Effect of Ultrasonic Vibration and Average Grain Size on the Deformability of T2 Copper in T-Shaped Micro-Upsetting

Abstract

Ultrasonic vibration (UV)-assisted forming technology has emerged as a significant advancement in the field of bulk micro-forming. This study presents a comprehensive experimental investigation into the micro-scale deformation behavior of metallic materials and its influence on size effects under UV, with a specific focus on the UV-assisted T-shaped micro-upsetting of T2 copper. Utilizing a custom-designed UV-assisted micro-upsetting apparatus, the flow stress, filling height, and microstructural evolution of T2 copper are systematically examined, considering various grain sizes, die opening angles, and ultrasonic amplitudes. The findings demonstrate that UV significantly mitigates the influence of grain size effects. Notably, the softening effect induced by UV becomes more pronounced with decreasing grain size, concomitantly leading to increased filling height. As the die opening angle expands, the required forming load increases. The enhancement of ultrasonic amplitude not only increases the V-groove filling height but also improves the surface quality. The optimal V-groove filling performance is achieved at an ultrasonic amplitude of 8.01 μm. It is crucial to note that increased ultrasonic amplitude generally improves forming performance, while excessive ultrasonic amplitude may lead to micro-crack formation within the material, thereby decreasing the formability of T2 copper. These results provide valuable insights into the complex interplay between ultrasonic parameters and material response in micro-forming processes, offering significant implications for the optimization of UV-assisted forming technologies in precision manufacturing applications.

1. Introduction

As metallic components are scaled down to the micrometer level, their plastic forming characteristics, including flow stress, interfacial friction, filling behavior, and surface roughness, become significantly influenced by size effects. These phenomena lead to a substantial deterioration in forming precision and part quality consistency, thereby imposing critical limitations on the broader application of micro-forming technology [1,2]. Wang et al. [3] demonstrated that the part geometry miniaturization results in a reduction in grain number within the material. This reduction leads to the dominance of individual grain anisotropy in determining the overall mechanical response and deformation behavior, consequently increasing the stochastic nature of formed part performance. In a complementary study, Wang et al. [4] investigated the surface morphology and microstructure of micro-extruded T2 copper components, revealing that the dimensional reduction in the extrusion rod or grain size enlargement can increase the non-uniform plastic deformation between the material’s inner and outer layers. Furthermore, the micro-extruded components exhibited noticeable bending deformation.

Numerous studies have been carried out to minimize the negative influence associated with size effects in polycrystalline materials [5,6,7], among which ultrasonic vibration (UV) has shown better performance. Ultrasonic energy fields offer several advantages, including low equipment costs, high energy density, and strong operability, making the technology promising for mitigating the adverse effects of size effects in the micro-forming processes of metal components [8,9,10]. The effects of UV on metal plastic deformation include the surface effect, which improves interfacial friction conditions, and the volume effect, which reduces material deformation resistance. These effects have been widely recognized [11,12]. Deshpande et al. [13] performed ultrasonic-assisted compression and tensile tests on pure aluminum, revealing that the low-angle grain boundaries increase with the enhancement of dislocation slip under UV, along with an increase in the volume fraction of subgrains. Xie et al. [14] conducted ultrasonic-assisted micro-ring compression experiments on aluminum alloy, showing that UV reduced the friction coefficient and improved surface quality. Bunget et al. [15] investigated the impact of UV on micro-extrusion processes, finding that forming forces were significantly reduced and the surface quality of parts was markedly improved under UV. Shiou et al. [16] significantly reduced surface roughness and achieved a nanoscale surface quality by applying UV-assisted polishing. Shimizu et al. [17] performed UV-assisted micro-indentation on pure copper with different grain sizes, noting that ultrasonic energy absorption was more pronounced in materials with larger grain sizes. Zhai et al. [18] conducted UV-assisted micro-cylinder compression experiments on copper, observing that the forming height of specimens increased with grain size. Wang et al. [19] carried out UV-assisted soft mold micro-bulging on 100 μm thick T2 copper sheets, demonstrating significant improvements in material deformation uniformity, forming accuracy, and forming limits under UV, along with enhanced surface quality. Pang et al. [20] performed UV-assisted micro-upsetting, showing that UV could reduce forces, accelerate material plastic deformation, improve forming efficiency, enhance surface morphology, and increase deformation uniformity. The abovementioned research indicates that UV significantly contributes to the reduction of forming force and the enhancement of surface quality, thereby facilitating the improvement of the forming quality of metal parts. However, the deformation laws and filling capabilities of materials at the micro-scale under the influence of UV are difficult to comprehensively characterize through conventional compression experiments using cylindrical specimens, especially for the plastic deformation behavior and size effect laws of materials in embossing processes. Therefore, a more representative fundamental experimental method is needed.

