**0 Preface**
With the rapid advancement of modern science and technology, brittle materials have become essential in various high-tech industries, such as aerospace, optics, and electronics. These materials often require extremely high precision and surface quality. However, processing brittle materials remains a significant challenge due to their high brittleness and low fracture toughness. The elastic limit and strength of these materials are very close, meaning that once the applied load exceeds the elastic limit, the material tends to crack or fracture, resulting in surface damage that negatively impacts performance [12, 13]. As a result, traditional methods like grinding and polishing are not only inefficient but also difficult to automate, limiting their ability to process complex curved surfaces. This has made it increasingly important to develop advanced techniques for ultra-precision machining of brittle materials.
In recent years, significant progress has been made in the processing of materials like germanium. With the development of diamond tooling and ultra-precision machine tools, it is now possible to achieve high-quality surface finishes through ultra-precision cutting. This method, which focuses on plastic deformation rather than brittle failure, offers advantages such as higher efficiency, better controllability, and the ability to handle complex geometries. This paper reviews the current state of research on ultra-precision machining of brittle materials and highlights some key challenges, aiming to inspire further exploration into plastic domain processing techniques.
**1 The Theory of Brittle-Plastic Deformation under Sharp Indenter**
The possibility of ultra-precision turning of brittle materials using sharp diamond tools relies on the fact that these materials can undergo plastic deformation under certain conditions. Over the past few decades, numerous indentation experiments have been conducted on hard and brittle materials. During these experiments, a diamond indenter is pressed into the material with a controlled force, and the resulting deformation is observed. A typical cycle of loading and unloading reveals the progression from initial plastic deformation to cracking, as shown in Figure 1 [1].
From the figure, it's clear that even brittle materials can exhibit some degree of plastic deformation under small loads. As the load increases, the material transitions from plastic deformation to brittle failure, leading to internal and surface cracks. The load at which this transition begins is called the critical load, and the corresponding depth is known as the critical depth. These parameters are crucial for understanding the behavior of brittle materials under external forces.
During the indentation process, intermediate cracks typically form first, extending perpendicular to the surface. These cracks cause the most severe damage. Researchers have studied the relationship between the length of these cracks and the applied load, deriving formulas that help predict crack propagation [4].
**2 Ultra-Precision Grinding of Brittle Materials**
Ultra-precision grinding is a modern technique used to machine brittle materials. It involves the use of diamond grinding wheels on high-rigidity machines. Evans and Marshall simulated the cutting action of abrasive grains on a diamond wheel by using a diamond indenter to shape the surface of brittle materials like glass. When the applied load exceeds the critical load, the brittle cracking system becomes evident, as shown in Figure 2 [5].
To achieve ultra-precision grinding, the goal is to remove material through plastic deformation rather than brittle fracture. The thickness of the abrasive grain is referred to as the critical cutting thickness. Many researchers have explored the transition from brittle to ductile behavior during grinding [6–8]. T. G. Bifano, for example, derived a formula for the critical cutting thickness based on extensive experiments on materials like glass and ceramics [6].
Japanese scholars like Naoya Ikawa have also contributed to this field, studying how different abrasive grain sizes affect the surface of single-crystal silicon and lithium niobate [9]. While this research shows promise, there is still much to learn about the impact of grain size on critical cutting thickness.
In the late 1980s, North Carolina State University developed an ultra-precision grinding machine with a spindle stiffness of 50 MN/m. This machine was used to grind various optically brittle materials, producing smooth surfaces without cracks [10]. Similarly, Japan and the UK have developed their own ultra-precision grinders, achieving superior surface quality compared to conventional polishing methods. However, challenges remain, such as ensuring uniform distribution of abrasive grains and preventing clogging, which can lead to increased grinding forces and surface cracks.
To address these issues, Japanese researchers proposed ELID (Electrolytic In-Process Dressing) grinding in 1987. This technique uses electrolysis to dress the grinding wheel during the process, maintaining its sharpness and enabling stable ultra-precision grinding. The grain size of the grinding wheel used in Japan has reached 5 nm, with surface roughness values below 1 nm [11].
