Calculation of stress intensity factor in two-dimensional cracks by strain energy density factor procedure

• Published in: Science China. Technological sciences 2018-04, Vol.61 (4), p.542-550
• Main Authors: Fang, Zhao, Li, AiQun, Bao, HaiYing, Wang, Hao
• Format: Article
• Language: English
• Subjects: Crack tips; Cracks; Density; Energy; Energy consumption; Engineering; Flux density; Heat treating; Mathematical analysis; Meshing; Strain energy; Stress intensity factors; Tips
• ISSN: 1674-7321; 1869-1900
• DOI: 10.1007/s11431-017-9186-9

In order to calculate the stress intensity factor (SIF) of crack tips in two-dimensional cracks from the viewpoint of strain energy density, a procedure to use the strain energy density factor to calculate the SIF is proposed. In this paper, the procedure is presented to calculate the SIF of crack tips in mode I cracks, mode II cracks and I+II mixed mode cracks. Meanwhile, the results are compared to those calculated by traditional approaches or other approaches based on strain energy density and verified by theoretical solutions. Furthermore, the effect of mesh density near the crack tip is discussed, and the proper location where the strain energy density factor is calculated is also studied. The results show that the SIF calculated by this procedure is close to not only those calculated by other approaches but also the theoretical solutions, thus it is capable of achieving accurate results. Besides, the mesh density around the crack tip should meet such requirements that, in the circular area created, the first layer of singular elements should have a radius about 0.05 mm and each element has a circumferential directional meshing angle to be 15°–20°. Furthermore, for a single element around the crack tip, the strain energy density factor is suggested to be calculated in the location where half of the sector element’s radius from the crack tip.