Study on the brittle-plastic transition of YAG crystals based on nano-scratch experiments

YAG crystals are typically hard and brittle materials that are prone to be damaged during optical processing. In order to improve processing quality, it is necessary to avoid brittle damage as much as possible so that the material is removed in the plastic domain, so it is particularly important to study the critical conditions for the brittle-plastic transition of YAG crystals. The brittle-plastic transition of the (100) and (111) crystal faces of YAG crystals was investigated by variable load and constant load nano-scratch experiments. By analyzing the scratch morphology and friction-scratch distance curves, the critical load of brittle plastic transition for each crystal surface is obtained. The results show that the critical loads of (100) and (111) crystal faces for brittle-plastic transformation under variable load nano-scratch experiments are 113.575 mN and 84.05 mN, respectively, and the different critical loads of the two crystal faces are due to the discrepancy of surface energy. According to Griffith’s fracture theory, because the surface energy of (100) crystal face is higher, the energy required for brittle fracture of the crystal surface is higher, so the critical load of brittle-plastic transition is larger. Finally, the correctness of the critical load was verified by constant load nano-scratch experiments.


Introduction
YAG (Yttrium aluminum garnet, Y 3 Al 5 O 12 ) crystal has the advantages of high thermal conductivity, excellent mechanical properties, high melting point, good light transmission performance, and can be doped with high concentrations, etc [1][2][3][4].It is the most widely used laser crystal material in solid-state lasers.The YAG crystal element needs to have extremely high optical processing accuracy in order to maintain the YAG laser's performance and service life [5].However, the YAG crystal is hard and brittle, which makes it a typically difficult material to process [6][7].The main processing techniques are still lapping and polishing, which relies on the mechanical action of hard abrasives to complete the removal of the material.This method has a low processing efficiency and is susceptible to brittle damage and results in some defects during processing, such as pit, chipping, and microcracking.In order to obtain better processing quality of YAG crystal components, brittle damage needs to be avoided as much as possible so that the material is removed in the plastic domain [8][9][10], so the study of the critical conditions for the brittle-plastic transition of YAG crystals is particularly important.
In this study, the nano-scratch testing technique [11] is used to examine the brittle-plastic transition of (100) and (111) crystal faces of YAG crystals.First, by conducting variable load nano-scratch experiments, the critical load of the brittle-plastic transition of the two crystal surfaces is determined.Next, by conducting constant load nano-scratch experiments, the results of the variable load nanoscratch experiments are confirmed.This work might serve as a theoretical guide for actually processing YAG crystal elements.

Experiment
The YAG crystals used in this experiment were grown by the Czochralski method at the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences.The samples selected for the experiments were YAG crystals with (100) and (111) crystal faces, all with dimensions of 15 mm × 15 mm × 3 mm.The test surface of the sample was lapped and polished until the surface is bright and free of scratches.On a G200 nanoindenter using a Berkovich diamond indenter, the nano-scratch studies were carried out.
First, a variable load nano-scratch test was conducted.In the variable load nano-scratch test, the linear load loading range is 0-180 mN, the scratch speed is 15 μm/s, and the scratch distance is 400 μm.During the scratching process, the nanoindentation equipment recorded parameters change such as scratching distance, load and friction.After the scratching procedure, the shape of the scratch was studied under a metallographic microscope.
For the constant load nano-scratch test, the scratch speed is 30 μm/s, and the scratch range is 150 μm.The choice of the load is based on the critical load for the brittle-plastic transition derived from the variable load nano-scratch test.The principle of the nano-scratch experiment is shown in Figure 1.It can be seen from Figure 2 that at the beginning of scribing, the load applied by the indenter to the crystal surface is minimal, the scribing depth is shallow, the scratch marks are not readily visible, and the material deformation is mainly elastoplastic deformation at this time.When the load steadily rises, the scratch groove widens and deepens, and material accumulation starts to emerge on both sides of the scratch, the material deforms plastically.When the load is raised over the critical load for brittle-plastic transformation, the material fractures, and lateral fissures start to show, and the crystal surface is badly damaged, and the material is removed in a brittle way.The (111) crystal face clearly cracks before the (100) crystal face, showing that the (111) crystal face's critical load for the brittle-plastic transition is lower than that of the (100) crystal face.

