Fractal analysis on machined surface morphologies of soft-brittle KDP crystals processed by micro ball-end milling

Qi Liu, Jian Cheng, Zhirong Liao, Mingyu Liu, Mingjun Chen, Linjie Zhao, Hongqin Lei, Wenyu Ding

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
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The micro-defects on KH2PO4 (KDP) optic surfaces are mainly repaired by the micro-milling technique, while it is very easy to introduce brittle cracks on repaired surfaces, as KDP is soft and brittle. To estimate machined surface morphologies, the conventional method is surface roughness, but it fails to distinguish ductile-regime machining from brittle-regime machining directly. To achieve this objective, it is of great significance to explore new evaluation methods to further characterize machined surface morphologies. In this study, the fractal dimension (FD) was introduced to characterize the surface morphologies of soft-brittle KDP crystals machined by micro bell-end milling. The 3D and 2D fractal dimensions of the machined surfaces and their typical cross-sectional contours have been calculated, respectively, based on Box-counting methods, and were further discussed comprehensively by combining the analysis of surface quality and textures. The 3D FD is identified to have a negative correlation with surface roughness (Sa and Sq), meaning the worse the surface quality the smaller the FD. The circumferential 2D FD could quantitively characterize the anisotropy of micro-milled surfaces, which could not be analyzed by surface roughness. Normally, there is obvious symmetry of 2D FD and anisotropy on the micro ball-end milled surfaces generated by ductile-regime machining. However, once the 2D FD is distributed asymmetrically and the anisotropy becomes weaker, the assessed surface contours would be occupied by brittle cracks and fractures, and corresponding machining processes will be in a brittle regime. This fractal analysis would facilitate the accurate and efficient evaluation of the repaired KDP optics by micro-milling.
Original languageEnglish
Article number1782
Number of pages15
Issue number5
Publication statusPublished - Mar 2023


  • KDP crystal
  • fractal dimension
  • box-counting approach
  • brittle-to-ductile transition
  • surface morphology analysis
  • material removal modes


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