is too small. The coupling effect of UV and dimension will be studied in depth in future investigations.

#### *3.2. E*ff*ect of UV on Properties of Specimens with Di*ff*erent Grain Sizes*

Uniaxial tensile tests were carried out with a punch speed of 0.3 mm/min and vibration amplitude of 0.48 μm using GB 5052 thin sheet specimens of 50 μm in thickness. The obtained curves of stress–strain for GB 5052 sheets with different grain sizes are shown in Figure 6 without and with UV, respectively. To analyze the effect of UV on the mechanical properties of GB 5052 thin sheet, yield stress, tensile strength, elongation, and harden exponent were obtained from the curves of stress–strain.

**Figure 6.** Curves of stress–strain of GB 5052 sheet. (**a**) Without UV; (**b**) With UV.

For the existing acoustic softening effect, the flow stress is reduced by UV. The yield stress and tensile strength are shown in Figures 7 and 8, respectively. We notice that the data in Figure 8 are different from those in Figure 5c for the same condition. The reason may be that the tests were carried out at a different time and using different batches of material.

**Figure 7.** Effect of UV on yield stress.

**Figure 8.** Effect of UV on tensile strength.

A softening effect can be observed from the two figures, and the reduction of flow stress is very small. The reason is that the softening effect depends on the level of acoustic intensity applied on specimens. A little acoustic energy used in these experiments, which is proportional to the vibration amplitude, accordingly leads to a small reduction of flow stress.

For different grain sizes, the effects of UV are almost similar. One reason is the small vibration amplitude. Another one, also important, is that the density of defects in thin sheets becomes very similar after heat treatment. Generally, defects in metallic materials can absorb acoustic energy and activate dislocations to move, which leads to a reduction of shear stress during plastic deformation. Thus, the effects of UV on yield stress and tensile strength are very small in this investigation.

The elongation of thin sheets indicates the limited plastic deformation ability of metallic materials, which is very important in thin sheet forming. The effect of UV on the elongation of thin sheet with different grain sizes is shown in Figure 9. It is found that the elongation of the thin sheet is decreased, and the reduction slightly increases with the increases of grain size. During the uniaxial tensile deformation, radial shrinkage will occur before the fracture of the specimen. The appearance of radial shrinkage means that the area of the cross-section becomes smaller. With the same vibration amplitude, as well as the same input acoustic energy, the acoustic energy density will be increased for the smaller area, which will improve the activation of dislocations and local plastic deformation. As a result, the elongation with UV becomes smaller.

**Figure 9.** Effects of UV on elongation.

The hardening exponent is another important parameter which indicates the ability of uniform plastic deformation of thin sheet. The effect of UV on the hardening exponent is shown in Figure 10. The experimental results showed that UV increases the hardening exponent, especially for specimens with a bigger grain size, which means that the uniform deformation ability is increased by ultrasonic vibration. The reason is that UV as a kind of energy can activate more dislocations to move, even dislocations in an unfavorable position, which is validated by Electron Backscattered Diffraction (EBSD) analysis [25]. The more dislocations are activated, the more uniform plastic deformation can be realized.

**Figure 10.** Effects of UV on the hardening exponent.

#### *3.3. E*ff*ect of UV Duration on Properties of Specimen*

The different duration of UV means a different acoustic energy applied on the specimen, and the effect of UV duration was analyzed in this investigation. With GB 5052 thin sheets of 50 μm in thickness treated on the temperature of 400 ◦C, UV-assisted uniaxial tensile experiments were carried out with a punch speed of 0.3 mm/min using a vibration amplitude of 5 μm under different durations of 20, 30, and 40 s, respectively. Experimental results showed that the flow stress can be decreased immediately during tensile deformation when UV is applied on the specimen as shown in Figure 11. This means that the acoustic softening effect occurs. The reduction of flow stress is almost the same for the same vibration amplitude. When UV is turned off, the flow stress goes back to that without UV. However, the flow stress becomes smaller after UV, which can be treated as a kind of residual effect because the acoustic energy forces dislocations to move in a preferred direction, and materials' properties undergo permanent changes [24].

**Figure 11.** Effect of UV duration on flow stress.

In Figure 11, the effect of UV duration on tensile strength and elongation can be obtained, as shown in Figures 12 and 13, respectively. The tensile strength can be obviously decreased from 77.6 MPa for 0 s to 72.5 MPa for 40 s; the reduction percentage is about 6.6%. Further, the elongation was reduced from 0.73 for 0 s to 0.21 for 40 s. Although UV is turned off, its effect on the tensile strength and elongation is very clear, which is called a kind of residual effect. This may be attributed to the permanent changes of the microstructure in metallic materials after UV-assisted deformation [24]. For a longer duration of UV, more acoustic energy was applied on the specimen, and its effect on the properties increased accordingly.

**Figure 12.** Tensile strength under different durations.

**Figure 13.** Elongation under different durations.

#### *3.4. E*ff*ect of Vibration Amplitude on Properties of Specimen*

As we know, acoustic energy is proportional to vibration amplitude, which has an obvious effect on the properties of materials. In this investigation, UV-assisted uniaxial tensile experiments were carried out with a punch speed of 0.3 mm/min using a duration of 30 s under different vibration amplitudes of 5, 5.6, and 6.2 μm, respectively. Further, the GB 5052 thin sheet of 50 μm in thickness treated on the temperature of 400 ◦C was selected, and the experimental results are shown in Figure 14. It was found that the flow stress decreases immediately. The reduction of flow stress was 16.43, 21.67, and 24.82 MPa, respectively. A higher level of acoustic intensity may provide more energy to motivate more dislocations to slide from their pinned points and also lead to a multiplication of dislocations [24]. As a result, the reduction of flow stress increases with the increase of vibration amplitude.

**Figure 14.** Curves of strain-stress under different vibration amplitudes.

#### **4. Conclusions**

In this investigation, UV-assisted uniaxial tensile tests were carried out utilizing GB 5052 thin sheets. The effects of UV on the properties of materials were analyzed in detail for specimens with different grain sizes and original thicknesses, respectively. An acoustic softening and residual effect was found in the investigation. The following conclusions can be obtained.

**Author Contributions:** Conceptualization, C.W.; Data curation, C.Z., X.W. and C.W.; Formal analysis, C.W., C.Z. and L.C.; Funding acquisition, C.W., X.W., W.Z. and H.H. (Haibo Han); Investigation, C.Z., W.Z., L.C. and X.W.; Methodology, C.W., X.W. and R.H.; Resources, C.W., W.Z. and H.H. (Haibo Han); Supervision, C.W.; Writing—original draft, C.W. and C.Z.; Writing—review & editing, C.W., C.Z., W.Z., and H.H. (Haidong He). All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was funded by the Natural Science Foundation of Jiangsu Province (BK20192007), National Science Foundation of China (No. 51875128, 51805497, 51605301, 51635005), and Six Talent Peaks in Jiangsu Province (GDZB-069).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Ultrasonic Vibration Facilitates the Micro-Formability of a Zr-Based Metallic Glass**

#### **Guangchao Han 1,2, Zhuo Peng 1, Linhong Xu 1 and Ning Li 3,4,\***

Received: 31 October 2018; Accepted: 12 December 2018; Published: 17 December 2018

**Abstract:** Thermoplastic microforming not only breaks through the bottleneck in the manufacture of metallic glasses, but also offers alluring prospects in microengineering applications. The microformability of metallic glasses decreases with a reduction in the mold size owing to the interfacial size effect, which seriously hinders their large-scale applications. Here, ultrasonic vibration was introduced as an effective method to improve the microformability of metallic glasses, owing to its capabilities of improving the material flow and reducing the interfacial friction. The results reveal that the microformability of supercooled Zr35Ti30Cu8.25Be26.75 metallic glasses is conspicuously enhanced by comparison with those under quasi-static loading. The more intriguing finding is that the microformability of the Zr-based metallic glasses can be further improved by tuning the amplitude of the ultrasonic vibration. The physical origin of the above scenario is understood, in depth, on the basis of ultrasonic vibration-assisted material flow, as demonstrated by the finite element method.

**Keywords:** metallic glasses; thermoplastic microforming; ultrasonic vibration; formability

#### **1. Introduction**

Thermoplastic microforming (TPMF) has broken through the bottleneck in the manufacture of metallic glasses (MGs), providing an alternative way to fabricate MG parts/components with high precision and excellent mechanical properties, which offers alluring prospects of MGs in microengineering applications [1–5], while the microformability of MGs is seriously hindered by the interfacial effect and high viscosity in the supercooled liquid region (SCLR, a temperature window between glass transition temperature *T*g and crystallization temperature *Tx*). The low viscosity and the spatiotemporally homogeneous flow are also regarded as critical parameters that significantly affect the thermoplastic formability of MGs in the supercooled liquid state [6–9].

To improve the microformability of supercooled liquid MGs, processing parameters such as temperature and strain rate are usually considered as crucial factors, because these parameters determine the flow characteristics of the MGs. In our previous research [10], we revealed an inherent relationship between the thermoplastic formability and the flow characteristics, namely, Newtonian flow facilitates the forming capability, while thermoplastic forming in a non-Newtonian flow regime tends to be difficult. However, it is noted that the MGs would have a very short forming time window during the high-temperature forming process, which induces the risk of possible crystallization during plastic forming. To reduce the viscosity of MGs and avoid the possible crystallization, rapid temperature increases [11,12] and fast cooling [2] have been introduced to avoid the interaction with

time–temperature–transformation (TTT) curve. On the other hand, in order to reduce the interfacial effect, the hot rolling method [13] and the thermoplastic blowing method [14] have been tried to reduce the physical contact area between MGs and the mold, while these methods are hard to be applied in the microforming of MGs. The method of adding lubricant has also been found to be very limited for reducing the interfacial friction. Therefore, a new method is urgent necessary to reduce the interfacial friction and lower the viscosity of MGs in the supercooled liquid region.

