Theory of rotational dynamic measurement of plastics



A theory which postulates a condition of combined constraints of constant stress and constant strain is developed for the rotating cantilever beam measurement of dynamic mechanical properties of rigid plastics. The theory provides operating equations for the rotating beam instrument of Maxwell equipped with a biaxial strain gage dynamometer. The storage component of the dynamic Young's modulus E′ = 64 L3F1/3πd4XtK1F1) and the mechanical loss tangent tan γ = [F2XtK1F1) + K2F1F2]/[F1XtK1F1) − K2(F2)2] are expressed in terms of the length L and diameter d of the circular rod specimen; the bending spring constants of the biaxial dynamometer K1K2; the imposed dynamometer displacement (ΔXt); and the cantilever beam storage and loss response forces F1, F2.