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A unique probabilistic theory is described to predict the uniaxial strengths andfracture properties of nanocomposites. The simulation is based on compositemicromechanics with progressive substructuring down to a nanoscale slice of ananofiber where all the governing equations are formulated. These equations havebeen programmed in a computer code. That computer code is used to simulateuniaxial strengths and fracture of a nanofiber laminate. The results are presentedgraphically and discussed with respect to their practical significance. Theseresults show smooth distributions from low probability to high