In recent years, vibration loading has been introduced to improve the microforming capacity of supercooled liquid MGs. It was found that low-frequency vibration (*f* ≤ 10 Hz) could effectively improve the plastic strain of MGs, owing to the vibration-assisted viscosity reduction and homogeneous flow [6]. Lateral extrusion experiments of Zr55 (Zr55Cu30Al10Ni5) MGs with low-frequency vibrations also revealed an enhanced microformability under vibration loading [15]. Ultrasonic vibration with high loading frequency of above 20 Hz has also been widely applied in metal microforming processes because of its superiority in enhancing formability via a reduction of the forming force and a decrease in friction at the interface [16–18], originating from the ultrasonic stress-softening effect, stress superposition effect, and periodic separation with ultrasonic vibration. Studies on ultrasonic vibration have been performed for shear formability of MGs [19]. This technique also exhibits potential applications in micro/nanoscale forming of MGs. By increasing loading frequency to about 20 KHz, Ma et al. [20,21] used high frequency ultrasonic beating method to fabricate micro- to macroscale structures, avoiding crystallization and oxidation of MGs, while the systemic investigation of ultrasonic vibration on microformability of metallic glasses is still lacking, and the underlying physical origin for ultrasonic-assisted thermoplastic forming of metallic glasses still remains unanswered.

In this work, ultrasonic vibrational loading was introduced as an innovative method to improve the thermoplastic microformability of Zr35Ti30Cu8.25Be26.75 MGs in a supercooled liquid state. It will be shown that the microformability of the supercooled liquid Zr-based MGs improves with increasing ultrasonic vibration amplitude, exhibiting an ultrasonic vibration-enhanced thermoplastic microformability. The physical mechanism of the phenomenon is rationalized in terms of the evolution of free volume concentration (*c*f) and flowing unit volume, which is further understood with assistance of finite-element-method (FEM) simulation. The present results provide an effective method to enhance the thermoplastic microformability of MGs.

#### **2. Experimental Setup and Procedure**

#### *2.1. Materials*

A Zr35Ti30Cu8.25Be26.75 (Zr35) MG system was selected for this research because of its excellent oxidation resistance, wide supercooled liquid region, and good glass-forming ability. Alloy cylinders with dimensions of φ 3 mm × 150 mm were fabricated by arc melting a mixture of pure Zr, Ti, Be, and Cu metals (purity > 99.5%) under a Ti-gettered argon atmosphere, followed by jet casting into a copper mold. The glassy structure of the as-cast alloy was verified by X-ray diffraction (XRD, Philips X'Pert Pro, Amsterdam, The Netherlands). The thermal response was determined by differential scanning calorimetry (DSC, TAQ2000, TA Instruments, New Castle, DE, USA) at a heating rate of 20 K·min−1, showing a glass transition temperature (*T*g) of 303.5 ◦C with a wide supercooled liquid region of 145 ◦C. The isothermal crystallization experiments revealed that the incubation time is more than 300 min at 370 ◦C [2,6,10,22]. The Zr35 samples with dimensions of φ 3 mm × 3 mm (strength of 1560 MPa) were sectioned from the bars, and the single factor experiments were completed for this research, such as ultrasonic power output, temperature, and forming velocity.

#### *2.2. Ultrasonic Microextrusion System*

To meet the requirements of ultrasonic vibration and equipment installation, we designed and fabricated a 20 kHz ultrasonic vibration system by ourselves. The ultrasonic vibration system included a TJS-3000 ultrasonic generator, two YP5020-4D ultrasonic transducers, two ultrasonic step horns (which were all produced by Hangzhou Success Ultrasonic Equipment Co., Ltd., Hangzhou, China), and a special porous sonotrode. In contrast to standard ultrasonic devices with a vertical arrangement, we designed an ultrasonic vibration system with a horizontally symmetrical arrangement, wherein a cylindrical ultrasonic horn and a microforming indenter were connected in sequence to the surface center of the porous sonotrode, as shown in Figure 1. The porous sonotrode could convert the horizontal input vibrations of the ultrasonic transducers into vertical output vibrations [23], and the indenter could have vertical ultrasonic resonance vibrations with the sonotrode. Additionally, the ultrasonic vibration system could be easily mounted with a press machine through two flange support seats without the need for specially designed mounting structures. The ultrasonic vibration modes in the vertical direction of both the unloaded ultrasonic vibration system and the forming tool (cylindrical ultrasonic horn and indenter)-loaded system were simulated by ANSYS software (version 13.0), and the results are shown in Figure 2. The results show that the frequency of the ultrasonic system is reduced from 19,661 Hz (shown in Figure 2a) to 19,573 Hz (shown in Figure 2b) with the increase in loading (frequency tracking range of the TJS-3000 ultrasonic generator (Hangzhou Success Ultrasonic Equipment Co., Ltd., Hangzhou, China) is 20 ± 0.5 kHz), and the maximum ultrasonic amplitude can be obtained at the end of the indenter (shown in Figure 2b with blue color), which means that the ultrasonic system is insensitive to load fluctuations and is fit for vertical ultrasonic micro-extrusion processes.

**Figure 1.** A schematic of the ultrasonic microextrusion system.

**Figure 2.** Models of the ultrasonic microextrusion systems in different situations: (**a**) model of the unloaded ultrasonic system; (**b**) model of the ultrasonic system loaded with a forming tool.

In addition to the ultrasonic vibration system, the microextrusion device was composed of an M-4050 universal test machine produced by Shenzhen REGER (Shenzhen, China) and a KSY-6D-16 electric heating device produced by Wuhan Yahua Electric Furnace Co., Ltd. (Wuhan, China) (the temperature range was 50–1000 ◦C, and the temperature control precision was ±1 ◦C). The ultrasonic amplitude of the indenter was adjusted by the power output percentage of the ultrasonic generator, and the power output percentages in the experiments were set to 30%, 40%, 50%, and 60%. The corresponding ultrasonic amplitudes at the end of the indenter in the vertical direction were detected by a V100 laser vibration meter from RION Co., Ltd. (Tokyo, Japan) and were 12, 16, 20, and 24 μm, respectively. The mold and the indenter were made from H13 hot-work die steel (Guangzhou Hengwei Electromechanical Equipment Co., Ltd., Guangzhou, China). The two parts of the mold were clamped together by bolts, and the microextrusion mold cavity was composed of 3 circular subsection slots, *L*1, *L*2, and *L*3, whose diameters were 2, 1, and 0.75 mm, and lengths 2, 4, and 23.5 mm, respectively. The structure diagram of the mold and the indenter are also shown in Figure 1. The experimental temperature was set at 370, 380, and 390 ◦C in supercooled liquid region,

while the microextrusion rate was set at 0.36 mm/min. The experimental microextrusion rate was set at 0.12, 0.24, 0.36 mm/min, while the temperature was set at 380 ◦C. During the ultrasonic microextrusion experiments, the mold was first heated to the setting temperature, and then the Zr35 sample was put into the mold, keeping the temperature for about 10 min, and the indenter contacted the sample with a pre-load of about 200 N. Then, the ultrasonic generator turned on, and the indenter started producing vertical ultrasonic vibration in addition to depressing the sample.

#### **3. Results**

#### *3.1. Effect of Ultrasonic Power Output*

Figure 3 illustrates the microextrusion results under different ultrasonic power outputs (which corresponds to various ultrasonic vibration amplitudes for the indenter) and the filling lengths of the 3 different circular slots and the entire extrusion length are shown in Table 1. From Figure 3a, the extrusion length (*L*) increases with increasing ultrasonic power output, such as *L* is only 3.43 mm for the supercooled liquid MGs formed under static loading, while the value of *L* increases to 15.42 mm under ultrasonic loading with power output of 60%. The detailed data are summarized in Table 1, from which the Zr35 alloy can be pushed into the *L*3 circular slot (0.75 mm diameter) when the ultrasonic power output is greater than 30%, which indicates that a sufficiently large ultrasonic vibration amplitude is necessary for enhancing microfilling capacities of the Zr35 MG.

**Figure 3.** Microphotos of extruded Zr35 alloy (**a**) and recalculated microextrusion lengths of samples at various ultrasonic power outputs (**b**).

**Table 1.** Microextrusion length of Zr35 alloy at various ultrasonic output powers.

According to the previous research [24], the microforming ability of MGs on mold filling in the SCLR can be described as,

$$P = 32\eta \times v \frac{L}{d^2} \tag{1}$$

where *P* is the flow stress of the MGs, η is the apparent viscosity of a fluid, *v* is the fluid velocity, *d* is the diameter of the cylinder groove, and *L* is the fluid filling depth.

Accordingly, a similar approach is introduced to describe the microfilling capacity of MG at various sections with different sectional areas. *L*∗ *i* is defined as the equivalent filling length of the different subsections, assuming that the whole equivalent microextrusion length is defined as *L\**, then,

$$L^\* = \sum\_{i=1}^3 L\_i^\* = \frac{L\_1}{d\_1^2} + \frac{L\_2}{d\_2^2} + \frac{L\_3}{d\_3^2} \tag{2}$$

where *L*1, *L*2, and *L*3 are the microfilling lengths of the different subsection slots shown in Figure 1, and *d*1, *d*2, and *d*3 are the corresponding diameters of these circular slots.

The extrusion lengths and the corresponding equivalent extrusion lengths are calculated, and summarized and described in Figure 3b. With increasing ultrasonic power output, it is clear that the equivalent extrusion lengths increase faster than the extrusion lengths. When the ultrasonic power output increased from 0% to 60%, the equivalent microextrusion lengths increased from 1.93 to 21.25 mm, which is 11 times longer than that of static loading, while the corresponding microextrusion length is just 4.5 times greater than that under static loading. Therefore, the equivalent extrusion length more objectively reflects the variation trends of the microfilling capacities of MGs at the microand nanoscales.

The true stress–strain curves of Zr35 MG extruded with different ultrasonic power outputs are depicted in Figure 4. The results show that the flow stress gradually reduces with increasing ultrasonic power output. Compared with the static loading process, the true stress is maximally decreased by 12.49%–60.17% when the ultrasonic power output increases from 30% to 60%.

**Figure 4.** True stress–strain curves for different ultrasonic power outputs.

#### *3.2. Ultrasonic Loading under Various Temperatures*

The ultrasonic microextrusion results with different supercooled liquid temperatures are shown in Figure 5, where the microextrusion rate is 0.36 mm/min and the ultrasonic power output is 40%. Figure 5a shows the microextrusion length (*L*) of Zr35 alloy at different supercooled liquid temperatures. Overall, the extrusion length increases with increasing supercooled liquid temperatures, wherein *L* with ultrasonic vibration at 370 or 380 ◦C is larger than that with static loading at 380 or 390 ◦C, which are marked with red and blue circles, respectively (the extrusion lengths for different temperatures are shown in Table 2). This phenomenon indicates that the ultrasonic vibration can improve the microfilling capacity of Zr35 MG similarly with temperature raising in the SCLR.

