Mechanisms and influencing factors of branch fracture in Caragana korshinskii: a numerical simulation using XFEM

Understanding the initiation and expansion of cracks in Caragana korshinskii branches (CKB) is crucial for investigating their cutting mechanisms. In this study, an extended finite element method (XFEM) model was developed to analyze the mechanical behavior associated with crack formation and growth in CKB under the influence of multiple factors. A mechanical model of the cutting tool was also established, and the effects of cutting speed and cutting angle on the cutting force were examined using MATLAB simulations. Beginning with the internal cracks present in the stems, the study employed a response surface methodology to investigate how various parameters affect the stress intensity factor and crack tip propagation. The results revealed that the cracks generally exhibit a mixed mode of type I–II, with mode I (opening mode) being dominant. The stress intensity factor varies significantly with the crack angle and increases with both crack length and applied load. Furthermore, crack propagation displays a characteristic “W”-shaped pattern as influenced by the crack angle and tends to increase with longer crack lengths and higher loads. To optimize crack propagation behavior, a central composite design experiment was conducted to achieve minimal crack expansion and a maximal stress intensity factor. The optimal parameter combination was determined to be a crack angle of 105°, a crack length of 0.5 mm, and a load of 44.62 N, which resulted in a crack expansion length of 6.30 mm and a stress intensity factor of 112.78 MPa·mm^1/2. This study offers a novel approach for analyzing the fracture behavior of CKB and provides valuable insights into optimizing their cutting performance.