Compared to traditional UV-assisted compression experiments, the UV-assisted T-shaped micro-upsetting experiment adopted in this study enables a more intuitive and comprehensive investigation into the mechanical properties and filling behavior of materials, representing an innovation in the research approach of this paper. In order to reduce the negative influence of size effect on metal materials, experimental research combining T-shaped micro-upsetting and UV is carried out to explore the micro-scale plastic deformation behavior of metal materials. Utilizing both the volume effect and surface effect induced by UV, an improvement of micro-scale filling performance and deformation ability is expected. Specifically, this paper conducts an experimental study on the UV-assisted T-shaped micro-upsetting of T2 copper. Through heat treatment, specimens with different grain sizes are obtained to investigate the variations in flow stress and filling height and to analyze the influence of UV on the grain size effect. Dies with different opening angles are designed to study the impact of UV on the mechanical properties of the material under various filling size conditions. Additionally, metallographic analysis is performed on the material under different ultrasonic amplitudes to determine the optimal forming process parameters.

2. Experimental

2.1. Experimental Setup

To study the influence of UV on the micro-upsetting deformation behavior of T2 copper, a UV-assisted micro-upsetting experimental setup was built, as shown in Figure 1. The experimental apparatus is based on a universal electronic materials testing machine (Load cell capacity: 100 kN) and includes a mold frame for fixing the UV device, an ultrasonic transducer, an ultrasonic horn, ultrasonic power, and a die with V-groove. The UV frequency is 19.70 kHz, and different ultrasonic amplitudes are generated by adjusting the output power. A laser vibrometer is used to measure the output amplitude, with a measured amplitude range of 1.6–15.2 μm. The die material is 45 steel with chemical composition listed in

Table 1. Chemical composition of 45 steel (wt.%).

C	Si	Mn	P	S	Cr	Ni	Cu
0.42–0.50	0.17–0.37	0.50–0.80	≤0.035	≤0.035	≤0.25	≤0.25	≤0.25

. There are four different die opening angles (α): 15°, 25°, 35°, and 45°, as shown in Figure 2. The opening width (L) is uniformly set to 1 mm, and the edge fillet radius (R) is 0.2 mm.

2.2. Experimental Material

T2 copper featured by corrosion resistance, strong electrical conductivity, and good ductility is widely used in the field of microelectronic devices. The chemical composition is listed in

Table 2. Chemical composition of T2 copper (wt.%).

Cu	Sn	Zn	Bi	Sb	Pb	Fe	As	S	O
≥99.90	≤0.002	≤0.005	≤0.002	≤0.002	≤0.005	≤0.005	≤0.002	≤0.005	≤0.006

. The experimental material is cold-drawn T2 copper rod with a diameter of 2 mm. Micro-cylindrical specimens with dimensions of Φ2 × 2 mm were prepared using wire cutting, as shown in Figure 3. To investigate the influence of grain size effects on the material deformation behavior, specimens were heat treated at different temperatures in vacuum conditions. Parameters of heat treatment are listed in

Table 3. Parameters of heat treatment and average grain size of specimens.

Heat Treatment	400 °C for 3 h	600 °C for 5 h	700 °C for 12 h
Average grain size	8.8 μm	43.5 μm	84.6 μm
Microstructure

. After mechanical polishing, the specimens were etched using a ferric chloride hydrochloric acid solution (FeCl₃:HCl:H₂O = 1:3:17). The microstructures were observed using a metallographic microscope. The average grain sizes were measured according to the methods specified in the ASTM E112 standard, and the measured average grain sizes along with the corresponding microstructures are presented in Table 3.

