Fatigue behavior of polystyrene (PS) analyzed from the Fourier transform (FT) of stress response: First evidence of I2/1(N) and I3/1(N) as new fingerprints

The fatigue behavior of polystyrene (PS) in strain controlled torsion rectangular oscillatory tests was analyzed via Fourier transform (FT) to better understand the time evolution of linear and nonlinear mechanical parameters, and to establish fingerprints related to failure onset. The tests were performed under large amplitude oscillatory shear (LAOS), so the stress response was no longer perfectly sinusoidal and higher harmonics could be detected and quantified in the FT spectra as a function of time or number of cycles N. A linear parameter, the storage modulus (G′(N)), was analyzed, as well as nonlinear parameters of the ratios of the second (I₂(N)) and the third (I₃(N)) harmonics over the fundamental one (I₁(N)). The nonlinear parameter I_2/1(N) is very low for undamaged samples, but its intensity was found to increase when defects were created in the structure to a point where cracks became visible in the sample. On the other hand, the I_3/1(N) parameter increased steadily during a test up to a local maximum where a macroscopic crack occurs in the sample. Both parameters I_2/1(N) and I_3/1(N) are proposed as new criteria to detect the onset of part failure under the conditions tested and can be used as safety limits for partial damage.