Probabilistic Failure Analysis of Composite Beams for Optimum Ply Arrangements under Ballistic Impact

The probabilistic analysis takes into consideration an effect of scatter in elastic and strength properties of composite beam, and velocity of impactor. The damage model is implemented in the FE (finite element) code by a VUMAT (user-defined subroutine). The inter ply failure is modeled using cohesive surfaces between the plies. Dynamic response is obtained using explicit time domain integration approach. SFEA (stochastic finite element analysis) is used to study the initiation of fiber failure analysis due to ballistic impact. SFEA provided the critical stress input in the limit state which is computationally solved using reliability software. The random variation in these properties is used for determining statistics of stress in the lamina. These are compared to the random strengths in the limit state function and probability failure surface is obtained by using GPRSM (Gaussian process response surface method). GPRSM is used to predict the Pf (probability of failure) for different ply lay-ups arrangement. The Pf of Chang-Chang initiation of fiber failure for simply supported composite beams with symmetric cross ply lay-ups are (88.9%, 1.47% and 58.1%) greater than the anti-symmetric cross ply, symmetric angle ply and anti-symmetric angle ply, respectively. Sensitivity analysis is also carried out for symmetric cross ply arrangements.