**Figure 5.** Ultrasonic microfilling length of Zr35 at different supercooled liquid temperatures: (**a**) microextrusion length (*L*); (**b**) equivalent extrusion length.

The equivalent extrusion lengths at different supercooled liquid temperatures are summarized in Figure 5b. The results reveal that the equivalent microextrusion lengths at 40% ultrasonic power output increase by 2, 5.83, and 7.13 respectively, compared with those of static loading under supercooled liquid temperatures of 370, 380, and 390 ◦C.

The true stress–strain curves of Zr35 extruded at different supercooled liquid temperatures are shown in Figure 6. The results illustrate that the flow stress of Zr35 gradually reduces with increasing supercooled liquid temperatures. Compared with the static loading process, the true stress at 40% ultrasonic power output is maximally decreased by 23.67%, 34.36%, and 34.92%, respectively, when the supercooled liquid temperatures are 370, 380, and 390 ◦C.

**Figure 6.** True stress–strain curves at different supercooled liquid temperatures.

#### *3.3. Effect of Microextrusion Rate*

Figure 7 illustrates the ultrasonic microextrusion lengths with various microextrusion rates, which is also summarized in Table 3, wherein the temperature is 380 ◦C and the ultrasonic power output is 40%. It is clear that the extrusion length reduces with the increasing of microextrusion speed. On the other hand, *L* is only 5.02 mm for the extrusion rate of 0.12 mm/min under static loading, while the value of *L* increases to 10.68 mm when the ultrasonic loading with power output of 40%, exhibiting an ultrasonic vibration dependence.

**Figure 7.** Ultrasonic extrusion length of Zr35 MG at various microextrusion rates.

**Table 3.** Extrusion length of Zr35 at different microextrusion rates.

Finally, the glassy structure of the microformed Zr35 alloys were characterized with X-ray diffraction, and one of the representative results of 380 ◦C and 60% ultrasonic power output is illustrated in Figure 8, wherein only a wide dispersion peak appears, demonstrating that the Zr35 alloy remains as amorphous structure after ultrasonic uniaxial compression.

**Figure 8.** XRD results of ultrasonic uniaxial compressed Zr35 sample.

#### **4. Discussion**

The above phenomena can be analyzed in terms of ultrasonic energy transmission. Actually, it is very difficult to directly measure the ultrasonic vibration characteristics of MGs during the ultrasonic microextrusion process. Therefore, the ultrasonic vibration energy of the alloy obtained from the ultrasonic microextrusion process could be estimated according to the ultrasound energy density between the ultrasonic vibrating indenter and the Zr35 sample.

According to Yao [25], the coefficient of the sound power transmission from the H13 indenter to the Zr35 sample can be expressed as in Equation (3).

$$\infty = \frac{4\mathfrak{p}\_{\text{H13}}\mathfrak{c}\_{\text{H13}}\mathfrak{p}\_{\text{Zr35}}\mathfrak{c}\_{\text{Zr35}}}{\left(\mathfrak{p}\_{\text{H13}}\mathfrak{c}\_{\text{H13}} + \mathfrak{p}\_{\text{Zr35}}\mathfrak{c}\_{\text{Zr35}}\right)^{2}} \tag{3}$$

where *C*H13 and *C*Zr35 are the longitudinal vibration wave velocities of H13 die steel and MG samples, respectively. According to the material properties of H13 steel [26] and Zr35 [27], the value of *C*Zr35 is 2861.5 m/s and the value of *C*H13 is 6072 m/s. Therefore, the value of αt is 0.739.

The sound energy density gained by the Zr35 sample can be calculated by Equation (4). The sound energy densities of the Zr35 samples at different ultrasonic power outputs are shown in Table 4.

$$E\_{\rm n} = \frac{1}{2} \xi\_{\rm H13}^2 \omega^2 \rho\_{\rm H13} \alpha\_{\rm t} \tag{4}$$

*E*n is the sound energy density of Zr35, ξH13 is the vibration amplitude of the indenter, and ω is the excitation angular frequency (ω = 2π*f* = 125,600 rad/s).

**Table 4.** The ultrasonic energy densities and amplitudes at different ultrasonic power outputs.

Based on the ultrasonic softening and thermal activation theories [25], the reduction of the material flow stress caused by the ultrasonic vibrations can be attributed to the ultrasonic volume effect, which is comprised of the acoustic softening and stress superposition effects. The total flow stress reduction by the ultrasonic volume effect can be expressed as in Equation (5).

$$
\Delta \sigma\_{\\$} = -K(\alpha\_l \xi)^n - 2\beta \dot{\pi} (E\_n/\dot{\pi})^m \tag{5}
$$

The negative sign indicates stress reduction, β and *m* are experimental constants of the material (*m* > 0), τˆ is the shear threshold of the material, which is equivalent to the shear strength of the material at absolute zero, αt is the sound power transmission coefficient, *n* is the hardening index and the value is 1, and *K* is the material strength coefficient, which is the slope of the curve of stress reduction and ultrasonic amplitude caused by the stress superposition.

The parameters of β, *m*, τˆ, *K*, and *n* are intrinsic parameters of the material, so the shear stress drop, σs, is only related and proportional to the ultrasonic energy density, *E*n*,* and ultrasound amplitude, ξ. With an increase in the indenter's ultrasonic vibration amplitude, the ultrasonic energy density, *E*n*,* absorbed by the Zr35 sample, should increase. Moreover, the value of the shear stress drop, σs*,* also increases, and the flow stress of Zr35 appears to decrease, which suggests that the ultrasonic volume effect on MGs is more obvious. Thus, the microforming capacity of Zr35 is greatly enhanced, and the equivalent whole extrusion length, *L\*,* becomes longer.

The phenomenon of true stress–strain various with ultrasonic power output in Figure 4 can also be illustrated with the Equation (5). With increasing of power output, the ultrasonic vibration amplitude of the indenter is increased, while the stress superposition effect generated by the high frequency intermittent impact between the indenter and Zr35 sample is also strengthened, which possibly increases the decrease of the true stress of MGs. It is worth noting that previous research revealed that as for the metallic glasses, the vibration induced softening responsible for the reduction of stress [6]. On the other hand, part of the absorbed ultrasonic energy converted into heat [28], which can improve the material flow of Zr35 alloy in the SCLR. Furthermore, the ultrasonic vibration of the indenter can generate the ultrasonic softening effect in Zr35 [29], which will reduce the deformation resistance and improve the microfilling capacity of Zr35. Therefore, improvement in the microfilling capacity of MGs should be the combined effect of the ultrasonic softening effect and increasing temperature, and should be more obvious for MGs at lower temperatures. This is the reason why the ultrasonic microextrusion process can have a similar effect on improving the microforming capacity of MGs in the SCLR as increasing temperature. The increase in the microfilling capacity of Zr35 by ultrasonic vibration reaches a maximum value at 390 ◦C.

Furthermore, the phenomenon of true stress–strain with respect to supercooled liquid temperature in Figure 6 can be explained with free volume theory and viscosity variation of MGs. The higher temperature can lead to the increment of free volume concentration in the Zr35 and the decrease of viscosity, which facilitates the thermoplastic forming of Zr35 alloy. When the ultrasonic vibration is superimposed on the Zr35 samples, atomic diffusion increases and, therefore, there is a more conspicuous softening phenomenon.

#### **5. FEM Analysis**

In order to analyze the ultrasonic flow deformation mechanism of MGs in the SCLR, ABAQUS software was used to simulate the effects of the ultrasonic vibration amplitude on the flow deformation behavior of Zr35 during ultrasonic TPMF in the SCLR. A constitutive relation based on the free volume model was selected [30] and expressed as:

$$\ln \tau\_{\sf s} = (m+n) \left[ \frac{W}{KT} + (\ln \gamma - \ln \gamma\_0) \right] + \ln \left[ s \left( \frac{1}{4} \right)^m \right] \tag{6}$$

where τs = 1/2σ is the shear stress, *m* = *n* = −1.31 × 10−3*T* + 1.00478 and *s* = 21.6 + 866 {1 + exp[(*T* − 674)/13.5] are the temperature-dependent parameters, and γ0 = 5.07 × 1033 s−1 is the reference strain rate of Vitreloy-1 BMG (i.e., Zr41.2Ti13.8Cu12.5–Ni10Be22.5 BMG). The Zr-based MGs studied in the present work have a similar composition to the Vitreloy-1 BMG, and the above parameters can be used in the calculation.

To eliminate the influence of friction on the flow deformation behavior of the MGs, the uniaxial tensile process of the MGs was simulated to study the ultrasonic-assisted flow deformation mechanism of the MGs. The sample for the FEM simulations was set to be a cylindrical Zr35 sample with a diameter of 3 mm and a height of 10 mm. An axisymmetric two-dimensional simulation model was used for quasi-static analysis because of the symmetrical structural characteristics of the sample. The upper end of the sample was stretched, and the lower end was fixed. The tensile stroke was set at 4 mm.

In the ultrasonic uniaxial tensile simulation experiments of Zr35, the supercooled liquid temperature was set to 370 ◦C, the ultrasonic frequency was set to 20 kHz, and the ultrasonic amplitudes were set to 0, 12, and 24 μm, in turn. A 20 mm/s drawing speed was applied to the upper end of the sample, and a sinusoidal displacement was superimposed onto the lower end of the sample for simulating the ultrasonic vibration. When the vibration amplitude was 12 μm, the superimposed displacement could be calculated as follows:

$$S = 0.012 \sin 125600t \tag{7}$$

The distribution of simulated equivalent stress of uniaxial tensile with ultrasonic vibration amplitudes of 0, 12, and 24 μm are shown in Figure 9a–c. The maximum equivalent stress at the different vibration amplitudes is 159.7, 138.2, and 114.0 MPa, respectively, which is a reduction of 13.5% and 28.6% with increasing ultrasonic amplitude. The distribution area of the maximum equivalent stress also decreased, which is shown in the red area of Figure 8. Additionally, the value of the equivalent strain is shown in Figure 10a–c, which was enhanced by the increasing ultrasonic vibration amplitude. The maximum equivalent strain increased by 16.74% and 33.38% when the ultrasonic vibration amplitude was increased to 12 and 24 μm, respectively. The maximum strain area exists in the upper and middle parts of the sample.

