Mechanical analysis of lateral uplift of aluminum film scribed by grating

During the diffraction grating scoring process, the stress change on the aluminum film greatly affects the groove morphology. In view of the current status of “trial and error” of grating scoring, in order to study the rule of lateral bulging of aluminum film in the process of grating scoring, this paper aims at the formation rule of groove topography during the process of grating scoring, which is affected by the change of the surface film material force. The slip line field theory and the speed upper limit field theory establish a simple model for the stress process of the material during the scoring process.


Introduction
The current diffraction grating scoring technology mainly adopts the "trial and error" method to determine the grating parameters, which not only wastes time but also increases costs, and it is difficult to say that it is scientific and effective. At the same time, there is a certain chance. Existing experience is not suitable for the grating scoring tasks with new parameters. The fundamental reason is that there is no deep understanding of the formation mechanism of the groove during the grating scoring process. And according to previous studies, the change of the stress on the aluminum film during the scoring process has a great influence on the change of the groove shape. Therefore, according to the mechanical scoring technology, the mechanical analysis of the grating scoring process can be used to realize the recognition of the groove formation process in the mechanical scoring process and the influence of the material flow law on the groove morphology and mechanical characteristics Law, so as to lay a solid foundation for grating scoring technology. Figure 1 is a schematic diagram of the groove cross section at a certain moment in the scoring process. The volume of the removed material is the G 1 area, and its volume is equivalent to 2G 2 material attached to the surface as a build-up material, forming a lateral bulge. For pure plow cutting, there is no material removal, only the material is moved to both sides. If the springback phenomenon at the bottom of the groove is not considered, G 1 =2G 2 .

Mechanical analysis of uplift
However, the grating scoring process is a complex three-dimensional process. Due to the inherent geometric complexity of plastic mechanics analysis, it is difficult to establish a mechanical analysis model that can simultaneously satisfy the equilibrium equation, the coordination equation and the plastic flow criterion. However, by considering that material flow occurs on the flow chip plane, the above problem can be simplified into a two-dimensional model. The material flow plane connects the front end of the tool and both sides.  Fig. 1(a). The material passes through the slip line B-P into the flow chip plane and flows out of the plane through the slip line G-R. Since the shape of the entrance cannot be known, the entrance is regarded as a single tangent line, as shown in Figure 1(b). The exit is regarded as a smooth transition plane. If it is only regarded as a single tangent line, the pressure of the vertices GRE will be too large, and the slip line field theory will no longer be applicable.
As the movement continues downward, and considering the flow phenomenon occurring in the C-C plane, there is not enough space to establish a slip line field. Therefore, the inlet and outlet of the material can be regarded as parallel tangents, and the upper limit method is used to solve the problem of material flow. Connect these tangents to get a shear plane. The upper surface of the upper limit model is a parallelogram, and the side gradually decreases toward the chip flow plane H-H, which connects the apex of the tool and the publicly constructed upper surface. The proposed plough cutting model is a combination of slip line field model and upper limit model.
When calculating the force, the force on the effective plane is calculated first, and then the force on the contact surface between the tool and the material is calculated according to the force on the effective plane. When using the slip line field model, the mechanical model on the contact surface can be solved by the stress generated by the free surface on the ridge. When applying the upper boundary field model, the energy consumed by the cutter surface and the shear plane is first calculated to solve the stress problem of the cutter.
The cutting force is the force on the effective plane. When it is in the range of 0-z, the upper field model is used; in the range of z-h, the slip line field model is used.  Figure 2, is the normal stress on BP. Considering the differential dω of the tool depth in the effective plane, the force on BP is

Mechanical analysis in the slip line field
Where k is the yield stress during cutting. The power on GE is Therefore, the positive pressure and shear force on the tool surface are The resultant force can be obtained by the above equation, simplify the above formula, eliminate the parameters t and dω on the tool surface, other factors remain unchanged, and the geometric relationship of the tool can be known as ( 7 ) Where is the limit height value of the effective plane obtained by measurement. At any point on z, the force on the tool surface can be calculated by the slip line field model, which can be obtained ( 8 ) Which ℎ The positive pressure and shear force on the tool surface are The dimensionless quantity of the force on the tool surface is (12) (13) The friction coefficient of the tool surface has a certain functional relationship with the above two forces. If the friction coefficient is μ, then there is (14) Therefore, if can be obtained, can be obtained by the above formula

Mechanical analysis in the upper field
When the tool surface ABGA is plastically deformed by the friction generating surfaces ABPHA and AGRHA, energy is lost. Let ABPHA, AGRHA, and ABGA areas be , , and , respectively. The total energy consumption is The magnitude of normal stress can be obtained.

Conclusion
In this paper, the influence of the groove formation process and material flow law on the groove shape and mechanical characteristics during mechanical scribing is explored. The complex three-dimensional scribing process is reduced to a simple two-dimensional model. The concept of the flow plane, based on the theory of the slip line field and the upper limit method, analyzes and solves the stress process of the material during the grating scoring process.