## Failure of fibrous composites: elastic and time-dependent stress analyses, Monte Carlo simulation, and probability modeling |

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applied load applied stress approximation asymptotic Beyerlein blocker blocking fiber broken fibers calculated ceramics comparing simulated strength composite failure composite fracture strength composite lamina composite strength crack tip creep deformation data with probability debonding decreases developed effects elastic failure mode failure probability failure stress fiber and matrix fiber breaks fiber composites fiber fractures fiber shape parameter fiber strength fiber stress Figure flaw tolerance fracture mechanics fracture resistance increases initial notch length intact fibers isolated break Laplace transform load profiles material metal matrix composites microcrack micromechanical modulus Monte Carlo simulation Newtonian viscous notch extension notch sensitivity notched composites Nt(y overload plot comparing simulated probability distributions probability models range region S. L. Phoenix scale sequence shear stress shown in Fig simulated strength data solution statistical strength distribution stress concentration technique tensile load tensile stress time-dependent toughening toughness unnotched upper tail variability in fiber weakest link Weibull distribution Weibull plot comparing