3. Results and Discussion

3.1. Effect of Grain Size

Micro-upsetting experiments with UV and without UV were conducted on specimens with three different grain sizes. Except for the grain size, all other experimental parameters remained constant. The die opening angle was 25°, the punch speed was 0.1 mm/s, the pressing displacement was 1.5 mm, and the ultrasonic amplitude was 3.12 μm. Each load-stroke curve was performed three times to ensure reproducibility, and the error is within ±0.061 kN. The load-stroke curves are shown in Figure 4. Under the same pressing displacement, the load significantly decreased as the grain size increased. The maximum load reduction under conditions without and with UV was 15.7% and 11.7%, respectively. The softening effect due to UV varied for specimens with different grain sizes. When the grain size was 8.8 μm, the load decreased by 0.39 kN under UV, whereas for a grain size of 84.6 μm, the load decreased by only 0.2 kN. This indicates that the UV softening effect is more pronounced for smaller grain sizes.

The deformation resistance increases with the decrease in grain size, which is one of the manifestations of the grain size effect. This is mainly related to the proportion of grain boundaries and can be explained by the following Hall–Petch relationship [21].

$${\sigma }_y={\sigma }_0+{\displaystyle \frac{k}{\sqrt{d}}}$$

(1)

where ${\sigma }_y$ is the yield stress (MPa). ${\sigma }_0$ is the lattice friction stress (MPa), representing the resistance to dislocation movement in a single crystal. k is the Hall–Petch slope (MPa∙mm^0.5), and d is the average grain size (mm). According to the Hall–Petch relationship, as the grain size d decreases, the term $k/\sqrt{d}$ increases, leading to a higher yield strength ${\sigma }_y$. This is because finer grains result in a larger number of grain boundaries, which act as barriers to dislocation motion, thereby increasing the material’s resistance to deformation. This relationship highlights the significant influence of grain size on the mechanical properties of materials, particularly in micro-forming processes.

Based on the linear elasticity dislocation theory under the interaction of dislocations and grain boundaries, the Hall–Petch slope k can be regarded as the energy required for dislocations to slip through grain boundaries, meaning the work required for a dislocation to move a certain distance from the grain boundary is essentially constant. This distance is proportional to the square root of the grain size. It is assumed that in UV-assisted forming, grain boundaries can absorb UV energy, causing changes in the strain energy of the grain boundaries and reducing the dislocation energy barrier, thereby decreasing the energy required for dislocations to be ejected from the grain boundary. Based on this assumption, the change in shear stress $\mathsf{\Delta }\tau$ caused by the grain size can be expressed as follows [22]:

$$\mathsf{\Delta }\tau ={\displaystyle \frac{E_{UV}}{xb}}$$

(2)

where $E_{UV}$ is the UV energy (J), x is the distance (nm) the dislocation slips from the grain boundary, and b is the Burgers vector (nm). The distance x is proportional to the square root of the grain size and can be expressed as follows [22]:

$$x={\displaystyle \frac{\sqrt{h}}{2}}\sqrt{d}$$

(3)

where h is the inter-dislocation spacing (nm), which depends on the inherent properties of the grain boundaries. By substituting Equation (3) into Equation (2), $\mathsf{\Delta }\tau$ can be expressed as follows:

$$\mathsf{\Delta }\tau ={\displaystyle \frac{{2E}_{UV}}{b\sqrt{hd}}}$$

(4)

It can be seen that under constant UV energy, the smaller the grain size, the greater the variation in shear stress, which macroscopically manifests as a more pronounced softening effect induced by UV. Simultaneously, this result also indicates that, compared to the case without UV, the variation amplitude of the load curve for specimens with different grain sizes under UV is reduced. In other words, UV can reduce the influence of grain size effects on deformation resistance.

