Probabilistic fracture mechanics with uncertainty in crack size and orientation using the scaled boundary finite element method

• We model shape sensitivity using the scaled boundary finite element method (SBFEM).
• Derivative of stress intensity factors with respect to crack geometry are computed.
• The Monte Carlo simulation and first/second-order reliability methods are applied.
• Efficiency and simplicity in modeling shape sensitivity is demonstrated.
• Results compare very well with those obtained from published literature.

The geometry of cracks in a structure are often difficult to determine accurately, leading to uncertainties in structural analysis. This paper presents a probabilistic fracture mechanics (PFM) approach to evaluate the reliability of cracked structures considering the uncertainty in crack geometry. The shape sensitivity analysis of the stress intensity factor (SIF) is performed efficiently using the scaled boundary finite element method (SBFEM). No remeshing is required as the size and orientation of a crack vary. Reliability is estimated using various probabilistic techniques. Numerical examples demonstrate the accuracy and simplicity of the present method.