**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 processing accuracy and surface quality. However, machining brittle materials remains a significant challenge due to their high brittleness, low fracture toughness, and the close proximity of their elastic limit and strength. When subjected to loads exceeding their elastic limit, brittle materials tend to fracture, resulting in cracks and surface damage that severely affect their performance and quality [12, 13]. As a result, traditional methods like grinding and polishing—once commonly used—have proven inefficient, difficult to control, and unsuitable for complex shapes. This has led to a growing need for more advanced and precise machining techniques.
In recent years, researchers have made significant progress in exploring the ultra-precision machining of brittle materials, particularly with the development of diamond tools and ultra-precision machine tools. One promising technique is ultra-precision cutting using diamond tools, which enables high-quality surface finishes by inducing plastic deformation on the material’s surface. This method offers advantages such as high efficiency, controllability, and the ability to process complex curved surfaces. This paper reviews the current state of research on ultra-precision machining of brittle materials and highlights some existing challenges, aiming to provide insights for future advancements in this field.
**1 The Theory of Brittle-Plastic Deformation Under Sharp Indenters**
The feasibility of ultra-precision turning of brittle materials using sharp diamond tools is based on the ability of these materials to undergo plastic deformation under small loads. Over the past few decades, numerous indentation experiments have been conducted on hard and brittle materials, where diamond indenters are pressed into the material at controlled forces to observe its response. During a full loading-unloading cycle, the cracking process from initial deformation to full failure is clearly visible (Fig. 1).
As shown in the figure, even brittle materials can exhibit some degree of plastic deformation under minimal load. As the force increases, the material transitions from plastic deformation to brittle failure, forming internal and surface cracks. The load at which cracks first appear is known as the critical load, and the corresponding indentation depth is called the critical depth. These parameters are crucial in understanding the transition from ductile to brittle behavior in brittle materials.
During the indentation process, intermediate cracks typically form first, extending perpendicular to the material surface. These cracks cause the most severe damage. Researchers have extensively studied the relationship between the length of these cracks and the applied load, leading to the following formula [4]:
$$ c = \beta P \phi $$
Where $ c $ is the crack length, $ P $ is the vertical load, $ \beta $ is a constant dependent on the indenter shape, and $ \phi $ is the half-vertex angle of the indenter.
These studies reveal that when the penetration depth is small, plastic deformation occurs, and cracks do not propagate into the ductile region of the material. This insight has paved the way for new machining strategies focused on controlling the transition between brittle and plastic deformation.
**2 Ultra-Precision Grinding of Brittle Materials**
Ultra-precision grinding is a relatively new method for machining brittle materials, utilizing high-rigidity and compact grinding machines equipped with diamond wheels. Evans and Marshall simulated the cutting action of abrasive grains on a diamond wheel by using a diamond indenter to shape brittle materials like glass. When the applied load exceeds the critical value, a brittle cracking system is observed (Fig. 2) [5].
To achieve ultra-precision grinding, the key is to induce plastic deformation rather than brittle fracture. The thickness of the abrasive grain, known as the critical cutting thickness, plays a vital role in determining the success of the process. Many researchers have explored the brittle-to-plastic transition under grinding conditions [6–8]. Based on extensive experiments on materials like glass and ceramics, T.G. Bifano derived the following formula for the critical cutting thickness [6]:
$$ d_c = K \frac{E}{H} $$
Where $ d_c $ is the critical cutting thickness, $ E $ is the elastic modulus, $ H $ is the hardness, and $ K $ is the fracture toughness.
Japanese researchers, including Naoya Ikawa, have also conducted indentation experiments on single-crystal silicon and lithium niobate using different abrasive grain sizes, revealing that the size of the abrasive grains significantly affects the surface quality [9]. Despite these findings, further research is needed to fully understand how abrasive grain size influences the 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 uses specially ground diamond wheels to process optically brittle materials like single-crystal silicon and amorphous glass, achieving smooth, crack-free surfaces [10]. Similar technologies have been developed in the UK and Japan, with notable achievements in producing high-quality surfaces through ultra-precision grinding. However, challenges remain, such as ensuring uniform distribution of abrasive grains and preventing clogging that could lead to increased grinding forces and surface damage.