**Figure 9.** The distribution of the simulated equivalent stress the uniaxial tensile of Zr35 at different ultrasonic vibration amplitudes: (**a**) 0 μm; (**b**) 12 μm; and (**c**) 24 μm.

**Figure 10.** The distribution of the simulated equivalent strain of the uniaxial tensile of Zr35 at different ultrasonic vibration amplitudes: (**a**) 0 μm; (**b**) 12 μm; and (**c**) 24 μm.

The reason for this phenomenon is mainly attributed to the ultrasonic softening effect of the material caused by the assisted ultrasonic vibration. In the process of ultrasonic plastic deformation, the stress field generated by the internal deformation of the material is superimposed over the periodic stress field of the ultrasonic vibration. With an increase in the ultrasonic amplitude, the effect of ultrasonic softening becomes more obvious, the plastic forming of the material becomes easier, and more free volume is generated in the plastic deformation process of the MGs. The higher free-volume concentration in the MGs means a lower viscosity for the MGs, together with smaller flow units in the sample under assisted ultrasonic vibration. The more homogeneous spatiotemporal distribution of flow units facilitates the thermoplastic microformability of the MGs, based on the above experimental results and theoretical analysis.

The profiles of the corresponding velocity distributions obtained from the above FEM simulation results are shown in Figure 11. The results show that the velocity is distributed heterogeneously along the uniaxial tensile direction due to the unidirectional stress. To further distinguish differences in the material flow during the ultrasonic uniaxial tensile process at different vibration amplitudes (i.e., 0, 15, and 30 μm), the velocities (*V*) at positions A–C (with an amplitude of 0 μm), A1–C1 (with an amplitude of 15 μm) and A2–C2 (with an amplitude of 30 μm) are calculated and compared, as shown in Figure 11a. As delineated in Figure 11b,c, the flowing velocity has a value ranging from 19.85 to 1869.99 mm/s at positions A1–C1, and a value ranging from 421.71 to 3874.21 mm/s at positions A2–C2, which are two orders of magnitude greater than the velocities with vibration in the A–C areas (0.21–19.85 mm/s). This indicates that a larger ultrasonic vibration amplitude corresponds to a greater change in the flow rate of the amorphous alloy.

**Figure 11.** The simulated velocity distribution under three ultrasonic amplitudes by assuming a temperature of 370 ◦C: (**a1**) 0 μm; (**a2**) 15 μm; and (**a3**) 30 μm. (**b**,**c**) present the corresponding speed distribution at various positions.

Kim proposed a free-volume constitutive model to characterize the internal atom changes in amorphous alloys by studying the deformation behavior of amorphous alloys [30]. The relationship between free volume and strain rate is expressed in Equation (8).

$$
v\_f^\* = \left[\frac{1}{v\_{fc}} - (c \ln \gamma + l)\right]^{-1} \tag{8}$$

Here, *v*∗ *f* is the steady state free volume, *v*fe = (*T* − *T*0)/*DT*0 is the balanced free volume, and *c* and *l* are temperature-related parameters.

From the above Equation (8), it can be concluded that an increase in the strain rate will lead to an increase in the steady-state free volume and a decrease in the viscosity of the amorphous alloy, and the occurrence of plastic deformation will also be easier.

In general, higher ultrasonic vibration amplitudes can achieve higher flow velocities and easier material flow of Zr35 MGs in the SCLR. Thus, the microplastic forming capacity of Zr35 can be gradually improved by increasing the vibration amplitude, which is in agreement with the analysis of the equivalent stress and strain above.

#### **6. Conclusions**

In this work, the ultrasonic vibration was introduced to the microextrusion processing of MGs. The ultrasonic microformability of Zr35 in the SCLR was studied with experiments and FEM. The conclusions are as follows.

**Author Contributions:** Data Curation, G.H. and L.X.; Formal Analysis, Z.P.; Supervision, N.L.; Writing−Original Draft Preparation, G.H.; Writing–Review & Editing, G.H. and N.L.

**Funding:** This research was funded by the Science and Technology Support Program of Hubei Province, China (No. 2015BAA019), the Open Research Fund Program of Shanxi Key Laboratory of Non-Traditional Machining (No. 2017SXTZKFJG01), and the Open Research Subject of Key Laboratory of Manufacturing and automation (No. szjj2017-006), and supported by the fund of the State Key Laboratory of Solidification Processing in NWPU (No. SKLSP201611).

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **A Numerical Study of Slip System Evolution in Ultra-Thin Stainless Steel Foil**

#### **Zhongkai Ren 1, Wanwan Fan 1, Jie Hou 2 and Tao Wang 1,\***

Received: 13 May 2019; Accepted: 3 June 2019; Published: 5 June 2019

**Abstract:** In order to quantitatively describe the effect of the initial grain orientation on the inhomogeneous deformation of 304 austenitic stainless steel foil during tension, a three-dimensional uniaxial tension model was established, based on the crystal plasticity finite element method (CPFEM) and Voronoi polyhedron theory. A three-dimensional representative volume element (RVE) was used to simulate the slip deformation of 304 stainless steel foil with five typical grain orientations under the same engineering strain. The simulation results show that the number and characteristics of active slip systems and the deformation degree of the grain are different due to the different initial grain orientations. The slip systems preferentially initiate at grain boundaries and cause slip system activity at the interior and free surface of the grain. The Brass, S, and Copper oriented 304 stainless steel foil exhibits a high strain hardening index, which is beneficial to strengthening. However, the Cube and Goss oriented 304 stainless steel foil has a low deformation resistance and is prone to plastic deformation.

**Keywords:** ultra-thin foil; slip system evolution; tensile process; crystal plasticity; numerical simulation; grain orientation

#### **1. Introduction**

Precision stainless steel foil with thickness ranging from 0.01 to 0.1 mm is a high-end steel product, which has been widely used in micro-manufacturing, micro-electromechanical, and other sophisticated micro-products [1]. With the increasing miniaturization of components, higher requirements are put forward for high-quality precision stainless steel, such as good ductility, high dimensional accuracy, and low surface roughness [2,3]. When the foil thickness is reduced to microscale, the anisotropy of the material increases, and the size effects become significant [4,5]. In this case, the grain morphology, size, orientation, and grain boundary have important impacts on the plastic deformation behavior [6,7]. Therefore, the traditional macroscopic plastic deformation theory appears to be no longer applicable to the plastic deformation analysis of the stainless steel foil in microscale.

The crystal plasticity finite element method (CPFEM) is widely used to homogenize the discrete dislocations and analyze the macroscopic effects of dislocation slip, based on the continuum theory, which reflects the microstructural characteristics of materials [8–11]. The mechanisms involved in the macro and micro-deformation of non-ferrous metal materials during tensile deformation have been studied by many scholars using CPFEM. Si et al. [12] established a polycrystalline model based on CPFEM and Voronoi polyhedron theory, and studied the effect of grain size on inhomogeneous deformation and grain rotation during the deformation process of polycrystalline aluminum. The results showed that the plastic deformation occurred preferentially at grain boundaries, and the multi-system slip caused local hardening near grain boundaries. Hama and Takuda [13,14] used CPFEM to analyze the hardening and unloading behavior of magnesium alloy strips during tensile deformation. They found that the pyramidal slip system dominated in the loading process, and only the base slip systems were activated during unloading. Ritz and Dawson [15] studied the effect of grain morphology on tensile deformation of aluminum alloys using CPFEM, and pointed out that grain morphology had little effect on the anisotropy of elastic deformation but significantly affected the micro-stress distribution in the grain interior and at the grain boundary. Pi et al. [16] analyzed the effects of polycrystalline model type and tensile strain rate on deformation, necking, and texture evolution of polycrystalline aluminum during the tensile process by CPFEM. Their results showed that the stress increased with the increase in strain rate, and the calculated results by CPFEM were closer to the experimental results.

In order to balance the relationship between the total central processing unit (CPU) calculation time and the model size, the representative volume element (RVE) model with the smallest number of grains was adopted by many scholars to reflect the mechanical behavior of macroscopic samples. Nakamachi et al. [17] proposed a crystalline homogenization algorithm based on multi-scale asymptotic series expansion, established the RVE model for a micro polycrystal structure that could satisfy the periodicity condition of crystal orientation distribution, and verified the accuracy of the RVE model through analytical and statistical examinations. Jigh et al. [18] applied the RVE model to predict the mechanical behavior of metal foams with real microstructure, and studied the effects of different boundary conditions on mechanical properties. Zheng et al. [19] established the RVE model based on CPFEM to predict the influence of structural parameters and relative density of multi-stage honeycomb on its equivalent elastic parameters. The accuracy of the RVE model was verified by comparing with the elastic parameters calculated by the relevant theoretical analytical formula. Kami ´nski et al. [20] used the iterative and generalized stochastic perturbation technique as a finite element method to determine the effective elasticity tensor for rubber reinforced with the carbon black particles, and applied this to the homogenization problem of the RVE model in such a composite. This study showed some significant differences between numerical and analytical homogenization methods in the context of geometrical uncertainty in the RVE of the composite.

Based on the above literature reviews, it is clear that grain size and morphology as well as strain rate do have an important effect on the plastic deformation behavior of materials. At present, research on the effect of grain orientation on the tensile deformation of 304 austenitic stainless steels, based on the three-dimensional CPFEM model, is still limited. In the present paper, a three-dimensional RVE uniaxial tension model is established based on the CPFEM and the Voronoi polyhedron theory. The effects of initial grain orientation on the inhomogeneous deformation and evolution of slip systems of 304 stainless steel foil during uniaxial tension are analyzed in detail.

#### **2. Crystal Plasticity Model**

The main physical mechanism of plastic deformation of the face-centered cubic (FCC) metal at room temperature is dislocation slip [21]. According to the visco-plasticity criterion proposed by Schmid's law [22], the relationship between the shear strain rate . γα and the resolved shear stress τα of each slip system is established in the form of the exponential function as:

$$\dot{\boldsymbol{\gamma}}^{\alpha} = \dot{\boldsymbol{\gamma}}^{\alpha} f^{\alpha} \left( \frac{\boldsymbol{\tau}^{\alpha}}{\boldsymbol{\tau}\_{c}^{\alpha}} \right) \tag{1}$$

where the resolved shear stress τα is the driving force of the slip motion. The slip system α starts when the resolved shear stress reaches the critical value τα *c* .

