Spontaneous Thermal Runaway as an Ultimate Failure Mechanism of Materials

The first theoretical estimate of the shear strength of a perfect crystal was given by Frenkel [ Z. Phys. 37 572 (1926)]. By assuming that two rigid atomic rows in the crystal would move over each other along a slip plane, he derived the ultimate shear strength to be about one-tenth of the shear modulus. Here we present a theoretical study showing that catastrophic failure of viscoelastic materials may occur below Frenkel’s ultimate limit as a result of thermal runaway. The thermal runaway failure mechanism exhibits progressive localization of the strain and temperature profiles in space, thereby producing a narrow region of highly deformed material, i.e., a shear band. We calculate the maximum shear strength σ_c of materials and then demonstrate the relevance of this new concept for material failure known to occur at scales ranging from nanometers to kilometers.