A master curve for tensile properties of thermoplastics

Ultimate mechanical properties of polymers can be characterized by a dimensionless Hooke number He ≡ σ_b/(E?_b), where σ_b is the ultimate tensile strength, E the tensile modulus, and ?_b the elongation at break. Hooke numbers are found to be a smooth function of ultimate elongations, independent of the chemical and physical structure of common thermoplastics. This master curve for fracture strengths and elongations can be described by He = [1 + (?_b/?_crit)^ab]^?1/b with empirically found parameters ?_crit = 0,0168, a = 0,918, and b ≈ 4. The decrease of He with increasing ?_b at ?_b > ?_crit reflects the shear flow on deformation. Hooke numbers depend on entanglement densities v_e according to He = 1,285·10³⁶ (v_e/cm^?3)^?1,846 for v_e > 3,65·10¹⁹ cm^?3. A correction for additional segment orientation during tensile testing brings the exponent to ?1,846/0,918 = ?2,01; i. e., a dependence of Hooke numbers on the reciprocal square of entanglement densities.