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We calculate analytically the phase diagram of a two-dimensional squarecrystal and its wrapped version with defects under external homogeneous stressas a function of temperature using a simple elastic lattice model that allowsfor defect formation. The temperature dependence turns out to be very weak. Theresults are relevant for recent stress experiments on carbon nanotubes. Underincreasing stress, we find a crossover regime which we identify with a crackingtransition that is almost independent of temperature. Furthermore, we find analmost stress-independent melting point. In addition, we derive an enhancedductility with relative strains before cracking between 200-400%, in agreementwith carbon nanotube experiments. The specific values depend on the Poissonratio and the angle between the external force and the crystal axes. We givearguments that the results for carbon nanotubes are not much different to thewrapped square crystal.

Modelling two-dimensional Crystals with Defects under Stress: Superelongation of Carbon Nanotubes at high Temperatures