The material rate sensitivity formula, established by Hutchinson [23], is as follows:

$$f^{\alpha} = \frac{\tau^{\alpha}}{\tau\_c^{\alpha}} \times \left| \frac{\tau^{\alpha}}{\tau\_c^{\alpha}} \right|^{\alpha - 1},\tag{2}$$

where . γ0 α is the reference shear strain rate of slip system α, *n* is the rate sensitive coefficient, n = 0 and n = ∞ correspond to viscoelasticity and rate-independent materials, respectively, τα is the resolved shear stress of the slip system α, τα *c* represents the dislocation slip resistance or critical resolved shear .

stress of the slip system α, which is the accumulation of the shear strain of the corresponding slip system on the hardening of the slip system α. τα *c* is expressed by:

$$\dot{\tau}\_c{}^{\alpha} = \sum\_{\beta=1}^{N} h\_{\alpha\beta} \left| \dot{\boldsymbol{\gamma}}^{\beta} \right| \tag{3}$$

where γβ is the shear strain rate of the slip system β and *h*αβ is the latent hardening coefficient.

In the present paper, the hardening model proposed by Bassani and Wu [24,25] was used to describe the interactions between different slip systems with different slip coefficients, which can accurately reflect the slipping process of all three hardening stages of FCC metal. The self-hardening moduli *h*αα can be expressed as follows:

$$h\_{\rm ant} = \left[ (h\_0 - h\_s) \text{sech}^2 \left( \frac{(h\_0 - h\_s) \gamma^\alpha}{\tau\_s - \tau\_0} + h\_s \right) \right] \times G \{ \gamma^\beta; \beta \neq \alpha \} \tag{4}$$

$$G\left(\boldsymbol{\upbeta};\beta\neq\alpha\right) = 1 + \sum\_{\beta=1\notin\alpha}^{N} f\_{\alpha\beta} \tanh\left(\frac{\boldsymbol{\upgamma}^{\beta}}{\boldsymbol{\upgamma}^{\alpha}}\right) \tag{5}$$

where *h*0 is the initial hardening modulus; *hs* is the hardening modulus in the easy slip stage; τ0 is the initial critical resolved shear stress; τ*s* is the critical shear stress saturation value; γ0 is the reference shear strain; and *f*αβ is the interaction coefficient between the α and β slip system. The factor depends on the geometric relationship of the two slip systems, which is represented by five constants *ai*(*i* = 1 ∼ 5).

The latent hardening moduli *h*αβ is given by:

$$h\_{a\emptyset} = qh\_{a\alpha\prime} \tag{6}$$

where *q* is the latent hardening parameter.

The above constitutive model was compiled into the user-defined material subroutine (UMAT) of ABAQUS finite element software by Fortran language for subsequent finite element simulation [26], and the combination of crystal plasticity constitutive theory and finite element method was realized. A numerical integration method using implicit differential equations was adopted to solve the rate-dependent crystal plasticity equation. The UMAT used the ABAQUS internal interface to communicate with the main solver. The specific process is shown in Figure 1.

**Figure 1.** The internal operation flow chart of ABAQUS finite element software.

#### **3. Finite Element Model for Stainless Steel Foil**

X-ray diffraction (XRD) phase analysis of the ultra-thin 304 stainless steel foil (0.05 mm) showed that the main phase constituent was FCC austenite. The elastic constants of single crystal austenite are C11 = 209 GPa, C12 = 133 GPa, C44 = 121 GPa [27]. Franciosi et al. [28] obtained the interaction coefficients between stainless steel slip systems by hardening experiments, which could be chosen as *a*1 = 0.625, *a*2 = 0.045, *a*3 = 0.045, *a*4 = 0.137, *a*5 = 0.122. The remaining unknown parameters could be determined by comparing the simulation results of RVE uniaxial tension with the measured stress–strain curves.

The average grain size and grain orientation information needed for simulation were obtained by the electron backscatter diffraction (EBSD) tests of the ultra-thin 304 stainless steel foil. EBSD diagrams of 304 stainless steel foil samples measured from the rolling direction (RD) and transverse direction (TD) are shown in Figure 2. The average grain size measured was 15 μm. The maximum density pole of the {111} pole figure was only 1.97 m.r.d (multiple random density), which indicates that the annealed 304 foil had little texture and the grain orientations were almost random. Therefore, the random grain orientations were applied to the polycrystalline model based on the Voronoi polyhedron theory.

**Figure 2.** Electron backscatter diffraction (EBSD) mapping of the transverse direction (TD) measured from the rolling direction (RD) of 304 stainless steel foil: (**a**) grain orientation map; (**b**) {111} pole figure.

The RVE model was established based on ABAQUS Standard. The effects of the number of grains and the number of elements in the grains on the tensile deformation accuracy of RVE model were analyzed, as shown in Figure 3. The RVE model contained 512 grains with a grain size of about 15 μm, and each grain contained 125 hexahedral elements (C3D8I), with average element dimensions of 3 × 3 × 3 μm3 (Figure 4b), which could guarantee the calculation accuracy. Different colors in the model represent different grain orientations, and the aggregates of the same orientation are one grain.

**Figure 3.** Effect of grain number (**a**) and unit number (**b**) on the representative volume element (RVE) model. The boundary conditions of the RVE uniaxial tension model are shown in Figure 4a:

All calculations were run on a workstation (2.6 GHz processor) with 20 multiple processors in parallel. The maximum number of increments was 100,000, to ensure convergence of the RVE model. It took around 5 h to complete one tension test of the RVE with 60% engineering strain.

According to the international standard ASTM-E345-16 [29], 0.05 mm thick 304 stainless steel foil tensile specimens were prepared and stretched using an INSTRON-5969 universal tensile testing machine (Instron corporation, Norwood, MA, USA). In the experiment, the stretching rate was 0.03 mm/min. The RVE model established above was subjected to uniaxial tensile simulation to an engineering strain of 60%. The obtained stress–strain curves were compared with the curves measured by tensile tests. The reasonable crystal plastic parameters were determined by optimization (see Table 1), and the comparison results shown in Figure 5 were obtained.

**Figure 4.** 304 stainless steel RVE tensile model: (**a**) boundary conditions in the simulation; (**b**) RVE model; (**c**) G411.

**Figure 5.** Comparison of the stress–strain curves between RVE simulation and experimental results.

**Table 1.** Constitutive model parameters of ultra-thin 304 stainless steel foil.

To study the effect of grain orientation on the motion of slip systems, five typical grain orientations (see Table 2) were assigned to the 411 grain (G411, Figure 4c) in the RVE model, and the other grains were given a random orientation, as shown in Figure 6. Then, the stress–strain curves of uniaxial tension to 60% engineering strain were obtained, as shown in Figure 7. It is clear that the five stress–strain curves coincide completely, indicating that a change of single grain orientation does not affect the mechanical properties of the stainless steel ultra-thin foil. The accuracy of the RVE model established in this paper is verified.

The 304 stainless steel had an FCC crystal structure. The dislocation slip motion occurred on the 12 slip systems {111} <110>, as shown in Table 3. The [100] direction of the crystal was consistent with the X-axis, with [010] and [001] corresponding to the Y-axis and Z-axis, respectively. According to the theory of crystal plasticity, the initiation of the slip system is always controlled by the shear strain rate on the slip system. The negative value of shear strain rate indicates that the slip should be along the opposite direction to the slip system [30].

**Figure 6.** {111} pole figure before RVE deformation with random orientation.

**Figure 7.** Stress–strain curves of G411 in the RVE model under five different grain orientations.

**Table 3.** Slip systems of face-centered cubic FCC metal.

#### **4. Results and Discussion**

#### *4.1. Microscopic Stress and Strain Distribution of G411*

Figure 8 shows the stress distribution of G411 under five typical grain orientations for the RVE models with 60% tensile engineering strain. It can be seen that the Brass, Copper, and S oriented grains had an obvious rotation phenomenon. The stress at the internal grain boundary was highly concentrated and the maximum stress value was high, even up to 2507 MPa for the Copper-oriented grain. The grain morphologies of the Cube and Goss oriented grains were similar after tensile deformation, which was mainly elongated along the tensile direction. The stress distribution was relatively uniform and the maximum stress value was small. The maximum stress value of the Cube oriented grain was 2004 MPa. It can be concluded that the different initial grain orientations led to the different degrees of the grain deformation under the same deformation conditions, and the microscopic stress distribution and the maximum stress value differed greatly.

**Figure 8.** Grain morphology and Mises stress distribution after the G411 deformation: (**a**) Brass; (**b**) Copper; (**c**) S; (**d**) Cube; (**e**) Goss.

Figure 9 shows the accumulative slip distribution of G411 under five typical grain orientations for the RVE models with 60% tensile engineering strain. As can be seen, the cumulative shear strain distributions of five typical oriented grains were not uniform, due to the restraint of adjacent grains, and there were obvious strain gradient characteristics. The strain was mainly concentrated in the boundary region with the internal grain contact. The Cube and Goss oriented grains had large deformations along the X-axis tensile direction. The cumulative shear strain distribution appeared to be more uniform and the cumulative shear strain value was small. The maximum cumulative shear strain value of the Cube oriented grain was 1.999. It can be seen that the initial grain orientation directly affected the cumulative shear strain distribution of the grains.

Considering the deformation coordination of polycrystalline, the grain deformation can be affected by the constraints of adjacent grains. Due to the different initial grain orientations, the order of grain deformation varies with the starting sequence of slip systems in different parts of the grain, so the deformation degree of the grain is different [31]. Compared with the resistance overcome by the slip of the grain internal dislocation, the slip at the grain boundary needs to overcome the resistance caused by the coordination of intergranular deformation, so the stress of polycrystalline plastic deformation is concentrated at the grain boundary [32].

**Figure 9.** Cumulative shear strain distribution after the G411 deformation: (**a**) Brass; (**b**) Copper; (**c**) S; (**d**) Cube; (**e**) Goss.

