Nonlinear viscoelasticity determined from internal friction

Departamento Materiales, Comisio ´n Nacional de Energia Atomica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentinaand Departmento de Fi´sica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabello´n I, Ciudad Universitaria,1428 Buenos Aires, Argentina Received 5 April 1996Internal friction IF peaks measured as a function of temperature or frequency are associated with nonlinearprocesses only if a systematic study determines the influence of the amplitude of the applied stress on therelaxation process. Nonlinear viscoelasticity, however, can be more easily determined just by noting incom-patibilities between experimental IF data and the postulates of linear viscoelasticity. The aim of this work is todemonstrate that the logarithmic derivative of the internal friction with respect to the frequency is a useful toolto establish whether a process is nonlinear. Effectively, if the absolute value of this derivative is greater thanone, then nonlinear mechanisms are involved in the relaxation process. Nothing can be said about the linearity,however, if the derivative is constrained to the interval 1,1 ; only measurements at different stress ampli-tudes should determine nonlinear effects. Not only the theoretical fundamentals are detailed but also severalexamples are shown as an application of the procedure developed to find nonlinear effects. Finally, thelinearity of the Snoek and Zener relaxations is analyzed through the calculation of the logarithmic derivativefrom IF measurements made as a function of both frequency and temperature. S0163-1829 96 06245-5I. INTRODUCTION