Description of specimens Variable load nano-scratch experiments
By analyzing the variation of the friction between the indenter and the scratching surface during the scratching process, the critical load for the brittle-plastic transformation of the material can be derived.Figure 3 shows the variation curve of friction with scratch distance in the variable load nano-scratching experiments of YAG crystal with different crystal faces.From Figure 3, it can be seen that the friction on both crystal faces increases with the increase in load, which is because the greater the load is, the deeper the scribing depth is, and the more material accumulates in front of the indenter, which hinders the movement of the indenter resulting in an increase in friction.At the beginning of the scribing, the load applied by the indenter is small, the change of friction on the two crystal surfaces is relatively gentle, and at this time the removal of material is plastic; scribing continues, the load further increases, when the load on (100) crystal face is 113.575mN, the load on (111) crystal face is 84.05 mN, the two curves begin to appear violent fluctuations, this is due to the brittle fracture that occurs at this time resulting in the fluctuation of friction; as the scratching continued, the fluctuation of the friction force became more violent, indicating that the removal method changed to complete brittle removal.The critical loads of the brittle-plastic transition on the (100) and (111) crystal face of the YAG crystal are 113.57mN and 84.05 mN, respectively.the critical load on the (100) crystal face is higher, indicating that the brittle fracture occurs later in the variable load nanoscratch experiment, which is consistent with the results in the micrograph.
The brittle-plastic transition of different YAG crystal faces shows obvious anisotropy, which is due to the differences in atomic arrangement and spacing on different crystal faces, resulting in different surface energies of different crystal faces.The surface energy is the energy per unit area required for the crystal to break into two semi-infinite crystals when it is deconstructed under the action of an external force and can reflect the stability of the surface.The surface energy of the (100) crystal face of the YAG crystal is greater than that of the (111) crystal face [12].According to Griffith's fracture theory, cracks need to consume energy in expansion, and if the surface energy of that surface is Γ, the energy required for crack expansion should be greater than 2Γ [13].Therefore, the energy required for brittle fracture on the crystal surface of YAG crystal (100) is higher, so the critical load for brittle-plastic transition on this crystal surface is larger.

Constant load nano-scratch experiments
The critical loads for the brittle-plastic transition of the YAG crystal (100) and (111) crystal faces were 113.575 mN and 84.05 mN, respectively, from the variable load nano-scratch experiments.In order to verify the correctness of the results, constant load nano-scratch experiments were performed on two crystal surfaces with selected loads of 50 mN, 90 mN, and 130 mN, respectively.Figure 4 shows the optical micrographs of the scratch morphology on the two crystal faces at different loading loads in the constant load nano-scratch experiment.When the loading load is 50 mN, the scratch morphology of both (100) and (111) crystal faces is clear and flat, and the scratch surface is smooth without cracks, which means that both crystal faces are plastic removed at this time.When the loading load is 90 mN, burrs and chips accumulate around the scratch of (100) crystal surface but no cracks appear, the material is still plastic removal, but small cracks start to appear on the side of the scratch of (111) crystal surface, indicating that brittle fracture has occurred.When the loading load was 130 mN, small cracks started to appear around the scratch on the (100) crystal face, and the number of cracks on the side of the scratch on the (111) crystal face increased and the crack length was larger, indicating that both crystal faces were brittly removed under this load.The critical load for the brittle-plastic transition determined by the variable load nano-scratch experiment is compatible with the phenomenon of constant load nano-scratch experiment, demonstrating the validity of the results.Figure 5 shows the curve of friction versus scratch distance for (100) crystal face under different loads in the constant load nano-scratch experiment.From Figure 5, it is clear that friction increases with the loading load.The curve fluctuates less and tends to be steady when the load is 50 mN because the indenter is pressed into a little depth and the material surface undergoes elastic-plastic deformation at this point.When the load is 90 mN, the fluctuation of friction increases, which is caused by the accumulation of debris in front of the indenter, which hinders the movement of the indenter.When the load is 130 mN, the friction changes abruptly, which is brought on by the material surface's brittle fracture.

Conclusion
In this paper, the brittle-plastic transformation mechanism of different YAG crystal faces was studied based on nano-scratch experiments.The critical loads for the brittle-plastic transition of YAG crystal (100) and (111) are 113.575mN and 84.05 mN, respectively, by analyzing the scratch morphology and friction-scratch distance curves of the nano-scratch experiment with variable load.The reason for the different brittle-plastic transition points of the two crystal faces is analyzed by using the surface energy and Griffith's fracture theory.The accuracy of the obtained critical loads is verified by constant load nanoindentation experiments, and the influence of different loads on the deformation mechanism is analyzed.The study's findings can serve as a theoretical basis for the selection of process parameters for ultra-precision optical machining of YAG crystal elements and are of great significance for the realization of plastic domain processing of YAG crystals.

Figure 1 .
Figure 1.Schematic diagram of the scratching process.

Figure 2 (Figure 2 .
a) and Figure 2 (b) show the optical micrographs of the surface morphology of (100) and (111) crystal faces of YAG crystals after scratching experiments with variable loads from 0 to 180 mN, respectively.Optical micrograph of scratch morphology at linear loading of load.(a) (100) Crystal face; (b) (111) Crystal face.

Figure 3 .
Figure 3. Variation curve of friction with scratch distance at linear loading of the load.

Figure 5 .
Figure 5. Variation curves of friction with scratch distance on (100) crystal face at different loads in constant load nano-scratch experiments.