Probability methods for the fracture of composite materials

The reliability calculation for a composite material may be performed using a variety of approximation methods. These methods are broadly divided into fast probability integration (FPI) methods of either first or second order, and the Monte Carlo-based simulation methods. Using the Tsai-Hill and Tsai-Wu failure criteria as examples, these methods are described and illustrated. The methods are compared for accuracy, difficulty of implementation, and sensitivity to uncertainty in the parameters of the strength (or stress) distributions. The two methods of choice for speed, accuracy and innate conservatism are: importance sampling simulation, and the FPI rotational parabaloid. Under most conditions, the results of a linear approximation are also acceptable.