#### *4.2. Slip System Evolution of G411 with the Typical Grain Orientations*

In order to investigate the relationship between grain orientation and shear strain rate of the slip systems during tensile deformation, a node on the outside surface of G411, shown in Figure 4c, was selected for analysis, and the results are shown in Figure 10. When the G411 grain orientation was Brass, Copper, or S-type, the number and motion state of the activated slip systems at the node were similar, because of the approximate angles between the three given orientations and the tensile direction. The slip systems a2 and c3 were activated in the above three orientations. Cube and Goss oriented grains had the largest number of activated the slip systems—eight. For the Cube oriented grain, the shear strain rates of slip systems a2, c2, c3, and d2 were large and slipped along their positive directions. The shear strain rates of slip systems a3, b1, b2, and d3 were small and slipped along their opposite directions. For the Goss oriented grain, the slip systems a1, b3, c1, and c2 slid along their opposite directions and the shear strain rates were large, while the slip systems a3, b2, d1, and d3 slid along their positive directions and the shear strain rates were small. It can be concluded that the number and motion state of the activated slip systems at the same position varied greatly because of the different initial grain orientations. The Cube and Goss oriented grains had the largest number of activated the slip systems in the uniaxial tensile stress state, which was beneficial to the occurrence of dislocation slip movement.

**Figure 10.** Shear strain rates of a node on the G411: (**a**) Brass; (**b**) Copper; (**c**) S; (**d**) Cube; (**e**) Goss.

The starting process of the 12 slip systems of FCC metal during uniaxial tension deformation is shown in Figure 11. When the grain orientation was Cube type, the local coordinate system of the crystal coincided with the global coordinate system of the sample and the angle between grain orientation and tensile force direction was zero. It can be seen that at this time the slip systems of a1, b3, c1 and d1 were perpendicular to the direction of the force. Thus, shear strain did not occur and the shear strain rate was zero. For the Goss grain orientation, the crystal coordinate system did not coincide with the sample coordinate system and the angle between grain orientation and tensile force direction was 90◦. At this time, the slip systems a2, b2, c3, d2 were perpendicular to the tensile direction and the shear strain rate was zero. As shown in Figure 10d,e, the other eight slip systems were activated except for the above four slip systems perpendicular to the tensile stress. The shear strain rates of each slip system are different due to the influence of grain morphology and adjacent grains. In summary, the movement of the slip systems in the process of tensile deformation was analyzed by simulation and theory, and the accuracy of the crystal plasticity finite element model was verified.

**Figure 11.** Illustration of {111} planes for initial tensile process: (**a**) (111) slip plane; (**b**) (-111) slip plane; (**c**) (1-11) slip plane; (**d**) (11-1) slip plane.

Figure 12 shows the evolution of the shear strain rate of the slip systems a2 and c3 during uniaxial tensile deformation of the Brass oriented G411. It can be observed that the shear strain rate distribution of the slip systems was inhomogeneous. The slip appea red in the opposite direction inside the single crystal grain, which is conducive to the formation of sub-crystallines. The shear strain rate distribution of different slip systems was also various. The a2 and c3 slip systems were activated first at the grain boundaries. With the rotation of the slip surface and direction of the tensile deformation, the internal and free surface slip systems started. The slip strain rate distribution of the slip system a2 varied greatly from −0.321 to 1.956. The outside surface nodes mainly moved along the opposite direction of the slip system a2. The difference of the shear strain rate of the slip system c3 in the whole grain was only 1.662, and the distribution was relatively uniform. It can be seen that the slip systems were activated at the grain boundary first and then caused the movement of the internal and free surface slip systems, and finally formed a slip band in the whole grain. At the same time, the above conclusions can be drawn from the analysis of the shear strain rate evolution process of the other four typical grain orientation slip systems.

Affected by grain orientation, morphology, and polycrystalline deformation compatibility, the number of the activated slip systems and the magnitude of shear strain at different locations are quite different. The motion state of the activated slip systems during plastic deformation is also different. These differences lead to inhomogeneous deformation of the grain and contribute to the stress–strain concentration zone [33].

**Figure 12.** Shear strain rate along active slip system a2 (a2-1, a2-2, a2-3) and c3 (c3-1, c3-2, c3-3) for the G411 of Brass with the tensile time 0.5 s (a2-1, c3-1), 30 s (a2-2, c3-2), 100 s (a2-3, c3-3).

#### *4.3. Stress and Strain Curves of Typical Texture Orientation Dominant Polycrystalline*

An RVE model with a typical texture orientation was established. The number of grains with each dominant orientation accounted for 50% of the total grains. The simulated stress–strain curves are shown in Figure 13. As can be seen, the yield strength of the RVE model with the dominant texture orientation was approximately 193 MPa, but its deformation resistance varied greatly. In the plastic deformation stage, the stress–strain curves of Brass, S, and Copper oriented dominant models were higher than those of random grain oriented models. The stress–strain curves of Cube oriented and Goss oriented RVE models coincide basically and are significantly lower than those of random oriented RVE models. Under the 60% strain condition, the stress values of the Brass, S, and Copper oriented dominant models are higher than those of random grain oriented model. The maximum stress value of the Copper-type orientation-dominated model is 618 MPa. The stress values of Cube-type and Goss-type orientation-dominated models are approximately 495 MPa, which is lower than that of the random grain orientation model (538 MPa). The results show that Brass, S, and Copper oriented stainless steel materials have large energy storage, large plastic deformation resistance, and a high strain hardening index, which are beneficial to strengthening. Cube-oriented and Goss-oriented stainless steels exhibit low strength and low deformation resistance, and are prone to plastic deformation.

**Figure 13.** Comparison of stress and strain curves of RVE models with typical texture orientation.

#### **5. Conclusions**

(1) Based on the crystal plasticity theory and microscopic characterization analysis, a crystal plastic RVE model of 304 stainless steel foil was established. By comparing the tensile stress–strain curves between the RVE simulation and experiment, the calibrated crystalline plastic parameters can accurately reflect the mechanical properties of 304 stainless steel foil. Combined with the simulation and theoretical analysis of the evolution of slip systems during the tensile deformation process, the accuracy of the crystal plastic finite element model was verified.

(2) The crystal plasticity RVE model was used to simulate the effect of typical grain orientation on the inhomogeneous deformation of ultra-thin 304 stainless steel foil during tension. The results show that the numbers of start-up and movement state of the slip systems at the same location are quite different due to the various initial grain orientations, resulting in a great difference in grain deformation degrees and stress–strain distribution. The effect of grain orientation on the plastic deformation of polycrystals is mainly manifested in the mutual constraints and coordination of various grain deformation processes. During the tensile deformation process, the stress distribution and the shear stress with different slip systems are different due to the different initial grain orientation. Therefore, the initiating sequence of the slip systems is different, resulting in different deformation orders and deformation degrees. The grains in favorable orientations slip first, and the grains in unfavorable orientations are difficult to slip.

(3) The change of stress–strain curves in the tensile process of 304 stainless steel foil RVE model with typical orientation was analyzed by CPFEM. The results show that the Brass, S, and Copper oriented dominant models exhibit a high strain hardening index and are beneficial to metal strengthening. However, Cube and Goss oriented dominant models have lower strength and low deformation resistance, so 304 stainless steel foil with these orientations are prone to plastic deformation.

**Author Contributions:** Z.R. conceived and guided the simulation analysis; W.F. wrote the paper; J.H. provided experiment data, materials and experimental equipments; T.W. revised the paper.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 51804215), the China Postdoctoral Science Foundation (Grant No. 2019M651074), the Shanxi Province Science and Technology Major Projects (Grant No.<PHONE_NUMBER>5,<PHONE_NUMBER>8), the Taiyuan City Science and Technology Major Project (Grant No. 170203) and the Natural Science Foundation of Shanxi Province (Grant No. 201801D221221).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Elucidation of Shearing Mechanism of Finish-type FB and Extrusion-type FB for Thin Foil of JIS SUS304 by Numerical and EBSD Analyses**

#### **Yohei Suzuki 1,\*, Tomomi Shiratori 1, Ming Yang 2 and Masao Murakawa 3**

Received: 3 June 2019; Accepted: 1 July 2019; Published: 3 July 2019

**Abstract:** A numerical analysis using FE (finite element) analysis was performed to clarify the shearing mechanism in the process of extrusion-type fine blanking (FB) for a thin foil of JIS SUS304 in this study. Extrusion-type FB, in which a negative clearance between the punch and the die has been developed and investigated experimentally to improve the quality of the sheared surface in the blanking of thin foils. The resultant sheared surface for extrusion-type FB indicated an almost completely sheared surface, and the fracture portion on the sheared surface was much smaller than that in conventional FB, the so-called finish-type FB. The material flow and fracture criteria in extrusion-type FB were analyzed in comparison with those in finish-type FB. The differences in material flow and so-called critical fracture value were verified for the two processes. The principal stress near the shearing surface has mostly compressive components in extrusion-type FB due to its negative clearance, and the critical fracture value was also less than that in finish-type FB, in which the principal stress near the shearing surface has mostly tensile components. Furthermore, SEM observation with EBSD (electron back-scatter diffraction) analysis of the shearing surface was performed to verify the phenomena. Reductions in deformation-induced crystal orientation rotation and martensite transformation in extrusion-type FB were confirmed in comparison with those in finish-type FB from the analysis results.

**Keywords:** fine blanking; metallic microgear; finite element analysis; electron backscatter diffraction; critical fracture value

#### **1. Introduction**

Recently, the notable miniaturization of electronic devices and medical instruments has been observed. Accordingly, the miniaturization of their components and their high-precision capability is also required [1]. The fabrication of microparts with complex profiles using stamping press machines is attractive owing to its high productivity. Blanking is one of the typical stamping processes used to rapidly cut parts with complex profiles from sheet metal, and fine blanking (FB) [2] can be used to make a part with a fine shearing surface. However, problems due to the miniaturization of parts arise in microblanking. As parts become smaller, the sheet becomes thinner. In general, the clearance between the punch and the die is expressed as the ratio to the thickness of the sheet, so the absolute value of the clearance also decreases as the sheet thickness decreases [3]. According to findings on the FB process at the macro scale, the clearance is assumed to less than 1% of the thickness *t* [4].  Furthermore, when the thickness of the work material decreases, fracture is likely to occur owing to the effects of the surface roughness of the material and the crystal grain size [6–9], which affects the product accuracy. To solve these problems, the authors previously developed a novel FB process and demonstrated its advantages by an experimental comparison with the conventional FB process using a general-purpose precision stamping press machine [10]. The conventional FB process is finish-type FB with an extremely narrow positive tool clearance and a counterpunch. The newly developed process is extrusion-type FB with a negative tool clearance and a counterpunch pressure pad. By comparing the results, the developed process was found to be superior from the most important viewpoint of suppressing the fracture of the surface. However, the material flow and fracture mechanism have not yet been clarified, and furthermore, the most important parameters in the process are unknown.