To address these issues, the Japanese Institute of Physical Chemistry introduced ELID (Electrolytic In-process Dressing) grinding in 1987. This technique uses electrolysis during the grinding process to maintain the sharpness of the diamond wheel, ensuring consistent performance and stable ultra-precision results. With ELID, grinding wheels with sub-5 nm grain sizes have achieved surface roughness values below 1 nm [11].
ELID technology has since gained global attention and is now widely used in the US, UK, Germany, and China. At Harbin Institute of Technology, researchers have successfully applied ELID to grind brittle materials like cemented carbide and optical glass, achieving nanometer-level surface roughness [12]. However, challenges such as oxide films on the grinding wheel surface and incomplete contact between the wheel and workpiece still exist and require further investigation.
**3 Ultra-Precision Turning of Brittle Materials**
Since 1987, Blake and Scattergood from North Carolina State University pioneered ultra-precision turning of brittle optical materials, such as single-crystal crucibles, achieving a surface roughness of 8 nm [13]. They proposed a model describing the relationship between the cutting geometry and the critical cutting depth when using a circular-arc diamond tool (Fig. 3). In this model, the feed rate $ f $, the distance $ z $ from the tool tip to the brittle transition zone, the crack length $ y_c $, and the cutting thickness $ t $ are all important parameters.
Due to the use of a circular-arc tool, the effective cutting thickness increases from zero at the tool tip to a maximum at the surface being machined. When the cutting thickness reaches a critical value $ d_c $, the material begins to fracture. Below this threshold, the material is primarily removed through plastic deformation. If the crack propagation depth $ y_c $ does not reach the machined surface, a smooth finish can be achieved. Any fractures formed on the arc surface will be removed during subsequent cutting passes.
Blake et al. proposed the following formula for the critical cutting depth:
$$ d_c = R f $$
Where $ f $ is the feed rate and $ R $ is the radius of the cutting tool.
Blackey later improved this model by considering the effect of the crack propagation depth $ y_c $, leading to a more accurate calculation of the critical cutting depth [14]. Experimental results showed that $ y_c $ is approximately 3 to 10 times $ d_c $, indicating a strong correlation between the two.
Further research by Blackey et al. using scanning electron microscopy revealed that chips near the tool tip are thin and continuous, indicating plastic deformation, while those farther from the tip are thick and discontinuous, showing brittle behavior. This observation supports the existence of a clear boundary between plastic and brittle deformation regions.
Nakasuji and others in Japan also studied the brittle-to-plastic transition in ultra-precision turning, finding similar results to Blackey’s work. However, they also observed that the surface roughness of single-crystal silicon exhibits a fan-shaped pattern, which is attributed to the anisotropic nature of the material. Experiments along different crystallographic directions showed varying cutting forces, which directly impact surface quality. While Takayuki Shibata explained this phenomenon in terms of slip systems, it is clear that the brittle nature of the material introduces limitations to purely plastic-based explanations.
Another factor influencing ultra-precision turning is the cutting edge radius, which is often comparable in size to the cutting thickness. Although some studies have examined the effect of the cutting edge on the cutting force, the influence of the edge radius on the brittle-to-plastic transition remains underexplored and requires further investigation.
KiovanolaJH found that using a -30° rake angle on a glass-cutting tool facilitates continuous chip formation and plastic deformation. Similarly, in ultra-precision turning of materials like single-crystal silicon, a large negative rake angle has been shown to promote plastic domain processing. Some Japanese researchers have even applied negative pressure to the workpiece surface to achieve plastic deformation. However, the underlying mechanism for this behavior is still not fully understood.
**4 Conclusion**
From the current state of research on ultra-precision machining of brittle materials, it is evident that significant progress has been made in understanding the cutting process. However, there remains a lack of deep theoretical insight into the brittle-to-plastic transformation under ultra-thin cutting conditions. Most studies rely on experimental measurements, 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 challenges remain, and further exploration is necessary to advance this field and improve the efficiency and quality of brittle material processing.
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