ELID grinding has gained attention worldwide and is now widely used for ultra-precision machining of brittle materials. In China, Harbin Institute of Technology began researching ELID grinding in 1993, achieving remarkable results in grinding brittle materials like ceramics and optical glass. Surface roughness values have reached the nanometer level, demonstrating the effectiveness of this technique. However, challenges such as oxide films on the grinding wheel surface and incomplete pressing of the surface layer still need further study.
**3 Ultra-Precision Turning of Brittle Materials**
Since 1987, Blake and Scattergood from North Carolina State University conducted pioneering ultra-precision turning experiments on brittle optical materials like single-crystal crucibles. They successfully achieved plastic deformation during the turning process, achieving a surface roughness of 8 nm [13]. Their work introduced the relationship between cutting geometry and critical cutting depth when using circular-arc diamond tools, proposing a brittle-to-ductile cutting model as shown in Figure 3.
Due to the use of a circular-arc tool, the effective cutting thickness increases from zero to a maximum value as it moves from the tool tip to the surface being machined. When the cutting thickness reaches a critical value, the material begins to fracture. Below this threshold, the material is primarily removed through plastic deformation. If the crack propagation depth does not reach the surface, a smooth finish can be achieved. The part of the fracture that occurs on the arc surface will be cut off during subsequent passes.
This model shows that plastic domain turning of brittle materials does not mean the entire material is plastically deformed. Instead, only the material near the cutting edge is removed through plastic deformation, while the rest is removed in a brittle manner. This distinction is crucial for achieving high-quality surfaces.
The feed rate plays a significant role in determining the critical cutting thickness. As the feed rate increases, the critical cutting thickness shifts along the tool edge, making it easier for cracks to propagate to the surface. Blake proposed a formula for the critical cutting thickness [13], which relates the feed rate and the radius of the turning tool.
Further studies by Blackey improved the accuracy of the critical cutting thickness calculation by considering the effect of crack propagation depth [14]. His experiments on single-crystal silicon showed that the crack propagation depth is approximately 3 to 10 times the critical cutting thickness.
Using a scanning electron microscope, Blackey analyzed the chip morphology of diamond-cut single-crystal crucibles. He found that chips near the tool tip were thin and continuous, indicating plastic deformation, while those farther away were thick and discontinuous, showing brittle deformation. The transition between these two states was clearly visible on the chips.
Nakasuji and others also studied the brittle-to-plastic transition in turning processes [16], finding results consistent with Blackey’s work. However, they also observed that the surface roughness of single-crystal silicon exhibited a fan-shaped pattern due to its anisotropic nature. Experiments along different crystal orientations showed varying cutting forces, which affected surface quality.
Takayuki Shibata explained this phenomenon in terms of slip systems, but the explanation was limited since brittle materials inevitably experience brittle failure during turning. Therefore, a more comprehensive approach is needed.
The cutting edge radius in ultra-precision machining of brittle materials is often comparable to the cutting thickness, making its influence significant. Although some studies have examined the effect of the cutting edge radius on cutting forces, further research is needed on its impact on the brittle-to-plastic transition.
KiovanolaJH found that a -30° rake angle facilitates continuous chip formation and plastic processing in glass. Similar findings were made in the ultra-precision turning of materials like single-crystal silicon, where a large negative rake angle promoted plastic deformation. Japanese researchers have also used negative pressure on the workpiece surface to achieve plastic domain processing on a precision lathe, though the mechanism remains unclear.
**4 Conclusion**
From the current research on ultra-precision machining of brittle materials, it is evident that significant progress has been made in understanding the cutting process. However, there is still a lack of deep theoretical insight into the brittle-to-plastic transformation under ultra-thin cutting conditions. Most critical depth calculations are based on experimental data, lacking a solid theoretical foundation.
Compared to the well-established field of ultra-precision machining of ductile materials, the study of ultra-precision machining of brittle materials in the plastic domain is still in its early stages. Many questions remain unanswered, and further research is needed to fully understand and optimize this process.
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