In this study, an FE analysis is performed to clarify the material flow and fracture mechanism in extrusion-type FB in comparison with finish-type FB, particularly from the viewpoint of suppressing fracture or cracking on the shearing surface during the FB process. Furthermore, the mechanism of fracture suppression was verified by SEM observation with EBSD (electron back-scatter diffraction) analysis, which enables the observation of the material deformation state using the information obtained by the orientation analysis of the crystallinity of the shearing surface of samples.

#### **2. FEM Simulation Model and Conditions**

Figure 1 shows SEM images of microgears fabricated by finish-type FB and extrusion-type FB [10]. As described previously, the shearing surface of the microgear processed by extrusion-type FB is smoothly sheared without fracture in comparison with that processed by finish-type FB.

(a) finish-type FB (b) extrusion-type FB

**Figure 1.** SEM images of the microgear [10]: (**a**) finish-type FB; (**b**) extrusion-type FB.

To elucidate the mechanism of fracture suppression, we developed an analysis model for both FB methods for use in FE simulation, and the model and its conditions are shown in Figure 2 and Table 1, respectively. The microgear was assumed to be axisymmetric about the gear centerline, and a two-dimensional model was applied in this simulation to reduce the calculation time. The commercially available FEM (Finite element method) code DEFORM2D (Ver.11.1) was utilized for the simulation. The punch force *Fp* was processed as a constant displacement type, i.e., *Fp* was calculated as the reaction force *Fm* of the workpiece. The workpiece used was a JIS SUS304 sheet with a thickness t of 0.178 mm, and a microgear workpiece having an outer diameter of ϕ*Dw* of 3.5 mm was used to correspond to the experiment at conditions of the press in the previous report [10]. In our present FE analysis, the outer peripheral edge of the workpiece was assumed to be constrained, as shown in Figure 2, since a coil material having sufficient width relative to the size of the microgear was used in the experiment, and there was no material flow in the width direction of the material. A die diameter ϕ*Dd1* of 1.752 mm (tool clearance *Cl* of 2 μm) was used for finish-type FB, and a die diameter ϕ*Dd2* of 1.732 mm (clearance *Cl* of −8 μm) was used for extrusion-type FB. The punch diameter ϕ*Dp* of 1.748 mm and the counterpunch diameter ϕ*Dc* of 1.720 mm were common to both processes. The punch, die and blank holder/stripper were assumed to be rigid bodies, and the workpiece was assumed to be elastoplastic. Approximately 15,000 four-node rectangular elements were generated on the workpiece. Since the deformation is concentrated in an extremely narrow range in the deformation area around

the cutting edge of the tool, there is significant distortion in the elements [11]. The simulation result in a previous FB study, which revealed the relationship between the mesh size and the clearance *Cl*, was referred to for the determination of the mesh size [12]. Specifically, the mesh size in the analysis was set to about 1 μm, which is smaller than the clearance *Cl*. In such a case where the deformation of the elements was apparently large, a remeshing function was adopted to rebuild the meshes.

**Figure 2.** FEM simulation model.

**Table 1.** FEM simulation conditions.

The material constants were derived from the data available from an actual experimental tensile test giving the flow stress-plastic strain curve shown in Figure 3. Furthermore, to verify and observe the fracture process in both FB methods, we used the damage value C (critical fracture value [13]) obtained from the ductile fracture criterion [14] of Cockcroft and Latham defined as the value of the integral corresponding to the evolution of the maximum principal stress as follows:

$$\mathcal{C} = \int\_0^{\overline{\varepsilon}} \frac{\overline{\sigma}\_{\text{max}}}{\overline{\sigma}} d\overline{\varepsilon} \tag{1}$$

where *C*: critical fracture value, σ*max*: maximum principal stress, σ: effective stress, and ε: effective strain.

**Figure 3.** Flow stress-plastic strain curve.

The friction coefficient was assumed to be 0.08, referring to the value recommended by DEFORM2D for cemented carbide dies. Although there was a concern that the friction may change significantly during the blanking process, as a result of examining them in the report of Sasada et al. [15]. It was reported that the FEM analysis agrees well with the blanking result even if the friction coefficient was constant. Accordingly, the coefficient of friction was set constant in this study. The temperature was set to be constant in this analysis. Although temperature changes occur in the tool and material during blanking, the ratio of heat flow to the material could be considered negligibly small owing to the small volume ratio of the material to the die at the microscale.

#### **3. FEM Simulation Results and Discussion**

Since fracture occurred at a punch stroke of about 80% of the sheet thickness t according to our previous experimental results [10] for finish-type FB, the damage values (critical fracture values) at a punch stroke of 80% were investigated for both processes. Figure 4 shows a comparison of the damage value between a) finish-type FB and b) extrusion-type FB in the case of the punch penetration. In the case of finish-type FB, the result shows that damage accumulated in the region connecting the punch shoulder and die. In the case of extrusion-type FB, the damage value was also high in the punch shoulder and punch side, but it was lower in other regions including the shearing zone, which means that some allowance remains to prevent fracture. This was in agreement with the experimental results obtained with an actual stamping press machine in which extrusion type FB did not cause any breakage or separation of the workpiece, even at 80% punch penetration through the sheet thickness *t* [10].

**Figure 4.** Comparison of damage value defined as the integration value corresponding to the evolution of the maximum principal stress σ*max* for 80%*t* punch penetration between finish-type fine blanking (FB) and extrusion-type FB: (**a**) finish-type FB; (**b**) extrusion-type FB.

The von Mises stress and maximum principal stress distributions for both FB methods are shown in Figures 5 and 6, respectively, for the same condition of punch penetration of 80% as in Figure 4. It was found that, although the von Mises stresses for both FB methods showed similar distributions, the maximum principal stress distributions were significantly different. It can be observed that, in the case of finish-type FB, in the area between the scrap and the product (being blanked out), a tensile stress distribution appears to prevail, while in the case of extrusion type FB, a compressive stress distribution prevails. These results are consistent with the results for the damage value shown in Figure 4, in which higher maximum principal stresses corresponded to higher damage values, consistent with previous knowledge that the compression stress distribution can reduce the damage value and suppress fracture in blanking processes even if the von Mises stress is similar [16].

**Figure 5.** Comparison of von Mises stress for 80%*t* punch penetration between the finish-type FB and extrusion-type FB in Figure 4: (**a**) finish-type FB; (**b**) extrusion-type FB.

**Figure 6.** Comparison of maximum principal stress for 80%*t* punch penetration between the finish-type FB and extrusion-type FB in Figure 4: (**a**) finish-type FB; (**b**) extrusion-type FB.

From the various reports thus far, it is known that the stress distribution within a material is related to the material flow in the processing. For example, Huang et al. have shown the effect of the tool clearance (either positive or negative) on the die roll during blanking [17], and Thipprakmas et al. have clarified the mechanism of fracture during FB, in which an extremely small but positive tool clearance was used [18]. However, they have not yet clarified the fracture mechanism, in which a positive clearance and a negative clearance might cause different fracture behaviors. The material flows in both FB processes were also compared at the same punch penetration of 80% sheet thickness and Figure 7 shows the resultant material flows in the shearing zone. In the case of finish-type FB, the workpiece located immediately under the punch flows almost perpendicularly to that in the die interior portion, inducing material flow on the scrap side that was parallel to the interior material flow. Accordingly, we concluded that this material flow behavior generates a tensile stress field between the scrap side of the workpiece (which is pressed down by the blank holder) and the blanked-out workpiece, resulting in a consequently high cumulative damage value, ultimately leading to the breakage of the workpiece. In the case of extrusion type FB, a change in the direction of the workpiece flow is observed near the die corner B. In particular, immediately adjacent to point B, owing to the material flow towards the die portion B, the workpiece behaves as if it were self-crushed. As a result, we consider that a compressive stress field is generated where fracture is suppressed.

**Figure 7.** Comparison of material flow for 80%*t* punch penetration between finish-type FB and extrusion-type FB, in an enlarged view: (**a**) finish-type FB; (**b**) extrusion-type FB.

#### **4. Discussion Based on EBSD Analysis**

The shearing surfaces were observed by SEM with EBSD (electron back-scatter diffraction) to clarify the shearing mechanism for both FB methods. EBSD analysis is an effective methodology for evaluating the deformation state of grains in a workpiece. In particular, the KAM (kernel average misorientation) is a value that indirectly represents the degree of plastic deformation via the amount of crystal orientation and can correspond to the equivalent plastic strain in plastic working [19]. Furthermore, it has been used to clarify the fracture generation mechanism during microshear processing [20]. Since it is known that JIS SUS304 transforms from a ductile austenite phase to a brittle martensitic phase depending on the processing strain, information on the phase transformation will be also useful for understanding the fracture mechanism.

For sample preparation for EBSD analysis, first of all, the cross section of workpieces of the microgear half-blanked by the punch that penetrated about 60% of the sheet thickness for both FB methods was fabricated. Next, it was cut to the area shown in Figure 8, and the surface was mirror-finished by mechanical polishing and ion milling. EBSD analysis was performed at an acceleration voltage of 20 kV and a measurement interval of 0.15 μm. Figure 9 shows the analysis results in the form of KAM maps for the finish and extrusion-type FB methods. Figure 10 shows the analysis results in the form of phase maps. It was found that the phase transformation from the austenite phase (red area) to the martensitic phase (green area) occurs in the areas with high strain in the KAM maps. It was found that areas with a high strain of five degrees red areas and different crystal orientations are distributed in the area connecting the punch edge and the die corner. Moreover, the phase transformations occurred in areas with high strain in both methods consistent with the results of FE analysis. However, the areas with high strain and phase transformation were concentrated in the shearing zone in the case of finish-type FB, while they shifted to the scrap side (left side) for extrusion-type FB. In these areas, compression stress is dominant and does not contribute to fracture, as described in the last section. By assuming that cracks occur along the vertical shearing line (white lines in Figures 9 and 10), a difference in strain concentration on the white line (length of about 80 μm) can be seen for the two methods. Figure 11 shows the KAM values along the line from point a to point b in Figure 9 for the two methods. In finish-type FB, the KAM values are mostly five degrees from point a to point b. On the other hand, in extrusion-type FB, the KAM values along Y axis are approximately two degrees around point a and increase toward point b. These findings indicate that strain has already accumulated in the area where shearing is going to proceed in finish-type FB, while there is less accumulation of strain in the area in extrusion-type FB. As a result, extrusion-type FB can prevent fracture from the viewpoint of the strain accumulation region and crystal grain phase field.