In micro-scale plastic forming processes such as micro-embossing, the microstructure filling height is one of the key factors for evaluating the quality of micro-forming. The T-shaped micro-upsetting experiment can intuitively reflect the micro-scale filling performance of materials. Figure 5 shows the V-groove filling height for specimens with different grain sizes. It can be seen that the smaller the grain size, the larger the filling height, and the filling height is further increased under UV. Since the V-groove size is in the micrometer range and comparable to the grain size of the specimen, the deformation behavior of individual grains has a greater impact on the overall forming performance, exhibiting a significant grain size effect, as shown in Figure 6. When the grain size is smaller, grain rotation and coordinated deformation within and between grains are more easily activated, thereby increasing the filling height. This result is consistent with the findings by Xu [23], who conducted micro-forming by using ultrafine-grain pure aluminum and found that the smaller the grain size, the better the filling effect and forming quality. The input of UV energy further enhances the material flowability and coordinated deformation ability, thus significantly improving the filling height under UV.

3.2. Effect of Die Opening Angle

Figure 7 illustrates the load-stroke curves for different die opening angles under conditions without UV and with UV. It can be observed that, at the same stroke, the load increases as the die angle increases. The deformation of the specimen during the upsetting process is divided into three stages. In stage I, the material primarily undergoes compressive deformation. As the stroke increases, the deformation force experienced by dies with different opening angles remains almost identical, indicating that the material extrusion deformation is extremely slow. Most of the material flows laterally, with only a small portion entering the V-groove and resulting in minimal contact with the sidewalls of the groove. Therefore, the deformation force of the material shows almost no variation under upsetting with dies of different opening angles. In stage II, the effect of material extrusion deformation gradually strengthens, and the extrusion height slowly increases. The contact area between the specimen and the sidewalls of the V-groove begins to expand, leading to increased friction and a slow rise in load. In stage III, the contact area between the specimen and both the die and the punch increases, causing the load to rise rapidly. The deformation mode of the specimen is dominated by extrusion, and the extrusion height further increases. Zhang et al. [24] carried out T-shaped compression tests on low carbon steel with die opening angles of 15°, 30°, and 90°, respectively, and found that the load increases when the angles become larger, which is consistent with the results in this work.

Compared to the case without UV, the application of UV resulted in load reductions of 15% and 17% for die angles of 45° and 15°, respectively. This indicates that under the same reduction in height, UV significantly decreases the forming load. This phenomenon can be attributed to two main factors. Firstly, the Blaha effect of UV enhances the activity of material dislocations and alleviates dislocation pile-ups, leading to a softening effect that reduces deformation resistance. Secondly, the friction at the interface between the die and the specimen is altered under UV. Ngaile et al. [25] investigated the influence of ultrasonic vibration on extrusion force and found that the maximum reduction in extrusion force was 23%, with a significant improvement in the surface quality of micro parts. This is primarily attributed to the surface effect of ultrasonic vibration, which alters the direction of friction between the mold and the workpiece surface. It is quite similar to the condition in this work, as illustrated in Figure 8. The vertical component of the vibrational load reduces the average contact stress at the specimen/die interface, while the horizontal component causes a periodic change in the direction of friction, significantly lowering the frictional force. The combined influence of these two factors results in a notable decrease in the load required for specimen forming and an improvement in the forming height. Consequently, the application of UV enhances the filling ability of the material.

3.3. Effect of Ultrasonic Amplitude

Ultrasonic amplitude is one of the key parameters in the UV-assisted forming process, representing the magnitude of the ultrasonic energy output by the transducer. Using the specimen with a grain size of 43.5 μm and a die opening angle of 25°, the effect of different ultrasonic amplitudes on the forming performance of the specimen during the T-shaped micro-upsetting process was investigated. Figure 9 shows the load-stroke curves under different ultrasonic amplitudes. When the ultrasonic amplitude is 13.97 μm, the load decreases by approximately 24%, and the load decreases further as the amplitude increases, which aligns with findings reported in numerous studies. At the microscopic level, higher ultrasonic energy density facilitates dislocation slip and annihilation by overcoming barriers such as grain boundaries, manifesting macroscopically as a reduction in deformation resistance. The decrease in deformation resistance indicates enhanced material flowability, which directly impacts the microstructural filling performance. During the T-shaped micro-upsetting process, the specimen material primarily flows in two directions: laterally and into the V-groove. To evaluate the filling performance of the material, the V-groove filling coefficient λ is introduced:

