We use large scale molecular dynamics (MD) simulations to determine the tensile yield mechanism of orthorhombic polyethylene (PE) crystals with finite chains spanning $10^2-10^4$ carbons in length. We find the yield stress $sigma_y$ saturates for long chains at 6.3 GPa, agreeing well with experiments. We show chains do not break but always yield by slip, after nucleation of 1D dislocations at chain ends. Dislocations are accurately described by a Frenkel-Kontorova model parametrized by the mechanical properties of an ideal crystal. We compute a dislocation core size $xiapprox25$AA and determine the high and low strain rate limits of $sigma_y$. Our results suggest characterizing the 1D dislocations of polymer crystals as an efficient method for numerically predicting the ultimate tensile strength of aligned fibers.
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