**Figure 8.** Observation area of microgear for electron back-scatter diffraction (EBSD) analysis.

**Figure 9.** Comparison of kernel average misorientation (KAM) map for 60%*t* punch penetration between finish-type FB and extrusion-type FB: (**a**) finish-type FB; (**b**) extrusion-type FB.

**Figure 10.** Comparison of phase map for 60%*t* punch penetration between finish-type FB and extrusion-type FB: (**a**) finish-type FB; (**b**) extrusion-type FB.

**Figure 11.** Comparison of KAM values between a and b of Figure 7: (**a**) finish-type FB; (**b**) extrusion-type FB.

From the discussion in Sections 3 and 4, we can conclude that the extrusion-type FB process can prevent fracture and improve the blanking quality by changing the material flow during the process. It is a high-potential process for blanking at the microscale. However, since the material is compressed in the negative clearance zone in addition to the shearing, the load on the punch in extrusion-type FB is higher than that in conventional FB. It is necessary to clarify design guidelines for the process parameters, such as the optimal negative clearance and the radius of the die corner, in further work.

#### **5. Conclusions**

An FE analysis was performed to clarify the material flow and fracture mechanism in extrusion-type FB, in which a negative clearance was applied, in comparison with that in finish-type FB, particularly from the viewpoint of suppressing the fracture and cracking on the shearing surface during the process. The critical damage value, an index showing the possibility of fracture in the workpiece during FB, was introduced as a critical fracture value. Furthermore, the SEM observation of the cross-section of blanked workpieces with EBSD analysis was performed to confirm the results of the analysis. The conclusions of this study are as follows:

(1) The perimeter of the workpiece under a punch flows almost perpendicularly towards the die interior in finish-type FB. This workpiece flow behavior generates a tensile stress field between the scrap-side workpiece (which is pressed down by the blank holder) and the blanked workpiece, with a consequent high damage accumulation value, ultimately leading to breakage of the workpiece.

(2) In contrast, in the case of extrusion-type FB, since the perimeter of the workpiece flow under the punch flows towards the end of the die radius, high compressive stress occurred in this region, which led to different material flow and reduced cumulative damage.

(3) The critical damage value for extrusion-type FB was less than that for finish-type FB owing to the difference in stress state near the shearing zone: compressive stress is dominant for extrusion-type FB, while tensile stress is dominant for finish-type FB.

(4) The difference in strain distribution between finish-type FB and extrusion-type FB was analyzed by EBSD. The relationship between the strain distribution and the occurrence of fracture was clarified.

**Author Contributions:** Conceptualization, Y.S., M.Y. and M.M.; Experiment, Y.S.; Writing—Original Draft, Y.S.; Writing—Review & Editing, M.Y., T.S. and M.M.

**Funding:** This research received no external funding.

**Acknowledgments:** We would like to express our sincere gratitude to the members of the R&D section of our company and also to Bastien Poitrimol, a French international student cooperating with us, for his valuable assistance in the experiment.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Optimum Clearance in the Microblanking of Thin Foil of Austenitic Stainless Steel JIS SUS304 Studied from Shear Cut Surface and Punch Load**

#### **Yohei Suzuki 1,\*, Ming Yang 2 and Masao Murakawa 3**

Received: 22 December 2019; Accepted: 31 January 2020; Published: 3 February 2020

**Abstract:** An extrusion-type fine blanking with a negative clearance was proposed by the authors instead of standard fine blanking for creating a full-sheared surface in the micro blanking process. In this study, micro blanking experiments and finite element analyses with narrow, zero and negative clearances are carried out for the optimizing the clearance at which a shear cut surface can be finished with a full-sheared surface with the minimized punch load. Fracture criterion, hydrostatic stress and maximum punch stress for the conditions with various clearances are investigated. As a result, it was clarified that the clearance at which the cut surface does not fracture and minimization of the punch load is achieved is gained by the use of clearance −4 μm.

**Keywords:** punch load; cut surface quality; optimum clearance; fine blanking; blanking experimental; finite element method analysis

#### **1. Introduction**

In recent years, attention has been paid to micro-processing technologies suitable for mass production. However, problems, such as the lowering of material forming limits due to thinner materials [1–4] and the lowering of dimensional accuracy (e.g., the fracture that occurs on the cut surface during shearing) due to the downsizing of product dimensions, have not been solved. Various research studies have been conducted on manufacturing methods for the microfabrication of small parts, such as laser processing, etching processing, and electron beam processing [5–7]. However, these microfabrication methods are not necessarily optimal from the viewpoint of productivity and cost. The authors have selected press stamping, which is excellent in terms of both productivity and cost, and examined the feasibility of a micropart manufacturing method. More specifically, an involute tooth profile part with a microsize and a complicated shape was selected as a representative example of a microsize part, and the so-called fine blanking (FB) [8,9] for the effect of hydrostatic pressure on the ductility of the metal [10], was used. In particular, the feasibilities of the finish-type FB using the narrow clearance, and the extrusion-type FB using the negative clearance, were verified, and the relationship between the difference between the narrow and negative clearances and the shear cut surface was investigated. The results revealed that it was possible to process full-sheared surfaces by adopting negative clearance [11]. In addition, the finite element method (FEM) and material crystal analysis by Electron Back Scatter Diffraction (EBSD) have also revealed the difference in the processing mechanism between the two FB methods [12].

However, according to the above-mentioned verification results, it was predicted that the load applied to the punch tip would be increased by adopting negative clearance. This suggests that, in general, punch breakage and wear will also increase [13]. Even in conventional shearing, punch breakage and wear are two of the most important issues, and various studies on punch load in conventional shearing have been conducted so far. For example, Aoki et al. studied the tool cutting edge wear mechanism by shear experiments [13], Maeda et al. verified the progress of the tool cutting edge wear [14], Koga et al. verified the relationship between clearance and tool wear [15], and the punch wear and quality of punched products, in punching thin sheets [16–20].

FE analysis has been used to elucidate various processing mechanisms, and it has been also used for punch load analysis in blanking. For example, Nakashima et al. obtained an equivalent stress on the tool by analyzing the axisymmetric model with the tool set to an elastic body [21], and Hambi reported tool wear results in press stamping using a finite element code wear prediction model [22]. Falconnet et al. reported punch wear in the blanking of a copper thin sheet [23,24]. However, the punch load due to the difference in negative clearance, including zero clearance in the FB proposed in previous reports [11,12], has not been verified or analyzed. In this study, we aim to derive the optimal clearance at which the shear cut surface can be finished with a full-sheared surface and the punch load can be minimized by experimental verification and finite element analysis at the narrow, zero, and negative clearances.

#### **2. Experimental Procedure**

#### *2.1. Blanking Condition*

From the blanking experiment at the narrow clearance, zero clearance, and negative clearance, the conditions under which the cut surface does not fracture were verified. At the same time, the load during blanking at each clearance was measured. The material to be processed was JIS SUS304 made by TOKUSHU KINZOKU EXCEL Co., Ltd. (Tokyo, Japan), with a plate thickness *t* of 0.1 mm and a width of 20 mm. Table 1 shows the mechanical properties of the material. Table 2 shows the material of tools' (punch and die) composition and mechanical properties, available from Fuji Die Co., Ltd. (Tokyo, Japan) Next, Figure 1 shows a schematic diagram of the blanking process using negative clearance developed for progressive machining in actual production to explicitly explain how negative clearance punching is technically feasible, and Table 3 shows the detailed specifications of the die comprehensive blanking experiment series, particularly from the viewpoint of various tool clearances. To explain from another viewpoint, of the aforementioned comprehensive experiment series, referring first to die-set production, the punch is processed, using a grinding machine for small to micro-precision tools and high-precision production parts, and then the die is roughly processed by a wire cutting process and finally lapped to remove the deformed superficial layer on the tooth surface. In addition, to secure the positional accuracy of the tool (punch/die), JIS-SKD11, which can ensure strength and dimensional stability against heat treatment, can be used for parts such as the stripper plate, punch plate, and die plate. Jig-grinding finish was used for drilling the relevant parts where a relative position relationship is required to align the punch and the die and, additionally, shim tape was used to move the die position in 1 μm unit. For blanking experiment series, a cemented carbide punch with *Dp1* = ϕ1.748 mm was combined with a cemented carbide die with an inner diameter (*Dd1*), such that the clearance (*CL)* values between the punch and the die were 2, 0, −2, −4, and −8 μm (2%*t*, 0%*t*, −2%*t*, −4%*t*, −8%*t*) respectively. At a positive clearance *CL*, a punch stroke greater than the plate thickness of the workpiece is technically feasible, as aforementioned with reference to Figure 1, but at zero and negative clearances, if the punch stroke exceeds the plate thickness, the punch and die could come into contact with each other. Strictly speaking, since the die radius corner has actually a radius value of 0.01 mm, the punch and die do not come into contact even if the punch stroke becomes equal to the plate thickness. Therefore, in the actual process, the punch stroke was stopped once it was at 99% of the plate thickness, and the remaining 1% was made into a progressive die structure that could be removed at the next stage of the die set.  The plate presser force was set to

a maximum of about 500 N using a coil spring, and the reverse presser force was set to a maximum of about 200 N by the same method. For measuring the punch load, a load cell was provided on the upper surface of the punch, and a load displacement diagram was obtained by measuring the slide displacement of the press plate with a laser displacement meter. The press machine itself was not exclusively designed for FB purposes; a general-purpose screw servo press machine (made by DT-J515 Microfabrication Research Laboratory with pressurization capacity of 50 kN) was used, in order to have the same functions. It should be stressed here that controlling the amount of punch stroke is important to prevent interference between the punch and the die. In this experiment, the slide displacement of the press machine, measured with a laser displacement meter, and a load cell set on the upper surface of the punch, could be controlled in an amount of 1 μm unit.

**Table 2.** Material of the tools' composition and mechanical properties.

**Figure 1.** Schematic of extrusion blanking used in the mass-production progressive die system [11].

**Table 3.** Blanking tool specifications.

#### *2.2. FEM Simulation Model and Conditions*