$$\lambda =a/b$$

(5)

where a is the maximum filling height (mm), and b is the maximum lateral width (mm). It is evident that a larger λ indicates more material flowing into the V-groove, resulting in better filling performance. Figure 10 shows the V-groove filling coefficient under different ultrasonic amplitudes. As the ultrasonic amplitude increases, λ first increases and then decreases. When the ultrasonic amplitude is 8.01 μm, the filling performance is the best. This result suggests that when the ultrasonic amplitude is too large, more material flows laterally, leading to a reduction in V-groove filling capacity.

The end surface appearances of specimens under different ultrasonic amplitudes were observed by scanning electron microscope (SEM), as shown in Figure 11. In the case without UV, the end surface appearance is flat and smooth, and the edge profile is clear. After the superposition of UV with the amplitude of 5.57 μm, no significant difference in morphological features at the end surface is observed. However, after increasing the ultrasonic amplitude to 13.97 μm, the lateral area appears visible cracks at an angle of 45 degrees. Additionally, the cracks are mainly concentrated in the surface rather than extending into the material. During the material deformation process, the internal region of the material is in a state of triaxial compressive stress, while the end surfaces are in a state of plane stress. The internal material is subjected to strong constraints, resulting in relatively uniform deformation. In contrast, the surface lacks such constraints, leading to lower resistance to material flow and thus causing non-uniform deformation. The application of high-amplitude UV further exacerbates this non-uniform deformation, resulting in significant stress concentration and ultimately leading to the formation of cracks. It should be noted that this phenomenon may also be observed in other metals. As reported by Xie et al. [26], proper ultrasonic amplitude can improve the formability of AZ31 magnesium alloy, while excessive ultrasonic amplitude may reduce the flow stress and plasticity of AZ31 magnesium alloy leading to the tendency of brittle fracture, which is attributed to the hardening effect caused by the excessive ultrasonic amplitude.

The central cross-section of the specimen was cut, ground, and polished, and the microstructure of the specimens under different ultrasonic amplitudes was observed. The metallographic structure is shown in Figure 12. In the case without UV, the V-groove filling height was 1099 μm. After applying UV, the filling height increased to 1125 μm and 1108 μm under the ultrasonic amplitude of 5.57 μm and 13.97 μm, respectively. Correspondingly, the lateral material height decreased while the width increased. This indicates that UV promoted the V-groove filling ability of the material. Further observation of the metallographic structure revealed that, in the case without UV, more micro-cracks appeared on the material surface at the corners. However, after applying UV with an amplitude of 5.57 μm, the micro-cracks were significantly reduced. This is attributed to the continuous change in the direction of friction at the specimen/die interface under UV, which reduces the frictional resistance on the material surface and promotes uniform deformation. When the ultrasonic amplitude increased to 13.97 μm, micro-cracks were observed in the lateral area, which is related to the unstable plastic flow of the material. When the ultrasonic amplitude is excessively large, significant stress concentration occurs at the local defect positions, reducing the ability of uniform plastic deformation and leading to premature fracture. Therefore, selecting an appropriate ultrasonic amplitude is crucial for improving the material plastic forming capability

4. Conclusions

• UV can effectively reduce the influence of grain size effects on material plastic forming. The smaller the grain size, the more obvious the softening effect of UV, and the better the V-groove filling performance of the material.
• The forming load in T-shaped micro-upsetting increases with the die opening angle, primarily due to the continuous change in the direction of friction at the specimen/die interface under UV, which reduces the load required for material plastic deformation.
• As the ultrasonic amplitude increases, the forming load monotonically decreases, while the V-groove filling coefficient λ initially increases and then decreases. The material exhibits optimal V-groove filling performance when the ultrasonic amplitude is 8.01 μm.
• An appropriate ultrasonic amplitude improves material flowability and reduces surface cracks. However, excessive ultrasonic amplitude can lead to stress concentration within the material, resulting in micro-cracks and premature fracture failure.