Numerical evaluation of structural relaxation-induced stresses in amorphous polymers

An attempt to calculate the internal stresses in a cylindrically shaped polystyrene component, subjected to an arbitrary cooling rate, will be described. The differential volume relaxation arising as a result of the different thermal history suffered by each body point was considered as the primary source of stresses build-Up. A numerical routine was developed accounting for the simultaneous stress relaxation processes assuming thermorheological simplicity. The volume relaxation kinetics were modelled by using the four-parameter TNM (Tool-Narayanaswamy-Mohynian) phenomenological theory, with optimum estimated values of the four model parameters, (A, Delta h, x, beta), obtained, once and for all, fitting the pressure-volume-temperature (PVT) liquid dilatometer measurements. The numerical routine was implemented within an Ansys environment. The algorithm translates the predictions of the TNM model for the volume at each body point, as applied non-mechanical loads, that acting, on the component generates a complex stress state possibly affecting the integrity of the system. Stress relaxation effects were modelled by a weighted exponential series. Specific boundary and initial conditions were also defined for the considered test case.