Application of scaled boundary finite element method in failure probability estimation of square nanographene sheet

Abstract

In recent years, so much attention has been drawn to the field of nano computational material science. Due to the extensive applications of nanographene sheets in various industries such as aerospace industry, fracture analysis of square nanographene sheets is of crucial importance. Stochastic analysis is widely applied in fracture mechanics because it helps the results to be more realistic. In the present work, probabilistic fracture analysis of nanographene sheets is done using scaled boundary finite element (SBFEM) that is a novel semi-analytical method. In order to apply the stochastic method, we need to select certain statistical parameters, the ones considered here include crack length and failure stress. The results using the stochastic response method are compared with those of the Monte Carlo, which shows good agreement. Average, variance, third and fourth moments of stress and the fracture probability are calculated for all the bonds in two states of crack angle 0°, 90°. The results indicate that the maximum crack-tip fracture probability for central crack θ = 90° is 95%, while for θ = 0° equals 58%. For central crack θ = 90°, the failure probability in crack tip bonds, bonds adjacent to the crack edge and other bonds equal 95%, 88% and 65%, respectively. For nanographene sheet having the central crack θ = 90°, probabilistic density function is Gaussian, which reaches the highest point at the displacement being 0.990 pm. The third moment of the stress turned out to be zero, which shows that the input uncertain variables are all normal. The results obtained from computing the failure probability of all the bonds indicates that the highest failure probability is in the tip and edges of the crack. The stochastic fracture sensitivity versus crack length is calculated which shows that the maximum sensitivity in central crack happens when θ = 90° and crack length ranges between 0.3 and 0.4.

Keywords

• Stochastic response analysis
• Nanographene
• Crack
• Monte Carlo method